,transcrib]'s ,note3 ,italics are indicat$ by und]scores4 ,,! ,,eng9e] ,,s]ies ,,! ,,gyroscopic ,,compass ,a ,,non-,,ma!matical ,,treatm5t ,,! ,,eng9e] ,,s]ies ,,! ,,gyroscopic ,,compass ,a ,,non-,,ma!matical ,,treatm5t ,,by ,t4 ,w4 ,,*alm]s1 ,b4,,sc41 ,a4,m4,i4,,me*4,e4 7,,on ,,! ,,editorial ,,/aff ,,( 8,,! ,,eng9e]07 ,,illu/rat$ ,,london ,,con/able ,,company1 ,,ltd4 #aj ,,orange ,,/reet1 ,,leice/] ,,squ>e4 ,w4,c4 #aibj ,pr9t$ 9 ,great ,brita9 ,,preface ,! *apt]s compos+ ?is book orig9ally appe>$ z a s]ies ( articles 9 ,! ,eng9e] dur+ ,janu>y1 ,febru>y1 & ,m>* ( ! curr5t ye>4 ,! articles 7 writt5 9 ! belief t _m read]s w\ld welcome a cle> & full1 non-ma!matical exposition ( ! gyroscopic compass1 its !ory & practical con/ruction4 ,! gyro-compass repres5ts at once ! mo/ involv$ & ab/ruse & ! mo/ important & valuable ( all ! practical applications to :i* ! gyroscope1 s f>1 has be5 put4 ,z a navigational in/rum5t x is n[ 9 practically univ]sal use 9 all ! *ief w> navies ( ! _w1 & is to-day be+ adopt$ by sev]al important repres5tatives ( ! m]cantile m>9e4 ,rem>kable figures 7 %[n to ! au?or rec5tly :i* demon/rat$ t n only 0 navigation by ! gyro-compass mu* m accurate ?an by ! magnetic compass1 b t ! increas$ accuracy r$uc$ ! l5g? ( ! voyage ( a m]cantile vessel to an ext5t t result$ 9 sav+ a quantity ( fuel ! value ( :i* on a s+le trip w\ld g a consid]able way t[>ds meet+ ! extra fir/ co/ ( ! gyro-compass4 ,be>+ ^! facts 9 m9d ! au?or f ! outset endeav\r$ n only to disp5se ) ma!matics b to avoid introduc+ any?+ except ! mo/ famili> physical pr9ciples & conceptions1 = 8 object 0 to expla9 ! mode ( action ( ! gyro-compass = ! b5efit prim>ily ( ! navigat+ (fic]--naval & m]cantile4 ,if "s read]s %\ld f9d ! treatm5t 9 places unduly prolix1 ! au?or tru/s !y w ex]cise l5i5cy & reg>d ! fault z be+ caus$ by ! au?or's unwill+ness to take any risks 9 exp\nd+ a subject1 no "p ( :i* c be und]/ood incompletely )\t grave hurt to ! und]/&+ ( ! :ole4 ,t4 ,w4 ,c4 ,,london1 ,may1 #aibj4 ,,cont5ts ,,*ap4 ,,page ,i4 ,,introduction #a ,,ii4 ,,elem5t>y ,,gyroscopic ,,ph5om5a #d ,,iii4 ,,! ,,gyroscope ,,& ,,! ,,rotation ,,( ,,! ,,e>? #ae ,,iv4 ,,damp+ ,,! ,,vibrations ,,( ,,! ,,gyro-,,compass #bi ,v4 ,,! ,,damp+ ,,sy/em ,,( ,,! ,,ans*,,tz 7#aiaj7 ,,compass #db ,,vi4 ,,! ,,damp+ ,,sy/em ,,( ,,! ,,sp]ry ,,compass #eb ,,vii4 ,,! ,,damp+ ,,sy/em ,,( ,,! ,,br[n ,,compass #ei ,,viii4 ,,! ,,latitude ,,error #fe ,,ix4 ,,! ,,nor? ,,/eam+ ,,error #ga ,x4 ,,! ,,balli/ic ,,deflection #ha ,,xi4 ,,! ,,quadrantal ,,error #ia ,,xii4 ,,! ,,elim9ation ,,( ,,! ,,quadrantal ,,error #ajg ,,xiii4 ,,c5trifugal ,,=ces ,,dur+ ,,quadrantal ,,roll+ #acj ,,xiv4 ,,! ,,ans*,,tz 7#aiaj7 ,,compass #ach ,,xv4 ,,! ,,sp]ry ,,compass #adb ,,xvi4 ,,! ,,br[n ,,compass #adh ,,xvii4 ,,! ,,ans*,,tz 7#aiab7 ,,compass #aed ,,index #afe ,,li/ ,,( ,,illu/rations ,,fig4 ,,page #a4 ,model gyroscope ) ?ree degrees ( fre$om #d #b4 ,model gyroscope ) ?ree degrees ( fre$om #g #c4 ,model gyroscope1 frictional transmission ( turn+ mom5t #i #d4 ,model gyroscope1 "o degree ( fre$om lo/ #aa #e4 ,model gyroscope1 second degree ( fre$om lo/ #ab #f4 ,model gyroscope1 lo/ degrees ( fre$om re/or$ #ac #g4 ,elem5t>y gyroscope at equator #ae #h4 ,gyroscopic clock #af #i4 ,elem5t>y gyro-compass #ah #aj4 ,elem5t>y compass at equator #bj #aa4 ,elem5t>y compass at #ee deg4 ,n4 ,lat4 #bd #ab4 ,compass at equator & ne> ,nor? ,pole #bf #ac4 ,p5dulum & compass #cb #ad4 ,damp$ & undamp$ vibrations #ce #ae4 ,damp$ p5dulum #cg #af4 ,air-bla/ damp+ sy/em ( ,ans*tz 7#aiaj7 compass #dc #ag4 ,free & damp$ motion ( axle #di #ah4 ,damp+ curve f ,ans*tz 7#aiaj7 compass #ej #ai4 ,damp+ sy/em ( ,sp]ry compass #ec #bj4 ,action ( exc5tric p9 9 ,sp]ry compass #ee #ba4 ,action ( exc5tric p9 9 ,sp]ry compass #eg #bb4 ,gyro-p5dulum ) axle tilt$ #fj #bc4 ,damp+ sy/em ( ,br[n compass #fb #bd4 ,! nor? /eam+ error at #j deg4 & #fj deg4 ,n4 #gb #be4 ,sp]ry correction me*anism = latitude & nor? /eam+ errors #gf #bf4 ,balli/ic =ce on compass :5 %ip's spe$ *anges #hc #bg4 ,balli/ic =ce on compass :5 %ip's spe$ *anges #hd #bh4 ,balli/ic deflection #hf #bi4 ,effect ( roll+ on due nor? c\rse #ic #cj4 ,effect ( roll+ on due we/ c\rse #id #ca4 ,ext]nal gimbal m\nt+ #ig #cb4 ,effect ( roll+ on a due nor? c\rse 7simple m\nt+7 #ih #cc4 ,effect ( roll+ on a due nor? c\rse 7ext]nal gimbal m\nt+7 #ii #cd4 ,%ip roll+ on ,n4,w4 c\rse #aja #ce4 ,sp]ry compass on ,n4,w4 c\rse #ajh #cf4 ,sp]ry balli/ic gyro #aaa #cg4 ,/abilis$ exc5tric p9 7,sp]ry compass7 #aab #ch4 ,diagram ( ,br[n compass #aac #ci4 ,oil control bottles 7,br[n compass7 #aae #dj4 ,br[n compass on we/ c\rse #aag #da4 ,diagram ( ,ans*tz 7#aiab7 compass #aba #db4 ,plans ( gyros 7,ans*tz compass7 #abb #dc4 ,c5trifugal =ces on a p5dulum #aca #dd4 ,! ,ans*tz 7#aiaj7 compass #aci #de4 ,! ,sp]ry compass remov$ f b9nacle #adc #df4 ,! ,sp]ry compass #add #dg4 ,! ,br[n compass remov$ f b9nacle #adh #dh4 ,! ,br[n compass remov$ f b9nacle #adi #di4 ,! ,br[n compass #aej #ej4 ,plan ( ,ans*tz 7#aiab7 compass #aee #ea4 ,sectional elevation ( ,ans*tz 7#aiab7 compass #aei ,,! ,,gyroscopic ,,compass3 ,a ,,non-,,ma!matical ,,treatm5t ,,*apt] ,i ,,introduction ,at ?is date x is1 or %\ld be1 unnecess>y to op5 an acc\nt ( ! gyroscopic compass ) a discussion ( ! defects ( ! ord9>y magnetic compass4 ,^! defects are too well kn[n to require m5tion4 ,rec5t advances 9 naval ar*itecture1 p>ticul>ly 9 w>%ip con/ruction1 & v especially ! build+ ( subm>9es1 h result$ 9 ! magnetic compass becom+ less & less useful = accurate navigation1 prim>ily because ( ! upsett+ influ5ce ex]cis$ ^u x by masses ( /eel or iron 9 its neighb\rhood4 ,x may /ill s]ve1 p]haps1 = ! surface navigation ( subm>9es1 b = subm]g$ runs ! use ( a gyro-compass is all b ess5tial4 ,9 w>%ips ! weight ( ! guns & turrets is n[ s heavy t ! magnetic compass c h>dly rema9 unaffect$ by !m & is mat]ially influ5c$ :5 ! guns are tra9$ to diff]5t directions4 ,! %ells !mselves z !y are dis*>g$ are also said to be a cause ( error 9 ! read+ ( ! magnetic compass1 = !y t5d 9 mo/ positions ( ! %ip to drag ! ne$le aft] !m by magnetic attraction z !y pass along ! bore ( ! gun4 ,! value ( ! gyro-compass is n1 h[ev]1 recognis$ only 9 ! _w's w> navies4 ,x is becom+ increas+ly appreciat$ 9 ! m]cantile m>9e1 & !re c be b little d\bt t ! device w soon be ext5sively employ$ on pass5g] l9]s & m]*antm5 g5]ally4 ,9 ! foll[+ pages we attempt to give an acc\nt ( ! work+ ( ! gyro-compass & to describe ! =ms assum$ by ! device 9 practice--suffici5tly fully to illu/rate ! !ory )\t go+ into any great detail on ! con/ructional side--& to d s )\t dep5d+ ^u ! read]'s possess+ ma!matical k4 ,x is to be rem>k$ t x is mu* easi] to treat ! gyroscope & all its practical applications ma!matically ?an non-ma!matically1 & t ! avoidance ( ma!matics g5]ally leads to a discussion ( ?is ess5tially ma!matical device :i* is unsci5tific1 uns\nd1 & ( v little practical value4 ,we tru/ t our acc\nt w be f\nd to avoid ^! defects & t x w prove useful & enlight5+ to ^? :o h s f> fail$ to und]/& ! behavi\r ( ! gyroscope & its applications by reason ( ! fact t hi!rto all tru/wor?y descriptions h be5 c\*$ 9 a highly ma!matical =m or h be5 m]e ma!matics ?9ly disguis$ 9 writt5 words4 ,x is admitt$ly n easy to und]/& gyroscopic ph5om5a ei!r ) or )\t ! aid ( ma!matics1 b on ! o!r h& _m ( ! difficulties ( ! subject are l>gely artificial4 ,?us ! ma!matician1 :5 deal+ ) x1 seems to be mu* m conc]n$ ) 8 equations ?an 9 creat+ a m5tal picture ( :at !y repres5t2 yet e "o ( 8 equations c be or %\ld be capable ( be+ repres5t$ physically4 ,^? :o set out to avoid ma!matics d n usually succe$ 9 giv+ a discussion suffici5tly complete to be ( any practical s]vice aft]w>ds to _! read]s4 ,?us 9 deal+ ) ! gyro-compass ! s-call$ 8popul>0 description 9 mo/ cases beg9s & ends ) an explanation ( :y ! device possesses directive =ce :5 x is set up at ! equator4 ,x is q easy to demon/rate ! exi/5ce ( su* =ce at ! equator4 ,x is n s easy to %[ non-ma!matically h[ ! directive =ce is g5]at$ & appli$ :5 ! compass is situat$ nor? or s\? ( ! equator4 ,! necessity = damp+ ! horizontal vibrations ( ! gyro-axle & h[ ! requir$ damp+ =ce is appli$ 9 practice are /ill m difficult to expla91 :ile ! errors to :i* ! gyro-compass is op5--su* z ! latitude & ! quadrantal errors--are ev5 m try+ to make cle>4 ,! latt] subjects are usually neglect$ 9 ! 8popul>0 acc\nt ( ! compass4 ,yet )\t "s means ( damp+ ! vibrations ref]r$ to or ( elim9at+ or all[+ = ! v>i\s errors1 ! compass1 ev5 ?\gh x c be %[n to possess directive =ce 9 all latitudes1 w\ld be utt]ly useless--especially on bo>d %ip--z a direction indicator4 ,f9ally1 x may be rem>k$ t :ile ! gyro-compass repres5ts to-day probably ! mo/ intricate & involv$ practical application ( ! gyroscope1 x is n ! only "o ( importance4 ,?is fact is to our advantage1 = if we succe$ 9 expla9+ ! !ory & work+ ( ! gyro-compass we %all h succe$$ 9 plac+ ! read] 9 a position enabl+ him readily to und]/& all o!r devices 9 :i* a gyroscope is employ$ or 9 :i* gyroscopic ph5om5a are develop$4 ,,*apt] ,,ii ,,elem5t>y ,,gyroscopic ,,ph5om5a ,let a :eel ,a 7,fig4 #a7 be m\nt$ on an axle ,b ,c j\rnall$ )9 a horizontal r+ ,d4 ,let ?is r+ 9 turn be m\nt$ on j\rnals ,e ,f )9 a v]tical r+ ,g &1 fur!r1 let ?is v]tical r+ be c>ri$ on j\rnals ,h ,j )9 a v]tical frame ,k4 ,?is arrangem5t con/itutes a gyroscopic sy/em hav+ ?ree degrees ( fre$om1 because relatively to ! frame ,k ! :eel may turn ab\t ?ree axes ,b ,c1 ,e ,f1 & ,h ,j mutually at "r angles to ea* o!r & because1 if ! :eel is set sp9n+ on its axle1 gyroscopic prop]ties w be manife/$4 ,illu/ration3 ,,fig4 #a4 ,model ,gyroscope1 ) ,?ree ,degrees ( ,fre$om4 ,! foll[+ is a brief /atem5t ( ! gyroscopic prop]ties manife/$ :5 ! :eel is spun on its axle3 7a7 ,let ! :eel be sp9n+ 9 ! direction ( ! arr[ ,l & let a weight ,w be hung on ! horizontal r+ at ! end ,b ( ! axle4 ,! movem5t produc$ by ?is weight is n a rotation ( ! horizontal r+1 & ! :eel )9 x1 ab\t ! axis ,e ,f4 ,in/ead1 ! horizontal r+ rema9s horizontal & ! :ole sy/em inside ! squ>e frame sets (f rotat+ at a uni=m spe$ ab\t ! axis ,h ,j 9 ! direction ( ! arr[ m>k$ ,m on ! horizontal r+4 ,?is rotation or precession1 z x is call$1 w be ma9ta9$ s long z ! weight ,w rema9s 9 action4 ,!re is "h no "q ( p]petual motion4 ,! "w exp5d$ 9 ov]com+ ! friction at ! v]tical j\rnals is d]iv$ f ! en]gy ( ! sp9n+ :eel1 & :5 ?is en]gy is exhau/$ ! ph5om5on ceases4 ,! ph5om5on c1 9 fact1 only be ma9ta9$ indef9itely by exp5d+ p[] to drive ! :eel aga9/ ! leakage ( en]gy ?r\gh friction at ! j\rnals ( ! axle & ! v]tical axis ,h ,j4 ,a clos] exam9ation ( ! ph5om5on w\ld %[ t !re is a slight rock+ motion ( ! horizontal r+ on its axis ,e ,f1 & !re=e an additional leakage ( en]gy at ! j\rnals ( ?is axis4 ,?is rock+ motion c be neglect$ = our pres5t purposes4 ,x is suffici5tly accurate to say t ! horizontal r+ rema9s horizontal4 7b7 ,! spe$ ( ! precession is proportional to ! weight ,w & to ! spe$ ( rotation ( ! :eel on its axle4 ,= in/ance1 d\bl+ ! weight d\bles ! spe$ ( precession4 7c7 ,if ! direction ( sp9 ( ! :eel is rev]s$ ! direction ( ! precession is also rev]s$4 7d7 ,if ! sp9 ( ! :eel is 9 ! direction ,l1 & if in/ead ( atta*+ a weight at ! end ,b ( ! axle we ex]t an upw>d =ce at ?is po9t ! precession develop$ w be oppos$ to ! direction ( ! arr[ ,m4 7e7 ,if in/ead ( try+ to rotate ! :eel ab\t ! axis ,e ,f by means ( a weight or =ce appli$ at ,b we attempt to turn x ab\t ! v]tical axis ,h ,j by apply+ a horizontal =ce ,v to ! out] r+1 ! :eel w n turn ab\t ! v]tical axis ,h ,j1 b ab\t ! horizontal axis ,e ,f1 ! end ,b ( ! axle ris+ up t[>ds ,h4 7f7 ,z be=e1 ! direction ( ?is movem5t is rev]s$ by rev]s+ ei!r ! direction ( sp9 ( ! :eel or action ( ! =ce ,v4 ,if bo? are rev]s$ simultane\sly ! direction ( ! movem5t produc$ by ! appli$ =ce is n alt]$4 ,! behavi\r set =? above c be summ>is$ 9 a g5]al rule z foll[s3--,if to a sp9n+ :eel possess+ ?ree degrees ( fre$om a =ce be appli$ t5d+ to turn ! :eel ab\t "s axis ,x ,x1 ! actual motion produc$ w n be ab\t ,x ,x b ab\t "s o!r axis ,y ,y2 ?is axis ,y ,y w be su* t rotation ab\t x w t5d to br+ ! axle ( ! sp9n+ :eel into co9cid5ce ) or p>allel ) ! axis ,x ,x2 ! direction ( ! rotation produc$ ab\t ,y ,y w be su* t :5 ! condition ( co9cid5ce or p>allelism is rea*$ ! sp9 ( ! :eel w co9cide 9 direction ) ! rotation we are attempt+ to produce ab\t ! axis ,x ,x4 ,tak+ case 7a7 7,fig4 #a71 x w be se5 t ! axis ,e ,f ab\t :i* we are attempt+ to produce rotation by means ( ! weight ,w1 toge!r ) ! weight ,w itself1 is ( necessity c>ri$ r\nd by ! precession 9 ! direction ,m at ! same rate z ! axle ( ! sp9n+ :eel4 ,! axle 9 ?is case _c !re=e place itself 9 co9cid5ce ) ! axis ( ! appli$ =ce4 ,b x does its be/ to d s4 ,! precession p]si/s & is an expression ( ! fruitless *ase ( ! axis ,e ,f by ! axle ,b ,c4 ,illu/ration3 ,,fig4 #b4 ,model ,gyroscope1 ) ,?ree ,degrees ( ,fre$om4 ,if1 h[ev]1 ! weight is atta*$ by "s k9d ( slid+ connection on ! horizontal r+ 9 su* a way t its l9e ( action rema9s /ation>y 9 space1 !n ! axis ab\t :i* we are attempt+ to produce rotation w also rema9 /ation>y 9 ! position occupi$ by ! axis ,e ,f be=e precession comm5ces4 ,9 ?is case x is q possible = ! axle ( ! :eel to place itself 9 co9cid5ce ) ! axis ( ! appli$ =ce4 ,precession ab\t ,h ,j ?r\gh #ij deg4 w accompli% ?is result1 z indicat$ 9 ,fig4 #b4 ,! weight ,w is n[ act+ at a po9t on ! horizontal r+ :]e x ceases to h any t5d5cy to turn ! :eel ab\t ! axis ,e ,f4 ,:51 !re=e1 ! position ( co9cid5ce is rea*$ precession ceases & ! sy/em comes to re/ 9 ?is position4 ,if ! exp]im5t 7 actually made x w\ld be f\nd t ! mom5tum acquir$ by ! sy/em dur+ ! #ij deg4 turn w\ld c>ry ! axle ?r\gh ! position ( co9cid5ce ) ! axis ( ! appli$ =ce4 ,b imm$iately ! axle passes to ! opposite side ! =ce ,w is ex]t$ on a po9t ( ! horizontal r+ betwe5 ,f & ,c4 ,! action ( ! =ce pass+ on to ?is1 ! opposite1 segm5t ( ! r+ rev]ses ! conditions "u :i* ! sy/em />t$ its movem5t & z a result precession 9 ! direction oppos$ to ! arr[ ,m is set up4 ,! axle ?us t5ds to recov] its position ( co9cid5ce & 9 ! end settles d[n to a vibratory motion f side to side ( ! axis ( ! appli$ weight4 ,friction at ! v]tical j\rnals w 8damp0 ?is vibratory motion1 ! amplitudes ( ! sw+s w decrease1 & ! axle w ultimately settle 9 /eady co9cid5ce ) ! axis ( ! appli$ =ce4 ,9 ?is condition ! =ce w h no fur!r effect on ! sy/em beyond ?r[+ a b5d+ mom5t on to ! v]tical axis4 ,illu/ration3 ,,fig4 #c4 ,frictional ,transmission ( ,turn+ ,mom5t4 ,in/ead ( try+ to make ! :eel rotate ab\t ! axis ,e ,f by apply+ a weight to ! inn] r+ z 9 ,fig4 #a1 let u1 z %[n 9 ,fig4 #c1 m\nt ! squ>e frame ,k on a horizontal axis ,n ,p & atta* ! weight ,w to an arm fix$ on ! frame4 ,! axes ,n ,p & ,e ,f be+--at lea/ initially--coll9e>1 ! effect ( ?is arrangem5t is to ?r[ a turn+ mom5t on to ! :eel ab\t ! axis ,e ,f j z does ! weight ,w 9 ,fig4 #a4 ,x is to be notic$1 h[ev]1 t ! mom5t ( ! weight ,w 9 ,fig4 #c ab\t ! axis ,n ,p is transmitt$ to ! inn] r+ z a mom5t ab\t ! axis ,e ,f solely because ( ! friction exi/+ at ! j\rnals ( ! axis ,e ,f4 ,?is friction may be v small1 s t ! turn+ mom5t receiv$ by ! :eel is only a v small fraction ( ! turn+ mom5t ex]t$ by ! weight ,w ab\t ,n ,p4 ,! effect ( ! arrangem5t is ?us exactly ! same z w\ld be produc$ 9 ! arrangem5t ,fig4 #a if we r$uc$ ! weight ,w to a hundr$? or a ?\s&? ( its value4 ,9 o!r words1 precession ab\t ! v]tical axis ,h ,j w set 9 9 ! direction ( ! arr[ ,m j z be=e1 b ! spe$ ( ?is precession w be only a hundr$? or a ?\s&? ( ! previ\s value4 ,x is n v important to trace out ! behavi\r ( ! sy/em %[n 9 ,fig4 #c beyond a v brief p]iod imm$iately aft] ! weight ,w is appli$4 ,! po9t ( importance is t ! precession produc$ by ! weight is v sl[1 & !re=e t 9 a giv5 int]val ( "t ! am\nt precess$ is v small4 ,fur!r1 ! rate ( ! precession dep5ds solely ^u ! friction at ! j\rnals ( ! axis ,e ,f & n ^u ! weight ,w or ! movem5t ( ! frame ,k except 9 s f> z ^! factors affect ! friction4 ,! less ! friction ! less w be ! rate ( precession & ! am\nt precess$ 9 a giv5 "t4 ,?us by m\nt+ ! axis ,e ,f on knife edges ! friction c be made s small t ! precession produc$ by ! weight ,w becomes immeasurable4 ,h5ce we d$uce t if friction is sub/antially abs5t at ! axis ,e ,f ! frame ,k might be viol5tly rock$ on ! axis ,n ,p or ev5 set into cont9u\s rotation )\t caus+ ! axle ( ! :eel ei!r to dip or to precess4 ,cont9u+ ! argum5t1 we might m\nt ! squ>e frame on a v]tical axis & attempt to produce rotation ( ! :eel ab\t ! axis ,h ,j by apply+ a horizontal =ce to "o side ( ! squ>e frame in/ead ( a =ce ,v on ! out] r+ z %[n 9 ,fig4 #a4 ,a simil> result w\ld be obta9$4 ,grant$ an all b total abs5ce ( friction at ! j\rnals ( ! v]tical axis ,h ,j1 ! precession produc$ ab\t ! horizontal axis ,e ,f w\ld be immeasurably small4 ,?us ! frame might be set into viol5t motion ab\t its v]tical axis )\t caus+ ! axle ei!r to rotate 9 a horizontal plane or to precess 9 a v]tical "o4 ,illu/ration3 ,,fig4 #d4 ,"o ,degree ( ,fre$om ,lo/4 ,f9ally1 if ! squ>e frame 7 m\nt$ on a horizontal axis coll9e> ) ! axle ,b ,c x might obvi\sly be rotat$ ab\t ?is axis )\t affect+ ! sy/em o!rwise ?an by increas+ or r$uc+ ! rubb+ spe$ ( ! axle ,b ,c 9 its be>+s4 ,s9ce pure translation ( ! frame 9 any direction _c apply a turn+ mom5t to ! sy/em ab\t any axis1 & z rotation ( ! frame ab\t any "o ( ! ?ree pr9cipal axes has no effect :i* is measurable on ! ori5tation ( ! axle1 x foll[s t1 giv5 sub/antial abs5ce ( friction at ! axes ,e ,f & ,h ,j1 ! axle ( ! :eel w rema9 con/antly po9t+ p>allel ) its orig9al position1 no matt] h[ ! frame ,k may be mov$ or turn$ ab\t4 ,illu/ration3 ,,fig4 #e4 ,second ,degree ( ,fre$om ,lo/4 ,! gyroscopic sy/em %[n 9 ,fig4 #a has1 z we h said1 8?ree degrees ( fre$om10 because its :eel is free to sp9 ab\t ?ree diff]5t axes mutually at "r angles4 ,x is to be c>efully not$ t x c only truly be said to h ?ree degrees ( fre$om s long z ! inn] r+ & ! p>ts inside x are n rotat$ on ! axis ,e ,f away f ! position :i* 9 ,fig4 #a !y are %[n z occupy+ relatively to ! out] r+4 ,?us rotation ( ! :eel on its axle or ( ! :ole sy/em inside ! squ>e frame on ! axis ,h ,j leaves ! ?ree axes ,b ,c1 ,e ,f1 ,h ,j undi/urb$ at "r angles to ea* o!r4 ,b rotation ( ! inn] r+ & ! p>ts inside x on ! axis ,e ,f t5ds to de/roy "o ( ! degrees ( fre$om4 ,if1 = in/ance1 ! inn] r+ is rotat$ ?r\gh #ij deg41 z %[n 9 ,fig4 #d1 ! axle ,b ,c & ! axis ,h ,j w co9cide 9 direction4 ,9 ?is position ! :eel _c be rotat$ ab\t a horizontal axis at "r angles to ,e ,f & has !re=e virtually only two degrees ( fre$om1 namely1 ab\t ! axis ,e ,f & ab\t ! axis ,h ,b ,c ,j4 ,aga91 if ) ! inn] r+ 9 ! position %[n 9 ,fig4 #d ! out] r+ is turn$ ?r\gh #ij deg4 relatively to ! squ>e frame1 ! sy/em assumes ! configuration %[n 9 ,fig4 #e & ! :eel loses ! p[] ( rotat+ ab\t a horizontal axis 9 ! plane ( ! squ>e frame4 ,illu/ration3 ,,fig4 #f4 ,lo/ ,degrees ( ,fre$om ,re/or$4 ,if1 !n1 9 any application ( ! gyroscope x is necess>y to gu>antee t ! sy/em %all h ?ree degrees ( fre$om 9 all possible configurations1 ! simple m\nt+ %[n 9 ,fig4 #a w n s]ve ! purpose4 ,x c be made to d s 9 ! mann] %[n 9 ,fig4 #f1 namely1 by m\nt+ ! squ>e frame inside a gimbal r+ ,x1 :i* 9 turn is support$ by a frame ,y1 ! two new axes ,t ,u & ,v ,w be+ at "r angles to ea* o!r4 ,9 ! position %[n 9 ,fig4 #d ! new axis ,t ,u w\ld re/ore ! lo/ ?ird degree ( fre$om1 :ile ! second new axis ,v ,w w\ld re/ore ! degree ( fre$om lo/ :5 ! sy/em assum$ ! configuration %[n 9 ,fig4 #e4 ,9 ! gyro-compass x is necess>y to gu>antee t ! sp9n+ :eel 9 all possible configurations %all h ?ree degrees ( fre$om1 & accord+ly we f9d ! :eel m\nt$ 9 a mann] reproduc+ ! features ( ,fig4 #f4 ,on ! o!r h&1 ! majority ( ! movem5ts :i* ! compass sy/em is call$ ^u to make d n entail any?+ except v small degrees ( rotation ( ! inn] r+ & :eel ab\t ! axis ,e ,f 7,fig4 #a71 & !re=e = mo/ purposes ! simple m\nt+ !re %[n reproduces ! requir$ ?ree degrees ( fre$om suffici5tly closely to p]mit u to use x = demon/ration purposes4 ,9 "o v important portion ( our subsequ5t discussion1 h[ev]--namely1 t deal+ ) ! effect on a m>9e gyro-compass produc$ by roll+ & pit*+ ( ! vessel--x w be necess>y = u to take cognisance ( ! fact t ! squ>e frame %[n 9 ,fig4 #a is n fix$ directly to ! %ip's deck1 b is really c>ri$ 9 gimbals z %[n 9 ,fig4 #f4 ,,*apt] ,,iii ,,! ,,gyroscope ,,& ,,! ,,rotation ,,( ,,! ,,e>? ,let u n[ suppose t ! gyroscopic sy/em %[n 9 ,fig4 #a--)\t ! weight ,w--is plac$ on ! equator z repres5t$ at ,p 7,fig4 #g71 & t ! axle is set po9t+ due ea/ & we/ z at ,b ,c4 ,at ! end ( an int]val ( "t1 say two h\rs1 ! e>? w h rotat$ ?r\gh "s angle 1 say #cj deg41 & w h c>ri$ ! gyroscope ) x to ! position ,q4 ,! squ>e frame has ?us cle>ly be5 incl9$ relatively to its orig9al position4 ,x has1 9 fact1 suff]$ ! exact equival5t ( a direct translation ,r toge!r ) a pure rotation ab\t a horizontal axis ?r\gh ,e ( am\nt 4 ,! translation leaves ! sy/em unaffect$1 b ! rotation ( ! frame results 9 ! frame mov+ relatively to ! axle1 :eel1 & inn] r+4 ,! axle1 9 fact1 rema9s p>allel ) its orig9al position at ,p4 ,x is /ill po9t+ ea/ & we/1 b ! frame is n[ incl9$ to x &1 relatively to ! horizontal surface ( ! e>? at ,q1 ! axle is dipp+ at an angle :i* is equal to --or #cj deg4 ,actually1 if we fix$ a disc to ! squ>e frame & a h& to ! inn] r+1 z indicat$ 9 ,fig4 #h1 ! sy/em z erect$ at ! equator w\ld =m a tw5ty-f\r h\r clock indicat+ /rictly accurate sid]eal "t z di/9ct f mean sol> "t4 ,to an obs]v] on ! e>? ! h& w\ld appe> to travel clockwise r\nd ! disc once 9 tw5ty-f\r h\rs4 ,actually1 h[ev]1 ! h& w\ld n rotate1 b w\ld rema9 con/antly p>allel ) its orig9al position1 :ile ! disc w\ld travel anti-clockwise relatively to ! h& & w\ld make "o complete turn 9 tw5ty-f\r h\rs4 ,! h& w\ld rema9 p>allel ) its orig9al position by virtue ( ! fact already /at$1 namely1 t ! =ce appli$ to ! inn] r+ ?r\gh its all-b-frictionless supports is v small1 & 9 any ev5t does n turn ! h& clockwise1 b causes ! :eel1 inn] r+1 & h& to precess ab\t ! v]tical axis ,h ,j4 ,! rate at :i* ?is precession took place w\ld be a measure ( ! success ) :i* we _h elim9at$ friction at ! horizontal axis ,e ,f4 ,illu/ration3 ,,fig4 #g4 ,elem5t>y ,gyroscope at ,equator4 ,illu/ration3 ,,fig4 #h4 ,gyroscopic ,clock4 ,x might be ?\ght t ! sy/em w\ld )\t fur!r addition s]ve z a compass1 = if x ma9ta9s its axle con/antly po9t+ 9 "o direction x is j z good z a compass :i* always po9ts its ne$le t[>ds ! magnetic nor?4 ,9 ! magnetic compass1 h[ev]1 ! ne$le has a directive =ce appli$ to x :i* enables x to recov] its /&>d direction if x %\ld be accid5tally deflect$ f x4 ,9 ! gyroscopic sy/em we h be5 consid]+ !re is no su* directive =ce4 ,! axle w rema9 po9t+ 9 "o direction1 x is true1 b ! sy/em is indiff]5t z to :at t direction may be4 ,if ! axle is accid5tally deflect$ x w rema9 po9t+ 9 ! new direction z consi/5tly z x did be=e 9 ! orig9ally set direction4 ,z a sub/itute = ! ord9>y compass1 !n1 ! success ( ! device w\ld dep5d ^u ! success ) :i* accid5tal deflect+ =ces 7 prev5t$ f act+ on ! axle aft] x _h be5 set 9 a kn[n direction4 ,9 practice1 z ,dr4 ,ans*tz f\nd 9 8 e>ly inve/igations1 x is excessively difficult1 if n q impossible1 to con/ruct a gyroscopic sy/em 9 :i* ! c5tre ( gravity & ! c5tre ( susp5sion are absolutely co9cid5t4 ,z a result a v m9ute gravity torque is ?r[n on ! sy/em1 & 9 consequ5ce ! axle v sl[ly precesses away f ! orig9al set direction4 ,?is fact & ! complication ( p>ts requir$ to give practical effect to ! idea l$ ,dr4 ,ans*tz to ab&on 8 e>ly attempts at provid+ a compass sub/itute ( ! app>5tly simple nature describ$ above4 ,illu/ration3 ,,fig4 #i4 ,elem5t>y ,gyro-,compass4 ,an addition to ! sy/em ( a v simple k9d 9 itself n only end[s ! axle ) directive =ce1 b makes ! direction :i* x seeks ! nor? & s\? "o1 & ?us conv]ts ! sy/em into a device possess+ ! famili> prop]ty ( ! compass4 ,?is addition consi/s ( a p5dulum-l weight ,s 7,fig4 #i71 atta*$ bel[ ! :eel by a /irrup fix$ to ! inn] r+ s t ! weight1 /irrup1 inn] r+1 axle1 & :eel may sw+ z a :ole on ! horizontal axis ,e ,f4 ,let u suppose t ! sy/em ) ?is addition is set up at ! equator & t ! axle ?is "t is align$ at "r angles to ! equator s t ! end ,b1 z %[n at ,i 7,fig4 #aj71 po9ts due nor?4 ,9 ?is condition ! inn] r+ is horizontal & ! weight ,s is v]tically bel[ ! p5dulum axis ,e ,f4 ,no turn+ mom5t is !re=e be+ appli$ by gravity to ! :eel4 ,if ?r\gh imp]fection ( workman%ip ! c5tre ( susp5sion ( ! sy/em is n absolutely co9cid5t ) ! c5tre ( gravity be=e ! weight ,s & its /irrup are atta*$1 !n ! m9ute gravity torque aris+ f ! lack ( co9cid5ce w be balanc$ automatically by ! weight1 ! inn] r+ tak+ up "s position m9utely incl9$ to ! horizontal4 ,!re w ?us "u all conditions be no resultant turn+ mom5t appli$ by gravity to ! sy/em z ?us set up4 ,9 addition1 ! axle1 ly+ nor? & s\? z x does1 is align$ p>allel ) ! e>?'s pol> diamet]4 ,consequ5tly ! rotation ( ! e>? c only move x p>allel ) its orig9al position1 & !re=e does n t5d to cause relative motion betwe5 x & ! squ>e frame4 ,we conclude1 !n1 t 9 ?is nor? & s\? position ( ! axle ! sy/em is n act$ ^u by any =ce or influ5ce t5d+ to cause ! axle to dep>t f ! nor? & s\? position4 ,illu/ration3 ,,fig4 #aj4 ,elem5t>y ,compass at ,equator4 ,n[ let u suppose t ! axle by "s ag5cy is =c$ into p>allelism ) ! equator s t ! end ,b po9ts due ea/ z indicat$ at ,,ii 7,fig4 #aj74 ,imm$iately aft] x takes up ?is position ! t5d5cy ( ! axle to rema9 p>allel ) ?is1 its new orig9al1 direction becomes manife/$ 9 attempt$ relative motion betwe5 ! axle1 :eel1 & inn] r+ on ! "o h& & ! squ>e frame on ! o!r4 ,?us z ! e>? rotates ! axle1 etc41 t5d to set !mselves relatively to ! frame 9 ! position %[n at ,,iii4 ,9 ?is position1 h[ev]1 ! weight ,s be+ rigidly susp5d$ f ! inn] r+1 is no long] v]tically bel[ ! p5dulum axis ,e ,f4 ,gravity act+ ^u ! weight !re=e applies a turn+ =ce to ! :eel1 etc41 ab\t ! axis ,e ,f4 ,! sy/em is ?us "u ! same conditions z ^? repres5t$ 9 ,fig4 #a1 :5 ! weight ,w is hung on ! inn] r+ at ,b4 ,precession ab\t ! v]tical axis !re=e sets 91 9 ! direction ,m 7,fig4 #a71 s t ! end ,b ( ! axle sw+s r\nd f ! ea/ t[>ds ! nor?4 ,let u reset ! sy/em 9 position ,i1 & !n by "s ag5cy cause ! axle aga9 to align itself p>allel ) ! equator1 ?is "t1 h[ev]1 ) ! end ,b po9t+ due we/ z %[n at ,,iv 7,fig4 #aj74 ,z be=e1 ! rotation ( ! e>? comb9$ ) ! t5d5cy ( ! axle to rema9 p>allel ) ! new we/ & ea/ position results 9 attempt$ relative motion betwe5 ! axle1 etc41 & ! squ>e frame1 s t 9 a little "t ! sy/em w\ld adopt ! configuration %[n at ,v4 ,9 ?is configuration1 h[ev]1 gravity z be=e applies ?r\gh ! weight ,s a turn+ =ce ab\t ! p5dulum axis ,e ,f4 ,n[1 comp>+ ! two configurations ,,iii & ,v1 x w be se5 t1 m]e ref]5ce lett]s or simil> di/+ui%+ m>ks be+ wa%$ out1 !y are indi/+ui%able except = "o fact3 ! :eel is rotat+ 9 opposite directions4 ,if ) ! sy/em z arrang$ 9 ,fig4 #a we rev]se ! direction ( sp9 ( ! :eel )\t rev]s+ ! direction ( ! appli$ =ce ,w1 !n1 z we "k already1 ! direction ( ! precession w be rev]s$4 ,precession ab\t ! v]tical axis w take place 9 ! direction oppos$ to ! arr[ ,m4 ,h5ce 9 ! configuration %[n at ,v 7,fig4 #aj71 ! precession induc$ by ! action ( gravity on ! weight ,s causes ! end ,b ( ! axle to sw+ up f due we/ t[>ds ! nor?4 ,we are ?us l$ to id5tify ! end ,b ( ! axle z ! nor?-seek+ end & ! end ,c z ! s\?-seek+4 ,) ,b po9t+ due nor? z at ,i1 !re is no =ce act+ on ! sy/em t5d+ to make ! axle dep>t f ! nor? & s\? direction4 ,if ,b is swung ov] to ! ea/ or we/--or int]m$iately1 z may be tak5 = grant$--a =ce is call$ into play t5d+ to move ! end ,b back t[>ds ! nor?4 ,x foll[s1 !re=e1 t ! re/+ position ( ! axle is ! nor? & s\? "o ) ! end ,b po9t+ nor?4 ,x may be said1 p]haps1 t we h neglect$ to discuss :at happ5s if f ! position ,i ! :eel is turn$ by "s ag5cy "r r\nd until ! end ,b ( ! axle po9ts due s\?4 ,9 ?is condition !re is no resultant gravity torque on ! p5dulum axis1 & ! axle is ly+ p>allel ) ! e>?'s pol> axis1 s t ! rotation ( ! e>? does n cause relative motion betwe5 ! :eel1 etc41 & ! frame4 ,j z 9 ! orig9al configuration ,i1 !re is ?us 9 ?is condition no =ce appli$ to ! sy/em t5d+ to make ! end ,b sw+ away f ! pole4 ,b z ! read] may readily e/abli% = himself by rev]s+ ! arr[s & ref]5ce lett]s 9 ! five diagrams ( ,fig4 #aj1 ! slighte/ dep>ture ( ! end ,b ( ! axle f ! s\?-po9t+ direction t[>ds ei!r side ( ! m]idian w call into play a =ce :i* w cause ! end ,b to precess up t[>ds ! nor?4 ,) ! :eel sp9n+ 9 ! direction we h %[n ?r\gh\t our illu/rations ! only /able position ( equilibrium = ! axle is ! nor? & s\? ) ! end ,b po9t+ nor?4 ,x may be po9t$ out t ! magnetic ne$le c1 l ! gyro-compass axle1 assume a position ( un/able equilibrium ) ! nor?-seek+ end po9t+ s\?4 ,a po9t ( v great practical importance into :i* to inquire is ! magnitude ( ! directive =ce1 ! exi/5ce ( :i*1 :5 ! axle is deflect$ f ! nor? & s\? position1 we h j demon/rat$4 ,?is directive =ce or re/or+ mom5t1 z w h be5 ga!r$ f our explanation1 increases ) ! deflection f ! nor?1 be+ a maximum :5 ! axle is ly+ ea/ & we/ or we/ & ea/4 ,its magnitude 9 any position ( ! axle dep5ds ^u 7a7 ! spe$ ( rotation ( ! e>? on its pol> axis1 7b7 ! spe$ ( ! sp9n+ :eel on its axle1 & 7c7 ! mass1 or1 m correctly1 ! mom5t ( in]tia1 ( ! :eel4 ,! fir/ item is small--#j4jjjg ( a revolution p] m9ute--& is q beyond our control4 ,! second factor is consequ5tly made z l>ge z possible1 :ile ! ?ird is also made l>ge1 b a limit is plac$ to our *oice by que/ions ( safety & temp]ature rise at ! high spe$s adopt$ = ! sp9 ( ! :eel4 ,9 ! foll[+ table we give ! values ( ^! factors = ?ree ( ! types ( gyro-compass to be describ$ lat]4 ,compass ,:eel diam4 ,:eel weight ,spe$ 94 lbs4 r4p4m4 ,ans*tz#a #f #aj #bj1jjj ,sp]ry #ab #de #h1fjj ,br[n #d #d #ae1jjj ,! value ( ! directive =ce = ! same ?ree gyro-compasses & = an ord9>y magnetic compass is giv5 9 ! next table1 7#a7 = ! axle--or ne$le--ly+ due ea/ & we/1 & 7#b7 = ! axle--or ne$le--deflect$ #a deg4 ea/ or we/ ( nor?--true or magnetic4 ,directive ,=ce at ,equator4 ,axle 7or ne$le7 ,axle 7or ne$le7 ,e4 & ,w4 #a deg4 ,e4 or ,w4 ( ,n4 ,=ce ,lev]age ,=ce ,lev]age ,gra9s 94 ,gra9s 94 ,ans*tz #ade #a #b #a ,sp]ry4 #aadj #a #bj #a ,br[n #ab #a #a ,magnetic#b #dj #a #a ,illu/ration3 ,,fig4 #aa4 ,elem5t>y ,compass at #ee deg4 ,n4 ,lat4 ,we h n[ to expla9 h[ ! gyro-p5dulum sy/em manife/s its compass-l prop]ty :5 x is transf]r$ f ! equator to "s degree ( latitude nor? or s\?4 ,9 ,fig4 #aa we repres5t ! sy/em z set up 9 ! latitude ( ! ,briti% ,isles4 ,! axle is horizontal & ! end ,b is po9t+ due ea/4 ,9 ?is configuration ! e>?'s rotation is1 ?r\gh ! action ( gravity on ! p5dulum bob ,s1 try+ to make ! :eel turn r\nd ! e>?'s pol> axis once e tw5ty-f\r h\rs4 ,z be=e1 9 accordance ) ! fundam5tal prop]ty ( ! gyroscope1 ! :eel w try to set its axle into co9cid5ce ) or p>allel ) ! axis ab\t :i* x is be+ =c$ to rotate4 ,9 o!r words1 ! :eel w endeav\r to turn 9 su* a way z to align its axle along ,v ,u ) ! end ,b t[>ds ,u4 ,?is movem5t c be effect$ by a rotation ab\t ! v]tical axis ,h ,j ?r\gh a "r angle comb9$ ) a rotation ab\t ! horizontal axis ,e ,f ?r\gh an angle equal to ! latitude ( ! /ation at :i* ! sy/em is set up4 ,! rotation ab\t ! v]tical axis ,h ,j does n result 9 deflect+ ! weight ,s away f ! plumb l9e1 & !re=e c be completely fulfill$4 ,! rotation ab\t ! horizontal axis does1 h[ev]1 affect ! bob4 ,! axle1 hav+ execut$ ! horizontal portion ( its movem5t1 is po9t+ its end ,b due nor?1 b ?is end1 unlike its behavi\r at ! equator1 manife/s a desire to rise v]tically s z to align ! axle along ,v ,u4 ,its desire to d s is resi/$ by ! bob ,s1 & ! axle !re=e fails to complete ! full movem5t4 ,! axle is ?us held sub/antially horizontal ) its end ,b po9t+ to ! nor?4 ,z ! e>? rotates ! desire ( ! axle to align itself p>allel ) ! pol> axis p]si/s4 ,9 attempt+ cont9u\sly to fulfil ?is desire x acquires a slight upw>d tilt1 :i* is suffici5t to br+ ! p5dulum weight into action4 ,) ! weight ?us slightly deflect$ t[>ds ! nor? a mom5t is appli$ to ! :eel :i* t5ds to turn ! :eel ab\t ! horizontal axis ,e ,f 9 su* a way z to br+ ! end ,b d[n aga9 to ! horizontal plane4 ,su* a mom5t1 z we "k f ! fundam5tal rule ( ! gyroscope1 w actually produce precession ab\t ! v]tical axis ,h ,j1 ! direction ( ?is precession be+ su* z to cause ! end ,b to move away f ! nor? t[>ds ! we/4 ,! fact1 !n1 t ! axle is prev5t$ f align+ itself completely p>allel ) ! e>?'s pol> axis ?us app>5tly results1 once x has f\nd ! nor?1 9 mak+ x w&]1 9 nor!rn latitudes1 t[>ds ! we/4 ,?is is n s4 ,once ! axle has f\nd ! nor? a /eady uni=m precession t[>ds ! we/ is requir$ to ma9ta9 x on ! nor?4 ,?us 9 ,fig4 #ab let ,a be ! :eel & axle ( ! compass :5 x f9ds ! nor?4 ,if ! axle ma9ta9$ ?is alignm5t !n "s "t lat] x w\ld assume ! position %[n dott$ at ,d2 t is to say1 x w\ld be po9t+ t[>ds ea/ ( nor?4 ,to ma9ta9 x on ! nor? x mu/ rotate we/w>dly ?r\gh ! angle 9 ! int]val betwe5 ,a & ,d4 ,z ?is angle gr[s ) ! int]val ! requir$ rotation is really equival5t to a /eady uni=m precession t[>ds ! we/4 ,illu/ration3 ,,fig4 #ab4 ,compass at ,equator & ne> ,nor? ,pole4 ,if ! compass 9 ,fig4 #ab is practically at ! nor? pole x is cle> t to hold ! end ,b ( ! axle on ! nor? ! axle has to precess ab\t ! v]tical axis ,h ,j ( ! compass m\nt+ at ! rate ( practically "o complete revolution p] tw5ty-f\r h\rs--t is1 #j4jjjg revolution p] m9ute4 ,at ! equator ! requir$ rate ( precession ab\t ,h ,j is z]o1 = any movem5t ab\t ?is axis w c>ry ! axle away f ! nor?4 ,at int]m$iate latitudes ! precession requir$ to hold ! axle on ! nor? has an int]m$iate value4 ,its value = any latitude is1 9 fact1 #j4jjjg s9 9 revolutions p] m9ute4 ,?us z ! latitude is *ang$ ! requir$ rate ( precession also *anges4 ,s1 too1 does ! angle 7,fig4 #aa71 by :i* ! axle fails to rea* p>allelism ) ! e>?'s pol> axis1 & consequ5tly s does ! /r5g? ) :i* ! axle desires to rea* ?is alignm5t4 ,z ! equator is left f>!r & f>!r beh9d1 !n1 ! axle comes to re/ po9t+ nor? ) a great] & great] upw>d tilt f ! horizontal4 ,! appli$ mom5t ( ! weight ,s ?us increases4 ,x increases j at ! rate necess>y to give ! requir$ rate ( we/]ly precession = ! p>ticul> latitude 9 :i* ! compass is at any mom5t /ation$4 ,%\ld any?+ prev5t ! axle f acquir+ ! tilt appropriate to ! latitude1 or %\ld ! we/]ly precession on ! v]tical axis caus$ by ?is tilt be oppos$ & r$uc$ 9 any way1 ! axle w fail to keep on ! nor? & w lag beh9d ! m]idian ) an ea/]ly deviation4 ,we %all see lat] on t ! precession ab\t ! v]tical axis is 9 "s designs ( gyro-compass unavoidably oppos$1 & t z a consequ5ce ^! compasses exhibit a latitude error4 ,we h ?us %[n t ! ef=t ( ! compass to set its axle p>allel ) ! e>?'s pol> axis1 comb9$ ) ! action ( gravity on ! p5dulum weight1 is necess>y to ! compass if ! axle once hav+ f\nd ! nor? is to rema9 on x1 & t ?is ef=t ( ! axle increases 9 /r5g? ! f>!r nor?--or s\?--! compass is mov$ f ! equator4 ,:at1 h[ev]1 ?is ef=t ga9s 9 /r5g? z ! angle ( latitude increases ! effective directive =ce on ! compass loses4 ,?us 9 ,fig4 #aa ! directive =ce may be repres5t$ z at f by a l9e p>allel ) ! e>?'s pol> axis4 ,?is l9e repres5ts ! magnitude ( ! compass's ef=t to set its axle p>allel ) ! pol> axis4 ,! spe$ ( ! sp9n+ :eel & its mom5t ( in]tia h n be5 alt]$ by mov+ ! compass away f ! equator1 nor has ! angul> spe$ ( ! compass r\nd ! e>?'s axis1 = al?\gh ! compass is mov+ 9 a circle ( r$uc$ radius ,t ,b1 & !re=e is travell+ ) less l9e> velocity ?an at ! equator1 x is /ill mak+ "o turn p] tw5ty-f\r h\rs r\nd ! pol> axis ( ! e>?4 ,?us ! ?ree factors fix+ ! magnitude ( ! 8directive =ce0 are unalt]$4 ,! =ce f is ?us ! same z t ex]t$ on ! compass at ! equator4 ,x does n1 h[ev]1 act z be=e1 purely ab\t ! v]tical axis ,h ,j1 b p>tly ab\t ,h ,j & p>tly ab\t ! horizontal axis ,e ,f4 ,x may be reg>d$ z a =ce appli$ at ! end ,b ( ! axle & !re=e z t5d+ to turn ! :eel ab\t an imag9>y axis a b4 ,we may resolve x into two compon5ts p & q1 p be+ at "r angles to ! axis ,h ,j & q at "r angles to ,e ,f4 ,! compon5t q repres5ts ! magnitude ( ! upw>dly tilt+ effect appli$ to ! axle by ! rotation ( ! e>?4 ,! compon5t p repres5ts ! effective directive =ce t5d+ to re/ore ! axle f ! deflect$ position repres5t$ t[>ds ! nor? 9 ! horizontal plane4 ,! angle betwe5 ?is effective compon5t & ! full =ce f is 1 ! angle ( latitude ( ! /ation at :i* ! compass is set up4 ,! effective directive =ce is ?us f cos 1 & !re=e dim9i%es f ! value f at ! equator t[>ds z]o z ! nor?--or s\?--pole is approa*$4 ,,*apt] ,,iv ,,damp+ ,,! ,,vibrations ,,( ,,! ,,gyro-,,compass ,review+ :at we h already e/abli%$1 we see t a gyroscopic sy/em possess+ 8?ree degrees ( fre$om0 & hav+ a p5dulum weight fix$ bel[ ! :eel manife/s a t5d5cy 9 all latitudes to pres]ve its axle po9t+ 9 ! nor? & s\? direction1 a 8directive =ce0 or re/or+ mom5t be+ develop$ & appli$ to ! axle if ! nor? & s\? position is dep>t$ f4 ,! magnitude ( ! directive =ce 9 any giv5 latitude increases ) ! deflection1 f z]o :5 ! axle is po9t+ nor? & s\? up to a maximum :5 x is align$ ea/ & we/4 ,at any giv5 angle ( deflection ( ! axle ! magnitude ( ! directive =ce v>ies ) ! latitude 9 :i* ! sy/em is /ation$1 be+ z]o at ! nor? or s\? 7true7 pole & a maximum at ! equator4 ,f9ally1 at any giv5 angle ( deflection ( ! axle & 9 any giv5 latitude ! magnitude ( ! directive =ce is det]m9$ by 7a7 ! spe$ ( rotation ( ! e>? on its pol> axis1 7b7 ! spe$ ( rotation ( ! sp9n+ :eel on its axle1 & 7c7 ! mass or mom5t ( in]tia ( ! sp9n+ :eel4 ,we h n[ to consid] sev]al important matt]s affect+ ! practical application ( ! gyroscope-p5dulum comb9ation z a sub/itute = ! magnetic compass4 ,! fir/ practical consid]ation :i* arises naturally 9 our m9ds is ! "q3 ,c a sy/em be devis$ & con/ruct$ suffici5tly robu/ to )/& ! trials & knocks ( e-day use & yet be suffici5tly delicate to respond to ! feeble directive =ces on ! effect ( :i* its action z a compass dep5ds8 ,f ! table giv5 previ\sly x w h be5 not$ t 9 ! ?ree *ief types ( gyro-compass s f> develop$ ! directive =ces develop$ are 9 two examples great] ?an ! correspond+ directive =ce appli$ to ! c>d ( a magnetic compass1 :ile 9 ! ?ird ! directive =ce is mat]ially l[]4 ,ev5 ?\gh !y 7 all consid]ably great] ?an ! =ce appli$ to ! ne$le ( a magnetic compass1 "s d\bt z to _! suffici5cy to effect _! "w w\ld rema91 = !y h to control s5sitive elem5ts1 compris+ a sp9n+ :eel1 axle1 support+ r+s1 etc41 weigh+ any?+ f #g lb4 to ab\t a hundr$weight1 :]eas 9 ! ord9>y compass ! s5sitive elem5t consi/+ ( ! c>d & its atta*$ magnetic ne$les weighs r\nd ab\t oz4 ,! actual weights ( ! s5sitive elem5ts are giv5 9 ! foll[+ table4 ,weight ( ,s5sitive ,elem5t4 ,ans*tz compass #ae lb4 ,sp]ry compass #ajj lb4 ,br[n compass #g lb4 ,?omson magnetic compass #agh gra9s ,:e!r or n ! directive =ce develop$ w be suffici5t to control ! movem5t ( ! s5sitive elem5t 9 a gyro-compass mu/ cle>ly dep5d v l>gely ^u ! degree ( success rea*$ 9 bani%+ friction f ! v]tical axis ab\t :i* ! s5sitive elem5t moves4 ,)\t = ! pres5t describ+ ! means actually adopt$ to secure virtually frictionless support 9 ! ?ree types ( gyro-compass1 we may say t 7 !y o!r ?an v ref9$ no compass action :atev] w\ld be manife/$4 ,9 ! e>ly !oretical days ( ! gyro-compass be=e suffici5tly ref9$ practical con/ructive me?ods _h be5 develop$1 ! exp]im5tal v]ification ( ! ma!matical results arriv$ at c\ld n be attempt$4 ,grant$ ! atta9m5t 9 practice ( a satisfactory frictionless me?od ( support+ ! s5sitive elem5t1 we h next to note t ! simple gyro-p5dulum sy/em :i* we h be5 consid]+ w\ld be q useless z a direction-f9d+ device ei!r at sea or on l& by virtue ( ! fact t ! v abs5ce ( friction at ! v]tical axis w\ld enc\rage ! s5sitive elem5t to oscillate f side to side ( ! m]idian "u ! lea/ provocation4 ,! p]iod ( oscillation w\ld be a prolong$ "o1 mu* too prolong$1 9 fact1 to p]mit ! true nor? to be det]m9$ by tak+ ! mean ( ! extreme positions rea*$ by ! gyro-axle 9 ! c\rse ( its oscillation4 ,we h se5 t ! simple gyro-p5dulum sy/em :i* we h s f> be5 consid]+1 :5 plac$ on ! equator1 manife/s a t5d5cy to set its axle nor? & s\?1 t if ! axle is deflect$ t[>ds ! ea/ a we/]ly turn+ directive =ce is develop$1 & t if ! axle is deflect$ t[>ds ! we/ an ea/]ly turn+ directive =ce is develop$4 ,9 an ord9>y v]tical p5dulum 7,fig4 #ac71 ! re/+ position ( ! bob is at d4 ,if x is swung to ! position e--t[>ds ! ea/1 let u say--! weight w ( ! bob supplies a mom5t ab\t ! axis at g1 t5d+ to re/ore ! p5dulum to its re/+ position2 :ile if x is swung t[>ds ! position f--t[>ds ! we/1 we may suppose--! mom5t is rev]s$ & aga9 acts to re/ore ! p5dulum to its re/+ position4 ,illu/ration3 ,,fig4 #ac4 ,p5dulum & ,compass4 ,! gyro-p5dulum sy/em z set up at ! equator is1 x w be se51 subject$ to an exactly analog\s set ( =ces :5 its axle is deflect$ ea/ or we/4 ,! sy/em1 9 fact1 con/itutes virtually a horizontal p5dulum1 ! v]tical axis ,h ,j be+ id5tifi$ ) ! axis at g 9 ! ord9>y p5dulum4 ,n[ we "k t if we deflect an ord9>y p5dulum to "s su* position z e & let x g x w sw+ ?r\gh ! re/+ position d to a position f equidi/ant on ! o!r side1 & w cont9ue to vibrate until friction at ! axis g1 air resi/ance1 etc41 sap its orig9al /ock ( en]gy communicat$ to x by ! initial deflection4 ,! p]iod ( vibration--! "t elaps+ betwe5 two successive passages ( ! bob 9 ! same direction ?r\gh ! re/+ position--is det]m9$ by ! l5g? ( ! p5dulum & rema9s con/ant ?r\gh\t1 ev5 :5 ! amplitude ( ! sw+ has fall5 (f virtually to no?+4 ,an exactly analog\s /ate ( affairs exi/s ) ! gyro-p5dulum sy/em4 ,if ! axle is deflect$ t[>ds ! ea/ & !n let g x w sw+ back "u ! action ( ! directive or re/or+ =ce ?r\gh ! nor? & s\? position ov] to an equal angle on ! we/]n side1 & w !reaft] vibrate back & =? ) a con/ant p]iod1 until frictional & o!r losses cause ! motion to die away4 ,! p]iod ( vibration is det]m9$ by a complication ( factors1 among :i* are ! spe$ at :i* ! :eel is sp9n+ on its axle1 ! spe$ ( rotation ( ! e>?1 & ! mass ( ! s5sitive elem5t4 ,if ! s5sitive elem5t c be reg>d$ z consi/+ solely ( ! :eel1 !n1 no matt] :at may be ! size ( ! :eel1 s long z x is 9 ! =m ( a circul> disc1 ! p]iod ( vibration is det]m9$ solely by ! spe$ ( ! :eel & ! spe$ ( rotation ( ! e>?4 ,= a :eel at ! equator runn+ at #bj1jjj revolutions p] m9ute ! p]iod ( vibration w\ld be ab\t elev5 seconds4 ,9 practice1 h[ev]1 ! weight ( ! axle1 ! inn] & out] support+ r+s--or _! equival5ts--! p5dulum bob & v>i\s o!r fitt+s & adjuncts ( a second>y nature h to be add$ to ! weight ( ! :eel 9 assess+ ! influ5ce ( ! s5sitive elem5t ^u ! p]iod ( vibration4 ,! great] ! mass--or m correctly1 ! mom5t ( in]tia--( ! s5sitive elem5t ! long] w be ! p]iod ( vibration4 ,9 ! e>ly--#aiaj--;,ans*tz gyro-compass ! s5sitive elem5t _h a mom5t ( in]tia su* t ! p]iod ( vibration at ! equator 0 j ov] #fa m9utes2 t is to say1 #ccd times z long z x w\ld h be5 if ! s5sitive elem5t _h consi/$ ( no?+ b ! sp9n+ :eel4 ,?is v prolong$ p]iod1 7 no?+ done to rectify matt]s1 w\ld be a v s]i\s objection 9 practice to ! use ( ! gyro-compass4 ,! axle1 if deflect$1 w\ld take ab\t half an h\r to rea* an equal position on ! opposite side ( ! m]idian4 ,h5ce1 if1 :5 a compass read+ 0 desir$1 ! axle 7 f\nd to be vibrat+1 at lea/ half an h\r w\ld be requir$ to det]m9e ! nor? & s\? direction by obs]v+ ! two extreme positions ( ! axle & tak+ ! mean4 ,! alt]native w\ld be to wait until ! vibration di$ away4 ,?is c\rse w\ld involve1 h[ev]1 a v mu* great] delay1 = ! virtual abs5ce ( friction at ! v]tical axis ( ! sy/em--an ess5tial1 z we h se51 if ! directive =ce is to be all[$ to come into play at all--results 9 ! vibration be+ practically un*eck$1 s t1 once />t$1 x w\ld cont9ue almo/ indef9itely4 ,"s means ( damp+ ! vibration analog\s to ! damp+ action ( ! liquid 9 a magnetic compass mu/ cle>ly !n be provid$4 ,ideally ! means %\ld be su* t if ! axle is deflect$ ?r\gh any angle x w return to ! nor? & s\? position 9 a 8dead-beat0 mann] & n sw+ across ! m]idian ov] to ! opposite side4 ,?is ideal _c be realis$ 9 practice4 ,return+ to ! simple p5dulum illu/rat$ 9 ,fig4 #ac we h to notice t ! influ5ce at "w caus+ ! vibration is ! weight ( ! bob act+ ab\t ! axis at g4 ,?is influ5ce is a maximum :5 ! bob is at ! extreme positions e f & is z]o :5 ! bob is at d4 ,on ! o!r h&1 ! velocity ( ! bob is z]o at ! two extreme positions e f & is a maximum at d4 ,dur+ ! sw+ f e to d ! vibrat+ influ5ce is help+ ! motion ( ! bob & ! velocity consequ5tly increases4 ,at d ! vibrat+ influ5ce disappe>s1 :ile dur+ ! sw+ f d to f x reappe>s & ?is "t opposes ! motion ( ! bob1 ! velocity ( :i* consequ5tly becomes less & less4 ,! movem5t ( ! bob f d to f 9 opposition to ! vibrat+ influ5ce is a*iev$ by ! mom5tum ( ! bob aris+ f ! velocity :i* x ga!rs dur+ its sw+ f e to d4 ,= ! angle d g f to be equal to ! angle d g e ! velocity ( ! bob z x passes ?r\gh ! position d mu/ j be a c]ta9 am\nt1 no m & no less1 namely1 ! velocity :i* a body w\ld acquire 9 fall+ f re/ at ! level ( ! bob at e v]tically d[nw>ds to ! level ( ! bob at d4 ,if ! velocity ( ! bob :5 x sw+s ?r\gh d is great] ?an ?is am\nt ! bob w sw+ beyond ! position f4 ,if x is less ! bob w fail to rea* f4 ,illu/ration3 ,,fig4 #ad4 ,damp$ & ,undamp$ ,vibrations4 ,! analogue ( ! problem to be solv$ 9 connection ) ! gyro-compass is to devise "s means t w rob ! p5dulum bob on ea* successive sw+ ( "s p]c5tage ( ! velocity ) :i* x pass$ ?r\gh ! re/+ position d dur+ ! prec$+ sw+4 ,by s do+ we %all obvi\sly decrease cont9u\sly ! angle to :i* ! p5dulum sw+s on ea* side ( ! position d4 ,?us in/ead ( ! sw+s z trac$ out on a piece ( pap] mov+ bel[ ! bob be+ z %[n at ,a 7,fig4 #ad71 !y w be ( ! =m repres5t$ at ,b4 ,! amplitudes1 in/ead ( rema9+ ( uni=m am\nt practically indef9itely1 w dim9i% ) ea* sw+ until !y become s small z to be invisible4 ,x is to be not$ t !oretically ! vibrations _c be completely suppress$ ev5 aft] an indef9ite numb] ( sw+s1 = if ! velocity at ! re/+ position is at ea* sw+1 say1 #ej p] c5t4 less ?an at ! previ\s passage1 x w always be some?+ & nev] become z]o4 ,x w1 h[ev]1 9 q a small numb] ( sw+s become s l[ t ! motion ( ! p5dulum w be practically undisc]nible4 ,?us ) a #ej p] c5t4 decrem5t ! velocity at ! eigh? passage ( ! bob ?r\gh ! re/+ position w be less ?an #a p] c5t4 ( :at x 0 at ! fir/ passage4 ,x is also to be not$ t :ile ! amplitudes are decreas$ 9 ! mann] indicat$ ! p]iods ( ! sw+s are n be+ made less4 ,9 an ord9>y p5dulum ! p]iod1 z we h said1 dep5ds solely ^u ! l5g? &--)9 q wide limits at lea/--rema9s ! same :atev] be ! angle to :i* we orig9ally deflect ! bob4 ,we %\ld !re=e expect t if ! sw+s are 8damp$0 9 ! way %[n at ,b 7,fig4 #ad71 ! p]iod ( ea* sw+ w\ld be ! same & equal to t ( ! undamp$ sw+s repres5t$ at ,a4 ,actually ! p]iod ( a damp$ vibration is always some:at great] ?an t ( ! same sy/em vibrat+ freely1 = by robb+ ! p5dulum ( "s ( its velocity at ea* sw+ we are virtually caus+ ! bob to pass ?r\gh ! re/+ position ) ! velocity ( a free sw++ p5dulum ( great] l5g? & !re=e ( increas$ p]iod4 ,! increase 9 ! p]iod ( ! damp$ p5dulum ov] ! same p5dulum :5 undamp$ is det]m9$ by ! /r5g? ( ! damp+ means employ$1 or1 9 o!r words1 by ! p]c5tage by :i* we r$uce ! velocity at ea* sw+4 ,9 ! e>ly 7#aiaj7 ,ans*tz compass ! p]iod ( vibration at ! equator )\t damp+ 01 z we h /at$ already1 ab\t #fa m9utes4 ,) its damp+ device 9 action ! p]iod ( ! compass at ! equator became approximately #gj m9utes4 ,9 lat] designs ( gyro-compasses ! p]iod ( ! damp$ vibration is delib]ately made #he m9utes or !reab\ts4 ,a practical advantage--to be expla9$ lat]--is secur$ by adopt+ ?is p>ticul> value4 ,x is ! p]iod :i* a simple p5dulum w\ld h if its l5g? 7 equal to ! radius ( ! e>?--#djjj miles or s4 ,illu/ration3 ,,fig4 #ae4 ,damp$ ,p5dulum4 ,a vibrat+ p5dulum 7,fig4 #ae7 w be satisfactorily damp$ if we c apply to ! bob 9 all positions ( its sw+ a =ce proportional to ! velocity ) :i* ! bob is mov+ at ea* giv5 in/ant & direct$ always s z to oppose ! motion4 ,at e1 ! position ( release aft] deflection1 ! bob has no velocity2 ! damp+ =ce %\ld !re=e be z]o4 ,z x travels f e to d ! bob is ga9+ velocity2 ! damp+ =ce %\ld !re=e gr[ f z]o to a maximum at d & be direct$ at ea* in/ant tang5tially to ! curve ( sw+ & act f d t[>ds e4 ,dur+ ?is portion ( its sw+ ! bob is ?us robb$ ( "s ( its velocity1 s t x fails to rise to ! position f & comes to re/ at "s po9t g4 ,9 travell+ f d to g ! velocity ( ! bob is decreas+ naturally1 & is /ill fur!r decreas$ by ! damp+ =ce :i*1 act+ 9 ! same direction z be=e1 falls f a maximum at d to z]o at g4 ,z x moves f g to d on ! return /roke ! bob ga9s velocity2 ! damp+ =ce %\ld !re=e increase f z]o at g to a maximum at d--( a l[] value ?an ! maximum at ! same po9t dur+ ! fir/ /roke--& %\ld be direct$ along ! curve 9 ! rev]s$ s5se1 namely1 f d t[>ds g4 ,dur+ ! sw+ f d to h ! damp+ =ce1 /ill rev]s$1 %\ld decrease f ! second maximum value once m to z]o4 ,at ! />t ( ! second sw+ ! damp+ =ce %\ld aga9 act f d t[>ds e & %\ld rise f z]o to a ?ird maximum value at d--less ?an ei!r ! second or fir/ maximum value1 & s on until ! amplitude ( ! sw+ is r$uc$ to ! requir$ degree4 ,x w be notic$ t 9 a damp$ vibration ! mean position ( ! bob on any "o sw+ is n co9cid5t ) ! re/+ position d1 b lies some:]e betwe5 ! re/+ position & ! position f :i* ! bob comm5ces ! sw+4 ,) ea* passage ( ! bob ?r\gh ! re/+ position d ! value ( ! damp+ =ce rises to a maximum1 ! value ( :i* becomes less & less on ea* successive sw+4 ,ultimately1 :5 ! bob settles 9 ! re/+ position1 ! maximum value becomes z]o4 ,9 o!r words1 ! damp+ =ce1 hav+ complet$ its "w by br++ ! bob to re/1 entirely disappe>s & leaves ! p5dulum exactly 9 ! same condition z x w\ld be "u 9 ! re/+ position if no damp+ =ce _h ev] be5 9 action4 ,! p5dulum is ?us z free z =m]ly to respond1 9 ! re/+ position1 to a vibrat+ influ5ce1 b z soon z x acquires motion ! damp+ =ce is aga9 call$ into exi/5ce to a degree directly dep5d5t on ! /r5g? ( ! vibrat+ influ5ce1 ) ! result t ! motion is fir/ *eck$1 & !n f9ally /opp$4 ,! damp+ =ce requir$ is1 z we h said1 "o :i* at all times is proportional 9 magnitude to ! velocity ( ! bob--or :at is ! same ?+1 to ! angul> velocity ( ! p5dulum z a :ole--& :i* at all times acts to oppose ! motion ( ! bob4 ,metallic friction--say1 at ! support+ axis ( ! p5dulum--x w\ld br+ ! motion to re/ soon] or lat]1 w\ld n provide a satisfactory damp+ =ce1 = solid friction is indep5d5t ( ! rubb+ velocity1 at lea/ at l[ spe$s su* z we are "h conc]n$ )4 ,! damp+ =ce provid$ by x be+ con/ant1 w\ld n be automatically adju/$ to ! velocity ( ! bob4 ,x w\ld vani%1 x is true1 :5 ! bob 0 at re/1 b z soon z ! slighte/ vibration set 9 x w\ld spr+ up to its full value /raight away & w\ld pres]ve ! same value ?r\gh\t a l>ge sw+ z ?r\gh\t a small "o4 ,9 any ev5t ! pres5ce ( metallic or o!r solid friction at ! po9t 9 ! gyro-compass correspond+ to ! axis ( ! p5dulum--namely1 at ! be>+s ( ! v]tical axis ,h ,j--_c be p]mitt$1 & mu/ be elim9at$ to ! utmo/ possible degree if ! directive =ce is to be suffici5t to control ! movem5t ( ! s5sitive elem5t4 ,fluid friction1 on ! o!r h&1 w\ld provide a satisfactory damp+ =ce1 = fluid friction is proportional to ! velocity1 at lea/ at l[ spe$s4 ,a p5dulum vibrat+ ) its bob 9 a vessel ( wat] or ! float+ c>d ( an ord9>y magnetic compass is satisfactorily damp$ by fluid friction4 ,9 ! gyro-compass1 h[ev]1 ! motion to be damp$ is1 z we h se51 an exce$+ly sl[ "o1 sl[] 9 fact ?an ! small h& ( a wat* if ! deflection ( ! axle f ! m]idian is initially less ?an #aa deg4 ea/ or we/4 ,a fluid damp+ =ce w\ld be proportionately l[1 s t )\t mak+ ! damp+ elem5ts ( enorm\s size ! =ce d]iv$ w\ld be insignificant & next to useless = practical purposes4 ,z an illu/ration ( ?is /atem5t x may be rem>k$ t 9 ! e>ly ,ans*tz compass ! s5sitive elem5t 0 virtually float$ 9 a b[l ( m]cury4 ,yet ! drag ( ! m]cury1 ! velocity ( ! vibration be+ s small1 did n measurably r$uce ! amplitudes ( ! vibration dur+ obs]vation ext5d+ ov] sev]al h\rs4 ,?is example is n q a good "o1 h[ev]1 = ! friction at ! surface ( a body imm]s$ 9 m]cury w\ld appe> to be n ( ! fluid description1 b ( ! solid type4 ,solid & fluid friction be+ ?us rul$ out1 at lea/ z direct means ( provid+ ! requir$ damp+ =ce1 we h to f9d "s o!r me?od ( apply+ x4 ,x is1 or %\ld be1 cle> t 9 :atev] way ! damp+ =ce is appli$ x %\ld orig9ate )9 ! s5sitive elem5t itself4 ,if x orig9ates outside1 !n its transmission to ! s5sitive elem5t _c1 9 view ( ! fact t its orig9ation1 gr[?1 & decay are to be controll$ by ! motion ( ! elem5t1 be effect$ 9 any conceivable way )\t ! introduction ( "s mat]ial connection betwe5 ! elem5t & ! outside s\rce ( ! =ce4 ,su* a connection c only be made frictionless if ! outside s\rce moves 9 exact unison ) ! s5sitive elem5t4 ,if x does s move x cle>ly ceases to be an outside s\rce & becomes really "p ( ! s5sitive elem5t itself4 ,?is consid]ation sugge/s g5]at+ & apply+ ! damp+ =ce gyroscopically by ! ex]tion ( "s suitable action on ! sp9n+ :eel itself4 ,,*apt] ,v ,,! ,,damp+ ,,sy/em ,,( ,,! ,,ans*,,tz 7#aiaj7 ,,compass ,9 ! prec$+ *apt] we demon/rat$ ! necessity = damp+ ! horizontal oscillatory movem5t ( ! gyro-compass axle & discuss$ ! nature ( damp$ vibrations 9 g5]al4 ,we n[ turn to describe ! damp+ means provid$ 9 ea* ( ! practical =ms ( gyro-compass s f> evolv$4 ,turn+ to ! e>ly 7#aiaj7 =m ( ,ans*tz compass1 we f9d t1 z %[n 9 ! purely diagrammatic sket* giv5 9 ,fig4 #af1 ! sp9n+ :eel is enclos$ )9 a metallic case =m$ ) tubul> j\rnals ,b ,c = ! axle1 & provid$ ) trunnions ,e ,f1 :]eby x is support$ )9 ! v]tical r+1 :i*1 z be=e1 is free to turn on a v]tical axis ,h ,j4 ,! cas+1 x w be se5 is1 s f> z ! support ( ! :eel is conc]n$1 exactly equival5t to ! horizontal inn] r+ ( our prec$+ illu/rations4 ,9 ! actual in/rum5t ! me?od ( support+ ! cas+ s z to p]mit x to turn ab\t a horizontal & a v]tical axis is n 9 ! lea/ l t %[n 9 our sket*4 ,! :eel1 runn+ at #bj1jjj revolutions p] m9ute1 al?\gh x is q pla91 has a p[]ful bl[]-l action4 ,on "o side ( ! cas+ an orifice ,d is =m$ = ! inlet ( air1 & on ! p]iph]y bel[ an outlet duct ,k1 direct+ ! air bla/ tang5tially away f ! cas+1 is provid$4 ,! exact value ( ! pressure ( ! bla/ 9 ! e>ly ,ans*tz compass is n kn[n to u1 b 9 ! ,br[n compass1 :]e9 a simil> bla/ is develop$1 ! :eel1 runn+ at #ae1jjj revolutions p] m9ute1 gives an air pressure equal to "s #c 94 ( wat]4 ,illu/ration3 ,,fig4 #af4 ,air ,bla/ ,damp+ ,sy/em ( ,ans*tz 7#aiaj7 ,compass4 ,! m\? ( ! outlet duct ,k is p>tially clos$ by a plate ,l fix$ at ! end ( a p5dulum arm susp5d$ frictionlessly1 or practically s1 f "s conv5i5t po9t on ! cas+1 s t :5 ! cas+ turns on ! v]tical axis ,h ,j ! arm & plate turn ) x4 ,! p5dulum arm is c>efully balanc$ 9 su* a way t :5 ! axle ( ! sp9n+ :eel is horizontal ! plate ,l exactly divides ! orifice ,k1 leav+ equal passages = ! air bla/ on ea* side4 ,9 ?is condition ! two passages ,m ,n be+ equal 9 area1 ! air bla/ is divid$ by ! plate into two /reams ( equal volume & mom5tum1 s t if _! free dis*>ge is n influ5c$ by surr\nd+ objects _! reactions on ! cas+1 "o on ! "o side ( ! v]tical axis ,h ,j1 ! o!r on ! opposite side1 w be equal4 ,let ! compass be deflect$ until its axle po9ts ea/ & we/1 ! end ,b be+ t[>ds ! ea/4 ,!n1 z we h se51 ! t5d5cy ( ! axle to rema9 p>allel ) its orig9al position1 comb9$ ) ! rotation ( ! e>?1 w cause ! axle to assume an incl9$ position relatively to ! e>?'s horizontal surface4 ,gravity act+ on ! p5dul\s weight ,s z ?us displac$ f ! plumb l9e w1 z we "k1 set up a precession ab\t ! v]tical axis ,h ,j1 s z to cause ! end ,b ( ! axle to move t[>ds ! nor?4 ,:51 h[ev]1 ! axle tilts 9 ?is mann] ab\t ! horizontal axis ,e ,f1 ! p5dulum plate ,l1 hang+ freely1 rema9s 9 ! plumb l9e4 ,consequ5tly ! equal areas ,m ,n become unequal1 z at ,p ,q1 ! l>g] ,p be+ t[>ds t end ( ! axle :i* has tilt$ upw>ds1 namely1 ! nor?-seek+ end ,b4 ,! reaction on ! cas+ ( ! portion ( ! air bla/ issu+ f ,p is n[ great] ?an t ( ! portion emitt$ ?r\gh ,q4 ,?is inequality results 9 ! application to ! s5sitive elem5t ( a =ce act+ ab\t ! v]tical axis ,h ,j4 ,! reaction ( a jet ( air or wat] or o!r fluid be+ oppos$ to ! direction 9 :i* ! jet is issu+1 ! =ce appli$ to ! cas+ is su* z to drive ,p into ! plane ( ! pap] & to br+ ,q out ( x--t is to say1 to t5d to rotate ! cas+ on ! v]tical axis 9 ! direction ( ! arr[ ,r4 ,! =ce ?us appli$ cle>ly t5ds to oppose ! return ( ! axle f ! ea/ t[>ds ! nor?4 ,on ! o!r h&1 if ! axle succe$s 9 turn+ r\nd until ! end ,b po9ts to ! we/1 ! rotation ( ! e>? w result 9 ! axle tilt+ z be=e1 b ) ! end ,b d[nw>ds4 ,consequ5tly ! area ,m dim9i%es & ! area ,n increases1 & ! reaction appli$ to ! cas+ is su* z to t5d to turn x 9 ! rev]se direction to ,r4 ,! appli$ =ce 9 ?is case !re=e opposes ! return ( ! axle f ! we/ t[>ds ! nor?4 ,! exact mann] 9 :i* ! opposition acts is to be not$4 ,a =ce appli$ to a simple gyroscope1 s z to t5d to make x turn ab\t ! v]tical axis ,h ,j 9 ! direction ,r 7,fig4 #af7 w1 z 0 /at$ 9 our second *apt]1 cause ! :eel to precess ab\t ! horizontal axis ,e ,f1 ! end ,b ( ! axle go+ d[n & ! end ,c up4 ,if ! =ce ab\t ,h ,j is rev]s$1 ! movem5t produc$ w be a precession ( ! :eel on ,e ,f su* t ! end ,b ( ! axle rises & ! end ,c falls4 ,! opposition betwe5 ! mom5t appli$ to ! s5sitive elem5t by ! air bla/ & ! mom5t appli$ to x by ! directive =ce is !re=e n q direct4 ,:5 ! end ,b ( ! axle is deflect$ t[>ds ! ea/ a directive =ce is call$ into be+ by virtue ( ! t5d5cy ( ?is end to rise4 ,! air bla/ reaction ab\t ,h ,j induces precession on ! axis ,e ,f1 caus+ ! end ,b to fall4 ,by ! am\nt by :i* ! air bla/ reaction succe$s 9 l[]+ ! end ,b ( ! axle1 by t am\nt w x r$uce ! normal magnitude ( ! directive =ce4 ,:5 ! axle sw+s ?r\gh ! m]idian t[>ds ! we/ a rev]s$ directive =ce is call$ into play by virtue ( ! t5d5cy ( ! end ,b to fall4 ,! opposition ( ! air bla/ reaction arises f ! fact t its t5d5cy n[ is to make ! end ,b rise4 ,?us on bo? sides ( ! m]idian ! opposition ( ! air bla/ reaction is effective because x t5ds to precess ! :eel on ! axis ,e ,f 9 ! direction oppos$ to t 9 :i* ! rotation ( ! e>? is try+ to tilt ! axle4 ,! tilt moves ! p5dul\s weight ,s away f ! v]tical1 s produc+ ! directive =ce2 ! air bla/ reaction r$uces ! tilt & s opposes ! directive =ce4 ,! reaction appli$ to ! s5sitive elem5t by ! air bla/ ?us fulfils "o requirem5t ( a satisfactory damp+ =ce2 its effect at all times is oppos$ 9 direction to ! direction 9 :i* ! axle is mov+4 ,! second requirem5t is t ! magnitude ( its effect %\ld always be proportional to ! velocity ) :i* ! axle is mov+4 ,9 connection ) ?is second requirem5t x is assum$ t ! mom5ta ( ! air jets issu+ f ! op5+s ,p ,q 7,fig4 #af7 are at all angles ( tilt equival5t to ! mom5tum ( a s+le jet issu+ f an imag9>y orifice ,u situat$ at "s di/ance d f ! axis ,h ,j on ! side ( ! l>g] op5+ ,p1 ! area ( ! imag9>y orifice ,r & ! velocity ( ! air ?r\gh x be+ con/ant at all angles ( tilt4 ,if ?is assumption is correct1 !n ! mom5t ab\t ,h ,j appli$ by ! reaction ( ! air bla/ is proportional to ! di/ance d--t is to say1 to ! angle ( ! tilt4 ,! assumption "h made is1 we believe1 sub/antially ju/ifi$ if ! angle ( tilt is nev] v great4 ,9 actual practice x is always small4 ,v>i\s consid]ations1 h[ev]1 sugge/ t ! reactions ( ! two jets ,p ,q are n equival5t /rictly to ! reaction ( a s+le jet ?r\gh an orifice ,r ( con/ant area4 ,?us f geometrical consid]ations we c %[ t ! sum ( ! areas ,p ,q is n equal to ! sum ( ! areas ,m ,n4 ,aga91 ! total weight ( air drawn 9 p] m9ute ?r\gh ! orifice ,d may be con/ant1 & !re=e ! total weight ( air deliv]$ p] m9ute ?r\gh ! comb9$ op5+s ,p ,q may be unaffect$ by ! tilt4 ,b ! ratio 9 :i* ! total volume divides itself betwe5 ! two op5+s ,p ,q & ! velocity ?r\gh ea* c]ta9ly v>y ) ! tilt4 ,a peculi> practical ph5om5on also has to be consid]$ 9 ?is connection4 ,9 ! #aiaj =m ( ,ans*tz compass ! p]iph]al spe$ ( ! sp9n+ :eel 0 #ejj ft4 p] second1 or #cdj miles an h\r4 ,! air friction at ?is spe$ 0 s v great t aft] ! :eel _h be5 run a few ?\s& h\rs its surface 0 f\nd to be noticeably smoo!r ?an x 0 :5 ! :eel left ! gr9d+ ma*9e on :i* x 0 f9i%$4 ,z a result ( ?is poli%+ effect1 we %\ld expect t ev5 ?\gh ! spe$ ( ! :eel rema9$ p]fectly con/ant1 its bl[]-l action w\ld decrease some:at until ! compass _h be5 9 use = a c]ta9 l5g? ( "t4 ,if ! bl[] action does s decrease ! magnitude ( ! air bla/ reaction on ! s5sitive elem5t at any giv5 angle ( tilt mu/ dim9i% ) "t4 ,we d n "k :e!r ! dim9ution w\ld be suffici5tly great to introduce a s]i\s error 9 ! read+ ( ! compass4 ,tak+ ! assumption to be correct1 at lea/ = small angles ( tilt1 we h next to /udy h[ ! angle ( tilt v>ies z ! axle sw+s f ! ea/ side ( ! m]idian ov] to ! we/ & back aga94 ,:5 ! axle is po9t$ due ea/ ! rotation ( ! e>?1 z we h se51 t5ds to make ! end ,b rise4 ,if x is po9t$ due we/1 ! end ,b t5ds to fall4 ,if x is ly+ dead on ! m]idian1 ! e>?'s rotation has no tilt+ effect at all on ! axle4 ,if ! axle is po9t$ 9 "s direction betwe5 due ea/ & due nor?1 ! tilt+ effect is less ?an x w\ld be if x 7 po9t$ due ea/1 b x is 9 ! same direction2 ! end ,b t5ds to rise4 ,simil>ly1 9 any position 9 ! nor?-we/ quadrant ! end ,b t5ds to tilt d[nw>ds "u a tilt+ influ5ce :i* is some:at less ?an t exp]i5c$ 9 ! due we/ position4 ,let1 !n1 ! axle be turn$ to po9t due ea/4 ,! end ,b beg9s at once to rise1 b imm$iately ! axle ?us leaves ! horizontal position x beg9s to feel ! directive =ce1 & x comm5ces to turn t[>ds ! nor?4 ,until x rea*es ! nor? ! tilt+ influ5ce ( ! e>?'s rotation cont9ues s t dur+ ! :ole "t ! axle is sw++ ?r\gh ! nor?-ea/ quadrant ! tilt is increas+ & ! end ,b is ris+1 high] & high]4 ,:5 ! nor? direction is rea*$ ! tilt+ influ5ce vani%es & ! end ,b ( ! axle t5ds to travel horizontally 9 its elevat$ position ov] into ! nor?-we/ quadrant "u ! influ5ce ( ! mom5tum acquir$ 9 t direction dur+ its movem5t ?r\gh ! nor?-ea/ quadrant4 ,b on pass+ to ! we/ side ( ! m]idian x aga9 comes "u ! tilt+ influ5ce ( ! e>?'s rotation1 :i* ?is "t t5ds to make ! end ,b fall4 ,:5 ! axle rea*es ! due we/ position1 ! tilt+ influ5ce be+ equal to t act+ ov] ! nor?-ea/ quadrant & rev]s$ 9 direction1 & hav+ act$ = ! same l5g? ( "t1 w j h wip$ out ! elevation ( ! end ,b1 & ! axle w aga9 be horizontal4 ,on ! return j\rney ?r\gh ! nor?-we/ quadrant ! tilt+ influ5ce is /ill rev]s$1 s t on rea*+ ! nor? position aga9 ! end ,b is z f> bel[ ! horizontal z x 0 above x on ! sw+ f ea/ to we/4 ,pass+ to ! ea/ side ( ! m]idian1 ! tilt+ action assumes its =m] direction1 ! end ,b beg9s to rise1 & :5 ! due ea/ position is rea*$ aga9 ! axle is once m horizontal4 ,! pa? trac$ out by ! end ,b dur+ a complete vibration f ea/ to we/ & back aga9 is ?us 9 ! nature ( an ellipse--or1 9 extreme cases1 a circle--su* z t %[n at a b c d e 9 ,fig4 #ag4 ,illu/ration3 ,,fig4 #ag4 ,free & ,damp$ ,motion ( ,axle4 ,on an ea/-to-we/ sw+1 !n1 ! end ,b ( ! axle 9 ,fig4 #af1 if ! air bla/ is out ( action1 tilts upw>ds f z]o to a maximum 9 ! mid position & !n aga9 falls to z]o4 ,if ! air bla/ is br\ght into play1 ! reaction1 be+1 z we h se5--at lea/ = all small angles ( tilt--proportional to ! angle ( tilt ( ! axle1 w correspond+ly increase f z]o to a maximum & aga9 fall to z]o4 ,on ! we/-to-ea/ sw+ ! reaction w simil>ly rise & fall 9 ! rev]s$ direction4 ,! unre/ra9$ movem5t ( ! s5sitive elem5t "u ! influ5ce ( ! directive =ce is1 z we "k1 analog\s to t ( a simple p5dulum1 s t ! velocity ) :i* ! axle moves is z]o 9 ! extreme positions & a maximum 9 ! mid position4 ,?us we see t ! air bla/ reaction n only con/antly opposes ! movem5t ( ! axle1 ) ! v>iation 9 ! velocity ) :i* ! axle moves4 ,! air bla/ reaction !re=e completely fulfils ! requirem5ts ( a satisfactory damp+ =ce4 ,:5 x is br\ght into play ! end ,b ( ! axle1 in/ead ( vibrat+ indef9itely 9 a clos$ elliptical pa? a b 444 e 7,fig4 #ag7 moves spirally1 z indicat$ at f g h 4441 until 9 a relatively %ort p]iod ( "t x comes virtually to re/ at m po9t+ t[>ds ! nor?4 ,illu/ration3 ,,fig4 #ah4 ,damp+ ,curve f ,ans*tz 7#aiaj7 ,compass4 ,an actual curve tak5 f an ,ans*tz 7#aiaj7 compass :ile x 0 settl+ d[n on ! m]idian aft] ! gyro-axle _h be5 deflect$ ne>ly #de deg4 to "o side is giv5 9 ,fig4 #ah4 ,! cre/s ,a ,b ,c occur at #gj-m9ute int]vals--! p]iod ( vibration ( ! sy/em :5 damp$1 z we h already /at$4 ,! oscillations are1 x w be se51 damp$ d[n v effectively1 be+ entirely elim9at$ 9 less ?an ?ree h\rs 9 ! c\rse ( ! ?ird complete vibration4 ,x foll[s t if ! :eel ( a gyro-compass is />t$ sp9n+ ) ! axle po9t+ else:]e ?an due nor?1 sev]al h\rs mu/ be all[$ to elapse be=e read+s are tak5 f ! c>d4 ,dur+ ! p]iod ( settl+ d[n1 & especially dur+ ! lat] portions1 ! movem5t ( ! axle t[>ds its re/+ position is extremely sl[1 & _c be detect$ by direct obs]vation4 ,x c1 h[ev]1 be inf]r$ f ! read+s ( a _s level plac$ on ! c>d1 =1 z we h se51 ! oscillations are accompani$ by a tilt+ ( ! :eel case on its horizontal axis4 ,,*apt] ,,vi ,,! ,,damp+ ,,sy/em ,,( ,,! ,,sp]ry ,,compass ,9 ! ,sp]ry gyro-compass ! damp+ sy/em adopt$ is me*anically ( a v diff]5t nature f t us$ 9 ! e>ly ,ans*tz1 al?\gh ! !oretical pr9ciple ( action 9 bo? cases is ! same4 ,! ,sp]ry me?od rules out ! employm5t ( air or o!r fluid 9 any %ape or =m z a means ( g5]at+1 apply+1 or transmitt+ ! damp+ =ce1 ! reason be+ t if air or o!r fluid is reli$ ^u1 ! damp+ =ce--or s ! ,sp]ry ,company holds--w n act 9 /rict unison ) ! oscillations1 b w inv>iably lag beh9d4 ,! details ( ! ,sp]ry me?od are indicat$ 9 a diagrammatic mann] 9 ,fig4 #ai4 ,z 9 ! ,ans*tz compass1 ! sp9n+ :eel revolves 9 a cas+ :i*1 be+ provid$ ) trunnions ,e ,f1 takes ! place ( ! inn] horizontal support+ r+ ( our elem5t>y gyroscope4 ,s9ce no bl[+ action is requir$ ( ! :eel 9 ?is compass ! cas+1 9 ord] to r$uce ! exp5diture ( p[] requir$ to drive ! :eel1 is exhau/$ ( air until a vacuum ( n less ?an #bf 94 is regi/]$ on a gauge :i* =ms a p]man5t fixture on ! cas+4 ,! exhau/ion is effect$ by atta*+ a h&-op]at$ vacuum pump to a nipple on ! cas+4 ,! vacuum produc$ at "o exhau/ion rema9s effective = at lea/ a mon? "u prop] treatm5t4 ,t x is v well wor? :ile exhau/+ ! cas+1 if ! g5]al design ( ! compass p]mits x1 is %[n by ! fact t 9 ! #aiaj ,ans*tz compass ov] #ie p] c5t4 ( ! "w done by ! motor driv+ ! sp9n+ :eel 0 sp5t aga9/ w9dage & air friction4 ,illu/ration3 ,,fig4 #ai4 ,damp+ ,sy/em ( ,sp]ry ,compass4 ,! out] r+ ,g 7,fig4 #ai7 )9 :i* ! cas+ is c>ri$ is1 z be=e1 m\nt$ on a v]tical axis ,h ,j4 ,a second out] r+ ,k--or 8phantom r+10 z x is call$--surr\nds ! r+ ,g1 & is m\nt$ co-axially ) x4 ,:ile ! r+ ,g1 z be=e1 moves along ) ! :eel & its cas+ relatively to ! squ>e frame "u ! influ5ce ( ! directive =ce1 ! r+ ,k is caus$ to foll[ x up 9 exact agreem5t by means ( a small electric motor1 ! p9ion ( :i* engages ) a ge> :eel ,l on ! upp] trunnion1 ! curr5t to ! motor be+ automatically controll$ by ! movem5t ( ! r+ ,g4 ,! compass c>d may be reg>d$ z atta*$ directly to ! top face ( ! ge> :eel4 ,a second p9ion ge>+ ) ! :eel ,l c be arrang$ to transmit ! read+ ( ! c>d to any numb] ( repeat] compasses /ation$ else:]e4 ,9 all our prec$+ illu/rations we h %[n ! p5dul\s weight ,s z be+ atta*$ by a /irrup directly on to ! inn] horizontal r+ or its equival5t1 ! :eel cas+1 s z to move 9 rigid connection !re)4 ,9 ! e>ly ,ans*tz compass ! design def9itely reproduces ?is arrangem5t1 b 9 ! ,sp]ry compass matt]s are o!rwise4 ,! p5dul\s weight ,s 7,fig4 #ai7 is c>ri$ on a /irrup1 :i* is =k$ at ea* end s z to span ! r+s ,g ,k1 & :i* is free to sw+ on pivots ,m ,n fix$ on ! phantom r+ ,k4 ,! pivots ,m ,n are exactly 9 l9e ) ! pivots ,e ,f1 & z ! phantom r+ ,k & ! r+ ,g always move 9 unison1 ! two sets ( pivots rema9 at all times coll9e>4 ,s f> ! arrangem5t ( p>ts is exactly simil> to t :i* w\ld be obta9$ 9 our simple gyro-p5dulum sy/em if ! /irrup ( ! p5dul\s weight 7 n fix$ rigidly to ! inn] horizontal r+1 b 7 swung freely on ! pivots ,e ,f4 ,x c be br\ght into complete id5tity ) ! arrangem5t ( our simple sy/em if ! p5dul\s weight ,s 7,fig4 #ai7 or 8bail10 z x is call$ by ! mak]s1 be provid$ ) a p9 at its mid po9t to engage ) a hole 9 ! p]iph]y ( ! cas+4 ,! sy/em1 z ?us arrang$1 w\ld m]ely be a di/9ctly complicat$ me*anical v>iation ( our simple gyro-p5dulum arrangem5t1 &1 z a compass1 w\ld be op5 to ! same practical objection1 namely1 ! p]si/5ce ) :i* any oscillation ( ! axle1 once set up1 w\ld cont9ue4 ,! vibrations w\ld1 9 fact1 be q undamp$4 ,! g5]ation & application ( a satisfactory damp+ =ce is accompli%$ 9 a v simple1 yet beautiful & really +5i\s1 mann] by displac+ ! p9 connect+ ! bail & ! cas+ f ! mid position to "s position ly+ ea/w>ds ( ! v]tical axis ,h ,j1 z %[n at ,q4 ,illu/ration3 ,,fig4 #bj4 ,action ( ,exc5tric ,p9 9 ,sp]ry ,compass4 ,9 ord] to foll[ ! action ( ?is arrangem5t1 let u consid] a disc 7,fig4 #bj7 swung on a horizontal axis ,e ,f on :i* !re is also swung a weight$ /irrup ,s1 ! /irrup & disc be+ connect$ by a p9 ,q4 ,let ?is sy/em ( p>ts be held horizontal1 & 9 ! fir/ in/ance let ! p91 z %[n 9 ! upp] view1 be arrang$ on ! c5tre l9e ( ! disc4 ,!n ! weight ,w ( ! /irrup applies to ! disc ?ree =ces1 namely1 a =ce ,w w act+ d[nw>ds at ! end ( ! p91 & two upw>d =ces ,p equal to ea* o!r at ! pivots ,e ,f1 z w readily be se5 by consid]+ ! /irrup z a lev] fulcrum$ at ! disc end ( ! p94 ,! only =ce t5d+ to turn ! disc is ! =ce ,w w act+ ab\t ! axis ,e ,f4 ,let1 n[1 ! p9 be situat$ exc5trically relatively to ! axis ,h ,j ( ! disc1 z %[n 9 ! l[] view4 ,! =ces appli$ to ! disc by ! weight ,w ( ! /irrup are aga9 ?ree 9 numb]4 ,! =ce appli$ at ! end ( ! p9 is1 z be=e1 ,w w1 b at ! pivot ,e ! =ce appli$ falls to ,p - p1 :ile ! =ce at ! pivot ,f rises to ,p p4 ,^! =ces apply turn+ mom5ts to ! disc4 ,ab\t ! axis ,e ,f ! turn+ mom5t1 z be=e1 is t ( ! =ce ,w w4 ,?is =ce1 ow+ to ! displacem5t ( ! p91 has n[1 9 addition1 a turn+ mom5t ab\t ! axis ,h ,j 9 ! direction ( ! arr[ ,r4 ,! upw>d =ce ,p - p on ! pivot ,e t5ds to turn ! disc 9 ! same direction1 :ile ! =ce ,p p on ! pivot ,f t5ds to turn x 9 ! oppos$ direction4 ,^! ?ree turn+ mom5ts ab\t ! axis ,h ,j exactly balance ea* o!r1 z c be confirm$ by work+ out _! values4 ,?us !re is no net alt]ation produc$ by %ift+ ! p9 f its c5tral position1 = 9 all positions ( ! p9 ! only effective mom5t appli$ by ! weight ,w to ! disc is t ( ! =ce ,w w ab\t ! axis ,e ,f4 ,n[1 9 ! ,sp]ry sy/em ! =ces ,p - p & ,p p are n all[$ to act on ! trunnions ,e ,f ( ! :eel cas+1 b are borne by ! phantom r+ ,k 7,fig4 #ai7 :5ce !y are transmitt$ back to =m "p ( ! load on ! foll[-up motor4 ,act+ on ! cas+1 !re=e1 !re rema9s only ! =ce ,w w4 ,?is =ce ex]ts a turn+ mom5t ab\t ! axis ,e ,f /rictly equal to t produc$ by a directly atta*$ p5dul\s weight4 ,9 addition1 x ex]ts a turn+ mom5t ab\t ! axis ,h ,j4 ,illu/ration3 ,,fig4 #ba4 ,action ( ,exc5tric ,p9 9 ,sp]ry ,compass4 ,z actually con/ruct$1 ! :eel cas+ & bail 9 ! ,sp]ry compass _c be plac$ 9 ! position %[n 9 ,fig4 #bj1 = ! =ks at ! end ( ! bail p]mit ! bail1 & !re=e ! cas+1 to sw+ only ?r\gh a small angle f ! v]tical position4 ,x is cle>1 h[ev]1 t if ! p>ts c\ld be mov$ into ! horizontal position ! mom5t ( ! =ce ,w w ab\t ! axis ,h ,j w\ld be a maximum1 j z 9 ?is position ! mom5t ( ! same =ce ab\t ! axis ,e ,f is a maximum4 ,x is also cle> t :5 ! p>ts are 9 ! v]tical position ! =ce ,w w has no turn+ mom5t ab\t ei!r axis4 ,9 an int]m$iate position 7,fig4 #ba7 ! mom5t ( ! =ce ,w w ab\t ! axis ,e ,f is proportional to a c--t is1 to ! compon5t ( a b p]p5dicul> to ! plane ( ! cas+ or disc--j z x w\ld be if ! p9 7 c5tral or if ! bail =m$ a rigid "p ( ! cas+4 ,! mom5t ( ,w w ab\t ! axis ,h ,j is likewise proportional to ! compon5t a c4 ,z ! value ( ! compon5t a c1 at lea/ = small angles ( sw+1 is proportional to ! angle ( sw+ 1 ! net result ( mak+ ! p9 exc5tric & introduc+ a phantom r+ is to apply to ! cas+ :5 x is deflect$ 7#a7 ! ord9>y mom5t ( ! weight ,w ab\t ! axis ,e ,f1 & 7#b7 an additional mom5t ab\t ! axis ,h ,j4 ,?is latt] mom5t is proportional to ! angle ( sw+ 1 & 9 ! position %[n 9 ,fig4 #ba t5ds to turn ! cas+ 9 ! direction ( ! arr[ ,r4 ,if ! deflection is t[>ds ! o!r side ( ! axis ,e ,f1 ! mom5t appli$ ab\t ,h ,j w cle>ly t5d to rotate ! cas+ 9 ! opposite direction1 z %[n at ,t4 ,comp>+ ,figs4 #ba & #af1 x w be se5 t ! exc5tricity ( ! p9 9 ! ,sp]ry compass secures exactly ! same result z ! air bla/ reaction produces 9 ! ,ans*tz compass4 ,x is to be not$ t ! exc5tric p9 9 ! ,sp]ry compass is displac$ t[>ds ! ea/ :5 ! axle is re/+ on ! m]idian4 ,if x 7 displac$ t[>ds ! we/ ! =ce appli$ ab\t ! v]tical axis w\ld be rev]s$ 9 its effect1 & w\ld t5d to increase ! oscillations ( ! s5sitive elem5t & n to damp !m1 z is ! int5tion4 ,,*apt] ,,vii ,,! ,,damp+ ,,sy/em ,,( ,,! ,,br[n ,,compass ,9 bo? ! ,sp]ry & ! e>ly ,ans*tz compass ! natural oscillation ( ! s5sitive elem5t ab\t ! v]tical axis is damp$ by apply+ a ret>d+ mom5t to ! elem5t ab\t ?is same axis1 ! /r5g? ( ! ret>d+ mom5t be+ at all times proportional to ! velocity ) :i* ! elem5t is mov+ 9 ! c\rse ( its vibration4 ,! opposition ex]cis$ by ! ret>d+ =ce is n1 h[ev]1 a direct "o4 ,! motion ( ! s5sitive elem5t arises f ! fact t ! sp9n+ :eel1 ! axle1 & ! p5dul\s weight are tilt$ ab\t ! horizontal axis ,e ,f4 ,! ret>d+ =ce is appli$ ab\t ! v]tical axis1 n because t is ! axis on :i* ! s5sitive elem5t is oscillat+1 b because a =ce s appli$ produces a movem5t ab\t ! horizontal axis t5d+ to wipe out ! tilt & s elim9ate ! cause ( ! oscillation4 ,illu/ration3 ,,fig4 #bb4 ,gyro-,p5dulum ) ,axle ,tilt$4 ,an alt]native me?od ( damp+ ! oscillation is possible4 ,! effectiv5ess ( ! p5dul\s weight may be damp$ by virtually r$uc+ ! weight ( ! p5dulum bob in/ead ( r$uc+ ! tilt at :i* x is act+4 ,9 ,fig4 #bb ! :eel ( a gyro-p5dulum sy/em is %[n tilt$4 ,! weight ,s is try+ to turn ! :eel on ! horizontal axis ,e ,f 9 ! direction ,r1 & z a consequ5ce is caus+ precession ab\t ! v]tical axis ,h ,j 9 ! direction ,t4 ,in/ead ( attempt+ to damp ?is precession by apply+ a =ce ab\t ! v]tical axis s z to r$uce ! tilt1 we might virtually r$uce ! weight ,s by apply+ an upw>d =ce ,w at ! end ,b ( ! axle1 or1 :at is ! same ?+1 a d[nw>d =ce ,v at ! o!r end4 ,su* a =ce1 if x 7 act+ alone1 w\ld t5d to turn ! :eel 9 ! direction oppos$ to t ( ! arr[ ,r1 & w\ld consequ5tly cause ! :eel to process on ! v]tical axis 9 ! direction oppos$ to t ( ! arr[ ,t4 ,act+ 9 conjunction ) ! weight ,s1 ! =ce ,w w\ld ?us damp ! natural motion by endeav\r+ to produce a c\nt] precession ( ! :eel ab\t ! v]tical axis4 ,?is alt]native me?od ( damp+ ! oscillations is adopt$ 9 ! ,br[n gyro-compass4 ,! me*anism ( ! ,br[n me?od is %[n diagrammatically 9 ,fig4 #bc4 ,! :eel1 z 9 ! e>ly ,ans*tz compass1 runs 9 an enclos+ case1 & acts z a bl[]1 develop+ a pressure ( ab\t #c 94 ( wat]4 ,at ea* side ( ! cas+ a bottle ,l1 ,m is atta*$ to ! h\s+ ( ! axle4 ,a pipe ,n connects ! bottoms ( ! bottles1 :ile a second pipe ,p jo9s _! upp] ends4 ,at its mid po9t ! pipe ,p is int]rupt$1 & a box ,q is ins]t$ 9 ! gap4 ,?is box1 z %[n sep>ately1 is op5 on ! und]side1 & is provid$ ) a c5tral p>tition4 ,! air f ! cas+ is deliv]$ ?r\gh ! holl[ trunnion ,f1 & passes upw>ds into ! box ,q f ! orifice ,r4 ,:5 ! axle is horizontal ! air bla/ ent]+ ! box ,q is divid$ into two equal portions by ! c5tral p>tition1 & ex]ts an equal pressure inside ! bottles4 ,^! two bottles are half-fill$ ) oil1 :i* "u ! equal air pressures & ! horizontal configuration ( ! sy/em lies at an equal level 9 ea* bottle1 & does n !re=e unbalance ! s5sitive elem5t on ! axis ,e ,f4 ,if1 h[ev]1 ! axle tilts ! balance is di/urb$4 ,?us if ! end ,b rises ! box tilt+ ) ! :eel w assume "s su* position relatively to ! nipple ,r--:i* is free ( ! trunnion ,f--z t %[n at ,t4 ,! c5tral p>tition w divide ! air jet unequally1 & a great] pressure w !re=e be ex]t$ inside ! bottle ,l ?an 9 ! bottle ,m4 ,?us ! oil level 9 ,l falls1 :ile ! oil level 9 ,m rises4 ,! diff]5ce 9 ! weights ( ! two bodies ( oil acts z a turn+ mom5t t5d+ to rotate ! cas+ ab\t ! horizontal axis ,e ,f 9 ! direction ,u--t is to say1 9 ! direction oppos$ to t 9 :i* ! p5dulum weight ,s is try+ to turn ! cas+4 ,s9ce ! p5dulum weight causes precession ab\t ,h ,j 9 ! direction ,v1 ! weight ( ! unbalanc$ oil w cause or t5d to cause precession ab\t ,h ,j 9 ! rev]se direction4 ,illu/ration3 ,,fig4 #bc4 ,damp+ ,sy/em ( ,br[n ,compass4 ,%\ld ! end ,b ( ! axle fall1 ! air jet w ex]cise excess ( pressure 9 ! bottle ,m1 ! oil level w rise 9 ! bottle ,l1 & z a consequ5ce w t5d to make ! sy/em precess ab\t ,h ,j 9 ! direction ( ! arr[ ,v4 ,?us 9 bo? cases ! precession :i* w\ld be produc$ by ! unbalanc$ weight ( oil if x act$ alone is 9 ! rev]se direction to t produc$ by p5dulum weight :5 ! axle tilts "u ! rotation ( ! e>?4 ,z ! excess ( pressure 9 ei!r bottle v>ies ) ! ratio 9 :i* ! c5tral p>tition ( ! box ,q divides ! air bla/1 & z t ratio v>ies ) ! angle ( tilt1 x foll[s t ! opposition ( ! appli$ precession increases ) ! angle ( tilt1 & !re=e ) ! rate at :i* ! s5sitive elem5t is turn+ on ,h ,j "u ! influ5ce ( ! p5dulum weight ,s4 ,! sy/em !re=e fulfils ! requirem5ts ( a satisfactory damp+ me?od4 ,x may be not$ t 7 ! air bla/ & ! box ,q suppress$ & ! pipe ,p made cont9u\s1 a tilt ( ! axle w\ld cause oil to fl[ f "o bottle to ! o!r 9 ! endeav\r ( ! liquid to pres]ve its surface horizontal4 ,?is fl[ might be con/rict$ by means ( a valve 9 ! pipe ,n1 & w\ld !n s]ve to damp ! oscillations1 = ! arrangem5t w\ld con/itute virtually an oil da%pot4 ,?is plan w\ld n prove satisfactory 9 practice1 because ! tilts :i* are atta9$ are s small t ! am\nt ( oil fl[+ betwe5 ! bottles w\ld be insignificant4 ,fur!r1 ! fl[ w\ld almo/ c]ta9ly lag beh9d ! movem5t to be damp$4 ,! application ( ! air bla/ to ! surface ( ! oil greatly increases ! rate ( fl[ ( ! oil & correctly syn*ronises x ) ! tilt4 ,! ext5t to :i* ! damp+ effect is all[$ to act on ! sy/em c be regulat$ by means ( a ne$le valve 9 "o ( ! bottles1 :i* valve is made to control ! orifice 9 ! bottom ( ! bottle ?r\gh :i* ! pipe ,n ent]s4 ,! damp+ sy/em adopt$ 9 ! late/ =m ( ,ans*tz compass _c v conv5i5tly be describ$ at ?is po9t4 ,x w be dealt ) lat] on 9 ,*apt] ,,xvii4 ,= ! pres5t x is suffici5t to say t ! sy/em us$ is 9 pr9ciple v simil> to t f\nd 9 ! ,br[n compass4 ,,*apt] ,,viii ,,! ,,latitude ,,error ,hav+ expla9$ ! necessity = damp+ ! horizontal vibrations ( ! gyro-compass axle & h[ ! damp+ =ce is g5]at$ & appli$ 9 ! ,ans*tz1 ,sp]ry1 & ,br[n compasses1 we are n[ 9 a position to discuss ! v>i\s errors to :i* ! gyro-compass is op5 & h[ ^? errors are 9 practice elim9at$1 r$uc$1 or all[$ =4 ,! fir/ error to :i* we %all turn our att5tion is t kn[n z ! latitude error4 ,?is error is a direct consequ5ce ( ! necessity we are "u ( damp+ ! horizontal vibrations ( ! compass axle4 ,x w be recall$ t 9 any latitude o!r ?an ! equator ! compass re/s on ! nor? ) a slight tilt up or d[n ( ! axle1 ! tilt increas+ progressively z ! poles are approa*$ & be+ upw>ds 9 nor!rn latitudes & d[nw>ds 9 s\!rn4 ,! tilt acquir$ 9 any latitude is p]=ce & automatically j suffici5t to precess ! axle we/w>dly or ea/w>dly at ! rate requir$ at t latitude to keep ! axle on ! nor? once x has f\nd x4 ,let u suppose1 !n1 t a compass ( ! e>ly ,ans*tz type is /ation$ 9 "s degree ( nor!rn latitude4 ,! axle 9 acquir+ ! appropriate tilt w cle>ly di/urb ! equilibrium betwe5 ! two sections ( ! air bla/4 ,z ! axle tilts its nor? end ,b upw>ds ! nor? section ( ! air bla/ w enl>ge & ! s\!rn dim9i% 9 area4 ,?us ! tilt+ ( ! axle br+s into play an air bla/ reaction :i* is appli$ z a mom5t t5d+ to turn ! s5sitive elem5t ab\t ! v]tical axis ,h ,j 9 su* a way z to make ! nor? end move ea/w>dly4 ,! actual movem5t produc$ w1 9 accordance ) ! fundam5tal rule1 be a precession ( ! axle ab\t ! horizontal axis1 ! end ,b go+ d[n4 ,?us ! tilt upw>ds ( ! axle requir$ = ! correct work+ ( ! compass is oppos$4 ,x is n all[$ to acquire ! full value :i* x %\ld h1 b in/ead /ops at ! po9t at :i* a balance is /ruck betwe5 ! upw>d mov+ t5d5cy ( ! axle result+ f ! e>?'s rotation & ! d[nw>d mov+ t5d5cy caus$ by ! unev5 air bla/ reaction4 ,! we/]ly precession ( ! axle ab\t ! v]tical axis is n[ t aris+ f ! r$uc$ angle ( tilt1 & is less ?an ! rate requir$ to keep ! end ,b po9t+ to ! nor?4 ,! result+ deviation is kn[n z ! latitude error4 ,its magnitude dep5ds ^u ! latitude & ^u su* factors z ! spe$ ( ! :eel1 its effici5cy z a bl[] & o!r items incid5tal to ! p>ticul> design ( ! compass4 ,9 ! ,sp]ry compass ! latitude error arises f an exactly simil> cause4 ,?us ! tilt ( ! axle is transmitt$ ?r\gh ! exc5tric p9 to ! cas+ z a mom5t ab\t ! v]tical axis ,h ,j1 t5d+ to make ! nor? end ( ! axle move ov] to ! ea/1 & !re=e caus+ ! axle to precess v]tically d[nw>ds until ! position ( balance is rea*$4 ,9 ! ,br[n compass1 on ! o!r h&1 x is claim$ t !re is no latitude error4 ,?us :5 9 nor!rn latitudes ! nor? end ( ! axle tilts upw>ds "u its unsatisfi$ desire to set itself p>allel ) ! e>?'s pol> axis1 ! air bla/ is divid$ unequally betwe5 ! two p>titions ( ! box4 ,excess pressure is ex]t$ inside ! damp+ bottle atta*$ to ! nor!rn face ( ! :eel cas+1 & z a result an excess ( oil accumulates 9 ! damp+ bottle on ! s\? side4 ,! weight ( ! excess oil applies a turn+ mom5t to ! sp9n+ :eel ab\t ! horizontal axis1 & t5ds to lift ! nor? end ( ! axle upw>ds 9 opposition to ! p5dulum weight1 :i* t5ds to turn x d[nw>ds ab\t ! same axis4 ,?us 9 ?is compass ! natural tilt ( ! axle is n int]f]$ ) by ! action ( ! damp+ arrangem5t1 = t action is appli$ ab\t ! horizontal axis ,e ,f1 & n1 z 9 ! ,ans*tz & ,sp]ry compasses1 ab\t ! v]tical axis ,h ,j4 ,! damp+ action 9 ! ,br[n compass is virtually equival5t to a subtraction f ! weight ( ! p5dulum bob1 & is n appli$1 z 9 ! o!r compasses1 to ! r$uction ( ! tilt ( ! axle4 ,x t5ds1 !re=e1 to r$uce ! natural rate ( we/]ly precession requir$ at ! giv5 latitude to keep ! axle on ! nor?4 ,actually1 h[ev]1 ! tilt acquir$ by ! axle w take cognisance ( ! r$uction 9 ! weight ( ! bob caus$ by ! weight ( ! excess oil4 ,! nor? end ( ! axle w rise until ! effective mom5t ( ! bob--t is1 ! mom5t due to its own actual weight less ! mom5t due to ! excess oil 9 ! s\!rn damp+ bottle--is su* z w automatically g5]ate ! requir$ rate ( we/]ly precession = ! giv5 latitude4 ,9 ! ,ans*tz & ,sp]ry compasses ! latitude error c be all[$ = by %ift+ ! position ( ! lubb] l9e relatively to ! %ip's longitud9al c5tre l9e 9 accordance ) calculat$ tables ( ! error4 ,! exact value ( ! error dep5ds ^u ! design ( ! compass1 b 9 bo? types x increases ) ! latitude4 ,analysis %[s t--at lea/ 9 ! e>ly ,ans*tz compass--! latitude error may be neglect$ if ! *ange ( latitude is less ?an #aj deg4 ,9 ! ,sp]ry compass1 z we %all see pres5tly1 ! movem5t ( ! lubb] l9e to correct ! latitude error is effect$ by a v pretty piece ( me*anism1 :i* also c control ! position ( ! lubb] l9e to all[ = a second error to :i* ! compass is op51 to wit1 ! s-call$ 8nor? /eam+ error40 ,9 "s respects z an alt]native to mov+ ! lubb] l9e1 ! latitude error may be completely elim9at$ = a p>ticul> latitude--! latitude ( mo/ frequ5t use w\ld naturally be *os5--by atta*+ a small weight to ! nor? side ( ! :eel cas+4 ,9 ! e>ly ,ans*tz compass su* a weight 0 provid$ z indicat$ at ,t 9 ,fig4 #af4 ,?is weight & its position 7 s *os5 t at #ej deg4 nor? ( ! equator its mom5t ab\t ! horizontal axis ,e ,f1 :5 ! axle ( ! compass 0 horizontal1 0 j suffici5t to supply to ! :eel ! am\nt ( we/]ly precession requir$ to keep ! axle po9t+ to ! nor?4 ,! axle be+ horizontal 9 t latitude1 ! air bla/ 0 equally divid$ by ! p5dulum %utt]1 & z a result ! rate ( we/]ly precession produc$ by ! weight ,t 0 n affect$ by ! exi/5ce ( ! damp+ sy/em4 ,at o!r latitudes1 ( c\rse1 ! latitude error arose1 & at ! equator--:]e ord9>ily !re %\ld be no latitude error--& s\? ( ! equator1 ! error became worse ?an x w\ld h be5 )\t ! addition ( ! weight1 unless ! weight & its position 7 adju/$4 ,) ! compass correct$ = #ej deg4 ,n4 latitude ! error _h ! foll[+ values3 ,latitude ,error #fj ,n4 4#f ,e4 #ej ,n4 ,z]o #dj ,n4 4#e ,w4 #bj ,n4 #a4a ,w4 #j #a4f ,w4 #bj ,s4 #b4a ,w4 #dj ,s4 #b4g ,w4 #fj ,s4 #c4h ,w4 ,9 ! ,sp]ry compass no attempt is made to elim9ate ! latitude error at any p>ticul> latitude1 ! correction appli$ to ! lubb] l9e be+ solely reli$ ^u to all[ = x4 ,9 ?is compass1 !re=e1 ! latitude error is z]o at ! equator4 ,at #ej deg4 nor? or s\? x am\nts to #b deg41 ea/]ly & we/]ly respectively4 ,a feature f\nd 9 ?is type ( gyro-compass ( a connect$ nature calls1 h[ev]1 = m5tion at ?is po9t4 ,?is feature consi/s ( m\nt+ ! pivots ,m ,n 7,fig4 #ai71 on :i* ! bail sw+s1 )9 exc5tric h\s+s & graduat+ ! edge ( ! h\s+s ) a scale ( latitudes4 ,9 ?is way ! pivots c be displac$ to "o side or ! o!r ( ! v]tical plane conta9+ ! axis ,h ,j by an am\nt proportional to ! latitude4 ,:5 ! sp9n+ :eel is at re/1 ?is displacem5t makes ! angle betwe5 ! axle ( ! :eel & ! plumb l9e ?r\gh ! c5tre ( gravity ( ! bail a little less or a little m ?an a "r angle1 & 9 nor!rn latitudes makes ! nor? end ( ! axle dip bel[ ! horizontal & 9 s\!rn latitudes rise above x4 ,! scale is s graduat$ t ! dip ( ! axle or its rise :5 ! :eel is n runn+ is j equal to ! natural rise or dip :i* ! axle w\ld acquire at any giv5 latitude ) ! :eel runn+ & ) ! bail pivots 9 ! mean position4 ,z a result1 :5 ! compass is 9 s]vice & ! bail pivots are adju/$ = ! latitude ( ! /ation1 ! natural rise or dip ( ! axle leaves ! axle horizontal1 b deflects ! bail weight f ! v]tical by ! am\nt requir$ to g5]ate ! correct degree ( ea/]ly or we/]ly precession4 ,?us 9 ! ,sp]ry compass ! axle1 if ! latitude bail correction is appli$1 is at all latitudes horizontal :5 re/+ on ! nor?4 ,sev]al advantages are ?us secur$1 ! *ief be+ t ! effect ( any *ange 9 ! spe$ ( ! sp9n+ :eel or ( a complete failure ( ! electric supply driv+ ! :eel is greatly r$uc$ or spread ov] a long] int]val4 ,7 ! axle z well z ! bail all[$ to acquire ! rise or dip prop] to ! latitude1 ! axle dur+ a *ange ( spe$ ( ! :eel w\ld t5d to deviate & develop an error :i* might prove mislead+4 ,if1 h[ev]1 ! axle is n all[$ to acquire ! rise or dip appropriate to ! latitude1 ! error introduc$ by a *ange 9 ! spe$ ( ! :eel takes long] to manife/ itself1 & is r$uc$ 9 magnitude4 ,z x is difficult to gu>antee t ! voltage ( ! curr5t suppli$ to ! compass w n v>y1 ?is feature ( ! ,sp]ry compass is und\bt$ly ( practical advantage4 ,,*apt] ,,ix ,,! ,,nor? ,,/eam+ ,,error ,! s\rce ( error :i* we h j discuss$ affects ! gyro-compass :e!r x is on l& or on a %ip4 ,we h n[ to discuss c]ta9 errors :i* are only met ) :5 ! compass is m\nt$ on bo>d a mov+ %ip4 ,! fir/ ( ^! errors to :i* we w ref] is sometimes call$ ! 8nor? /eam+ error10 al?\gh x is equally associat$ ) a due s\? c\rse4 ,imag9e ! vessel on :i* ! gyro-compass is fitt$ to be sail+ due ea/ along ! equator4 ,if its spe$ is1 say1 #bj knots x w\ld1 if x c\ld1 circumnavigate ! globe 9 #de days4 ,its velocity r\nd ! e>?'s axis ap>t f ! rotation ( ! e>? is ?us #j4jjjjae revolution p] m9ute4 ,z ! spe$ ( ! e>? on its pol> axis is #j4jjjg revolution p] m9ute1 ! actual rate at :i* ! gyro-axle is be+ c>ri$ r\nd 9 space is #j4jjjgae revolution p] m9ute4 ,if ! vessel is sail+ due we/ its spe$ opposes t ( ! e>?1 s t ! actual rate at :i* ! gyro-axle is be+ c>ri$ r\nd 9 space is #j4jjjfhe revolution p] m9ute4 ,z comp>$ ) ! same gyro-compass on l&1 ! only effect ( ! %ip's spe$ on ^! c\rses is 9 ! "o case to increase ! magnitude ( ! directive =ce & 9 ! o!r case to r$uce x1 ! increase & r$uction bo? be+ q small--ab\t #b p] c5t4 actually4 ,sail+ due ea/ or we/ 9 latitude #fj deg4 nor? or s\?1 its spe$ w\ld cause ! vessel to circumnavigate ! globe 9 #bb days4 ,on ^! c\rses 9 ei!r ( ^! latitudes1 !re=e1 ! directive =ce w\ld be increas$ or dim9i%$ respectively by ab\t #d p] c5t4 ,illu/ration3 ,,fig4 #bd4 ,! ,nor? ,/eam+ ,error at #j ,deg4 & #fj ,deg4 ,n4 ,if1 n[1 ! vessel />ts at ! equator & sails due nor?1 its spe$ is at "r angles to ! spe$ ) :i* ! rotation ( ! e>? is c>ry+ ! gyro-compass r\nd 9 space4 ,! spe$ ( ! %ip--#bjbf ft4 p] m9ute--may be repres5t$ by ,a ,b 7,fig4 #bd7 & ! spe$ ( rotation ( ! e>?--#ib1djj ft4 p] m9ute--by ,a ,c4 ,! actual spe$ & direction 9 :i* ! gyro-compass is be+ c>ri$ r\nd 9 space is ,a ,d1 & ! actual axis ab\t :i* x is be+ c>ri$ r\nd is n ! e>?'s pol> axis ,n ,s1 b an axis ,n ,s at "r angles to ,a ,d4 ,! gyro-axle w settle1 !re=e1 on ! l9e ,n ,s1 & n on ! true nor? & s\? m]idian4 ,! true nor? w be to ! ea/ ( ! indicat$ nor? by ! angle ,n ,a ,n1 :i* = ! %ip spe$ 9 "q--#bj knots--w be #a4be deg4 ,if ! %ip />t+ f ! equator sails due s\?1 ! deviation w be t[>ds ! opposite side1 ! true nor? ly+ #a4be deg4 to ! we/ ( t indicat$ by ! compass4 ,if ! c\rse is nei!r due nor? or s\? nor due ea/ or we/1 ! deviation w h "s int]m$iate value betwe5 z]o & #a4be deg41 ! true nor? ly+ to ! ea/ ( ! indicat$ on all c\rses ) a nor!rn compon5t & to ! we/ on all c\rses ) a s\!rn compon5t4 ,if ! %ip is 9 latitude #fj deg4 nor?1 & is /eam+ nor?1 its spe$ w c>ry x1 z be=e1 #bjbf ft4 nor?w>d p] m9ute1 z at ,e ,f1 b1 z its di/ance f ! e>?'s pol> axis is n[ only half :at x 0 at ! equator1 ! e>?'s rotation is c>ry+ x r\nd at only half ! equatorial spe$1 namely1 ) a velocity ,e ,g ( #df1bjj ft4 p] m9ute4 ,! compass is !re=e be+ c>ri$ r\nd 9 space ) a velocity repres5t$ 9 magnitude & direction by ,e ,h--t is to say1 x is be+ rotat$ n actually ab\t ! e>?'s pol> axis ,n ,s1 b ab\t an axis ,n ,s at "r angles to ! resultant velocity ,e ,h4 ,! axle w !re=e align itself p>allel ) ,n ,s1 & n ) ,n ,s4 ,?us 9 t latitude at ! giv5 spe$ ! true nor? w lie #b4e deg4 ea/w>d ( t indicat$ by ! compass4 ,on nor?-ea/]ly or nor?-we/]ly c\rses at #fj deg4 nor? latitude ! deviation w lie betwe5 z]o & #b4e deg41 :ile on all c\rses ) a s\!rly compon5t ! true nor? w be to ! we/ ( ! indicat$ nor? by "s am\nt betwe5 ! same two limits4 ,our demon/ration is n /rictly accurate1 =1 aris+ f ! rotundity ( ! e>?1 ! spe$ ,e ,f ( ! %ip is n really 9 ! plane ( ! pap]1 b %\ld be drawn incl9$ ) ! end ,f bel[ ! level ( ,e4 ,accurate analysis1 h[ev]1 %[s t ! deviation arriv$ at by neglect+ ?is fact is sub/antially correct4 ,9 ! tables issu$ 9 connection ) ! e>ly ,ans*tz compass ! deviation at #bj knots due nor? or s\? 9 latitude #fj deg4 ,n4 is giv5 z #b4e deg41 :ile ^? issu$ by ! ,sp]ry ,company give x1 by int]polation1 z #b4da deg4 ,x w be se5 t ?is error is a natural "o--t is to say1 x is n caus$ by any peculi>ity 9 ! design ( ! compass 9 use4 ,! table ( deviations on v>i\s c\rses1 at v>i\s spe$s1 9 v>i\s latitudes1 compil$ = "o type ( compass w\ld be equally applicable to any o!r design4 ,9 ! case ( ! e>ly type ( ,ans*tz compass ! 8nor? /eam+ error0 0 correct$ solely by means ( su* tables--t is to say1 to f9d ! exact be>+ on :i* ! %ip 0 sail+ ! compass 0 read1 & f its read+ !re 0 subtract$1 or to x !re 0 add$1 ari?metically1 ! appropriate figure tak5 f ! tables1 ! uncorrect$ read+ be+ a suffici5tly accurate indication ( ! true c\rse to p]mit x to be assum$ z ! true c\rse = ! purpose ( extract+ ! correction f ! tables4 ,9 ! ,sp]ry design ! use ( simil> tables 9 a simil> way is p]missible & is provid$ =4 ,9 addition1 h[ev]1 provision is made :]eby ! tables may be entirely disp5s$ ) & ! correction appli$ by mov+ ! lubb] l9e relatively to ! %ip's =e & aft direction4 ,9 ! case ( ! e>ly ,ans*tz compass ! lubb] l9e c\ld be mov$ ?r\gh #d deg4 on ea* side ( ! position 9 :i* x 0 p>allel ) ! %ip's =e & aft c5tre l9e4 ,?is movem5t 01 h[ev]1 = ! purpose ( correct+ ! latitude error1 & n ! nor? /eam+ error4 ,9 ! ,sp]ry compass provision is made = mov+ ! lubb] l9e s z to correct = bo? errors4 ,! latitude error dep5ds ^u ! design ( ! compass & ! latitude4 ,! nor? /eam+ error is indep5d5t ( ! design ( ! compass1 & is det]m9$ by ! spe$ ( ! %ip1 ! latitude 9 :i* x is sail+1 & ! c\rse :i* x is foll[+4 ,latitude ?us comes into bo? errors1 be+ ! sole v>iable caus+ "o1 & "o ( ! ?ree v>iables caus+ ! o!r4 ,x is elim9at$ simultane\sly = bo? errors1 by op]at+ "o dial4 ,a second dial is set to suit ! spe$ ( ! %ip1 :ile ! ?ird factor 9 ! nor? /eam+ error1 ! be>+ ( ! %ip's c\rse1 is automatically br\ght into ! movem5t ( ! lubb] l9e by means ( an incl9$ r+ c>ri$ r\nd ) ! compass c>d4 ,a diagram ( ! ,sp]ry correction me*anism is giv5 9 ,fig4 #be4 ,! lubb] r+ on :i* ! lubb] l9e is engrav$ is %[n at ,a4 ,! latitude corrector dial ,b is m\nt$ to rotate ab\t its c5tre & to read aga9/ a fix$ scale4 ,x is slott$ radially to engage a p9 ,c on a rod ,d ,e1 "o end ( :i* c slide 9 a fix$ guide ,f1 :ile ! o!r is pivot$ to a l9k ,e ,g p9n$ at ,h to ! lubb] r+4 ,if ! end ,g ( ?is l9k be imag9$ pivot$ to "s fix$ po9t x is cle> t rotation ( ! dial ,b w communicate a correspond+ rotation to ! lubb] r+4 ,! proportions ( ! p>ts & ! positions ( ! pivots & p9s are su* t by sett+ ! dial to ! latitude 9 :i* ! vessel is sail+ ! lubb] r+ is rotat$ ?r\gh ! angle by :i* ! local latitude error causes ! gyro-axle to deviate 9 its re/+ position f ! true nor? & s\? direction4#c ,illu/ration3 ,,fig4 #be4 ,sp]ry ,correction ,me*anism = ,latitude & ,nor? ,/eam+ ,errors4 ,if ! end ,g ( ! l9k ,e ,g 7 pivot$1 z we h suppos$ x to be1 to "s fix$ po9t1 !n ! latitude ,error c\ld be appli$ by itself to ! lubb] r+4 ,x is n1 h[ev]1 s fix$1 b is pivot$ to a l9k1 ! end ,j ( :i* c>ries a p9 work+ 9 a curv$ slot ext5d+ f ! c5tre ( ! spe$ corrector dial ,k to its edge4 ,! radius ( ?is curv$ slot is /ruck f ! po9t ,g z c5tre4 ,x foll[s1 !re=e1 t ) ! spe$ corrector dial 9 ! position %[n ! end ,j ( ! l9k ,g ,j may be fix$ at any po9t 9 ! curv$ slot )\t affect+ ! position ( ! po9t ,g4 ,if1 h[ev]1 ! spe$ corrector dial be rotat$ ab\t its c5tre1 ! movem5t ( ! po9t ,g w v>y 9 magnitude ) ! position at :i* ! p9 ,j is fix$ 9 ! curv$ slot4 ,?is position is set aga9/ ! scale ( spe$ 9 knots on ! edge ( ! slot1 b ! sett+ is )\t effect until ! spe$ corrector dial is rotat$ f ! position %[n 9 ! diagram4 ,:5 x is s rotat$ a correspond+ movem5t is communicat$ to ! lubb] r+ ?r\gh ! l9k ,g ,e1 ! end ,e ( :i* is n[ to be reg>d$ z ! fix$ fulcrum4 ,! two dials ,b ,k are connect$ by means ( a l9k ,l ,m ( l5g? equal to ! di/ance betwe5 ! dial c5tres4 ,! end ,l ( ?is l9k is pivot$ to a fix$ po9t on ! dial ,b1 b ! end ,m is provid$ ) a p9 :i* works )9 a slot 9 ! dial ,k4 ,?us ! sett+ ( ! dial ,b to any latitude w n produce rotation ( ! dial ,k1 b w m]ely cause ! p9 ,m to slide 9 its slot4 ,if1 h[ev]1 ! l9k ,m ,n is mov$ upw>ds1 ! angle ?r\gh :i* su* movem5t w rotate ! dial ,k w dep5d ^u ! exact position ( ! p9 ,m 9 its slot--t is to say1 ^u ! sett+ ( ! latitude dial4 ,?us a movem5t ( ! l9k ,m ,n w rotate ! lubb] r+ by an am\nt proportional to ! movem5t ( ,m ,n1 to ! sett+ ( ! p9 ,j 9 ! curv$ slot ( ! spe$ dial1 & to ! sett+ ( ! latitude dial4 ,! l9k ,m ,n is p9n$ to a lev] ,p ,q1 ! end ,p ( :i* is pivot$ to a fix$ po9t4 ,! end ,q c>ries a roll]1 :i* engages )9 ! flanges ( a r+ ,r p]man5tly fix$ 9 an incl9$ position on ! phantom r+ ( ! compass4 ,! high] end ( ?is r+ is situat$ directly above ! nor?-seek+ end ( ! gyro-axle1 & ! l[] end directly above ! s\?-seek+ end1 its ea/ & we/ diamet] be+ align$ horizontally4 ,9 ! position %[n 9 ! diagram ! %ip is suppos$ to be sail+ due we/4 ,"u ?is condition1 z we "k1 no nor? /eam+ error is involv$1 ! latitude error only apply+4 ,! dial ,b c !re=e be set to ! latitude 9 :i* ! vessel is sail+ s z to apply ! latitude correction by itself to ! lubb] r+4 ,at ! same "t ! p9 ,j c be set to read ! %ip's spe$--#ag knots 9 ! case %[n4 ,! movem5t ( ! l9k ,j ,g involv$ 9 ?is sett+ w1 z we h se51 n alt] ! sett+ ( ! lubb] r+1 nor w ! sett+ ( ! dial ,b rotate ! dial ,k f ! position %[n4 ,! two sett+s are1 h[ev]1 ready to modify ! adju/m5t ( ! lubb] r+ z soon z any movem5t ( ! l9k ,m ,n occurs4 ,su* a movem5t arises if ! vessel alt]s c\rse t[>ds ! nor? or s\? or int]m$iately1 = :5 ! c\rse is alt]$ ! l9ks1 dials1 & lubb] r+ move ) ! %ip1 :ile ! compass c>d & ! c\rse corrector r+ ,r rema9 /ation>y4 ,! roll] at ,q !re=e rises or falls t[>ds ! nor? or s\? end ( ! r+1 & produces a rotation ( ! dial ,k4 ,! am\nt ( ! modification ?us produc$ 9 ! sett+ ( ! lubb] r+ relatively to ! %ip's c5tre l9e w dep5d ^u 7#a7 ! sett+ ( ! p9 ,m--t is to say1 ! sett+ ( ! latitude dial2 7#b7 ! sett+ ( ! p9 ,j on ! spe$ dial2 & 7#c7 ! ext5t ( ! turn t[>ds ! nor? or s\?4 ,9 ?is way ! correction = ! nor? /eam+ error is automatically add$ to or subtract$ f ! correction = ! latitude error to ! correct am\nt on all occasions :5 ! %ip's c\rse is alt]$ s z to h a nor!rly or s\!rly compon5t1 ! adju/m5t = ! error be+ automatically wip$ out 9 all latitudes :5 ! %ip's c\rse is aga9 br\ght ea/ & we/4 ,! me*anism1 x w be se51 m]ely by ! sett+ ( two dials1 takes cognisance ( ?ree indep5d5t v>iables1 ( :i* "o ent]s into ! requir$ adju/m5t 9 a tw(old way4#d ,! total correction is indicat$ on ! corrector scale ,s atta*$ to ! b9nacle indep5d5tly ( ! lubb] r+4 ,x w be se51 !n1 t nei!r ! latitude error nor ! nor? /eam+ error is 9 ! /rict s5se ( ! ^w elim9at$1 b is only all[$ =1 automatically or ari?metically1 :5 ! compass is read--t is to say1 no attempt is made to =ce ! gyro-axle to re/ 9 ! true nor? & s\? position 9 all latitudes at all spe$s on all c\rses4 ,! crucial angle by :i* ! %ip is navigat$ is ! angle betwe5 its longitud9al c5tre l9e & ! true m]idian4 ,a con/ant /raight c\rse w be held if ?is angle is ma9ta9$ con/ant4 ,if ! indicat$ m]idian on ! compass is op5 to error1 ! con/ancy ( ! navigat+ angle may be pres]v$ by introduc+ a simil> error into ! degree ( co9cid5ce betwe5 ! lubb] l9e & ! longitud9al c5tre l9e ( ! %ip4 ,! read+s ( ! ma/] compass may !re=e be us$ = ! purpose ( ma9ta9+ ! %ip on a giv5 c\rse or = sett+ x on a new "o4 ,b = tak+ ! be>+ ( "s pass+ object1 ! fact t x may n be indicat+ true nor? may r5d] ! obs]vation some:at m tr\blesome ?an x ne$ be4 ,to ov]come ! difficulty "h involv$ ! repeat]s s]v$ by ! ma/] compass are arrang$ to indicate true nor? "u all conditions1 provid$ ! latitude & spe$ dials on ! ma/] compass are correctly set4 ,! repeat]s are op]at$ electrically1 ! fir/ elem5t 9 ! transmission sy/em betwe5 !m & ! ma/] compass be+ a p9ion me%+ ) ! ge> :eel atta*$ to ! phantom r+ b5ea? ! ma/] compass c>d4 ,?is p9ion is m\nt$ on ! lubb] r+1 & !re=e rotates ) ! %ip r\nd ! c>d :5 ! c\rse is alt]$4 ,b1 z x is m\nt$ on ! lubb] r+1 x also p>takes ( ! movem5t ( ?is r+ relatively to ! %ip produc$ by ! correction me*anism4 ,?us ! net indication transmitt$ to ! repeat]s :5 ! %ip *anges c\rse or latitude or spe$ is comp\nd$ ( ! relative motion ( ! ma/] compass c>d & ( ! lubb] r+4 ,! read+ ( ! repeat]s ?us %[s ! true nor?4 ,a pelorus or dummy compass may be comb9$ ) ! repeat]s to facilitate ! tak+ ( be>+s4 ,9 w> vessels ! actual navigation ( ! %ip is pref]ably conduct$ f a repeat]1 ! ma/] compass = safety 9 action be+ dispos$ bel[ ! arm\r$ deck4 ,! ,sp]ry compass is peculi>ly complete 9 ! provision made = tak+ acc\nt ( ! latitude & nor? /eam+ errors4 ,! ,br[n compass1 z we h se51 is free f latitude error1 s t ! nor? /eam+ error alone has to be dealt )4 ,?is error may be all[$ = ari?metically 9 ! usual way by means ( tables ( corrections to be appli$ to ! read+s ( ! ma/] compass4 ,z reg>ds ! repeat]s1 ! error is elim9at$ by a me?od involv+ ! m\nt+ ( ! repeat] c>ds exc5trically1 ! exc5tricity be+ v>i$ to suit ! latitude1 spe$1 & c\rse4 ,,*apt] ,x ,,! ,,balli/ic ,,deflection ,hav+ consid]$ ! effect ( ! %ip's spe$ ^u ! read+s ( ! gyro-compass1 we h next to discuss ! effect ( ! conditions :i* arise :5 ! spe$ is *ang$4 ,x is cle>1 ( c\rse1 t if ! %ip's spe$ is *ang$1 say f #bj to #aj knots1 ! nor? /eam+ error appropriate to ! c\rse & latitude w fall to half its value :5 ! new spe$ has be5 atta9$4 ,two que/ions1 h[ev]1 may be ask$4 ,:at happ5s 9 ! p]iod dur+ :i* ! spe$ is *ang+1 & :at "t elapses betwe5 ! atta9m5t ( ! new spe$ & ! atta9m5t by ! compass ( ! new nor? /eam+ error prop] to ! new spe$8 ,if an ord9>y simple p5dulum 7 hung f ! ro( ( a railway c>riage x w\ld be f\nd t s long z ! tra9 0 travell+ smoo?ly at uni=m spe$ ! p5dulum w\ld hang v]tically )\t oscillat+ j z x w\ld d if ! tra9 7 at re/4 ,if ! tra9 increas$ its spe$ ! in]tia ( ! p5dulum--t is to say1 its t5d5cy to g on mov+ ) ! old velocity--w\ld cause ! p5dulum to assume an incl9$ position beh9d ! v]tical1 ! deflection be+ proportional to ! rate at :i* ! tra9 0 ga!r+ spe$4 ,at ! in/ant at :i* ! tra9 ceas$ to ga!r spe$1 & aga9 assum$ a uni=m velocity1 ! t5d5cy = ! p5dulum to rema9 incl9$ to ! v]tical w\ld vani%1 b ! deflection x possess$ at t in/ant w\ld result 9 its acquir+ an oscillation :i* w\ld p]si/ until friction1 etc41 damp$ x out4 ,if :5 ! p5dulum 7 aga9 /eady & hang+ v]tically1 ! tra9 began to sl[ d[n1 a simil> s]ies ( ev5ts w\ld occur1 only on t occasion ! in]tia ( ! bob w\ld cause ! p5dulum :ile ! tra9 0 los+ spe$ to assume a =w>dly incl9$ position1 ! angle ( :i* w\ld be a measure ( ! rate at :i* ! spe$ 0 be+ r$uc$4 ,on ! atta9m5t ( ! new uni=m spe$ ! p5dulum w\ld oscillate = a "t1 z be=e4 ,! gyro-compass is 9 "p a p5dul\s body1 & on a %ip *ang+ spe$ or acquir+ spe$ f re/ or com+ to a /op x is op5 to ! action ( in]tia =ces j z is our railway c>riage p5dulum4 ,z a result ! compass dur+ ! *ange ( spe$ may exhibit an error--! balli/ic error1 z x is call$--on top ( ! exi/+ nor? /eam+ error4 ,s9ce ! spe$ ( a %ip1 at lea/ ( a m]*ant %ip1 _c be *ang$ v quickly1 & s9ce1 fur!r1 ! spe$ ( a %ip1 at lea/ on long voyages1 is n liable to be *ang$ v (t51 x might be ?\ght t ?is transi5t balli/ic error c\ld be neglect$4 ,x probably c\ld be safely neglect$ if its effect 7 /rictly conf9$ to ! actual p]iod ( ! *ange 9 ! spe$1 b x is n s conf9$4 ,we h to be> 9 m9d ! subsequ5t vibration ( ! railway c>riage p5dulum4 ,a simil> oscillation is set up 9 ! gyro-compass aft] ! new spe$ is atta9$4 ,s9ce ! p]iod ( oscillation ( ! compass is ab\t #he m9utes1 & z two or ?ree complete sw+s h to be made be=e ! damp+ arrangem5ts c suppress ! vibration1 x foll[s t ! compass w n settle 9 its re/+ position aga9 until two or ?ree h\rs aft] ! new spe$ has be5 atta9$1 al?\gh ! actual *ange ( spe$ may h be5 effect$ inside five m9utes or less4 ,illu/ration3 ,,fig4 #bf4 ,balli/ic ,=ce on ,compass :5 ,%ip's ,spe$ ,*anges4 ,if ! %ip is sail+ on an ea/-we/ c\rse1 z repres5t$ 9 ,fig4 #bf1 any *ange ( spe$ w t5d to cause ! p5dulum weight ,s to move 9 ! direction ,r or ,t1 accord+ z ! *ange ( spe$ is a decrease or an increase4 ,su* a t5d5cy w m]ely ?r[ /resses on to ! j\rnals at ,e ,f & ,h ,j1 or1 if ! equival5t ( ! squ>e out] frame is c>ri$ on gimbals1 z x actually is 9 practice1 !n ! t5d5cy to rotate w be translat$ into an actual movem5t ( ! s5sitive elem5t on ! axis ( ! out] m\nt+ co9cid5t or p>allel ) ! axle ,b ,c ( ! :eel4 ,su* a movem5t w h no gyroscopic effect on ! compass1 = ! axle is n subject$ by x to any non-p>allel displacem5t4 ,no balli/ic deflection w !re=e occur on t c\rse4 ,illu/ration3 ,,fig4 #bg4 ,balli/ic ,=ce on ,compass :5 ,%ip's ,spe$ ,*anges4 ,if ! %ip *anges spe$ :ile on a we/ to ea/ c\rse1 ! *ange is simil>ly )\t effect on ! compass4 ,/rictly speak+1 we ought to say t ! *ange ( spe$ w h no effect on ! compass if ! %ip's c\rse is at "r angles to ! direction 9 :i* ! axle ( ! :eel is po9t+4 ,only at ! equator w\ld ?is c\rse be due ea/ or we/4 ,9 o!r latitudes ! latitude error has to be reckon$ )1 s t ! p>ticul> c\rse on :i* *anges ( spe$ are )\t effect on ! compass mu/ be slightly s\? or nor? ( due ea/ or we/4 ,if1 n[1 ! %ip is /eam+ due nor?1 z indicat$ 9 ,fig4 #bg1 a r$uction ( its spe$ w t5d to make ! p5dulum weight sw+ =w>d ab\t ! ea/ & we/ axis ,e ,f 9 ! direction ,p4 ,?is t5d5cy is cle>ly equival5t to ! application ( an upw>d =ce to ! end ,b ( ! axle1 & h5ce1 z we "k1 w cause ! :eel to precess1 ! end ,b ( ! axle go+ ea/w>ds4 ,z ?is precession cont9ues x is oppos$ by ! ev]-increas+ re/or+ mom5t ( ! directive =ce1 s t 9 ! end ! axle assumes a position 9 :i* ! directive =ce j balances ! balli/ic deflective =ce4 ,?is balli/ic deflection rema9s con/ant all ! "t ! %ip's spe$ is fall+4 ,:5 ! spe$ rea*es ! new /eady value ! axle sl[ly oscillates back to ! true re/+ position4 ,x is cle> t a r$uction ( spe$ on a nor!rly c\rse & an increase ( spe$ on a s\!rly produce balli/ic deflections 9 a l direction1 ! nor? end ( ! axle mov+ t[>ds ! ea/4 ,an increase ( spe$ on a nor!rly c\rse or a decrease ( spe$ on a s\!rly produces a we/]ly balli/ic deflection4 ,on int]m$iate c\rses deflections ( a l k9d1 b ( int]m$iate value1 are caus$1 = ! nor? & s\? compon5t ( ! *ange ( spe$ is alone effective 9 tilt+ ! :eel ab\t ! ea/ & we/ axis ,e ,f4 ,imag9e a %ip /eam+ due nor? at #bj knots & *ang+ its spe$ to #aj knots dur+ a p]iod ( five m9utes4 ,z x is /eam+ nor? !re w be a nor? /eam+ error1 ! axle po9t+ we/w>ds ( true nor? by an am\nt dep5d5t ^u ! spe$ ( ! %ip & ! latitude 9 :i* x is sail+4 ,let ,o ,n 7,fig4 #bh7 be ! direction ( true nor?1 & let ,o ,a be ! direction 9 :i* ! axle ( ! gyro-compass aligns itself :5 ! spe$ is #bj knots1 ! angle ,n ,o ,a be+ ! comb9$ latitude & nor? /eam+ errors4 ,let ,o ,b be ! re/+ position = ! axle :5 ! %ip's spe$ is #aj knots1 ! angle ,n ,o ,b be+ ! latitude error--:i* has n alt]$--plus ! nor? /eam+ error--:i* is n[ less because ( ! r$uc$ spe$4 ,z ! spe$ is be+ r$uc$1 ! balli/ic action ( ! p5dulum weight causes ! axle tempor>ily to turn ea/w>ds f ! true re/+ position & to align itself 9 "s direction ,o ,c4 ,:5 ! %ip has settl$ d[n to #aj knots1 ! axle leav+ ! position ,o ,c vibrates ab\t ,o ,b ) amplitudes :i* are be+ cont9ually r$uc$ by ! action ( ! damp+ sy/em4 ,illu/ration3 ,,fig4 #bh4 ,balli/ic ,deflection4 ,! po9t ( importance to notice is t ! tempor>y balli/ic deflection ,o ,c is ea/w>d ( ,o ,a1 j z is ,o ,b ! new re/+ position = ! axle4 ,?is result is a g5]al "o4 ,_h ! spe$ be5 increas$ in/ead ( decreas$1 ! balli/ic deflection w\ld h be5 we/w>d ( ,o ,a1 j z w\ld be ! new re/+ position = ! axle at ! increas$ spe$4 ,simil>ly1 on due s\!rly c\rses or on quadrantal c\rses ! balli/ic deflection produc$ by any *ange ( spe$ is always 9 ! same direction z t 9 :i* ! axle moves 9 pass+ f ! old to ! new nor? /eam+ error4 ,?is be+ s1 x is conceivable t at lea/1 "u c]ta9 conditions1 ! balli/ic deflection position ,o ,c may co9cide ) ! new position ,o ,b = ! axle "u ! new nor? /eam+ error4 ,%\ld su* a result be obta9$1 ! balli/ic action w1 on a *ange ( spe$ occurr+1 sw+ ! axle /raight away into ! new re/+ position4 ,?us ,o ,c & ,o ,b be+ co9cid5t1 !re w be no t5d5cy = ! axle to oscillate ab\t ,o ,b :5 ! spe$ assumes ! new /eady value1 s t ! axle w sw+ into ! new re/+ position 9 a 8dead-beat0 mann]4 ,! effect ( ! balli/ic action w ?us be conf9$ to ! p]iod dur+ :i* ! spe$ is be+ *ang$--five m9utes 9 our example--& w n influ5ce ! read+s ( ! compass = a p]iod ( any?+ up to two or ?ree h\rs aft] ! new spe$ is rea*$4 ,! balli/ic deflection ( a p5dulum hung f ! ro( ( a railway c>riage is dep5d5t ^u ! l5g? ( ! p5dulum1 & !re=e ^u its p]iod ( natural vibration4 ,s1 too1 ! balli/ic deflection ( ! gyro-compass is dep5d5t ^u ! p]iod ( its vibration ab\t ! nor? & s\? direction4 ,once ! *>act]i/ics ( ! compass are det]m9$1 !re=e1 ! angle ,a ,o ,c 7,fig4 #bh7 ( ! balli/ic deflection is settl$ by 7#a7 ! direction ( ! %ip's c\rse1 & 7#b7 by ! rate at :i* ! %ip's spe$ t[>ds ! nor? or s\? is be+ *ang$4 ,x is n affect$ by ! latitude 9 :i* ! %ip is sail+1 ! deflection produc$ by a *ange ( #aj knots 9 five m9utes be+ ! same at ! equator z 9 #fj deg4 or any o!r latitude4 ,com+ to ! diff]5ce betwe5 ! old & ! new nor? /eam+ errors1 x w be se5 f our previ\s explanation ( ! errors !mselves t ! magnitude ( ! angle ,a ,o ,b is indep5d5t ( ! design ( ! compass 9 use4 ,x w v>y ) 7#a7 ! direction ( ! %ip's c\rse1 & 7#b7 ! ext5t by :i* ! %ip's spe$ is *ang$4 ,9 addition1 x w also v>y ) 7#c7 ! latitude 9 :i* ! %ip is sail+4 ,f ^! consid]ations x is argu$ t by suitably select+ ! p]iod ( vibration ! balli/ic deflection c be made = "o p>ticul> latitude j equal to ! diff]5ce betwe5 ! nor? /eam+ errors = any initial & any new spe$ on any c\rse4 ,9 practice ! latitude select$ is #dj deg4 nor? or s\?4 ,x is f\nd by calculation t ! p]iod ( vibration :i* mu/ be giv5 to ! compass to secure ?is dead-beat balli/ic deflection is su* t 9 ?is latitude ! compass %\ld oscillate 9 ! same p]iod z w\ld a simple p5dulum1 ! l5g? ( :i* 0 equal to ! radius ( ! e>?4 ,x is = ?is reason t all mod]n gyro-compasses h a p]iod ( vibration ( approximately #he m9utes4#e ,9 latitudes o!r ?an #dj deg4 nor? or s\? ! balli/ic deflection w n be dead-beat1 b by tak+ ?is latitude z ! mean ! subsequ5t oscillation aft] a *ange ( spe$ is--9 m]cantile vessels at lea/--suffici5tly small to introduce no error ( great importance1 except = purposes ( v accurate obs]vation1 9 :i* case ! obs]vation1 if possible1 w\ld n be made until ! vessel _h be5 runn+ = two or ?ree h\rs aft] ! la/ consid]able *ange ( spe$4 ,x is to be notic$ t ! balli/ic error may arise :5 ! %ip is alt]+ c\rse )\t alt]+ its spe$4 ,?us1 if x is sail+ nor? & makes a %>p turn ea/w>ds or we/w>ds1 ! spe$ nor?w>ds dur+ ! turn falls progressively f a maximum at ! beg9n+ to z]o at ! end ( ! turn1 ev5 al?\gh ! actual l9e> spe$ ( ! %ip rema9s con/ant ?r\gh\t4 ,turn+ 9 ei!r direction is ?us equival5t to a decel]ation ( ! %ip's nor!rly spe$1 s t an ea/]ly balli/ic deflection may be expect$ 9 bo? cases4 ,on ! o!r h&1 a turn t[>ds ! nor? f a due ea/ or we/ c\rse is equival5t to an accel]ation ( ! %ip's nor!rly spe$1 &1 z a result1 a we/]ly balli/ic deflection is produc$4 ,9 latitude #dj deg4 nor? or s\? bo? ^! balli/ic deflections w\ld be dead-beat 9 a mod]n gyro-compass1 be+ j suffici5t 9 ! "o case to elim9ate & 9 ! o!r to apply ! appropriate nor? /eam+ error4 ,9 a v rec5t improvem5t1 x is und]/ood1 x has be5 f\nd possible to provide means :]eby ! balli/ic deflection is made dead-beat 9 all latitudes4 ,,*apt] ,,xi ,,! ,,quadrantal ,,error ,let a /one be ti$ to ! end ( a /r+ & be flung =w>d :ile ! free end ( ! /r+ is held 9 ! h&4 ,let ! h& hold+ ! free end be mov$ =w>d at fir/ ) ! same spe$ z ! /one 9 its flight1 & !n let ! h& be drawn back4 ,we "k t z soon z ! /r+ becomes taut--if x 7 n already fully ext5d$--! h& w\ld feel a pull ex]t$ on x 9 ! direction 9 :i* ! /one 0 initially project$4 ,?is pull arises f ! fact t ! /one has be5 giv5 mom5tum 9 ! direction ( its flight1 & :ile ?is mom5tum is be+ tak5 out ( x by ! backw>d pull ( ! h& & new mom5tum 9 ! backw>d direction is be+ communicat$ to x ! /one reacts =cibly on ! /r+ & !re=e on ! h&4 ,9 ! gyro-compass ! p5dulum weight may be lik5$ to ! /one1 ! /irrup c>ry+ ! weight to ! /r+1 & ! sp9n+ :eel to ! h&4 ,:ile ! %ip is /eam+ at a uni=m spe$1 ! sy/em is 9 ! condition exi/+ j aft] ! /one has be5 project$ f ! h&1 & :ile ! h& is foll[+ x ) equal spe$4 ,a *ange 9 ! %ip's spe$--a r$uction ( its spe$ to be q correct 9 our analogy--is comp>able ) ! draw+ back ( ! h&4 ,! pull ( ! /one ex]t$ on ! h& at ?is in/ant is repres5t$ by ! t5d5cy ( ! weight to cont9ue mov+ at ! =m] spe$1 & ! resultant 8kick0 :i* by its attempt to d s x applies to ! sp9n+ :eel4 ,?is kick is communicat$ to ! sp9n+ :eel ?r\gh /iff memb]s & rigid connections1 & n ?r\gh a flexible /r+4 ,x really acts at ! c5tre ( gravity ( ! p5dulum weight1 & is !re=e felt by ! sp9n+ :eel1 n z a /raight pull1 b z a =ce t5d+ to turn ! :eel ab\t ! horizontal axis ,e ,f4 ,! kick ( ! weight :5 ! %ip *anges spe$ on any c\rse hav+ a nor? or s\? compon5t produces1 z we h se51 a transi5t balli/ic error :i* may influ5ce ! correctness ( ! compass read+s = "s h\rs aft] ! *ange ( spe$ has be5 complet$4 ,we h n[ to %[ t simil> kicks occur "u o!r conditions1 & may simil>ly affect ! accuracy ( ! read+s4 ,! subject :i* we are ab\t to discuss is ! s-call$ quadrantal error :i*1 unless /eps are tak5 to elim9ate x1 appe>s 9 ! compass read+s :5 ! %ip is sail+ 9 a r\gh sea on any c\rse o!r ?an due nor?1 s\?1 ea/1 or we/4 ,x is caus$ by ! roll+ & pit*+ ( ! %ip4 ,! ef=ts made to elim9ate x h influ5c$ ! evolution ( ! gyro-compass to a great] ext5t ?an probably ^? direct$ t[>ds ov]com+ or all[+ = all ! o!r errors comb9$ to :i* ! device is op54 ,illu/ration3 ,,fig4 #bi4 ,effect ( ,roll+ on due ,nor? ,c\rse4 ,! gyro-compass on bo>d %ip is usually1 al?\gh 9 no way necess>ily1 m\nt$ above ! vessel's metac5tres--transv]se & longitud9al--ab\t :i* roll+ & pit*+ take place4 ,9 ,fig4 #bi we %[ a section1 look+ aft1 ( a vessel /eam+ due nor? ) a gyro-compass m\nt$ on its deck4 ,x is cle> t1 s f> z ! weight ,s is conc]n$1 x may be reg>d$ :5 ! %ip rolls z ! bob ( an inv]t$ p5dulum vibrat+ 9 an ea/ & we/ plane1 ?r\gh an angle equal to ! angle ( ! %ip's roll4 ,f :at we h already said1 x w be se5 t at ! end ( a roll to port ! h& hold+ ! /r+ atta*$ to ! fly+ /one1 hi!rto foll[+ x1 beg9s its )drawal to ! ea/4 ,! weight *eck$ 9 its movem5t to ! we/ communicates a kick to ! s5sitive elem5t4 ,?is kick1 a we/w>d =ce1 is appli$ at ! c5tre ( gravity ( ! weight1 & cle>ly does no?+ m ?an ?r[ a /ress on to ! j\rnals at ,e ,f & ,h ,j1 & ?r\gh ! squ>e frame on to ! deck4 ,x does n !re=e affect ! direction 9 :i* ! gyro-axle is po9t+4 ,if1 z is actually ! case 9 practice1 ! equival5t ( ! squ>e frame is n fix$ directly to ! deck1 b is m\nt$ inside ! b9nacle on a?w>t%ip & longitud9al gimbals1 ! squ>e frame w sw+ on ! longitud9al gimbal axis4 ,! weight ,s w1 h[ev]1 /ill act dur+ ! %ip's roll z an inv]t$ p5dulum1 z at ,z ,z1 9 :i* ! bob rema9s m or less p>allel ) its orig9al direction4 ,"u ^! conditions ! kick ( ! weight at ! end ( a roll to port w rotate ! frame 9 ! direction ( ! curv$ arr[ ab\t ! longitud9al gimbal axis4 ,z ?is axis is co9cid5t or p>allel ) ! gyro-axle1 ! gyro-axle is n mov$ o!rwise ?an p>allel ) itself ei!r by ! actual roll ( ! %ip or by ! kick ( ! weight at ei!r out position4 ,?us a %ip /eam+ nor? may roll ) impunity )\t affect+ ! accuracy ( ! direction 9 :i* ! gyro-axle is po9t+4 ,illu/ration3 ,,fig4 #cj4 ,effect ( ,roll+ on due ,we/ ,c\rse4 ,x is cle> t roll+ on a due s\? c\rse or pit*+ on a due ea/ or we/ c\rse is simil>ly )\t effect on ! gyro-compass4 ,n[ consid] ! case ( ! %ip roll+ :5 on a due we/ c\rse 7,fig4 #cj74 ,x is cle> t "h aga9 ! weight ,s may by itself be consid]$ z ! bob ( an inv]t$ p5dulum vibrat+ ?r\gh ! angle ( ! %ip's roll1 ?is "t 9 a nor? & s\? plane4 ,! weight ,s has1 9 addition1 its own p5dulum action on ! horizontal axis ,e ,f1 & t5ds to keep ! gyro-axle horizontal ?r\gh\t ! roll4 ,at ! end ( a roll to port ! kick ( ! weight ,s1 a s\!rly =ce act+ at ! c5tre ( gravity ( ! weight1 t5ds to turn ! sp9n+ :eel 9 ! direction ,r ab\t ! horizontal ea/ & we/ axis ,e ,f4 ,?is kick is cle>ly equival5t to ! application ( an upw>d =ce at ! end ,c ( ! axle or a d[nw>d =ce at ! end ,b1 & !re=e1 z we "k1 w cause ! axle n to turn ab\t ,e ,f1 b to precess ! nor? end ,b t[>ds ! we/ ab\t ! axis ,h ,j4 ,! roll to />bo>d n[ takes place1 & at its end ! kick ( ! weight occurs 9 ! nor!rly direction4 ,?is kick w t5d to turn ! sp9n+ :eel ab\t ! ea/ & we/ axis ,e ,f 9 ! direction ,t1 & is cle>ly equival5t to ! application ( an upw>d =ce at ! end ,b ( ! axle4 ,su* a =ce1 z we "k1 w cause ! end ,b ( ! axle to precess t[>ds ! ea/4 ,x w ?us be se5 t ! we/]n deflection ( ! axle produc$ by ! precession :i* occurs at ! end ( ! roll to port is c\nt]balanc$ & automatically elim9at$ by ! ea/]n deflection produc$ by ! precession occurr+ at ! end ( ! roll to />bo>d4 ,! only effect on ! compass caus$ by ! roll+ ( ! %ip is !re=e a vibration ( ! axle ab\t ! nor? & s\? direction4 ,we %\ld really say t ! only effect is ! application to ! s5sitive elem5t ( a vibratory influ5ce 9 tune ) ! roll+ ( ! %ip4 ,z ! %ip's p]iod is v small comp>$ ) t ( ! compass ab\t ! axis ,h ,j--ab\t #e to #ab seconds z comp>$ ) ab\t #he m9utes--?is vibratory influ5ce practically fails to di/urb ! /ead9ess ) :i* ! axle po9ts to ! nor?4 ,x is cle> t pit*+ ( ! %ip :5 on a due we/ c\rse has ! same effect--or lack ( effect--on ! compass z roll+ on a due nor? c\rse1 & t pit*+ on a due nor? c\rse has ! same effect z roll+ on a due we/ c\rse4 ,x is fur!r cle> t due s\? & due ea/ c\rses are simil> 9 ?is respect to due nor? & due we/ c\rses4 ,?us :5 ! %ip is on a c>d9al c\rse nei!r pit*+ nor roll+ di/urbs ! axle ( ! sp9n+ :eel f its nor? re/+ position4 ,matt]s are q o!rwise1 h[ev]1 :5 ! c\rse is an int]-c>d9al1 or quadrantal1 "o4 ,! discov]y ( ?is unlikely fact 0 9 l>ge "p due to ! inve/igations ( ! ,compass ,dep>tm5t ( ! ,briti% ,admiralty4 ,x does n appe> to h be5 kn[n1 or at lea/ its full significance does n seem to h be5 appreciat$1 9 ! e>li] days ( gyro-compass con/ruction4 ,at lea/ "o e>ly design ( compass--! ,ans*tz ( #aiaj--;did n include means ( elim9at+ or all[+ = ! 8quadrantal error10 & soon became obsolete z a result prim>ily ( ! omission4 ,t ! lat] design ( ,ans*tz compass successfully ov]comes ! difficulties introduc$ by ?is error is %[n by ! admitt$ excell5ce ( ! navigation ( ! ,g]man subm>9es1 :i* vessels 7 univ]sally fitt$ ) compasses ( ?is design1 & :i*1 l all _! class1 suff] mu* f roll+ & pit*+4 ,illu/ration3 ,,fig4 #ca4 ,ext]nal ,gimbal ,m\nt+4 ,s f> we h be5 able to use a v simple model to demon/rate ! prop]ties & errors ( ! gyro-compass4 ,we h n[ rea*$ a subject :i*1 if x is to be expla9$ correctly1 requires u to adopt a model ( a m elaborate nature1 "o 9 :i* ! out] squ>e frame ( our simple model is itself m\nt$ on a pair ( gimbal axes4 ,we h already ref]r$ to ?is type ( m\nt+ 9 our second *apt] & above 9 connection ) ,fig4 #bi4 ,9 ,fig4 #ca we %[ x ) ! p5dul\s weight add$ to ! s5sitive elem5t4 ,we may take x t ! axis ,t ,u1 ab\t :i* ! entire compass sy/em may sw+1 is p>allel ) ! longitud9al c5tre l9e ( ! %ip1 & t ! frame ,y is fix$ to ! deck4 ,illu/ration3 ,,fig4 #cb4 ,effect ( ,roll+ on a ,due ,nor? ,c\rse 7,simple ,m\nt+74 ,illu/ration3 ,,fig4 #cc4 ,effect ( ,roll+ on a ,due ,nor? ,c\rse 7,ext]nal ,gimbal ,m\nt+74 ,9 ord] to make q cle> ! diff]5ce betwe5 ! two =ms ( m\nt+1 we give 9 ,figs4 #cb & #cc two correspond+ sets ( views %[+ ! compass sy/em on a %ip :ile /eam+ due nor? & roll+4 ,) ! simple m\nt+ 7,fig4 #cb7 ! weight ,s con/antly rema9s radially bel[ ! c5tre ( ! sp9n+ :eel1 & ! kicks :i* x applies at ! out port & out />bo>d positions m]ely /ress ! compass m\nt+s4 ,) ! m elaborate m\nt+ 7,fig4 #cc7 ! weight t5ds to rema9 con/antly 9 ! v]tical bel[ ! c5tre ( ! sp9n+ :eel1 b ! kicks occurr+ at ! out positions1 if ! roll+ is cont9u$ = any l5g? ( "t1 cause x to sw+ beyond ! v]tical1 s t z ! %ip rolls ! :ole compass sy/em acquires an oscillation on ! axis ,t ,u 7,fig4 #ca7 9 tune ) ! rolls4 ,x is to be not$ t ! p]iod ( vibration ( ! compass sy/em ab\t ! axis ,t ,u is v mu* less ?an t ( ! s5sitive elem5t ab\t ! axis ,h ,j4 ,! latt]1 z we h se51 is ab\t #he m9utes1 & is det]m9$1 9 "p at lea/1 by ! high spe$ ( ! sp9n+ :eel4 ,ab\t ,t ,u ! vibration1 h[ev]1 does n call any gyroscopic =ce into play1 = x takes place )\t caus+ ! axle ( ! sp9n+ :eel to alt] its direction4 ,! p]iod ( ?is vibration is !re=e n affect$ by ! spe$ ( ! sp9n+ :eel4 ,x may be q small--f "o to two seconds--& !re=e comp>able ) ! %ip's roll+ p]iod4 ,if1 !n1 no /eps are tak5 to prev5t x1 ! compass sy/em z a :ole w acquire a sw+ on ! axis ,t ,u 7,fig4 #ca7 :5 ! %ip is /eam+ nor?--or s\?--& roll+4 ,its p]iod ( vibration on ?is axis is n /rictly t :i* x w\ld h 7 x set oscillat+ ab\t ! axis ,t ,u ) ?is axis m\nt$ on a fix$ frame1 = ! vibration is n a free "o1 b is a =c$ vibration "u ! impulses communicat$ by ! roll+ ( ! %ip4 ,:atev] may be ! exact free p]iod ( sw+ ( ! compass sy/em on ! axis ,t ,u1 s long z x is some:]e ne> t ( ! %ip's roll or a small sub-multiple ( ! roll+ p]iod1 ! t5d5cy is = ! compass sw+s to settle d[n 9 su* a way t1 z repres5t$ 9 ,fig4 #cc1 ! p5dulum weight ,s rea*es its extreme out positions simultane\sly ) ! %ip's arrival at its extreme port & />bo>d heels4 ,9 ! c\rse ( "o complete roll ( ! %ip1 h[ev]1 ! compass sy/em may make m ?an "o complete vibration ab\t ,t ,u4 ,x is cle> t :e!r ! bob ,s rema9s radially bel[ ! c5tre ( ! :eel1 z 9 ,fig4 #cb1 or rema9s v]tically bel[ x1 or sw+s pa/ ! v]tical1 z 9 ,fig4 #cc1 ! effect ( roll+ :5 ! %ip is on a due nor? c\rse is z e/abli%$ 9 connection ) ,fig4 #bi4 ,ei!r a t5d5cy to rotate ! :eel ab\t an axis co9cid5t ) its axle or an actual rotation ( ! :eel ab\t ?is axis results f ! kicks ( ! weight ,s at ! out positions4 ,:i*ev] x is1 !re is no gyroscopic effect call$ into play1 & ! axle is n subject$ to any influ5ce caus+ x to move away f ! due nor? direction4 ,we h n[ to discuss :at happ5s if ! vessel rolls or pit*es :5 sail+ on an int]-c>d9al or quadrantal c\rse4 ,9 ,fig4 #cd we %[ 9 plan a vessel /eam+ on a nor?-we/ c\rse4 ,:5 ! %ip rolls ! compass oscillates 9 ! pa? ,a ,d1 a pa?1 t is to say1 at "r angles to ! %ip's c5tre l9e & curv$ upw>dly by reason ( ! fact t ! compass is m\nt$ above ! roll+ c5tre ( ! %ip4 ,! axle ( ! compass dur+ ?is movem5t t5ds to po9t /eadily t[>ds ! nor? "u ! action ( ! directive =ce4 ,! :eel !re=e oscillates f ,a to ,d ) its axle askew relatively to ! pa? ( oscillation1 & n at "r angles to x1 z 9 ,fig4 #bi1 or p>allel ) x1 z 9 ,fig4 #cj4 ,! oscillation ,a ,d c1 h[ev]1 be resolv$ into two compon5ts1 namely1 a nor? & s\? oscillation ,d ,k1 9 :i* ! axle is p>allel ) ! pa?1 & an ea/ & we/ oscillation ,k ,a1 9 :i* x is at "r angles to ! pa?1 bo? pa?s be+ curv$ upw>dly4 ,illu/ration3 ,,fig4 #cd4 ,%ip ,roll+ on ,n4,w4 ,c\rse4 ,! oscillation ,d ,k1 tak5 by itself1 is cle>ly exactly equival5t to t %[n 9 ,fig4 #cj4 ,! s\?w>d kick ( ! weight at ! 8out position0 ,d 7,fig4 #cd7 j neutralises ! di/urb+ effect ( ! nor?w>d kick at ! 8out position0 ,k4 ,simil>ly1 ! oscillation ,k ,a1 tak5 by itself1 is exactly equival5t to t %[n 9 ,fig4 #bi or its modification1 ,fig4 #cc4 ,! ea/w>d kick ( ! weight at ,a & ! we/w>d kick at ,k _c d m ?an turn ! m\nt+ r\nd ! axle ( ! sp9n+ :eel4 ,!y d n t5d to *ange ! direction ( ! axle4 ,h5ce1 tak5 sep>ately1 ea* compon5t oscillation ,d ,k & ,k ,a is )\t di/urb+ effect ^u ! direction 9 :i* ! axle is po9t+4 ,tak5 toge!r1 h[ev]1 _! unit$ effect is n ! sum ( _! sep>ate effects1 z we might ha/ily assume4 ,we mu/ n suppose t ! nor? & s\? kicks prop] to ! nor? & s\? compon5t ( ! oscillation are )\t effect ^u ! ea/ & we/ compon5t or vice v]sa4 ,at ! out position ,d ( ! compon5t oscillation ,k ,d ! weight is n only kick$ s\?w>ds1 b also receives a we/w>d kick f ! o!r compon5t oscillation ,a ,k4 ,at ,k x receives bo? a nor?w>d kick & an ea/w>d kick4 ,simil>ly1 at ! out position ,k ( ! compon5t oscillation ,a ,k ! weight is kick$ n only to ! we/ b also to ! s\?1 by virtue ( ! oscillation f ,k to ,d4 ,at ! o!r out position ,a ( ?is compon5t ! weight is kick$ ea/w>dly1 & also to ! nor?4 ,if we take cognisance ( ^! additional kicks1 we may treat ! compon5t oscillations sep>ately & add ! sep>ate results to get ! true effect ( ! actual oscillation ,a ,d4 ,return+1 !n1 to ,fig4 #cj1 let u suppose t 9 ! oscillation !re %[n1 ! equival5t ( ! compon5t ,k ,d1 we apply a we/w>d kick to ! weight ,s :5 ! %ip rea*es its port out position--t is to say1 a kick out ( ! pap]--& t at ! />bo>d out position x receives an ea/w>d kick into ! plane ( ! pap]4 ,x is cle> t ^! additional kicks d no?+ m ?an t5d to rotate ! :eel ab\t its axle or an axis co9cid5t or p>allel ) its axle4 ,!y _c !re=e call any gyroscopic effect into action1 & z a result d n di/urb ! direction 9 :i* ! axle is po9t+4 ,! compon5t oscillation ,d ,k1 ev5 ) ! extra kicks add$1 is ?us h>mless4 ,tak+ ,fig4 #cc r ?an ,fig4 #bi z ! equival5t ( ! compon5t oscillation ,a ,k1 let u suppose t at ! port out position ! weight is subject$ to an additional kick to ! s\?--t is1 into ! plane ( ! pap]--& t at ! />bo>d out position x receives an extra kick to ! nor?1 or out ( ! plane ( ! pap]4 ,! s\?w>d kick on ! weight at ! port out position w t5d to cause ! end ,b ( ! axle to turn d[n t[>ds ,j1 b1 9 accordance ) ! fundam5tal gyroscopic rule1 ! actual motion ( ! s5sitive elem5t w n be a rotation ab\t ! axis ,e ,f1 b a precession ab\t ! axis ,h ,j1 ! end ,b ( ! axle mov+ 9 ! direction ,k4 ,simil>ly1 ! nor?w>d kick at ! />bo>d out position w t5d to cause ! end ,b ( ! axle to rise t[>ds ,h1 & w !re=e produce precession 9 ! direction ,l4 ,n[ ^! two precessional movem5ts1 ,k & ,l1 c be resolv$ into horizontal & v]tical compon5ts ,n ,m & ,q ,p respectively1 z %[n sep>ately1 & ( ^! compon5ts x is cle> t ! movem5t ,n cancels ! movem5t ,q4 ,on ! o!r h&1 ! two compon5ts ,m & ,p are 9 ! same direction1 & !re=e d n cancel ea* o!r4 ,_! effect is cumulative1 & ) ea* succe$+ roll ! end ,b ( ! axle t5ds to rise high] & high] 9 ! true v]tical plane ,b ,r4 ,x may be expla9$1 p]haps1 t ?is motion is possible1 9 spite ( ! fact t !re is no actual axis 9 ! m\nt+ ( ! compass at "r angles to ! true v]tical plane1 except at ! in/ant :5 ! compass is pass+ ?r\gh ! ev5 keel position 9 ! c\rse ( its sw+ f side to side4 ,z ! roll+ ( ! %ip />t+ f z]o increases up to a m or less /eady value1 ! end ,b ( ! axle rises sl[ly at fir/ & !n at a con/ant rate1 z exagg]at$ at ,t4 ,su* ( ?is upw>d movem5t z occurs :ile ! compass is pass+ ?r\gh ! ev5 keel position c be effect$ by means ( a rot>y motion purely ab\t ! axis ,e ,f4 ,else:]e 9 ! sw+ ( ! compass f side to side x is accommodat$ by a p>tial rotation on ,e ,f & a p>tial rotation ab\t ,h ,j4 ,^! two axes betwe5 !m p]mit ! end ,b ( ! axle to rise 9 a v]tical plane at any po9t ( ! compass sw+ j z effectively z w\ld an axis :i* 0 at "r angles to ! v]tical plane ,b ,r4 ,to appreciate ! significance ( ?is v]tical rise ( ! nor? end ,b ( ! axle1 let u consid] ! condition ( ! compass z x is pass+ ?r\gh ! ev5 keel position4 ,! elevation ( ! end ,b out ( ! horizontal plane causes ! weight ,s to sw+ =w>d t[>ds ! nor?1 & !re=e to apply a turn+ mom5t to ! sp9n+ :eel ab\t ! axis ,e ,f4 ,?is turn+ mom5t w t5d to br+ ! end ,b d[n aga9 to ! horizontal1 b1 z we "k1 ! actual motion produc$ w be a precession ab\t ! axis ,h ,j1 ! end ,b mov+ we/w>ds4 ,look+ at ,fig4 #cd1 x w ?us be se5 t ! net effect ( ! roll+ ( ! %ip is to deviate ! axle ( ! compass 9 ! direction %[n at ,v--t is to say1 9 ! direction requir$ to set ! plane ( ! sp9n+ :eel p>allel ) ! plane ( ! roll+ by ! %orte/ possible c\rse--9 our example by a rotation we/w>d ?r\gh #de deg4 ,) ! axle s deflect$ ! e>?'s rotation1 ( c\rse1 calls a directive =ce into play1 t5d+ to re/ore ! axle to ! nor? & s\? l9e1 b if ! %ip is roll+ viol5tly ! deviat+ =ce w be mu* /rong] ?an ! directive =ce until a v consid]able angle ( deflection is rea*$4 ,:5 ! balance is /ruck1 ! axle settles d[n ) a /eady deviation t[>ds ! we/1 :i* w rema9 con/ant z long z ! roll+ is ma9ta9$4 ,9 practice ! viol5ce ( ! roll+ v>ies almo/ f roll to roll1 = x repres5ts a conflict betwe5 ! natural p]iod ( roll+ ( ! %ip & ! p]iod ( ! waves4 ,z a consequ5ce1 ! deviation ( ! compass v>ies some:at dur+ ! roll+1 b x is always we/w>dly if ! c\rse is 9 ! nor?-we/ quadrant4 ,a little consid]ation w %[ t if ! %ip is /eam+ t[>ds ! nor?-ea/ ! additional kick on ! weight ,s 7,fig4 #cc7 at ! port out position w be t[>ds ! nor? & at ! />bo>d out position t[>ds ! s\?4 ,! end ,b ( ! axle is !re=e precess$ v]tically d[nw>ds in/ead ( upw>ds1 & z a result ! deviation ( ! axle is ea/w>dly4 ,9 g5]al1 if ! %ip is /eam+ on any c\rse 9 ! nor?-we/ or s\?-ea/ quadrant1 ! deviation caus$ by h] roll+ w be t[>ds ! we/4 ,x w be t[>ds ! ea/ if ! c\rse is 9 ! nor?-ea/ or s\?-we/ quadrant4 ,! effect ( pit*+ on a quadrantal c\rse is to cause a deviation ( ! axle 9 ! direction oppos$ to t ( ! deviation caus$ by roll+1 s t if ! vessel be bo? roll+ & pit*+1 ! deviation is some:at less ?an x w\ld be if roll+ only _h to be consid]$4 ,x may p]haps be ?\ght t ! quadrantal error is an effect produc$ by ! d\ble gimbal m\nt+ ( ! compass1 & t _h we adh]$ to our simple model1 z %[n 9 ,fig4 #cb1 x w\ld n arise4 ,?is is n s4 ,if ,fig4 #cb be tak5 z repres5t+1 aft] ! mann] ( ,fig4 #cc1 ! nor? view ( ! compass on a %ip /eam+ due nor?-we/1 x w be se5 t ! s\!rn kick at ! port out position causes ! axle to precess 9 ! direction ,k & ! nor!rn kick at ! />bo>d out position 9 ! direction ,l4 ,resolv+ ^! movem5ts z be=e1 we see t1 :ile ! horizontal compon5ts ,n ,q aga9 cancel1 ! v]tical compon5ts ,m ,p are1 z 9 ,fig4 #cc1 cumulative 9 effect1 b ?is "t !y result 9 ! end ,b ( ! axle mov+ d[nw>ds1 & !re=e f9ally cause x to precess ea/w>ds in/ead ( we/w>ds1 z be=e4 ,! quadrantal error is !re=e n elim9at$1 b m]ely rev]s$ 9 direction by adopt+ ! simpl] m\nt+ = ! compass4 ,,*apt] ,,xii ,,! ,,elim9ation ,,( ,,! ,,quadrantal ,,error ,f our description ( ! cause ( ! quadrantal error x %\ld be cle> t x is ( a v>iable erratic nature1 or at lea/ t1 unlike ! latitude & nor? /eam+ errors1 its magnitude _c be =eca/ f a k ( ! %ip's spe$1 c\rse1 latitude1 or o!r factors4 ,its direction is det]m9$ by ! direction ( ! %ip's c\rse1 b its am\nt is settl$ by ! viol5ce ( ! roll+ & pit*+1 & _c !re=e be calculat$ & tabulat$ 9 a practically useful way4 ,x foll[s1 !re=e1 t to get rid ( ! upsett+ influ5ce ( ! quadrantal error we _c resort to 8correct+0 ! compass read+s = x1 b mu/ entirely elim9ate x4 ,9 ! e>ly 7#aiaj7 ,ans*tz compass !re 7 no means ( elim9at+ ! quadrantal error1 = ! exi/5ce ( ! error1 or at lea/ ! importance to be atta*$ to x1 0 n at fir/ recognis$4 ,! compass1 we believe1 %[$ errors f ?is cause ( z mu* z #bj deg4 to #dj deg4 ,z a result1 )9 a v %ort "t ! design 0 disc>d$1 & :at am\nt$ to an entirely diff]5t compass 0 sub/itut$ = x4 ,! #aiab ,ans*tz compass w be briefly describ$ lat] on1 b "h x may be said t ! quadrantal error 9 x is elim9at$ by add+ two m gyro-:eels to ! s5sitive elem5t4 ,! !ory ( ?is compass is n v easy to und]/&1 s t x w be be/ if we expla9 fir/ h[ ! quadrantal error is elim9at$ 9 ! ,sp]ry & ! ,br[n compasses4 ,! e>ly ,sp]ry1 l ! e>ly ,ans*tz compass1 0 op5 to ! full action ( ! quadrantal error4 ,9 ! =m n[ 9 use1 h[ev]1 x is prev5t$ f tak+ effect by controll+ automatically ! position ( ! exc5tric p9 connect+ ! weight or 8bail0 to ! gyro cas+4 ,9 ! ,sp]ry compass1 z we "k1 ! weight ,s 7,fig4 #ce7 is n hung f ! inn] support+ r+ or its equival5t1 b f ! foll[-up or phantom r+1 its p5dul\s effect be+ communicat$ to ! cas+ & !nce to ! sp9n+ :eel ?r\gh ! exc5tric p9 ,a4 ,! kicks ( ! weight at ! out positions dur+ ! roll+ ( ! %ip are also transmitt$ ?r\gh ! p9 to ! cas+ & :eel inside x4 ,illu/ration3 ,,fig4 #ce4 ,sp]ry ,compass on ,n4,w4 c\rse4 ,let u suppose1 z %[n 9 ,fig4 #ce1 t at ! port out position ( ! compass sw+ ! exc5tric p9 is ea/ ( ! axis ,h ,j by ! am\nt requir$ j to br+ x v]tically bel[ ! c5tre ( ! sp9n+ :eel4 ,!n ! s\?w>d kick ( ! weight :5 ! vessel rolls on a nor?-we/ c\rse is transmitt$ to ! cas+ z a s\?w>d =ce appli$ at ! po9t ,a4 ,?is =ce1 act+ ab\t ! axis ,e ,f z be=e1 produces precession 9 ! direction ,k1 &1 z be=e1 we may resolve ?is movem5t into ! compon5ts ,n ,m4 ,! =ce at ,a has1 h[ev]1 9 addition1 a turn+ mom5t ab\t ! axis ,h ,j1 = x is appli$ to ! cas+ at a po9t ly+ at a di/ance ,a ,d f ?is axis1 & n1 z 9 ,fig4 #cc1 at a po9t virtually on x4 ,?is mom5t ab\t ,h ,j w\ld t5d to make ! end ,b ( ! axle turn 9 ! direction ( ,f1 & !re=e results1 9 accordance ) ! rule ( ! gyroscope1 9 an actual movem5t ab\t ! axis ,e ,f1 ! end ,b ( ! axle precess+ d[nw>ds t[>ds ,j1 t is1 9 ! direction ,r4 ,we may resolve ! precession ,r into two compon5ts ,t ,u4 ,simil>ly1 at ! />bo>d out position1 let u suppose t ! exc5tric p9 is ?is "t we/w>ds ( ! axis ,h ,j by exactly ! am\nt requir$ aga9 to br+ x v]tically bel[ ! c5tre ( ! :eel4 ,z be=e1 9 ! case %[n 9 ,fig4 #cc1 ! nor?w>d kick ( ! weight act+ ab\t ,e ,f results 9 a precession ,l1 :i* may be resolv$ into ! compon5ts ,p ,q4 ,! kick1 h[ev]1 z at ! port out position1 also has a mom5t ab\t ! axis ,h ,j4 ,! kick is rev]s$ 9 direction1 b ! po9t ( its application to ! cas+ is n[ on ! o!r side ( ,h ,j4 ,consequ5tly ! kick t5ds to rotate ! cas+ ab\t ,h ,j--& !re=e produces precession ab\t ,e ,f--9 ! same direction z does ! kick at ! port out position4 ,! precession produc$ is repres5t$ by ,v1 & c be resolv$ into ! compon5ts ,w ,x4 ,consid]+ n[ ! f\r pairs ( compon5t precessions1 we see t !y cancel out 9 pairs4 ,?us ,n & ,q cancel1 ,u cancels ,x1 ,t wipes out ,m1 & ,w does ! same to ,p4 ,! two compon5ts ,m ,p1 :i* 7 ! cause ( ! quadrantal error1 are j balanc$ by ! two additional compon5ts ,t ,w4 ,! axle !re=e does n rise v]tically1 b rema9s horizontal1 & z a result no quadrantal error c arise4 ,x w be se5 t ! ,sp]ry me?od ( elim9at+ ! quadrantal error requires ! exc5tric p9 to be movable relatively to ! bail & cas+4 ,to be m precise1 :ile ! cas+1 ! bail1 ! phantom r+1 & all ! o!r p>ts ( ! compass may sw+ r\nd ! axle ( ! sp9n+ :eel1 or ! ext]nal gimbal axis co9cid5t or p>allel ) ! axle1 matt]s h to be arrang$ 9 su* a way t :5 ! %ip rolls ! exc5tric p9 %all n p>take ( ?is motion1 b rema9 con/antly 9 ! v]tical bel[ ! c5tre ( ! sp9n+ :eel4 ,we h to rememb]1 h[ev]1 t ! ,sp]ry me?od ( damp+ ! horizontal vibrations ( ! axle hangs ^u ! p9 be+ displac$ t[>ds ! ea/ ( ! axis ,h ,j :5 ! compass is 9 ! ev5 keel position4 ,! two requirem5ts are met by s controll+ ! position ( ! p9 relatively to ! bail & cas+ t :5 ! bail1 cas+1 etc41 sw+ sideways "u ! influ5ce ( ! roll+ ( ! %ip1 ! p9 is ma9ta9$ at a fix$ di/ance ea/w>ds ( ! true v]tical ?r\gh ! c5tre ( ! sp9n+ :eel at all po9ts 9 ! oscillation ( ! bail1 cas+1 etc4 ,illu/ration3 ,,fig4 #cf4 ,sp]ry ,balli/ic ,gyro4 ,! /abilisation ( ! exc5tric p9 9 ?is mann] is effect$ gyroscopically by means ( ! atta*m5t %[n 9 ,fig4 #cf4 ,?is device consi/s ( a small high-spe$ electrically driv5 gyroscope runn+ inside a cas+ :i* is m\nt$ rotatably on a v]tical axis inside a /irrup frame4 ,?is frame1 z %[n 9 ,fig4 #cg1 is hung p5dulum-wise on ! nor? side ( ! ma9 gyro cas+1 ! axis ( its susp5sion be+ coll9e> ) ! axle ( ! ma9 gyro-:eel4 ,! axle ( ! small gyro-:eel is ?us align$ 9 ! ea/ & we/ direction4 ,! /irrup bracket is turn$ up horizontally bel[ ! cas+ ( ! small gyro1 & at its end is fitt$ ) guides1 c>ry+ a pair ( roll]s4 ,^! roll]s con/itute ! exc5tric p9 &1 z %[n 9 ,fig4 #cg1 engage )9 two curv$ *annel-section$ tracks atta*$ "o to ! bail & "o to ! ma9 gyro cas+4 ,if :5 ! bail1 cas+1 etc41 sw+ "u ! influ5ce ( ! %ip's roll+ ! exc5tric p9 %\ld attempt to foll[ suit--ei!r by reason ( friction at ! axis ( susp5sion ( ! /irrup bracket or at ! track roll]s--! :eel & cas+ ( ! small gyro w />t process+ r\nd ! v]tical axis inside ! /irrup1 = ! attempt is equival5t to an endeav\r to tilt ! small gyro-axle 9 an ea/ & we/ v]tical plane1 & !re=e calls =? ! usual gyroscopic reaction4 ,! precession ( ! small gyro on its v]tical axis is made to react on ! /irrup bracket by means ( a spr+ connection betwe5 ! bracket & ! cas+1 z %[n 9 ,fig4 #cf4 ,! direction ( sp9 ( ! small gyro-:eel is su* t ! =ce ?us appli$ to ! /irrup bracket opposes & j balances ! frictional or o!r =ce try+ to make x sw+ ) ! bail1 cas+1 etc41 ( ! ma9 gyro4 ,9 ?is way ! exc5tric p9 z ! vessel rolls is caus$ to ma9ta9 its orig9al di/ance f ! v]tical l9e ?r\gh ! c5tre ( ! sp9n+ :eel4 ,illu/ration3 ,,fig4 #cg4 ,/abiliz$ ,exc5tric ,p9 7,sp]ry ,compass74 ,! suppression1 or r ! avoidance ( ! quadrantal error 9 ! ,br[n compass1 is a*iev$ 9 a mann] :i* is me*anically v di/9ct f t adopt$ = ! same purpose 9 ! ,sp]ry compass4 ,illu/ration3 ,,fig4 #ch4 ,diagram ( ,br[n ,compass4 ,an elem5t>y diagram ( ! ,br[n compass is giv5 9 ,fig4 #ch4 ,9 ?is sket* ,a is ! cas+1 inside :i* ! gyro-:eel m\nt$ on ! axle ,b 7,c7 rotates 9 ! direction ( ! dott$ arr[--,b1 z be=e1 repres5t+ ! nor?-seek+ end ( ! axle4 ,! cas+ is support$ on an ea/ & we/ horizontal axis ,e ,f inside a v]tical r+1 ?is r+ be+ j\rnall$ at ,h ,j inside a frame ,d1 ! equival5t ( ! squ>e frame 9 our simple model4 ,to obta9 complete fre$om = ! gyro ! frame ,d is m\nt$ on an a?w>t%ip axis ,g ,k1 :i* is itself c>ri$ inside a r+ j\rnall$ )9 ! b9nacle on an axis ,l p>allel ) ! %ip's longitud9al c5tre l9e4 ,! p5dulum weight ,s is fix$ to ! l[e/ po9t ( ! frame ,d4 ,if ! weight ,s & frame ,d be set sw++ on ! axis ,g ,k1 ! sw++ movem5t w1 ( c\rse1 be directly communicat$ ?r\gh ! j\rnals ,h ,j to ! v]tical support+ r+1 b1 z ! trunnions ,e ,f ( ! cas+ are really support$ on knife edges1 ! sw++ movem5t ( ! frame ,d _c be communicat$ f ! v]tical r+ ?r\gh ! trunnions ,e ,f to ! cas+ ,a1 & !nce to ! :eel4 ,yet x is ess5tial t ! weight ,s %\ld be able to act p5dulum-wise on ! cas+ & :eel1 = o!rwise1 z we "k1 ! sy/em w\ld be )\t directive =ce4 ,illu/ration3 ,,fig4 #ci4 ,oil ,control ,bottles 7,br[n ,compass74 ,! connection betwe5 ! weight & ! cas+ is n a me*anical "o1 b is effect$ by mak+ use ( ! air bla/ creat$ by ! fan-l action ( ! :eel inside ! cas+4 ,z we h expla9$ 9 connection ) ! damp+ sy/em adopt$ 9 ?is compass1 ! trunnion ,f is holl[1 & deliv]s ! air bla/ ?r\gh a nozzle ,m1 fix$ relatively to ! v]tical support+ r+1 into a divid$ box ,n4 ,f ?is box pipes are l$ to two oil bottles--"o ( :i* is %[n at ,p--fix$ to ! cas+ on ! ea/ side ( ! axle1 "o bottle be+ on ! nor? face ( ! cas+ & ! o!r on ! s\?4 ,! pressure ( ! air bla/ act+ unequally ^u ! oil 9 ^! two bottles :5 ! cas+ tilts ab\t ! axis ,e ,f results1 z we h already expla9$1 9 any horizontal oscillation ( ! s5sitive elem5t ab\t ! axis ,h ,j be+ damp$4 ,9 a simil> way two bottles ,q ,r half-fill$ ) oil are fix$ to ! nor? & s\? faces ( ! cas+ on ! we/ side ( ! axle ( ! sp9n+ :eel4 ,^! bottles are also connect$ to ! box ,n1 b ! connect+ pipes are cross$ s z to jo9 ea* bottle ,q ,r to ! division ( ! box remote f x1 & n to ! adjac5t division1 z 9 ! case ( ! damp+ bottles ,p4 ,:51 !re=e1 ! weight ,s & frame ,d are swung sl[ly p5dulum-wise on ! axis ,g ,k1 z %[n 9 ! fir/ view 9 ,fig4 #ci1 ! nozzle ,m1 be+ fix$ to ! v]tical r+1 deliv]s m air into "o division ( ! box ,n ?an ! o!r1 & !re=e a great] air pressure is ex]t$ inside "o bottle ?an inside ! o!r4 ,consequ5tly oil fl[s ?r\gh ! connect+ pipe ,t f ! =m] bottle to ! latt] until ! columns ( oil are suffici5tly unequal to balance ! diff]5ce ( pressure ( ! air inside ! bottles4 ,x w be notic$ t ! cross+ ( ! pipes connect+ ! bottles ) ! box ,n results 9 ! oil be+ accumulat$ 9 t bottle1 :i* lies away f ! side to :i* ! weight ,s has be5 swung4 ,h5ce1 al?\gh !re is no me*anical connection betwe5 ! weight & ! cas+ ( ! sp9n+ :eel1 ! effect :5 ! weight ,s is swung sl[ly is ?us sub/antially ! same z x w\ld be if !re 71 = ! weight ( ! extra oil =c$ into ! bottle ,r ex]ts a turn+ mom5t on ! cas+ ab\t ! axis ,e ,f1 & t5ds !re=e to make ! cas+ foll[ ! deflection ( ! weight ,s & frame ,d4 ,simil>ly1 %\ld ! axle ,b ,c dip1 z %[n 9 ! second view 9 ,fig4 #ci1 extra oil w accumulate 9 ! bottle :i* has be5 elevat$ by ! dipp+1 & z a result a re/or+ mom5t ab\t ! axis ,e ,f w be appli$ to ! cas+1 j z x w\ld be if ! weight ,s _h be5 directly connect$ to ! cas+ & _h be5 deflect$ by ! dipp+ movem5t4 ,! second view 9 ,fig4 #ci illu/rates ! g5]ation ( ! directive =ce 9 ! ,br[n compass4 ,let u suppose t ! compass is at ! equator1 & t by "s ag5cy ! axle is turn$ s t its end ,b po9ts due we/4 ,! rotation ( ! e>? w cause ! axle to dip sl[ly into "s su* position z t %[n4 ,dur+ ?is sl[ dipp+ movem5t oil w fl[ sl[ly f ! bottle ,q into ! bottle ,r4 ,! unbalanc$ weight ( oil w apply a turn+ mom5t to ! s5sitive elem5t ab\t ! axis ,e ,f & w !re=e produce actual motion ab\t ! axis ,h ,j1 :i* w precess ! end ,b ( ! axle t[>ds ! nor?4 ,any t5d5cy = ! axle to vibrate ab\t ! nor? & s\? l9e z a result ( ! mom5tum acquir$ by ! s5sitive elem5t :ile com+ up f ! we/ w be damp$ by ! air bla/ act+ ^u ! oil 9 ! two o!r bottles ,p fix$1 z %[n 9 ,fig4 #ch1 on ! ea/ side ( ! axle4 ,illu/ration3 ,,fig4 #dj4 ,br[n ,compass on ,we/ ,c\rse4 ,! po9t we require "h to notice especially ab\t ?is action is t1 z ! tilt+ ( ! axle produc$ by ! rotation ( ! e>? takes place v sl[ly--x _c exce$ ! spe$ ( rotation ( ! e>? on its pol> axis1 namely1 #j4jjjg ( a revolution p] m9ute--! fl[ ( oil f ! bottle ,q to ! bottle ,r takes place v sl[ly also4 ,! oil !re=e acquires practically no mom5tum1 & rises 9 ! bottle ,r 9 /rict accordance ) ! tilt acquir$ by ! axle4 ,if ! tilt+ motion be /opp$ or rev]s$1 ! oil w\ld rema9 9 ! bottle ,r at j ! level x _h rea*$1 or w\ld imm$iately beg9 to fl[ back aga91 = its mom5tum be+ negligible1 x has n suffici5t k9etic en]gy to rise high] 9 ! bottle ,r aft] ! upw>d motion ( ! bottle has ceas$4 ,on ! o!r h&1 :5 ! %ip rolls1 say1 on a due we/ c\rse1 z repres5t$ 9 ,fig4 #dj1 ! out] gimbal r+ support+ ! a?w>t%ip axis ,g ,k1 ! frame ,d c>ry+ ! weight ,s1 & ! v]tical support+ r+ w acquire an oscillation ab\t ! =e & aft axis ,l 9 tune ) ! rolls ( ! %ip4 ,! air bla/ w ?us be direct$ into ! two divisions ( ! box alt]nately1 & !re=e oil w fl[ f "o bottle to ! o!r4 ,x is to be notic$1 h[ev]1 t ! roll+ motion ( ! %ip induces 9 ?is mann] a fl[ ( oil f "o bottle to ! o!r at a v mu* great] rate ?an does ! tilt+ action ( ! e>?'s rotation dealt ) above4 ,a %ip roll+ ?r\gh #de deg41 out to out1 9 a complete p]iod ( #aj seconds rotates ab\t its roll+ c5tre ) an av]age velocity equival5t to #a4e revolutions p] m9ute--or ov] #bjjj times z fa/ z ! spe$ ( rotation ( ! e>? on its pol> axis--& at ! mid po9t ( its roll x w move ) an actual velocity ( ab\t twice ! av]age4 ,! mom5tum acquir$ by ! oil 9 fl[+ f bottle to bottle is !re=e 9 ?is case n negligible4 ,9 fact1 :5 ! %ip rea*es "o ( its out positions & />ts to return1 ! oil does n imm$iately beg9 to fl[ back into ! o!r bottle1 b is c>ri$ by its k9etic en]gy to a /ill high] level 9 ! bottle 9 :i* x has be5 ris+4 ,z a result1 ! oscillation ( ! oil betwe5 ! two bottles lags beh9d ! oscillation ( ! p5dulum weight ,s1 & !re=e t ( ! %ip itself4 ,! lag acquir$ is su* t ! oil is j level 9 ! two bottles :5 ! %ip is at ei!r ( its out positions1 & :5 ! %ip is at ! mid po9t1 or ev5 keel position ( its roll1 al?\gh ! air bla/ is = ! mom5t ev5ly di/ribut$ betwe5 ! two comp>tm5ts ( ! divid$ box1 ! oil is /&+ at its maximum level 9 ! bottle on t side ( ! :eel f :i* ! %ip is recov]+ h]self4 ,! action ( ! oil 9 ! bottles dur+ a rapid oscillation ( ! compass sy/em is1 9 fact1 q analog\s to t ( ! wat] 9 ! ,frahm sy/em ( anti-roll+ tanks4 ,x w ?us be se5 t ! net effect ( transmitt+ ! 8kicks0 d]iv$ dur+ roll+ f ! p5dul\s weight ( ! :eel ?r\gh ! ,br[n oil bottle arrangem5t is simply to delay ! application ( ! kicks to ! gyro-:eel by a con/ant am\nt1 namely1 by ! "t tak5 = ! %ip to roll f ei!r out position to ! mid position or a qu>t] ( a complete p]iod4 ,?us z ! %ip sail+ due we/ rolls ?r\gh ! mid position f />bo>d to port ! compass sy/em exp]i5ces ! turn+ mom5t ab\t ! axis ,e ,f1 :i* ) a rigidly fix$ p5dulum x w\ld receive at ! />bo>d out position f ! nor?w>ds kick ( ! weight4 ,simil>ly1 ! equival5t ( ! s\?w>ds kick ( ! weight at ! port out position is felt by ! :eel :5 ! compass is pass+ ?r\gh ! ev5 keel condition on ! subsequ5t roll f port to />bo>d4 ,x is cle> t ) ! %ip sail+ due we/--or ea/--?is delay+ ( ! kick does n affect ! result e/abli%$ previ\sly = a rigidly connect$ p5dul\s weight4 ,any t5d5cy = ! axle to precess t[>ds ! we/ :5 ! compass is pass+ ?r\gh ! ev5 keel position 9 "o direction is completely annull$ by ! t5d5cy to precess t[>ds ! ea/ at ! succe$+ passage ?r\gh ! ev5 keel position 9 ! opposite direction4 ,on quadrantal c\rses1 h[ev]1 ! delay 9 ! application ( ! kick is mo/ important1 = :5 ! %ip rolls x results 9 ! elim9ation ( ! quadrantal error4 ,t x does s c easily be und]/ood by ref]5ce to ,fig4 #cc4 ,! kicks1 be+ receiv$ :5 ! compass is pass+ ?r\gh ! ev5 keel position1 & n at ! out positions1 precess ! :eel ab\t ! axis ,h ,j at a "t :5 ?is axis is truly v]tical1 & n :5 x is incl9$4 ,! precessional movem5ts h !re=e no v]tical compon5ts ,m ,p4 ,!y are repres5t$ completely by ! horizontal compon5ts ,n ,q4 ,! axle ?us does n dep>t f ! horizontal plane1 & any movem5ts 9 ?is plane aris+ f ! t5d5cy to precess 9 ! directions ,n ,q cancel ea* o!r at successive passages ( ! compass ?r\gh ! mid position4 ,! e>ly =m ( ,ans*tz compass 0 foll[$ by ! #aiab patt]n 9 :i* ! quadrantal error 0 successfully elim9at$4 ,an example ( ! #aiaj =m 0 obta9$ by ,messrs4 ,elliott ,bro!rs1 ( ,lewi%am1 f ,ans*tz & ,co41 ( ,kiel1 & 01 we believe1 fitt$ on bo>d ,h4,m4,s4 ,new ,zeal&4 ,its defects becom+ app>5t1 its manufacture 9 ?is c\ntry 0 n proce$$ )1 b ^u ! appe>ance ( ! improv$ type 9 #aiab1 ,messrs4 ,elliott took up its con/ruction & suppli$ sev]al to ! ,admiralty4 ,! ,sp]ry compass1 h[ev]1 secur$ ! pref]5ce 9 ! ,briti% ,navy1 & ) ! outbreak ( ! w> ,messrs4 ,elliott ceas$ practically to make ,ans*tz compasses4 ,on ! o!r h&1 ! ,g]man ,navy cont9u$ to use ! #aiab type ( ,ans*tz compass1 ) v little alt]ation or addition1 "r ?r\gh\t ! w>4 ,9 view ( ! fact t e ,g]man subm>9e 0 fitt$ ) a compass ( ?is =m1 & be>+ 9 m9d ! high degree ( excell5ce atta9$ 9 ! navigation ( ! enemy's und]wat] craft1 !re c be no d\bt t ! mod]n ,ans*tz compass is a v satisfactory device4 ,9 ,fig4 #da we give a purely diagrammatic repres5tation ( ! compass4 ,! out] squ>e frame may1 z usual1 be reg>d$ z m\nt$ )9 ext]nal gimbal r+s1 provid+ a =e-&-aft axis & an a?w>t%ip axis4 ,! squ>e frame conta9s a v]tical r+ free to turn ab\t ! axis ,h ,j & itself conta9+ a horizontal r+ m\nt$ on an ea/ & we/ axis ,f ,e4 ,! p5dulum weight ,s is atta*$1 z usual1 to ! inn] horizontal r+4 ,! ess5tial diff]5ce betwe5 ! #aiab & ! #aiaj =ms ( ,ans*tz compass lies 9 ! fact t1 z %[n 9 our diagram1 ! inn] r+1 or its equival5t1 does n surr\nd a s+le gyro-:eel1 b has atta*$ to x ! cas+s ( ?ree di/9ct gyros4 ,illu/ration3 ,,fig4 #da4 ,diagram ( ,ans*tz 7#aiab7 ,compass4 ,z %[n 9 ! fir/ plan--9 ,fig4 #db--! ?ree gyros are situat$ at ! corn]s ( an equilat]al triangle4 ,"o gyro ,k is plac$ at ! s\? end ( ! m]idional diamet] ( ! horizontal r+1 ) its axle po9t+ t[>ds ! c5tre ( ! r+4 ,! two o!r gyros ,l ,m are plac$ at #fj deg4 ea/ & #fj deg4 we/ ( nor?1 ) _! axes po9t+ t[>ds ! c5tre ( ! gyro ,k--n t[>ds ! c5tre ( ! r+4 ,! :eels ( all ?ree gyros rotate anti-clockwise1 z se5 f ! nor?1 look+ s\?--t is1 !y rotate 9 ! same direction z d ! :eels ( all s+le-gyro compasses z se5 f ! same /&po9t4 ,illu/ration3 ,,fig4 #db4 ,plans ( ,gyros4 ,if we neglect ! two gyros ,l ,m = ! mom5t1 imag9+ !m to be replac$ by simple deadweights to c\nt]balance ! weight ( ! gyro ,k1 x w be se5 t ?is sy/em diff]s f t ( ! e>ly ,ans*tz compass only 9 ! fact t ! gyro-:eel has be5 r$uc$ 9 size1 & has be5 displac$ f ! c5tre ( ! horizontal r+ to ! s\!rn edge4 ,! displacem5t ( ! :eel 9 ?is mann] 9 no way affects ! ess5tial work+ ( ! compass4 ,9 a s+le-gyro compass we might ) "s advantage simil>ly displace ! sp9n+ :eel1 = by s do+ & by c\nt]balanc+ ! displac$ weight we %\ld1 at lea/ p>tially1 get rid ( ! conc5tration ( mass ab\t ! ea/-we/ axis1 :i*1 z we %all see1 introduces1 if n correct$1 an additional s\rce ( error into ! compass read+s :5 ! %ip rolls on quadrantal c\rses4 ,! r$uction 9 ! size ( ! gyro-:eel w\ld1 ( c\rse1 r$uce ! magnitude ( ! directive =ce4 ,9 ! #aiab design ! :eels ( all ?ree gyros run at #bj1jjj revolutions p] m9ute--t is1 at ! same spe$ z ! :eel 9 ! #aiaj design4 ,b ea* :eel is only #e 94 9 diamet] in/ead ( #f 941 & weighs1 ) its axle1 #e lb4 #b oz41 or only half z mu* z ! :eel 9 ! e>li] =m4 ,! gyro ,k consid]$ alone w\ld !re=e supply a directive =ce ( b half ! =m] am\nt4#f ,x foll[s1 obvi\sly1 t if a second gyro ( ! same spe$ & size z t at ,k be fix$ 9 accurate alignm5t at ! nor? end ( ! m]idional diamet] ( ! horizontal r+ ! directive =ce at any angle ( horizontal deflection away f ! nor? w be d\bl$1 t is1 w be made equal to t develop$ 9 ! #aiaj design4 ,su* a compass might be con/ruct$1 b x w\ld exhibit ! quadrantal error--or at lea/ ! in]tia =ce portion ( t error--j z badly z did ! e>ly ,ans*tz4 ,! ess5ce ( ! #aiab design lies 9 ! fact t n "o b two gyros are atta*$ to ! nor? side ( ! horizontal r+1 & 9 ! additional fact t ! axles ( ^! two gyros are n p>allel ) b are incl9$ to ! axle ( ! s\? gyro ,k4 ,:5 ! s5sitive elem5t ( ?is compass is 9 ! nor? re/+ position1 ! axle ( ! gyro ,k is align$ ) ! m]idian & !re=e ! rotation ( ! e>?--! compass be+ suppos$ at ! equator--m]ely moves ! axle p>allel ) itself4 ,on ! o!r h&1 ) ! s5sitive elem5t 9 ! nor? re/+ position1 ! axles ( ! gyros ,l ,m are incl9$ to ! m]idian at #cj deg4 ,! gyro ,l is virtually 9 ! condition ( a s+le-gyro compass1 ) ! nor? end ( its axle p>tially turn$ t[>ds ! ea/4 ,"u ?is condition1 z we "k1 ! rotation ( ! e>? w t5d to make ! nor? end ,b ( ! axle rise above ! horizontal plane4 ,conv]sely1 ! gyro ,m is 9 ! condition ( a s+le-gyro compass1 ) ! nor? end ( its axle p>tially turn$ t[>ds ! we/4 ,! e>?'s rotation 9 ?is case t5ds to make ! nor? end ( ! axle dip bel[ ! horizontal plane4 ,?us1 9 ! #aiab ,ans*tz compass1 :5 ! s5sitive elem5t is 9 ! nor? re/+ position1 ! gyro ,k "u ! rotation ( ! e>? is )\t effect on ! p5dul\s weight ,s1 ! gyro ,l is /riv+ to sw+ x t[>ds ! nor?1 & ! gyro ,m is try+ ) an equal ef=t to sw+ x t[>ds ! s\?4 ,! weight1 !re=e1 rema9s 9 ! plumb l9e & applies no turn+ mom5t to any ( ! gyros4 ,z !re is no turn+ mom5t1 !re is no precessional t5d5cy4 ,! s5sitive elem5t rema9s direct$ t[>ds ! nor?4 ,?is alignm5t1 z 9 a s+le-gyro sy/em1 is ! true re/+ position1 & "u x no directive =ce is appli$ to ! s5sitive elem5t4 ,to /udy h[ ! ?ree gyros act toge!r to re/ore ! s5sitive elem5t to ! nor? re/+ position %\ld x be deflect$ !refrom1 let u suppose t ! deflection suff]$ is "o ( #cj deg4 t[>ds ! ea/4 ,z %[n 9 ! second plan 9 ,fig4 #db1 ! effect ( su* a deflection is to place ! ?ree gyros ,k ,l ,m 9 ! condition respectively ( a s+le-gyro sy/em :5 ! axle is 7k7 deflect$ #cj deg4 to ! ea/1 7l7 deflect$ #fj deg4 to ! ea/1 & 7m7 align$ on ! nor?4 ,at ?is deflection1 !n1 ! gyro ,m contributes no re/or+ =ce4 ,! directive =ce contribut$ by ! gyro ,k is half t contribut$ by ! s+le gyro ( ! #aiaj design :5 ! deflection is #cj deg41 = ! mass--or mom5t ( in]tia--( ! :eel is half ! e>li] value4 ,! directive =ce contribut$ by ! gyro ,l is some?+ great] ?an t contribut$ by ! gyro ,k1 = ! virtual deflection ea/w>ds is #fj deg4 in/ead ( #cj deg41 &1 z we "k1 ! directive =ce increases ) ! deflection4 ,?us1 ! ?ree gyros tak5 toge!r supply a directive =ce1 :5 ! s5sitive elem5t is deflect$ ?r\gh #cj deg41 :i* is some:at great] ?an t suppli$ by ! s+le d\ble-siz$ :eel ( ! #aiaj design4#g ,?is result is a g5]al "o4 ,:atev] ! deflection may be1 ! directive =ce suppli$ by ! ?ree-gyro compass is always ab\t "o-?ird great] ?an ! directive =ce ( ! #aiaj design at ! same deflection4 ,?is increas$ =ce is develop$ ev5 if ! deflection be less ?an #cj deg4 ,9 su* cases ! gyro ,m w1 ( c\rse1 supply a =ce1 a non-re/or+ =ce1 to ! s5sitive elem5t4 ,only :5 ! deflection exce$s #cj deg4 ea/w>ds does ! gyro ,m assi/ ! gyros ,k & ,l to re/ore ! s5sitive elem5t to ! nor? re/+ position4 ,if ! deflection be to ! we/1 h[ev]1 ! gyro ,m is ! *ief assi/ant ( ! gyro ,k1 a lagg>d's "p be+ play$ by ! gyro ,l until #cj deg4 ( we/]ly deflection is rea*$4 ,! mann] 9 :i* ?is ?ree-gyro sy/em avoids ! quadrantal error c n[ be discuss$4 ,! quadrantal error1 x may be recall$1 arises :5 ! %ip rolls on an int]c>d9al c\rse1 & is prim>ily caus$ by ! fact t ! :ole compass sy/em c sw+ on its ext]nal gimbal axis 9 tune ) ! rolls ( ! %ip4 ,if we c\ld s arrange matt]s t dur+ ! roll ( ! %ip f side to side ! compass sy/em w\ld sw+ on ! ext]nal gimbals1 no m & no less ?an ! am\nt requir$ j to keep ! axis ,h ,j truly v]tical at all po9ts ( ! roll1 !n ! nor? & s\? 8kicks0 receiv$ on ! weight ,s at ! out positions ( ! roll w\ld cause ! s5sitive elem5t to precess fir/ "o way1 !n ! o!r1 b always 9 a horizontal plane4 ,!re w\ld be no v]tical compon5t 9 ! precession1 ! cumulative effect ( :i*1 z we h se51 produces ! quadrantal error4 ,9 ! ,br[n compass1 ! quadrantal error is elim9at$ by delay+ ! effect ( ! 8kicks0 on ! weight ,s until ! axis ,h ,j is truly v]tical--t is to say1 ! 8kicks0 on ! weight are n transmitt$ to ! sp9n+ :eel until ! compass sy/em is pass+ ?r\gh ! ev5 keel position4 ,9 ! ,sp]ry compass ! weight ,s is virtually %ift$ back & =? f ea/ to we/ ( ! axis ,h ,j 9 tune ) ! roll+ ( ! %ip 9 su* a way z to introduce a second compon5t ( v]tical precession1 :i* 9 am\nt & direction is j suffici5t to nullify ! v]tical compon5t caus+ ! quadrantal error4 ,9 ! #aiab ,ans*tz compass1 ! object aim$ at is ! ma9t5ance ( ! axis ,h ,j truly v]tical at all times dur+ ! roll+ condition4 ,?is object is a*iev$1 z we %all n[ %[1 by sett+ ! axles ( ! gyros ,l ,m--,fig4 #da--;incl9$ to ! axle ( ! gyro ,k4 ,9 a s+le-gyro compass1 or 9 ! #aiab ,ans*tz compass ) ! gyros ,l ,m suppress$1 ! sy/em is v /iff aga9/ vibrations on ! ea/-we/ axis ,e ,f1 b is q easily set vibrat+ ab\t ! nor?-s\? axis provid$ by ! ext]nal gimbal m\nt+4 ,! reason is1 ( c\rse1 t any vibration ab\t ! axis ,e ,f is met by ! resi/ance ( ! gyro-:eel1 = ! vibration causes ! axle to alt] its direction1 :]eas no gyroscopic resi/ance is call$ into play by ! vibration on ! nor? & s\? axis1 = ?is axis is co9cid5t or p>allel ) ! gyro-axle4 ,?us1 9 ! #aiaj ,ans*tz compass ! p]iod ( vibration ab\t ! ea/-we/ axis 0 some?+ l #gj m941 :]eas ! p]iod ab\t ! nor? & s\? axis 0 only "o or two seconds4 ,! smallness ( ! latt] p]iod readily result$ 9 ! compass sy/em gett+ into a sw+ 9 tune ) ! p]iod ( roll+ ( ! %ip--f five to twelve seconds or s4 ,7 ! axles ( ! gyros ,l ,m 9 ! #aiab =m set p>allel ) t ( ! gyro ,k1 !re w\ld /ill be no gyroscopic resi/ance ex]t$ aga9/ vibration on ! nor?-s\? axis4 ,z x is1 ! incl9ation ( ! axles ( ^! two gyros1 tak5 toge!r1 has virtually ! same effect z w\ld be obta9$ by ! addition to ! s5sitive elem5t ( a sep>ate s+le gyro1 ) its axle align$ at "r angles to ! axle ( ! gyro ,k4 ,! gyroscopic /iffness aga9/ vibration ab\t ! ea/-we/ axis ,e ,f is h>dly affect$ by ! incl9ation ( ! gyros ,l ,m at ! angle *os5 by ! design]s4 ,! resi/ance1 in/ead ( be+ t contribut$ by ?ree gyros1 is equival5t to t suppli$ by ab\t #b gyros4 ,! p]iod ( vibration on ?is axis ,e ,f is arrang$ to be ! /&>d #he m94 ,ab\t ! nor? & s\? axis we h virtually ! resi/ance ( "o gyro4 ,! p]iod ( vibration ab\t ?is axis1 in/ead ( be+ only "o or two seconds1 is ab\t #hj sec4 ,) ?is l5g!n$ p]iod ( vibration !re is practically no *ance ( ! compass sy/em gett+ into a sw+ 9 tune ) ! roll+ ( ! %ip1 = e #b to #f seconds ! vibrat+ influ5ce is rev]s$ 9 direction1 & 9 ?is int]val ( "t ! sy/em _c acquire any sub/antial degree ( sw++ motion4 ,?us1 z ! compass1 foll[+ ! rolls ( ! %ip1 moves f side to side1 x suff]s a pure translational movem5t4 ,! axis ,h ,j rema9s truly v]tical at all in/ants dur+ ! roll1 & !re=e ! nor? & s\? kicks ( ! p5dul\s weight at ! out positions ( ! roll precess ! gyro-axle ab\t ,h ,j 9 purely a horizontal plane1 ! precessional t5d5cy at "o out position cancell+ t at ! o!r4 ,!re is no v]tical compon5t 9 ! precession1 & !re=e !re c be no quadrantal error4 ,x is ( int]e/ & ( "s amusem5t to note t dur+ ! w> ! ,g]mans appli$ a f\r? gyro to ! ,ans*tz compass1 & t ?is additional gyro 0 c>efully remov$ f e compass be=e !y surr5d]$ _! subm>9es to u4 ,! deceit 01 h[ev]1 ( no avail1 = ! application ( ! f\r? gyro 0 kn[n to u long be=e ! w> end$1 a complete compass s fitt$ hav+ be5 recov]$ f a sunk5 subm>9e & repair$ & c>efully /udi$4 ,! f\r? gyro 0 appli$ to ! ext]nal gimbal r+s4 ,^! r+s1 :5 ! subm>9e roll$1 7 f\nd to acquire at times a viol5t oscillation ( _! own1 =1 ( c\rse1 !y receiv$ no /abilisation f ! gyroscopic elem5ts ( ! compass4 ,on bo>d subm>9es ! viol5ce ) :i* ! r+s vibrat$ w\ld occasionally ?reat5 to wreck ! compass4 ,by add+ a gyroscope to ! gimbal r+s1 ! p]iod ( vibration ( ! r+s 0 l5g!n$ to ab\t #af sec41 s t little or no opportunity to sw+ 0 left to !m4 ,) ! exception ( ?is addition1 ! ,ans*tz #aiab compass 0 us$ by ! ,g]mans ?r\gh\t ! w> practically )\t alt]ation4 ,,*apt] ,,xiii ,,c5trifugal ,,=ces ,,dur+ ,,quadrantal ,,roll+ ,9 addition to ! 8kicks0 ( ! p5dul\s weight1 :i* dur+ quadrantal roll+1 z we h se51 react gyroscopically ^u ! compass & t5d to make ! axle deviate f ! nor?1 !re is a second influ5ce at "w on ! compass1 :i*1 :5 ! vessel rolls on an int]c>d9al c\rse1 likewise t5ds to deviate ! axle4 ,! two deviations are always 9 ! same direction1 s t we _c arrange ! "o to r$uce or elim9ate ! o!r4 ,! second deviation arises f ! c5trifugal =ces develop$ 9 ! compass p>ts dur+ quadrantal roll+4 ,^! =ces1 l ! kicks ( ! p5dul\s weight1 react gyroscopically ^u ! sp9n+ :eel1 & if n *eck$ w deviate ! axle away f ! nor?4 ,illu/ration3 ,,fig4 #dc4 ,c5trifugal ,=ces on a ,p5dulum4 ,let u consid] ! some:at unusual type ( p5dulum %[n 9 ,fig4 #dc1 a p5dulum ! rod ,a ( :i* is fix$ rigidly to ! b> ,b c>ri$ on knife edges1 & ( :i* ! 8bob0 is 9 ! =m ( a cyl9d] susp5d$ at its mid po9t f ! rod ,a 9 su* a way z to p]mit ! bob to turn horizontally on ! be>+ at ,c1 sub/antially )\t friction4 ,9 ! fir/ in/ance1 let ! p5dulum be set sw++ ab\t ! knife edges ) ! cyl9drical bob set p>allel ) ! axis ,b4 ,ea* portion ( ! bob is ?us caus$ to sw+ ab\t t po9t on ! axis ,b :i* is v]tically ov] ! portion :5 ! bob is at re/4 ,! c5trifugal =ce develop$ on ea* portion is at all positions ( ! sw+ direct$ radially f su* po9t4 ,! c5trifugal =ce on ea* portion is a maximum :5 ! bob is pass+ ?r\gh ! mid position1 & falls1 ) ! velocity1 to z]o at ea* ( ! out positions4 ,at ! mid position ! c5trifugal =ce on ! two extreme portions ,l ,m ( ! bob may be repres5t$ by ,d ,e4 ,^! two =ces are equal & are direct$ v]tically d[nw>ds4 ,on all o!r simil> portions ! c5trifugal =ce at ! same in/ant is simil> 9 magnitude & direction4 ,! net effect ( ! c5trifugal =ces on all ! portions is ?us simply a t5d5cy to b5d ! bob ends d[nw>ds ab\t ! c5tral l9e at ,c4 ,!y h cle>ly no t5d5cy ei!r at ! mid position ( ! sw+ or at any o!r to turn ! bob r\nd ! axis ,c at ! foot ( ! rod4 ,let u n[ set ! p5dulum sw++ ) ! bob arrang$ at "r angles to ! knife-edge axis1 z %[n 9 ! second view ( ,fig4 #dc4 ,ea* & e portion ( ! bob is n[ sw++ ab\t ! "o po9t ,f on ! axis4 ,at any in/ant 9 ! sw+ ! c5trifugal =ce on any portion is direct$ along ! l9e jo9+ ! po9t ,f to ! c5tre ( t portion4 ,tak+ ! two extreme end portions ,l ,m z ! bob passes ?r\gh ! mid position1 ! c5trifugal =ces are z indicat$ at ,g ,h4 ,!y are n n[ v]tical nor p>allel ) ea* o!r1 b1 aga91 !y h no t5d5cy to turn ! bob horizontally ab\t ! axis at ,c4 ,resolv+ !m into v]tical & horizontal compon5ts1 we see t ! net effect ( all ! c5trifugal =ces is to try to b5d ! ends ( ! bob d[nw>ds--! effect ( ! v]tical compon5ts--comb9$ ) ! application to ! bob ( a horizontal /ret*+ =ce--! effect ( ! horizontal compon5ts4 ,let u1 h[ev]1 rotate ! bob ab\t ! axis at ,c ?r\gh some?+ less ?an #ij deg4 f ! fir/ position--say1 ?r\gh #de deg41 z indicat$ 9 ! ?ird sket*4 ,consid] aga9 ! two extreme end portions z ! bob is pass+ ?r\gh ! mid position ( its sw+4 ,let ,j ,k be a l9e ?r\gh ! c5tre ( ! bob p>allel ) ! knife-edge axis4 ,f ! c5tres ( ! end portions1 let l9es ,l ,n & ,m ,p be drawn at "r angles to ,j ,k4 ,f ,n & ,p draw l9es upw>ds p>allel ) ! rod ,a to meet ! knife-edge axis at ,q & ,r4 ,!n ,q & ,r are ! po9ts ab\t :i* ! two extreme portions ( ! bob are sw++4 ,! c5trifugal =ces on ^! portions are direct$ along ! l9es ,q ,l & ,r ,m1 & are indicat$ at ,s & ,t4 ,^! =ces may1 z %[n1 be resolv$ into v]tical compon5ts--p>allel ) ,q ,n & ,r ,p--& horizontal compon5ts--p>allel ) ,n ,l & ,p ,m4 ,treat+ ! o!r portions ( ! bob simil>ly1 x w be se5 t :ile ! v]tical compon5ts ( ! c5trifugal =ces1 z be=e1 m]ely t5d to b5d ! ends ( ! bob d[nw>ds1 ! horizontal compon5ts are no long] p>allel ) ! l5g? ( ! bob1 z 9 ! second sket*4 ,!y are incl9$ to ! bob & cle>ly apply to x a mom5t :i* w turn x ab\t ! axis at ,c 9 ! direction ( ! arr[ ,u until ! bob rea*es ! position %[n 9 ! second sket*4 ,x is obvi\s t any rotation ( ! bob on ! axis at ,c away f ! position %[n 9 ! fir/ sket*1 ev5 a slight "o1 w call into action horizontal compon5ts ( c5trifugal =ce aft] ! mann] %[n 9 ! ?ird sket*4 ,! equilibrium ( ! bob 9 ! position %[n 9 ! fir/ sket* is !re=e un/able4 ,) ! bob 9 ! second position a movem5t ( ! end ,l to ! left w1 z we "k1 call into action horizontal compon5ts ( c5trifugal =ce1 t5d+ to turn ! bob ab\t ,c 9 ! direction ( ! arr[ ,u4 ,if ! end ,l is mov$ to ! "r ! horizontal compon5ts1 z c easily be v]ifi$ by repeat+ ! argum5t1 w t5d to turn ! bob ab\t ,c 9 ! direction oppos$ to ! arr[ ,u4 ,?us deflection to ei!r side ( ! second position calls =? =ces :i* lead ! bob to recov] t position4 ,we conclude1 !re=e1 t ! second position is "o ( /able equilibrium4 ,x may fur!r be %[n by repeat+ ! argum5t t if ! bob is rotat$ ab\t ,c f ! fir/ position 9 su* a way z to s5d ! end ,l to ! re> ! horizontal compon5ts call$ into action t5d to set ! bob into ! second position ) ! end ,l po9t+ backw>ds1 & t :5 ! bob is s align$ relatively to ! knife-edge axis ! equilibrium is aga9 /able4 ,?us1 altoge!r1 if ! bob is p>allel ) ! knife-edge axis1 ! equilibrium is un/able4 ,if x is at "r angles ! equilibrium is /able4 ,if x is set into any int]m$iate position1 =ces are call$ into play :i* endeav\r to align x at "r angles to ! knife-edge axis4 ,let a second cyl9drical bob ( ! same size & weight be atta*$ to ! fir/ at "r angles to x & 9 ! same plane4 ,!n 9 all positions ( ! bobs relatively to ! knife-edge axis ! equilibrium w be /able1 = at any sett+ ( ! bobs ! rot>y =ce ab\t ,c develop$ by ! "o bob w be equal & oppos$ 9 direction to t develop$ by ! o!r bob4 ,! above discussion cov]s a pr9ciple ( consid]able g5]al importance 9 ma!matical physics4 ,briefly put1 x %[s u t a body susp5d$ p5dulum-wise 9 ! mann] sket*$ w develop a t5d5cy :5 swung to set its long] axis p>allel ) ! plane ( ! sw+1 & t to avoid ?is t5d5cy 9 a sw++ body m\nt$ 9 ! mann] we h indicat$1 ! mass ( ! body mu/ be di/ribut$ symmetrically & equally ab\t ! p5dulum rod1 s t !re %all be no 8long] axis40#h ,s f> z ! gyro-compass is conc]n$1 ! circum/ances describ$ necessitate--at lea/ 9 ! ,sp]ry & ,br[n compasses--! addition ( comp5sator weights to repres5t ! second cyl9drical bob to :i* we h ref]r$ above4 ,! masses compos+ ! gyro-compass are n dispos$ symmetrically & equally ab\t ! v]tical axis--! axis :i* we h ?r\gh\t call$ ,h ,j4 ,z se5 9 plan1 ! masses are conc5trat$ t[>ds ! ea/ & we/ plane conta9+ ! sp9n+ :eel1 & are defici5t t[>ds ! nor? & s\?4 ,by virtue ( ! pres5ce ( ! p5dul\s weight1 or its equival5t1 bel[ ! sp9n+ :eel1 ! :ole mass ( ! compass is capable ( sw++ p5dulum-wise1 ! axis ( ?is sw+ be+ "o or o!r ( ! axes ( ! ext]nal gimbal m\nt+4 ,fur!r1 ! sw++ mass is free--if ! :eel is n sp9n+--to turn ab\t ! v]tical axis :i* we h call$ ,h ,j4 ,ref]5ce to ,fig4 #ca w make ^! /atem5ts q cle>4 ,?us ! compass & its sy/em ( m\nt+ inevitably reproduce ! ess5tial features ( ! p5dulum %[n 9 ,fig4 #dc4 ,tak+ ! second sket* 9 t engrav+1 ! bob repres5ts ! masses ( ! compass conc5trat$ 9 ! ea/ & we/ plane4 ,! gyro-axle be+ at "r angles to ?is plane is p>allel ) ! knife-edge axis ,b4 ,?is axis ,b may be reg>d$ z repres5t+ ! longitud9al axis ( ! ext]nal gimbal m\nt+1 s t 9 ! conditions imag9$ ! %ip is suppos$ to be sail+ due nor? or s\?4 ,x is cle> t :5 ! %ip rolls on ei!r ( ^! c\rses1 ! fact t ! mass ( ! compass is conc5trat$ 9 ! ea/ & we/ plane w n t5d to deviate ! axle1 = ! 8p5dulum bob0 is 9 its position ( /able equilibrium4 ,! fir/ sket* simil>ly repres5ts ! condition ( matt]s exi/+ :5 ! %ip rolls on an ea/ or we/ c\rse1 ! knife-edge axis ,b aga9 be+ id5tifi$ ) ! longitud9al axis ( ! ext]nal gimbal m\nt+4 ,! p5dulum bob is n[ 9 its position ( un/able equilibrium1 s t if ! mass di/ribution ( ! compass is n correct$ by ! addition ( comp5sator weights1 a t5d5cy = ! axle to deviate away f ! nor? may occur4 ,if we id5tify ! knife-edge axis ,b ) ! a?w>t%ip axis ( ! ext]nal gimbal m\nt+1 ! second sket* 9 ,fig4 #dc illu/rates ! condition ( matt]s exi/+ :5 ! %ip pit*es on an ea/ or we/ c\rse1 :ile ! fir/ w repres5t pit*+ on a due nor? or s\? c\rse4 ,on quadrantal c\rses1 failure to correct ! inequality ( ! mass di/ribution1 if t di/ribution is n uni=m1 w inevitably result 9 ! axle deviat+ :5 ! %ip rolls4 ,?us1 ! ?ird view 9 ,fig4 #dc repres5ts ! conditions prevail+ :5 ! %ip rolls on a due nor?-we/--or s\?-ea/--c\rse4 ,look+ at ! plan1 ! l9e ,j ,k repres5ts ! direction ( ! longitud9al axis ( ! ext]nal gimbal m\nt+ & !re=e ! direction ( ! %ip's c\rse1 :ile a l9e at "r angles to ! p5dulum bob w\ld repres5t ! gyro-axle1 & !re=e ! nor? & s\? direction4 ,:5 ! %ip rolls ! compass masses oscillate p5dulum-wise ab\t ! ext]nal longitud9al gimbal axis--repres5t$ by ! b> ,b--b ! directive =ce ( ! compass t5ds to pres]ve ! g5]al plane ( ! oscillat+ masses incl9$ at #de deg4 to ! direction ( ! b> ,b4 ,z a result1 ! horizontal compon5ts ( ! c5trifugal =ces develop$ 9 ! compass masses apply to ! :eel1 cas+1 etc41 a turn+ mom5t 9 ! direction ( ! arr[ ,u4 ,?is mom5t1 x w be se51 t5ds to turn ! s5sitive elem5t 9 ! same direction z t 9 :i* ! 8kicks0 ( ! weight at ! out positions ( ! sw+ endeav\r to deviate ! axle on ! same c\rse4 ,! c5trifugal mom5t w\ld1 h[ev]1 cause an actual deviation 9 ! direction ,u 9 a direct mann] only if ! gyro-:eel 7 n sp9n+4 ,z x is1 ! c5trifugal mom5t causes ! nor? end ( ! gyro-axle to precess upw>ds & !re=e leads to a deflection ( ! p5dul\s weight ( ! nor?4 ,?is deflection ?r[s a turn+ mom5t on to ! :eel ab\t ! horizontal axis--! axis we h call$ ,e ,f ?r\gh\t--&1 f9ally1 ?is turn+ mom5t precesses ! axle horizontally 9 ! direction ( ! arr[ ,u4 ,?us1 ) ! :eel sp9n+1 ! c5trifugal mom5t actually does produce rotation 9 ! direction ,u1 b its action is n direct4 ,z we h said1 ! t5d5cy ( ! axle to deviate dur+ roll+ on quadrantal c\rses z a result ( ! action ( c5trifugal =ces1 is correct$ 9 ^? compasses requir+ x by ! addition to ! compass masses ( comp5sator weights on ! nor? & s\? sides ( ! s5sitive elem5t4 ,^! weights are adju/$ = mass & position 9 su* a way z to make ! mass di/ribution ( ! s5sitive elem5t sub/antially ! same 9 ! nor? & s\? direction z 9 ! ea/ & we/4 ,9 ?is way ! c5trifugal =ces t5d+ to cause deviation are neutralis$ on all c\rses1 bo? dur+ roll+ & pit*+4 ,,*apt] ,,xiv ,,! ,,ans*,,tz 7#aiaj7 ,,compass ,"s few words ( description fall to be made reg>d+ c]ta9 me*anical & electrical features ( ! pr9cipal types ( gyro-compass--features1 t is1 :i*1 n be+ prim>ily connect$ ) ! gyroscopic behavi\r ( ! compass1 h n s f> be5 m5tion$ 9 our discussion ( ! g5]al !ory ( ! device4 ,a sectional diagrammatic view ( ! e>ly =m ( ,ans*tz compass is giv5 9 ,fig4 #dd4 ,?is compass1 al?\gh x is n[ obsolete by reason ( ! fact t no provision 0 made 9 its design = ! quadrantal error1 is /ill1 we ?9k1 ( int]e/ f o!r ?an ! hi/orical po9t ( view4 ,illu/ration3 ,,fig4 #dd4 ,! ,ans*tz 7#aiaj7 ,compass4 ,! gyro-:eel is %[n at ,a4 ,! axle is c>ri$ 9 be>+s inside ! cas+ ,b4 ,?is cas+ is atta*$ to a tubul> /alk ,c1 :i* is fix$ to a head ,d c>ry+ ! compass c>d ,r4 ,?is sy/em ( p>ts z a :ole is float$ 9 m]cury ,q conta9$ inside a circul> /eel b[l ,k1 ! flotation be+ secur$ by means ( a holl[ /eel r+ ,s jo9$ to ! head ,d by a dome-%ap$ memb] ,e1 :i* is p]=at$ all ov] = ! sake ( lightness4 ,z ! float ,s is completely imm]s$ 9 ! m]cury1 ! exact level to :i* x w s9k c be delicately settl$ by controll+ ! =m ( ! bore inside ! head ,d4 ,! c5tral position ( ! float inside ! b[l is controll$ by means ( a /eel /em ,t fix$ at its upp] end to ! c5tre ( ! glass ,g cov]+ ! c>d & po9t$ at its l[] end to dip into a cup conta9+ m]cury :i* is fix$ c5trally inside ! /alk ,c4 ,! /em ,t is insulat$1 & is enclos$ )9 a tube1 ! upp] end ( :i* is also atta*$ to ! glass ,g & ! l[] end ( :i* is splay$ out to dip into a second m]cury cup surr\nd+ b insulat$ f ! fir/4 ,?r\gh ?is tube & its m]cury cup "o phase ( a ?ree-phase curr5t is l$ to ! motor driv+ ! gyro-:eel f ! t]m9al ,f4 ,! second phase rea*es ! motor f ! t]m9al ,h by way ( ! /em ,t1 :ile ! ?ird phase is transmitt$ ?r\gh ! b[l1 ! m]cury ,q1 & ! float4 ,! b[l is provid$ ) knife-edge be>+s at ,l1 :]eby ! :ole sy/em %[n is m\nt$ )9 two gimbal r+s provid+ ! ext]nal longitud9al & a?w>t%ip axes4 ,! out] gimbal r+ is support$ inside ! b9nacle by means ( spr+s1 ! atta*m5ts ( ^! spr+s1 z well z ! gimbal supports1 be+ insulat$ on acc\nt ( ! me?od adopt$ = transmitt+ ! ?ird phase ( ! curr5t to ! gyro-motor4 ,! gyro-axle runs on ball be>+s4 ,! driv+ motor comprises a /ator c>ry+ ! w9d+s & fix$ inside ! cas+ ,b & a rotor =m+ a rigid "p ( ! gyro-:eel itself4 ,x w be se5 t ?is design ( compass does n explicitly reproduce ! horizontal axis ,e ,f1 nor ! p5dul\s weight ,s ( our simple model4 ,! float is1 h[ev]1 free to tilt )9 ! b[l 9 any direction1 s t ! sy/em ( susp5sion is practically equival5t to ! provision ( an inf9ite numb] ( horizontal axes ,e ,f4 ,z reg>ds ! app>5t abs5ce ( ! p5dul\s weight1 x is to be not$ t ! c5tre ( gravity ( ! float+ sy/em is bel[ its metac5tre1 & !re=e t ! p5dulum effect is exactly reproduc$4 ,! damp+ details are n %[n 9 ! engrav+1 b !y are sub/antially z we h describ$ !m previ\sly4 ,9 view ( ! high spe$1 #bj1jjj revolutions p] m9ute1 at :i* ! gyro-:eel runs1 giv+ a /ress 9 ! rim ( ab\t #aj tons p] squ>e in* & a p]iph]al velocity ( #cdj miles an h\r1 x is ( int]e/ to note t dur+ a te/ to de/ruction ! :eel did n fail until x 0 be+ driv5 at a spe$ involv+ ! supply to x ( five times ! normal driv+ p[]4 ,a special motor g5]ator _h to be built to enable ?is te/ to be c>ri$ out4 ,ev5 ! normal motor driv+ ! gyro-:eel _h to be specially design$1 = no motor capable ( runn+ at #bj1jjj revolutions 0 at ! "t comm]cially available1 :ile ! small space )9 :i* x _h to be accommodat$ r5d]$ ! "q ( temp]ature rise a v s]i\s "o4 ,x 0 f\nd1 x may be add$1 t 9 design+ ! motor ! usually accept$ magnetic con/ants = ! iron 9 ! motor did n hold good ) a p]iodicity z high z #ccc cycles p] second4 ,! flotation ( ! s5sitive elem5t 9 m]cury is a simple & conv5i5t me?od ( obta9+ a practically frictionless support = ! v]tical axis--! axis ,h ,j ( our elem5t>y model4 ,! abs5ce ( friction arises f ! facts t ! drag ( ! m]cury on ! p>ts ( ! s5sitive elem5t ) :i* x is 9 contact is proportional to ! velocity ) :i* ! p>ts move ?r\gh x1 & t ?is velocity is always extremely sl[4 ,if ! m]cury is fre%ly di/ill$1 !re is1 x w\ld appe>1 sub/antial abs5ce ( frictional drag4 ,b 9 c\rse ( "t du/1 oil1 etc41 may collect on ! surface ( ! m]cury1 & may introduce a drag on ! s5sitive elem5t ( suffici5t am\nt to int]f]e ) ! accuracy ( ! compass read+s4 ,! susp5sion ( ! v]tical axis by flotation has1 h[ev]1 ! advantage t no ext]nal gimbal r+s ne$ be provid$ to give ! s5sitive elem5t ?ree degrees ( fre$om 9 all configurations4 ,! s5sitive elem5t1 z we h said1 is virtually provid$ ) an inf9ite numb] ( horizontal axes1 s t )9 ! b[l itself !re is always a longitud9al & an a?w>t%ip axis ab\t :i* ! s5sitive elem5t may turn4 ,! ext]nal gimbal axes provid$ 9 ?is compass p]mit ! b[l to rema9 horizontal :5 ! %ip rolls or pit*es2 !y are n ess5tial gyroscopically4 ,a simil> rem>k applies to ! lat] =m ( ,ans*tz compass 9 :i* ! s5sitive elem5t is also float$ 9 m]cury4 ,,*apt] ,,xv ,,! ,,sp]ry ,,compass ,a g5]al view ( ! ,sp]ry compass z remov$ f ! b9nacle is giv5 9 ,fig4 #de4 ,?is view depicts ! compass z x w\ld be se5 look+ =w>d on a vessel /eam+ t[>ds ! s\?-we/4 ,at ,a is %[n ! comp5sator weight on ! nor? side ( ! s5sitive elem5t1 & at ,b ! balli/ic gyro is to be se54 ,! r+ ,c is ! inn] ( ! two ext]nal gimbal r+s1 & c>ries on an a?w>t%ip axis ,d ! spid] ,e1 f :i* ! s5sitive elem5t is susp5d$4 ,at ,f may be se5 "o ( ! be>+s :]eon ?is r+ is swung on a longitud9al axis )9 ! out] gimbal r+4 ,! out] r+1 9 turn1 is hung on spr+s atta*$ to ! inside ( ! b9nacle4 ,! spe$ & latitude corrector dials are to be se5 directly above ! be>+ ,f1 :ile beh9d !m ! incl9$ cos9e r+ or c\rse corrector r+ is visible4 ,! phantom r+ is %[n at ,g4 ,?is r+ 9 section is *annel-%ap$1 & 9 ! view hides ! v]tical r+ )9 :i* ! cas+ ( ! gyro-:eel is j\rnall$ on ! horizontal ea/ & we/ axis4 ,x is to be c>efully not$ t ! lugs ,h1 by :i* ! comp5sator weights are atta*$ to ! s5sitive elem5t1 are n fix$ to ! phantom r+1 b pass ?r\gh easy-fitt+ holes !re91 & are directly secur$ to ! v]tical r+ inside4 ,! bail weight lies )9 ! phantom & v]tical r+s1 & c be se5 at ,j1 ! tracks = ! exc5tric p91 "o on ! bail & ! o!r on ! :eel cas+1 be+ %[n at ,k4 ,! /irrups ,l are fix$ to ! ends ( ! bail1 & c>ry ! p9s :]eon ! bail is swung f ! phantom r+4 ,! bail latitude corrector dial1 :]eby ! bail is all[$ to assume ! tilt appropriate to ea* latitude )\t di/urb+ ! horizontality ( ! gyro-axle1 is visible beh9d ! /irrup4 ,! horizontality ( ! axle is indicat$ on a level atta*$ at ?is po9t to two brackets spr++ f ! :eel cas+4 ,illu/ration3 ,,fig4 #de4 ,! ,sp]ry ,compass ,remov$ f ,b9nacle4 ,illu/ration3 ,,fig4 #df4 ,! ,sp]ry ,compass4 ,( ! non-gyroscopic me*anical details ( ?is compass1 *ief int]e/ probably c5tres 9 ! me?od ( provid+ ! v]tical axis ab\t :i* ! s5sitive elem5t may turn relatively to ! spid] ,e 9 a sub/antially frictionless mann]4 ,9 ,fig4 #df we give a diagram ( ! compass z we w\ld see x look+ aft on a %ip /eam+ due s\?4 ,x w be se5 f ?is diagram t ! phantom r+1 %[n 9 black section1 is ext5d$ at ! top to =m a horizontal flange4 ,on ?is flange ! angul> divisions ( ! compass c>d are engrav$4 ,! phantom r+ is also =m$ ) a c5tral holl[ /alk :]eby x is hung on ball be>+s )9 ! c5tral boss ( ! spid]4 ,a torsionless wire compos$ ( sev]al /r&s ( /eel is secur$ at "o end to a cap fix$ ov] ! top ( ! /alk1 & at ! l[] end is secur$ to a ball-borne p9 =m+ "p ( ! v]tical r+4 ,diametrically bel[1 ! v]tical r+ & ! phantom are unit$ by a pivot p94 ,! gyro case1 z we h expla9$ be=e1 is c>ri$ on a horizontal axis )9 ! v]tical r+1 :ile ! bail is swung on ! phantom4 ,! phantom & all )9 x may be reg>d$ z ! s5sitive elem5t1 ! con/ant alignm5t ( :i* 9 ! nor? & s\? direction gives ! device its utility z a compass4 ,! spid] c>ry+ ! lubb] r+ & all outside x move r\nd ! wire-&-pivot-p9 v]tical axis ) ! %ip :5 ! c\rse is alt]$4 ,:5 su* a movem5t occurs ! abs5ce ( any direct me*anical connection ( a rigid nature betwe5 ! phantom r+ on ! "o h& & ! re/ ( ! s5sitive elem5t on ! o!r w\ld t5d to result 9 ! phantom r+ foll[+ ! movem5t ( ! spid]1 b9nacle1 & %ip r ?an 9 its rema9+ /ation>y ) ! :eel1 cas+1 & v]tical r+4 ,! susp5sion wire w\ld ?us be twi/$4 ,z we h previ\sly expla9$1 h[ev]1 ! phantom r+ is =m$ j bel[ ! c>d ) a circul> rack ) :i* !re me%es a p9ion driv5 ?r\gh r$uction ge>+ by a small electric motor--! azimu? motor--atta*$ to ! spid]4 ,! />t+ & /opp+ ( ?is motor & ! direction ( its rotation are controll$ automatically by means ( gold-rimm$ :eels on two trolley heads fix$ to ! v]tical r+ & c]ta9 gold-fac$ contactors on ! phantom4 ,?us :5 ! %ip's c\rse is alt]$ ! azimu? motor is />t$ up 9 ! direction requir$ to take ! twi/ out ( ! susp5sion wire & br+ ! phantom into alignm5t ) ! re/ ( ! s5sitive elem5t4 ,:5 ?is alignm5t is rea*$ ! motor is automatically cut out4 ,9 actual use ! phantom ov]%oots ! exact position ( alignm5t by a v small am\nt1 br++ ! rev]se contactors into action & />t+ ! motor 9 ! rev]se direction4 ,! phantom1 9 fact1 oscillates ab\t ! position ( alignm5t ) ! s5sitive elem5t ?r\gh1 r\ghly1 a qu>t] ( a degree4 ,?is small vibration is transmitt$ to ! repeat] compasses else:]e 9 ! %ip1 & is ( practical value 9 t its visibility is "s assurance t ! ma/] compass is work+ correctly4 ,x w be se51 !n1 t ! abs5ce ( friction ab\t ! v]tical axis ( ! ,sp]ry compass is secur$ by susp5d+ ! s5sitive elem5t )9 a memb]--! phantom r+--! frictional drag on :i* is elim9at$ by driv+ x by p[] 9 su* a way t x foll[s all ! movem5ts ( ! s5sitive elem5t relatively to ! support+ spid] 9 an automatic & sub/antially in/antane\s & dead-beat mann]4 ,! repeat] compasses are op]at$ electrically f ! ma/] compass ?r\gh a transmitt] & a p9ion me%+ ) ! circul> rack on ! phantom4 ,! p9ion is j\rnall$ on a p9 dep5d+ f ! lubb] r+1 & !re=e transmits to ! repeat]s n only ! relative movem5t betwe5 ! phantom & ! b9nacle1 b1 z we h be=e expla9$1 any movem5t ( ! lubb] r+ relatively to ! b9nacle :i* may be made to correct ! read+ ( ! ma/] compass = ! latitude & nor? /eam+ errors4 ,9 ?is way ! repeat] compasses always indicate true nor? bo? = c\rse-sett+ purposes & = ! purpose ( tak+ be>+s on pass+ objects4 ,x is reg>d$ z outside ! scope ( ?is discussion to describe ! me*anical features ( ! repeat] compasses4 ,x may1 h[ev]1 be rem>k$ t ! fact t !y may be fitt$ 9 any numb] & 9 any position1 & t automatic c\rse record]s & simil> devices may also readily be l9k$ up ) ! gyro-compass1 =ms a v /rong reason 9 itself = recomm5d+ ! adoption ( ! gyroscopic r ?an ! magnetic compass on bo>d %ip4 ,,*apt] ,,xvi ,,! ,,br[n ,,compass ,! ,br[n compass is ! inv5tion ( ,mr4 ,s4 ,g4 ,br[n1 ,f4,r4,s41 ( ,nor? ,acton1 ) ,pr(essor ,john ,p]ry1 ,f4,r4,s41 9 association z te*nical advis] & co-pat5tee4 ,x has be5 evolv$ aft] five ye>s ( labori\s exp]im5tal "w1 & is claim$ to be ! only ,briti% gyroscopic compass s f> con/ruct$ & appli$ on bo>d %ip4 ,illu/ration3 ,,fig4 #dg4 ,! ,br[n ,compass ,remov$ f ,b9nacle4 ,illu/ration3 ,,fig4 #dh4 ,! ,br[n ,compass ,remov$ f ,b9nacle4 ,illu/ration3 ,,fig4 #di4 ,! ,br[n ,compass4 ,9 ,fig4 #dg we %[ ! ,br[n compass z se5 look+ =w>d on a vessel /eam+ due nor?4 ,! s\? end ( ! gyro-axle is po9t+ t[>ds ! read]4 ,9 ,fig4 #dh x is %[n z x w\ld be se5 :5 look+ =w>d on a vessel /eam+ due we/4 ,! nor? end ( ! axle is po9t+ to ! "r 9 ?is view4 ,9 ! l9e engrav+ 7,fig4 #di7 we are suppos$ to be look+ =w>d on a vessel /eam+ due s\?4 ,! nor? end ( ! axle is !re=e po9t+ t[>d u4 ,9 ! half-tone engrav+s ! compass is %[n remov$ f its ext]nal gimbal r+s4 ,! axis ,a 7,fig4 #dg71 x w be und]/ood1 is ! a?w>t%ip axis ( ! ext]nal m\nt+4 ,x is m\nt$ on ball be>+s )9 a c\ple ( small brackets :i* by means ( f\r screws are atta*$ to ! inn] gimbal r+1 z %[n 9 ,fig4 #di4 ,?is inn] r+1 9 turn1 is c>ri$ on a longitud9al axis inside an out] gimbal r+1 :i*1 f9ally1 is hung on spr+s f ! b9nacle4 ,! frame ,b1 )9 :i* ! s5sitive elem5t prop] is m\nt$1 is v mu* z we h repres5t$ x to be 9 our previ\s diagrams1 except t x sw+s p5dulum-wise on ! axis ,a--or ! o!r axis ( ! ext]nal m\nt+--n because ( ! atta*m5t to x at its l[e/ po9t ( an actual bob weight1 b because its c5tre ( gravity is design$ly bel[ ! axis ( susp5sion1 & because at its l[e/ po9t x c>ries a cas+ conta9+ an electric motor & o!r adjuncts possess+ a degree ( weight4 ,z %[n be/ 9 ,fig4 #di1 ! frame ,b supports a v]tical r+ ,c c>ry+ ! compass c>d1 & )9 :i* ! cas+ ,d conta9+ ! gyro-:eel is m\nt$ on a horizontal1 ea/ & we/1 knife-edge axis4 ,! ea/]ly end ( ?is knife-edg$ axis--t[>ds ! left 9 ! engrav+--has associat$ ) x ! nozzle & divid$ air box1 :]eby1 z we h expla9$1 ! pressure ( ! air bla/ g5]at$ inside ! cas+ by ! sp9n+ :eel is transmitt$ by op5 & cross$ pipes respectively to ! oil-damp+ bottles ,e & ! oil control bottles ,f4 ,:at we reg>d z ! mo/ int]e/+ non-gyroscopic feature ( ! ,br[n compass is ! mann] 9 :i* ! v]tical r+ ,c is support$ )9 ! frame ,b4 ,! r+ at its highe/ po9t is =m$ ) a v]tical trunnion1 :i* at its top is guid$ )9 a ball be>+ fix$ 9 ! c5tral boss ( ! frame ,b4 ,?ree slip r+s l[] d[n on ! trunnion act+ 9 conjunction ) ?ree m]cury contact r+s atta*$ to ! frame s]ve to conduct ?ree-phase curr5t to ! s5sitive elem5t4 ,at ! l[] side ! v]tical r+ is also provid$ ) a trunnion1 :i* is ( ! nature ( a foot-/ep be>+4 ,9 reality1 h[ev]1 ! trunnion is nev] all[$ to t\* ! bottom ( its be>+1 = x--& ) x ! v]tical r+1 ! compass c>d1 & ! :ole ( ! s5sitive elem5t--is =c$1 by means ( a supply ( oil deliv]$ bel[ x1 to vibrate up & d[n ?r\gh ab\t an eigh? ( an in* at ! rate ( "s #ahj times a m9ute4 ,be=e ! trunnion c fall to ! foot ( its be>+ x gets a fre% kick up by ! oil1 s t no actual metal-to-metal contact is e/abli%$4 ,! oil supply is drawn f & return$ to ! res]voir ,g by a pump driv5 f an electric motor ,h4 ,! slight rapid vibratory motion ?us communicat$ to ! s5sitive elem5t has no appreciable effect ^u ! ease or accuracy ) :i* ! compass c>d may be read4 ,on ! o!r h&1 x is suffici5t to relieve ! frictional resi/ance to turn+ at ! upp] & l[] trunnions ( ! v]tical r+ 9 accordance ) ! well-kn[n fact t if we ov]come friction 9 "o direction we ov]come x also 9 ! direction at "r angles to ! fir/4 ,a second me*anical feature ( ! ,br[n compass ( out/&+ int]e/ is ! me?od adopt$ = transmitt+ ! indications ( ! ma/] compass c>d to ! repeat] compasses4 ,! problem to be solv$ 9 ?is matt] is to e/abli% connection ) ! ma/] compass c>d 9 a mann] :i* %all impose no frictional or o!r drag on t c>d4 ,to ?is end 9 ! ,br[n compass ! air bla/ g5]at$ by ! sp9n+ :eel is call$ ^u to fulfil a function additional to ^? to :i* we h already ref]r$4 ,! air bla/ is deliv]$ n only f ! ea/]n1 b also f ! we/]n end ( ! horizontal axis ( ! cas+4 ,x is ?us direct$ ?r\gh a nozzle ,j aga9/ ! face ( a contact mak] ,k conta9+ a pair ( disc-l plung]s work+ 9 balanc$ connection )9 two cyl9d]s4 ,opposite ea* plung] is a slot1 & :5 no movem5t has to be transmitt$ to ! repeat] compasses ! air bla/ is direct$ aga9/ ! blank wall betwe5 ^! two slots or ent]s ea* slot 9 equal proportion4 ,?us ! plung]s be+ balanc$1 nei!r makes contact4 ,if1 h[ev]1 ! %ip's c\rse is alt]$1 ! contact mak] ,k1 be+ atta*$ to a r+ ,l b5ea? ! lubb] r+1 moves ) ! %ip1 :ile ! nozzle ,j rema9s /ation>y ) ! s5sitive elem5t4 ,?us ! air bla/ ex]ts unequal pressures on ! plung]s1 & "o ( !m is =c$ back to make contact4 ,z a result1 a /ep-by-/ep electric motor ,m c>ri$ on ! frame ,b & 9 me% ?r\gh r$uction ge>+ ) a rack on ! r+ ,l is />t$ up & turns ! r+ 9 ! direction requir$ to make ! two slots aga9 divide ! air bla/ equally4 ,:5 ?is neutral position is rea*$ ! motor is cut out4 ,z 9 ! ,sp]ry compass1 ! foll[-up motion is op5 to a little hunt+ movem5t z a result ( ! mom5tum acquir$ by ! p>ts4 ,ignor+ ?is hunt+ movem5t1 ! r+ ,l & ! contact mak] ,k are ?us driv5 to rema9 /ation>y 9 fix$ relation%ip ) ! s5sitive elem5t no matt] to :at ext5t ! frame ,b may move ) ! %ip :5 ! c\rse is alt]$4 ,! relative movem5t betwe5 ! r+ ,l & ! frame ,b is communicat$ to ! repeat] compasses 9 an electrical mann]4 ,! details ( ! electrical transmission are outside ! ambit ( ?is discussion1 b we may say t ! movem5ts communicat$ to ! repeat] compasses are d]iv$ f a di/ributor on ! compass swit*bo>d1 ?is di/ributor be+ arrang$ to op]ate 9 exact syn*ronism ) ! foll[-up r+ ,l4 ,x is claim$ = ! ,br[n sy/em ( transmission betwe5 ! ma/] & ! repeat] compasses t ev5 %\ld ! :ole repeat] sy/em break d[n ! correct action ( ! ma/] compass w n !reby be affect$4 ,,*apt] ,,xvii ,,! ,,ans*,,tz 7#aiab7 ,,compass ,a plan & sectional elevation ( ! mod]n =m ( ,ans*tz compass are giv5 9 ,figs4 #ej & #ea4 ,! cas+s ( ! ?ree gyros ,k ,l ,m hang by v]tical /alks bel[ a triangul> spid] ,a at ! c5tre ( :i* is affix$ a float ,b imm]s$ 9 a b[l ,c conta9+ m]cury4 ,aft] ! mann] foll[$ 9 ! #aiaj =m1 ! float & all atta*$ to x are c5tralis$ relatively to ! b[l by means ( a rod ,d fix$ c5trally to ! cov] ( ! compass4 ,z be=e1 ?is rod ,d is compos$ ( a c5tral core & a l9] insulat$ f ! core4 ,! ends ( ! core & l9] dip into two conc5tric m]cury cups c>ri$ )9 ! float 9 ord] t two phases ( ! ?ree-phase curr5t driv+ ! gyro-motors may be transmitt$ ?r\gh ! core & l9] ( ! rod ,d4 ,! ?ird phase is transmitt$ ?r\gh ! m]cury & float by e>?+ ! b[l ,c4 ,matt]s are s arrang$ t ! c5tre ( flotation ( ! float ,b & its atta*$ p>ts is above ! c5tre ( gravity ( ! float+ p>ts4 ,^! float+ p>ts--! spid] ,a1 ! float ,b1 ! ?ree gyros1 & o!r items n yet m5tion$--con/itute ! s5sitive elem5t1 s t ?is elem5t1 z 9 ! #aiaj =m1 does n ne$ ! addition ( a sep>ate weight to provide ! requir$ p5dulum action ab\t a horizontal axis ?r\gh ! c5tre ( flotation4 ,in/ead ( !re be+ b "o su* horizontal axis--! ea/ & we/ axis ,e ,f ( our models & diagrams--x is cle> t ! support ( ! s5sitive elem5t by means ( a float provides ! elem5t ) an ea/ & we/ horizontal axis & an inf9ite numb] ( o!r horizontal axes4 ,illu/ration3 ,,fig4 #ej4 ,plan ( ,ans*tz 7#aiab7 ,compass4 ,atta*$ to ! spid] ,a--& !re=e =m+ a portion ( ! s5sitive elem5t--is a %eet metal annul> cas+ ( ! section %[n at ,e ,e or ,f ,f4 ,! gyros are enclos$ )9 ?is cas+4 ,v5tilat+ tubes & baffles ,g are provid$ at po9ts on ! cas+ betwe5 ea* pair ( gyros4 ,! compass c>d--9 ! =m really ( a r+--is atta*$ to ! cas+ at ,h4 ,reg>d+ ! cas+ & ! spid] ,a z ! equival5t ( ! horizontal r+ %[n 9 our diagram 7,fig4 #da71 x w be notic$ t ! gyro cas+s are n fix$ rigidly to x1 b are really m\nt$ on ball be>+s surr\nd+ _! /alks1 s t !y may rotate ab\t a v]tical axis relatively to ! re/ ( ! s5sitive elem5t4 ,z %[n 9 ! plan view1 h[ev]1 ! cas+ ( ! gyro ,k is connect$ by two spr+s ,j to ! re/ ( ! s5sitive elem5t1 s t 9 :i*ev] way ! gyro turns on ! ball be>+s x applies ?r\gh "o or o!r ( ! spr+s a =ce 9 ! same direction to ! annul> cas+1 etc4 ,! gyro is !re=e sub/antially1 ?\gh n actually1 rigidly connect$ to ! re/ ( ! s5sitive elem5t1 ! spr+s be+ introduc$ to provide a yield+ connection :i* w prev5t ! full =ce ( a sudd5 turn ( ! %ip f be+ ?r[n all at once on to ! gyro4 ,! gyros ,l ,m are simil>ly connect$ to ! re/ ( ! s5sitive elem5t1 b 9 _! case "o pair ( spr+s is made to s]ve bo? gyros by employ+ l9ks & a bell-crank lev]4 ,! spr+s1 x may be rem>k$1 und\bt$ly d play a "p 9 ! transmission ( ! directive =ce f ! gyros to ! c>d & 9 ! avoidance ( ! quadrantal error4 ,b _! pres5ce is n ess5tial to ! fundam5tal pr9ciple ( action ( ! compass4 ,! damp+ sy/em ( ! #aiab design is ( a v simple nature1 & repres5ts a great improvem5t ov] ! air bla/ me?od previ\sly us$4 ,al?\gh ! :eels are n requir$ to act z bl[]s1 _! cas+s are n exhau/$ ( air4 ,! cas+s1 9 fact1 are p]=at$ ) f\r l>ge holes on ea* side1 ! cool+ effect ( ! circulat+ air be+ reg>d$ z ( m value 9 practice ?an ! sav+ ( p[] :i* w\ld result if ! :eels 7 run 9 an exhau/$ atmosph]e4 ,! damp+ =ce is suppli$ by ! weight ( a body ( oil conta9$ )9 a tr\gh ,n ext5d+ "r r\nd ! foot ( ! annul> cas+ conta9+ ! gyros4 ,?is tr\gh1 a circle z se5 9 plan1 is block$ by eight bulkheads1 "o ea* bel[ ! nor? & s\? po9ts ( ! compass c>d1 & ! o!rs equally spac$ r\nd ! tr\gh4 ,?r\gh ea* bulkhead a %ort pipe passes1 s t ! oil 9 ! tr\gh may fl[ f "o comp>tm5t to ano!r4 ,) ! exception1 h[ev]1 ( ! nor? & s\? bulkhead pipes1 :i* are q free 9 ! bore1 ! passage ( ! oil is re/rict$ by means ( a wire p>tially fill+ ! bores ( ! pipes4 ,by v>y+ ! size ( wire us$1 ! re/riction to ! fl[ ( ! oil f "o comp>tm5t to ! o!rs1 & !re=e ! rate at :i* ! oil w fl[ :5 ! s5sitive elem5t tilts1 c be regulat$ to give ! degree ( damp+ requir$ or to suit any *ange ( viscosity 9 a fre% supply ( oil4 ,! sy/em 9 pr9ciple has mu* 9 common ) ! ,br[n me?od ( damp+4 ,%\ld ! compass c>d suff] an ea/]ly deflection1 ! nor? po9t ( ! c>d w1 z we "k1 t5d to rise "u ! influ5ce ( ! e>?'s rotation1 & w cont9ue to rise until ! turn+ mom5t appli$ by ! deflect$ p5dulum weight precesses ! c>d back to ! m]idian1 :]eaft] ! nor? po9t ( ! c>d pass+ ov] t[>ds ! we/ w beg9 to fall t[>ds ! horizontal plane1 & !n1 desc5d+ /ill f>!r1 x w once m come back to ! m]idian4 ,dur+ ?is comp\nd motion ! oil 9 ! tr\gh fl[s backw>ds & =w>ds1 accumulat+ bel[ ! s\? po9t ( ! c>d :5 ! nor? po9t ( ! c>d is ris+ & ga!r+ bel[ ! nor? po9t :5 ! nor? po9t is fall+4 ,9 o!r words1 !re is an excess weight ( oil bel[ ! s\!rn po9t ( ! c>d ?r\gh\t ! complete half-sw+ f ea/ to we/1 ! maximum excess occurr+ :5 ! c>d is cross+ ! m]idian4 ,on ! half-sw+ f we/ to ea/ ! excess weight ( oil is bel[ ! nor!rn po9t ( ! c>d1 ! maximum excess occurr+1 z be=e1 :5 ! c>d is cross+ ! m]idian4 ,! excess weight ( oil at all times ?us t5ds to increase ! rise or dip ( ! nor? po9t ( ! c>d above or bel[ ! horizontal plane1 :]eas ! p5dulum weight at all times t5ds to dim9i% su* rise or dip4 ,h5ce ! excess weight ( oil tries to precess ! c>d 9 ! direction oppos$ to t 9 :i* ! p5dulum weight is precess+ x4 ,! vibration ( ! c>d 9 ?is compass1 z 9 ! ,br[n design1 is !re=e damp$ by ! g5]ation ( a c\nt]-precessional t5d5cy1 & n1 z 9 ! e>ly ,ans*tz & ! ,sp]ry designs1 by precess+ ! s5sitive elem5t 9 ! direction requir$ to r$uce ! angle by :i* ! p5dulum weight is tilt$ away f ! plumb l9e4 ,f :at we h already said reg>d+ ! ,br[n sy/em ( damp+1 x w readily be inf]r$ t !re is no latitude error 9 ! ,ans*tz #aiab compass4 ,! damp+ =ce is equival5t to a r$uction 9 ! weight ( ! p5dulum 8bob10 & is n appli$ directly to r$uce ! tilt ( ! bob4 ,! tilt ( ! p5dulum weight requir$ 9 nor? or s\? latitudes to provide ! appropriate rate ( we/]ly or ea/]ly precession is n oppos$ by ! damp+ =ce call$ into play by su* tilt4 ,in/ead1 ! damp+ =ce m]ely makes ! bob light]1 s t ! tilt has to be c>ri$ f>!r be=e ! effective weight ( ! bob c balance ! tilt+ action ( ! e>?'s rotation4 ,! balance w be automatically /ruck :5 ! mom5t ( ! effective weight ( ! bob is j suffici5t to g5]ate ! requir$ rate ( we/]ly or ea/]ly precession appropriate to ! latitude4 ,! arrangem5t ( ! ?ree gyros at ! corn]s ( an equilat]al triangle & ! g5]al =m giv5 to ! annul> cas+ & ! re/ ( ! s5sitive elem5t results 9 ! di/ribution ( ! mass ( ! s5sitive elem5t 9 a v uni=m mann] ar\nd ! v]tical axis4 ,!re is no excessive conc5tration ( ! mass t[>ds ! ea/ & we/ plane1 & z a result x is unnecess>y to add comp5sator weights to ?is compass 9 ord] to avoid ! effects ( c5trifugal =ce dur+ quadrantal roll+4 ,illu/ration3 ,,fig4 #ea4 ,sectional ,elevation ( ,ans*tz 7#aiab7 ,compass4 ,! gyro-:eels are made ( a special quality ( nickel /eel1 & are m\nt$ on axles ( ! de ,laval type--t is to say1 !y are tap]$ & made ( v small diamet] 7ab\t #j4ae 94 at ! p>allel ends7--9 ord] t !y may yield a little %\ld ! c5tre ( gravity ( ! :eel n be truly co9cid5t ) ! c5tre l9e ( ! %aft4 ,! :eels are #e 94 9 diamet]1 weigh #e lb4 #b oz41 & run at #bj1jjj revolutions p] m9ute4 ,! motors are ( ! squirrel-cage type ) ! rotor w9d+s fix$ to ! :eels inside a recess conc5tric ) ! axle4 ,! field coils are fix$ relatively to ! gyro cas+4 ,x is ( int]e/ to note t :5 ! gyro-:eel is be+ run up to its full spe$--an op]ation tak+ ab\t five m9utes to complete--! axle passes ?r\gh ?ree critical spe$s4 ,^! spe$s are approximately #gjjj1 #aa1jjj1 & #ad1jjj revolutions1 & are believ$ to be associat$1 ! fir/ ) "o end ( ! axle1 ! second ) ! o!r end1 & ! ?ird ) a comb9$ action at bo? ends4 ,dur+ ! p]iod ( runn+ up ! gyros ! />t+ curr5t is1 ( c\rse1 heavi] ?an ! curr5t tak5 to drive ! :eels at ! top spe$1 & z a result a consid]able temp]ature is develop$ 9 ! :eels & _! cas+s4 ,:51 h[ev]1 ! gyros h be5 runn+ = "s "t at ! top spe$ ! temp]ature drops1 & ?r\gh\t ! compass rema9s fairly con/ant at ab\t #aej deg4 ,fahr4 ,! viscosity ( ! damp+ oil1 on ! con/ancy ( :i* ! con/ancy ( ! damp+ =ce dep5ds1 is !re=e less affect$ by ext]nal atmosph]ic *anges ( temp]ature ?an might be expect$4 ,! oil us$ is a m9]al "o4 ,x s]ves n only to damp ! vibrations ( ! c>d1 b also to lubricate ! gyro-axles4 ,to ?is end1 z %[n 9 ,fig4 #ea1 pipes are l$ d[n f ea* end ( ea* axle to dip into ! oil tr\gh1 ! fl[ ( oil be+ induc$ by means ( wicks inside ! pipes4 ,! me?od adopt$ = ! transmission ( ! read+s f ! ma/] compass to ! repeat]s is ( consid]able int]e/4 ,! b[l ,c conta9+ ! m]cury & ! float is surr\nd$ by two semi-cyl9drical /rips ,p ,q ( silv]-plat$ brass4 ,at "o ( ! gaps betwe5 ^! /rips ! two abutt+ edges are fac$ ) plat9um4 ,! gap betwe5 ^! plat9um faces is #j4aa 94 9 wid?1 & into x !re is ins]t$1 z %[n 9 ! plan view1 a plat9um-iridium ball ,r1 measur+ #j4jie 94 9 diamet]4 ,on ! swit*bo>d s]v+ ! compass !re is a rev]sible motor1 two ( ! w9d+s ( :i* are con/antly connect$ to a g5]ator--! same g5]ator z s]ves ! gyro-motors4 ,! contact ball ,r is connect$ to ! ?ird phase ( ! g5]ator1 :ile ! two /rips ,p ,q are connect$ to ! ?ird w9d+ ( ! rev]sible motor1 ?is w9d+ be+ duplicat$ 9 su* a way t ! motor revolves 9 "o direction or ! o!r1 accord+ z ! circuit is complet$ at ! ball ,r ?r\gh ! /rip ,p or ! /rip ,q4 ,a commutator is m\nt$ on ! axle ( ! rev]sible motor1 & f x curr5t is di/ribut$ to ! motors op]at+ ! repeat]s & to ! 8foll[-up0 motor ,s 7,fig4 #ea74 ,! latt] motor is ge>$ to ! %aft c>ry+ ! b[l ,c1 & :5 />t$ up by ! rev]sible motor turns ! b[l 9 ! direction requir$ to re/ore ! ball ,r to ! middle ( its slot1 & s break ! connection ) ! /rip ,p or ,q4 ,?us :5 ! %ip's c\rse is alt]$ ! b[l t5ds to rotate ) ! %ip1 b ! ball ,r is m\nt$ on ! s5sitive elem5t1 & !re=e ma9ta9s its position4 ,contact is ?us e/abli%$ betwe5 ! ball & "o ( ! /rips ,p ,q1 ! rev]sible motor is set rotat+ 9 ! appropriate direction1 & curr5t is di/ribut$ to ! 8foll[-up0 motor ,s to rotate ! b[l relatively to ! %ip until ! ball ,r is once m ly+ midway 9 ! gap4 ,! t5d5cy ( ! b[l to rotate ) ! %ip is ?us c\nt]act$2 ! action ( ! 8foll[-up0 motor practically results 9 ! b[l be+ held 9 con/ant relation%ip to ! s5sitive elem5t sub/antially z ?\gh x 7 "p !re(4 ,simultane\sly ! c>ds ( ! repeat]s are prev5t$ f rotat+ ) ! %ip1 s t virtually !y1 too1 act z if rigidly connect$ to ! s5sitive elem5t1 )\t1 h[ev]1 any frictional drag be+ ?r[n f !m on to ! s5sitive elem5t4 ,z illu/rat+ ! ref9$ con/ruction ( ! entire compass1 ! design ( ! ball contact may be notic$4 ,! ball is c>ri$ at ! end ( a tap]$ spiral spr+4 ,x is free to rotate on ! spr+ end1 b is prev5t$ f mov+ axially !reon4 ,! spr+ end is provid$ ) a button4 ,! ball is drill$ out & bead$ ov] ! button4 ,to ensure good electrical contact at all times betwe5 ! ball & ! spr+ a drop ( m]cury is c>ri$ inside ! ball betwe5 x & ! button4 ,%\ld ! %ip turn v sudd5ly ! ball may spr+ out ( ! gap & be dragg$ across ! face ( "o or o!r ( ! /rips ,p ,q4 ,x is = ?is reason t ^! /rips are silv]-plat$4 ,! repeat] compasses are provid$ n only ) an ord9>y c>d graduat$ f #j deg4 to #afj deg41 b also ) an inn] dial :i* makes "o revolution = an alt]ation ( #aj deg4 9 ! %ip's c\rse4 ,?is dial is graduat$ to #a_/aj deg41 & p]mits v small dep>tures f ! set c\rse to be imm$iately notic$ & correct$4 ,an elaboration ( ! same idea is provid$ 9 ! multiple repeat] ( ! ,br[n compass4 ,9 ?is repeat] ! inn] dial is ! ord9>y #cfj deg4 c>d4 ,! out] annul> dial makes f\r revolutions = e complete turn ( ! %ip4 ,) ! %ip sail+ due nor? ! graduations on ! out] dial are numb]$ f #j to #de r\nd ! ea/ half ( ! dial1 & f #cfj to #cae r\nd ! we/ half4 ,! numb]s1 h[ev]1 are n m>k$ on ! dial itself1 b on ! edges ( discs se5 ?r\gh slots 9 ! dial4 ,z ! %ip turns f ! nor? t[>ds ! ea/1 ! discs on ! we/ side ( ! dial are successively rotat$ "o /age z ! s\? end ( ! lubb] l9e passes ov] !m1 s z to exhibit numb]s =m+ a cont9uation ( ! numb]s on ! ea/ side ( ! dial4 ,! out] magnifi$ dial is ?us ( itself suffici5t = navigational purposes4 ,9 ! ,ans*tz equipm5t arrangem5ts are made = atta*+ an azimu? mirror to ! repeat] dial = ! purpose ( provid+ an artificial horizon dur+ ! tak+ ( be>+s4 ,a sep>ate gyroscopically /abilis$ artificial horizon device1 su* z is sometimes to be f\nd on bo>d %ips1 is ?us r5d]$ unnecess>y4 ,,index ,abs5ce ( latitude error 9 ,ans*tz 7#aiab7 compass1 #aeh ,abs5ce ( latitude error 9 ,br[n compass1 #ff ,action ( exc5tric p9 9 ,sp]ry compass1 #ee et seq4 ,air-bla/ pressure1 ,br[n compass1 #fa ,ans*tz 7#aiaj7 compass-- ,air-bla/ damp+ sy/em1 #db et seq4 ,damp+ curve1 #ej ,latitude error1 cause (1 #fe -- -- correction =1 #fg -- -- value (1 #fh ,magnitude ( directive =ce at equator1 #bc ,non-gyroscopic details1 #ach ,p]iod ( vibration ( axle1 #cc1 #cg ,p]iph]al spe$ ( :eel1 #dg ,quadrantal error1 #if1 #ajg1 #abj ,weight1 diamet]1 & spe$ ( :eel1 #bc ,weight ( s5sitive elem5t1 #cj ,:eel te/$ to de/ruction1 #adj ,ans*tz 7#aiab7 compass-- ,abs5ce ( latitude error1 #aeh ,directive =ce1 value (1 #abe ,f\r? gyro type1 #abh ,gyro-:eels1 details (1 #aei ,non-gyroscopic details1 #aed ,oil damp+ sy/em1 #aef ,quadrantal error1 #ajg1 #abj1 #abf ,repeat] compasses1 #afb ,temp]ature rise1 #afj ,weight1 diamet]1 & spe$ ( :eels1 #abc ,balli/ic deflection & error1 #ha et seq4 ,balli/ic deflection1 dead-beat1 #hg ,balli/ic deflection1 te/s by ,briti% ,admiralty1 #hi ,balli/ic gyro1 ,sp]ry compass1 #aaa ,br[n compass-- ,abs5ce ( latitude error1 #ff ,air-bla/ pressure1 #fa ,comp5sator weights1 #acd ,damp+ bottles1 #fa -- sy/em1 #ei et seq4 ,g5]ation ( directive =ce1 #aaf ,magnitude ( directive =ce at equator1 #bc ,non-gyroscopic details1 #adh ,oil control bottles1 #aac ,on due we/ c\rse1 #aag ,quadrantal error1 #aac1 #abf ,repeat] compasses1 #aed1 #afb ,weight1 diamet]1 & spe$ ( :eel1 #bc ,weight ( s5sitive elem5t1 #cj ,c5trifugal =ces dur+ quadrantal roll+1 #acj et seq4 ,clock1 gyroscopic1 #af ,comp5sator weights1 #acd ,correction me*anism = latitude & nor? /eam+ errors1 #ge ,c\rse correction or cos9e r+1 #gg ,damp$ & free motion ( gyro-axle1 #di ,damp$ & undamp$ vibrations1 #ce et seq4 ,damp+ curve1 #ej -- sy/ems1 #db1 #dc1 #eb1 #ei1 #aef -- vibrations ( gyro-compass1 #bi ,dead-beat balli/ic deflection1 #hg ,details ( gyro-:eels1 #bc1 #aei ,directive =ce1 value (1 at equator1 #bc1 #abe ,directive =ce1 effective1 #bh ,effect ( roll+ on due we/ c\rse1 #ic1 #ih1 #ii ,effect ( roll+ on due nor? c\rse1 #id ,effect ( roll+ on nor?-we/ c\rse1 #aja ,elem5t>y gyro-compass1 #ah -- -- at equator1 #bj1 #bf -- -- at #ee deg4 ,n4 lat41 #bd -- -- ne> ,nor? ,pole1 #bf ,elem5t>y gyroscope at equator1 #ae ,elem5t>y gyroscopic ph5om5a1 #d et seq4 ,elim9ation ( ! quadrantal error1 #ajg ,exc5tric p91 action (1 #ee et seq4 -- -- /abilisation (1 #aaj1 #aab ,ext]nal gimbal m\nt+1 #ac1 #ig ,f\r? gyro type ( ,ans*tz compass1 #abh ,free & damp$ motion ( gyro-axle1 #di ,friction1 solid & fluid1 #ci1 #dj ,g5]ation ( directive =ce1 #ah1 #aaf ,g]man subm>9es1 #if1 #abj1 #abh ,gimbal m\nt+1 ext]nal1 #ac1 #ig ,gyro-axle1 free & damp$ motion (1 #di ,gyroscope at equator1 #ae -- ) ?ree degrees ( fre$om1 #d et seq4 ,gyroscope & rotation ( ! e>?1 #ae ,gyroscopic compass at equator1 #bj1 #bf ,gyroscopic compass at #ee deg4 ,n4 lat41 #bd ,gyroscopic compass ne> ,nor? ,pole1 #bf ,gyroscopic ph5om5a1 elem5t>y1 #d et seq4 ,gyro-:eels1 details (1 #bc1 #aei ,latitude bail corrector1 #fi -- corrector dial1 #gf -- error1 #fe -- -- abs5ce (1 #ff1 #aeh -- -- cause (1 #fe1 #ff -- -- correction (1 #fg1 #ge -- -- value (1 #fh1 #fi1 #ge ,magnetic compass1 #a1 #bc1 #cj ,magnitude ( directive =ce at equator1 #bc1 #abe ,nor? /eam+ error1 #gj -- -- -- correction me*anism1 #ge -- -- -- value (1 #gd1 #gi ,oil control bottles1 #aac -- damp+ sy/em1 #aef ,p5dulum1 simple1 #ca1 #ha ,p]iod ( roll+ ( a %ip1 #ie -- -- vibration ( gyro-axle1 #cc1 #cg1 #hh ,p]iph]al spe$ ( gyro-:eel1 #dg ,phantom r+1 #ec ,quadrantal error1 #ia1 #if1 #ajg1 #abj ,quadrantal error1 elim9ation (1 #ajg1 #ajh1 #aac1 #abj1 #abf ,quadrantal error1 value (1 #ajg -- roll+1 c5trifugal =ces dur+1 #acj et seq4 ,repeat] compasses1 #gi1 #hj1 #adf1 #aeb1 #afb ,roll+ ( a %ip1 p]iod (1 #ie -- on due nor? c\rse1 #ic1 #ih1 #ii -- -- -- we/ c\rse1 #id -- -- nor?-we/ c\rse1 #aja -- quadrantal1 c5trifugal =ces dur+1 #acj et seq4 ,rotation ( ! e>? & ! gyroscope1 #ae ,simple p5dulum1 #ca1 #ha ,sp]ry compass-- ,bail1 #ed ,balli/ic gyro1 #aaa ,comp5sator weights1 #acd ,c\rse corrector or cos9e r+1 #gg ,damp+ sy/em1 #eb ,directive =ce1 magnitude at equator1 #bc ,exc5tric p91 action (1 #ee et seq4 ,exc5tric p91 /abilisation (1 #aaj1 #aab ,latitude bail corrector1 #fi -- corrector dial1 #gf -- error1 cause (1 #ff -- -- correction (1 #fg1 #ge ,latitude error1 value (1 #fi ,non-gyroscopic details1 #adb ,nor? /eam+ error1 correction (1 #ge1 et seq4 ,on nor?-we/ c\rse1 #ajh ,phantom r+1 #ec ,quadrantal error1 #ajh1 #abf ,repeat] compasses1 #adf ,spe$ correction dial1 #gg ,vacuum 9 :eel cas+1 #eb ,weight1 diamet]1 & spe$ ( :eel1 #bc ,weight ( s5sitive elem5t1 #cj ,subm>9es1 ,g]man1 #if1 #abj1 #abh ,temp]ature rise 9 ,ans*tz compass1 #afj ,te/ ( ,ans*tz :eel to de/ruction1 #adj ,vacuum 9 ,sp]ry cas+1 #eb ,vibration p]iod ( ,ans*tz compass1 #cc1 #cg ,vibration p]iod ( gyro-axle1 /&>d1 #hh ,vibrations1 damp$ & undamp$1 #ce et seq4 ,weight1 diamet]1 & spe$ ( gyro-:eel1 #bc1 #abc ,weight ( s5sitive elem5t1 #cj ,pr9t$ 9 ,great ,brita9 at ,! ,mayfl[] ,press1 ,plym\?4 ,william ,br5don ,son1 ,ltd4 ,,footnotes #a ,e>li] =m z 9 use 9 #aiaj4 #b ,approximate4 ,diff]s 9 diff]5t compasses4 #c ,! value ( ! latitude error is b tan ,l1 :]e ,l is ! angle ( latitude & b a con/ant dep5d5t ^u ! design ( ! compass4 ,9 ! ,sp]ry correction me*anism ! value ( ! quantity b is repres5t$ by ! di/ance betwe5 ! c5tre ( ! dial ,b & ! c5tre ( ! p9 ,c :5 ! radial slot 9 ! dial is ly+ at "r angles to ! b> ,d ,e4 #d ,! value ( ! nor? /eam+ error is num]ically equal to 7a ,k cos ,c7_/cos ,l1 :]e ,k is ! %ip's spe$1 ,l ! angle ( latitude1 ,c ! angle betwe5 ! c\rse & ! nor? & s\? direction1 & a a con/ant involv+ ! spe$ ( rotation ( ! e>?4 ,9 ! ,sp]ry correction me*anism ! value ( ! quantity a is repres5t$ by ! radius at :i* ! p9 ,l lies f ! c5tre ( ! latitude dial4 #e ,! balli/ic deflection is dep5d5t ^u ! rate at :i* ! nor!rly compon5t ( ! %ip's spe$ is be+ *ang$4 ,! diff]5ce 9 ! nor? /eam+ errors is dep5d5t ^u ! initial & f9al values ( ! spe$ t[>ds ! nor?1 & w\ld n appe> to be affect$ by ! l5g? ( "t occupi$ 9 *ang+ ! spe$4 ,x w\ld seem1 !re=e1 t ! balli/ic deflection c only be dead-beat 9 ! *os5 latitude if ! spe$ t[>ds ! nor? is r$uc$ or increas$ at "o p>ticul> rate4 ,?us if ! %ip is /eam+ due nor? at #bj knots & *anges its spe$ to #aj knots 9 7a7 #aj m9utes or 7b7 #e m9utes1 ! initial & f9al values ( ! nor? /eam+ error w be ! same 9 bo? cases1 s9ce ! initial & f9al spe$s are ! same1 b ! balli/ic deflection w be great] 9 ! second case ?an 9 ! fir/1 s9ce ! rate at :i* ! spe$ is *ang$ is great]4 ,if1 !n1 ! balli/ic deflection is dead-beat 9 ! fir/ case x _c be s 9 ! second4 ,! /atem5t t ! balli/ic deflection 9 ! *os5 latitude is dead-beat ?us appe>s1 x may be sugge/$1 to require qualification4 ,on ! o!r h&1 ! ,briti% ,admiralty 9 connection ) ! use ( gyro-compasses on de/roy]s & simil> fa/-manuvr+ vessels :]e9 ! balli/ic deflection is a factor ( v great importance has c>ri$ out l5g?y exp]im5ts on ! matt]1 &1 al?\gh ! results h n be5 divulg$1 x is und]/ood t ! balli/ic deflection 0 f\nd to be dead-beat indep5d5tly ( ! rate at :i* ! spe$ 0 *ang$4 #f ,! :eels 9 ! two designs be+ simil> 9 =m1 _! mom5ts ( in]tia--! real factors det]m9+ ! magnitude ( ! directive =ces--are proportional to ! f\r? p[]s ( _! diamet]s4 ,! f\r? p[] ( #e is to ! f\r? p[] ( #f z #a is to #b approximately4 #g ,! directive =ce is proportional to ! s9e ( ! angle ( deflection4 ,! gyros ,k ,l ,m !re=e supply at #cj deg4 deflection a total directive =ce ( ,d s9 #cj deg4 ,d s9 #fj deg4 ,d s9 #j deg41 or #a4cff ,d4 ,= a s+le-gyro compass1 hav+ a :eel ( twice ! in]tia ( ,k ,l or ,m sep>ately1 ! directive =ce at #cj deg4 deflection w\ld be #b ,d s9 #cj deg4 or ,d4 #h ,m precisely1 ! mom5t ( in]tia ( ! body mu/ h a con/ant value ab\t ! l9e ,j ,k1 ,fig4 #dc1 at all angles ( sett+4 ,transcrib]'s ,notes ,simple typographical errors 7 correct$4 ,:5 necess>y1 illu/rations h be5 mov$ betwe5 p>agraphs1 s "s ( ! page ref]5ces 9 ! ,li/ ( ,illu/rations are (f by a page or two4 ,l9ks to ^? illu/rations are correct4 ,index n *eck$ = prop] alphabetization or correct page ref]5ces4