,,! ,,:ys ,,& ,,:]e=es ,,( ,,navigation ,,! ,,:ys ,,& ,,:]e=es ,,( ,,navigation ,,by ,,g]%om ,,brad=d #b;d ,navigat+ ,(fic] & ,s5ior ,in/ructor ,new ,york ,/ate ,nautical ,s*ool%ip 8,newport10 ,late ,nautical ,exp]t1 ,hydrographic ,(fice1 ,u4 ,s4 ,n4 ,,illu/rat$ ,illu/ration3 colophon ,,new ,,york ,d4 ,,van ,,no/r& ,,company #be ,,p>k ,,place #aiah ,copyright1 #aiah1 by ,d4 ,,van ,,no/r& ,,company ,,press ,,( ,,braunwor? ,,co4 ,,book ,,manufactur]s ,,brooklyn1 ,n4 ,y4 ,,to ,,! ,,am]ican ,,sub-,,patrol ,,^: ,,w> ,,zone ,,record ,,( ,,skill ,,& ,,d>+ ,,has ,,! ,,au?or',s ,,pr(\nd ,,respect ,,& ,,admiration ,,preface ,:5 tak+ into consid]ation ! numb] ( excell5t works n[ publi%$ on navigation !re w\ld seem to be a small *ance ( f9d+ a diff]5t angle f :i* to discuss ! subject4 ,! purpose ( ! majority ( su* books is to give in/ruction to beg9n]s4 ,?is book1 h[ev]1 is writt5 p>ticul>ly = ! m5 :o d _! "w mo/ly by rote & wi% to "k m ( ! reasons2 or1 p]haps1 = s*ool%ip graduates :o may "h f9d a *ance to ext5d _! horizons4 ,i h n consid]$ x desirable to avoid repetition & 9 ord] to closely foll[ a l9e ( ?\ght h freely repeat$ _m po9ts already tak5 up4 ,?is has 9 a numb] ( cases avoid$ ! di/raction ( seek+ a page ( ref]5ce else:]e4 ,i h _h 9 m9d t x s]ve z supplem5t>y read+ to ! ,am]ican ,practical ,navigator1 ,b[dit*1 t great bulw>k ( navigation :i* = ov] a hundr$ ye>s has protect$ ,am]ican %ips ?r\gh e de$ ( valor & e comm]cial adv5ture4 ,x is plac$ beyond criticism by its v5]able "n & its rem>kable record &1 z a ref]5ce book = ! navigator1 x /&s )\t a pe]1 b z a text book x f\nd]s ! /ud5t4 ,if to su* m>9]s z ^! a little insight is giv5 to ! 8,:ys & ,:]e=es0 ( _! "w1 ,i %all be well repaid = ! "w ( _m wat*es bel[4 ,^! discussions appe>$ sev]al ye>s ago1 9 a less ext5d$ =m1 9 ! ,ma/]1 ,mate & ,pilot1 ! magaz9e =m]ly publi%$ by ! ,am]ican ,association ( ,ma/]s1 ,mates & ,pilots4 ,i h freely consult$ ! foll[+ /&>d works3 ,am]ican ,practical ,navigator1 ,b[dit*2 ,wr9kles 9 ,practical ,navigation1 ,lecky2 ,! ,!ory & ,practice ( ,navigation1 ,dunrav52 ,g5]al ,a/ronomy1 ,"y2 ,navigation & ,compass ,adju/m5t1 ,muir2 ,guide to ! ,m>9e ,bo>d's ,exam9ations1 ,re$4 ,i h receiv$ & am grateful = v valuable help & sugge/ions f ,mr4 ,george ,w4 ,littlehales1 ,hydrographic ,eng9e]1 ,u4,s4,n41 ,mr4 ,felix ,ries5b]g1 ,c4,e41 ,comm&] ,new ,york ,/ate ,s*ool%ip ,newport1 & ,george ,a4 ,collie 7deceas$71 ,nautical ,exp]t1 ,hydrographic ,(fice1 ,u4,s4,n4 ,g4 ,b4 ,,new ,,york1 ,april #ae1 #aiah4 ,,cont5ts ,,page ,,*apt] ,i ,,introductory ,,rem>ks #a ,,*apt] ,,ii ,,nautical ,,a/ronomy #e ,,*apt] ,,iii ,,decl9ation ,,& ,,"r ,,asc5sion1 ,,includ+ ,,precession #ae ,,*apt] ,,iv ,,"t #cc ,,*apt] ,v ,,corrections ,,= ,,obs]v$ ,,altitudes #fh ,,*apt] ,,vi ,,latitude #gh ,,*apt] ,,vii ,,azimu?s ,,& ,,amplitudes #ic ,,*apt] ,,viii ,,longitude #aja ,,*apt] ,,ix ,,sumn] ,,me?od1 ,,includ+ ,,new ,,navigation #ajg ,,*apt] ,x ,,! ,,moon #aci ,,*apt] ,,xi ,,*>ts #adf ,,index #afa ,,! ,,:ys ,,& ,,:]e=es ,,( ,,navigation ,,*apt] ,i ,introductory ,rem>ks ,9 emb>k+ ^u ! /udy ( navigation famili>ity ) ! compass is ! fir/ logical /ep3 ! quick m5tal conv]sion ( a c\rse or direction giv5 9 po9ts to ! same direction 9 degrees express$ 9 quadrants z ,s4 #ce ,e41 & aga9 into a sy/em by :i* direction is indicat$ by degrees f #j to #cfj4 ,a m>9] w enc\nt] all ?ree ( ^! sy/ems & w f9d con/ant conv]sion necess>y back & =? = v>i\s purposes4 ,! #j to #cfj sy/em is ! mo/ up-to-date & ! simple/ =m ( h&l+ direction4 ,foll[+ ! compass may be tak5 up ! use & description ( o!r nautical in/rum5ts ) :i* e m>9] is suppos$ to be famili>4 ,dead reckon+ is ! fir/ calculation to appe> & ?is involves ! correction ( ! compass c\rses back & =? betwe5 true1 magnetic & compass directions4 ,?is is dealt ) "u ,azimu?s & ,amplitudes4 ,9 practical navigation a vessel comm5ces h] voyage & attempts to sail 9 a c]ta9 direction1 b ! well-kn[n elem5ts ( compass error1 v>iation & deviation1 curr5t1 w9d1 seas & poor /e]+ all div]t ! vessel f ! project$ c\rse4 ,9 dead reckon+ a navigator /rives to keep track ( 8 position by keep+ a record ( actual c\rses /e]$ & di/ances run4 ,he !n is oblig$ to guess at ! am\nt ! vessel has div]t$ bo? 9 direction & di/ance until an a/ronomical obs]vation sets him /raight aga94 ,x is "h p>ticul>ly %[n t navigation becomes an art ( e/imat+ position & ! bett] ! navigator's bump ( locality1 ! great] 8 success4 ,?is is a peculi> gift & usually is born 9 ! man1 at lea/ x _c be le>n$ f books4 ,! process ( f9d+ latitude & longitude by dead reckon+ is suppos$ to be already well kn[n to ! read] & w n be detail$ at l5g?4 ,h[ev]1 e c\rse angle is laid (f f a m]idian 7:i* is true ,n4 & ,s47 & t]m9ates 9 a p>allel ( latitude4 ,?is m]idian & p>allel int]sect at "r angles2 h5ce ^! ) ! di/ance run 7:i* is ! hypo!nuse7 =m a plane "r angle triangle1 plane because ! curvature ( ! e>? is n consid]$ 9 %ort di/ances4 ,to solve ?is triangle1 we h ! c\rse angle & "o side--! di/ance run4 ,) ^! ! o!r two sides are easily f\nd by computation1 b m easily by tables ,no4 #a & #b1 ,b[dit*4 ,! side along ! m]idian is repres5t$ by ! column head$ ,lat4 7diff]5ce ( latitude7 & ! side ly+ 9 ! p>allel is 9 ! column head$ ,dep4 7dep>ture74 ,?us ! values ( ! sides ( ! triangle are giv5 9 miles & t5?s1 %[+ ! di/ance good made ,n4 or ,s4 & ,e4 or ,w4 ,x w be not$ t at ! top ( ! pages ( ^! tables are f\r diff]5t c\rses & at ! bottom are likewise f\r c\rses mak+ ! same page s]ve = eight diff]5t c\rses4 ,?is is accompli%$ by ! fact t triangles =m$ by ^! p>ticul> eight c\rses are ! same 9 %ape4 ,?us ,n4 #cj ,e41 = in/ance1 makes a simil> triangle to ,n4 #cj ,w4 7#ccj72 ,s4 #cj ,e4 7#aej72 or ,s4 #cj ,w4 7#baj74 ,!y h id5tically ! same diff]5ce ( latitude & dep>ture4 ,if ?is fact is n cle> draw a diagram & be conv9c$4 ,9 ! cases ( ,n4 #fj ,e4 7#fj72 ,n4 #fj ,w4 7#cjj72 ,s4 #fj ,e4 7#abj72 ,s4 #fj ,w4 7#bdj71 ! same %ap$ triangle z above is f\nd1 b rev]s$ 9 t :at 0 ! diff]5ce ( latitude side n[ has become ! dep>ture side4 ,! values ( ^! sides are read f ! bottom ( ! page & are f\nd 9 ! rev]se columns to fit ! rev]se triangle4 ,! latitude value read f ! top ( ! page z #cj becomes a dep>ture value :5 read f ! bottom ) #fj4 ,! subject ( ,sail+s is "o ( ! e>ly problems confront+ ! /ud5t ( navigation & w be consid]$ briefly4 ,! above rem>ks on dead reckon+ cov] ! pr9ciple ( plane sail+1 ! simple me?od :]e ! sph]ical surface ( ! e>? is ignor$ & a flat ocean sub/itut$4 ,?is me?od w n s]ve = any?+ b %ort di/ances ( a few hundr$ miles )\t suffici5t error to r5d] x impracticable4 ,trav]se sail+ is a s]ies ( plane sail+ c\rses made1 = in/ance1 by a sail+ vessel beat+ to w9dw>d4 ,9 p>allel sail+ ! vessel pursues a true ,e4 or ,w4 c\rse & runs along a p>allel ( latitude4 ,?us all h] progress is 9 ! t]ms ( dep>ture ) no diff]5ce ( latitude4 ,z all m]idians conv]ge f ! equator t[>ds ! poles ! l5g? 9 miles ( a degree ( longitude keeps on dim9i%+ z ! poles are approa*$ &1 conv]sely1 miles ( dep>ture h an increas+ value 9 degrees ( longitude4 ,s 9 p>allel sail+ :at we desire to "k is :at is ! value 9 ! p>ticul> latitude ( our c\rse ( our dep>ture 7miles7 9 ( longitude4 ,hav+ ?is & apply+ x to ! longitude left w give ! longitude 94 ,middle latitude sail+ is v simil> to p>allel sail+ 9 t x is assum$1 = ! purpose ( gett+ ! diff]5ce ( longitude1 t ! :ole dep>ture ( ! c\rse or c\rses sail$ has be5 made 9 ! mean or middle latitude1 because ! great] value 79 ! nor!rn hemisph]e7 9 diff]5ce ( longitude ( a mile nor?w>d ( ! middle latitude is c\nt]act$ by ! correspond+ less] value s\?w>d ( ! middle latitude4 ,m]cator sail+ is p]haps ! mo/ ext5sively us$1 z ! ,m]cator pr9ciple is employ$ almo/ univ]sally 9 ! con/ruction ( navigational *>ts4 ,x is describ$ "u ,*>ts 9 ?is book4 ,also "u ,*>ts is a description ( ! ,gnomonic ,*>t :i* is also call$ ! ,great ,circle ,*>t & us$ 9 ,great ,circle ,sail+1 also ref]r$ to 9 ^? pages4 ,! "y navigator is c\nsell$ nev] to "k :]e 8 vessel is1 le/ ?r\gh ov] confid5ce he be l$ into close & dang]\s qu>t]s4 ,,*apt] ,,ii ,nautical ,a/ronomy ,! sun is ! c5t] ( ! sol> sy/em1 ) all ! planets1 includ+ ! e>?1 revolv+ ar\nd x1 "s ) orbits great] & o!rs less ?an t ( ! e>?4 ,! planets 9 "s in/ances h satellites revolv+ 9 turn ar\nd !m1 z ! moon 9 ! case ( ! e>?4 ,! movem5ts ( ! e>? w be1 p]haps1 m readily und]/ood by assum+ a position at ! ,nor? ,pole2 "h b5ea? ! obs]v] ! e>? is rotat+ left-h&$--aga9/ ! h&s ( a wat*1 once ea* day2 :ile at ! same "t x is spe$+ onw>d ?r\gh space 9 a left-h&$ curve1 :i* 9 ! c\rse ( a ye> resolves itself into a complete revolution ar\nd ! sun4 ,! sun & />s are consid]$ to be /ation>y = all navigational purposes1 ! app>5t movem5ts ( ^! bodies be+ entirely due to ! motions ( ! e>?4 ,! result ( our daily rotation f we/ to ea/ is1 t ! heav5ly bodies m>* pa/ our m]idian 9 a maje/ic procession = #bd h\rs1 aft] :i* ! p]=mance is repeat$4 ,! un9itiat$ are "h =ew>n$ aga9/ becom+ confus$ by ! assumption us$ = conv5i5ce by navigators t ! heav5s revolve ar\nd ! e>?4 ,! planets & moon jo9 ! sun & />s 9 ! daily p>ade pa/ our m]idian1 b _! app>5t movem5ts are n entirely an illusion1 = !y h motions ( _! own t some:at affect ! precision ( _! daily revolution4 ,?is is readily obs]v$ 9 ! moon's h\r ( ris+1 :i* is v p]ceptibly lat] ea* ev5+4 ,h] actual revolution ar\nd ! e>?1 be+ f we/ to ea/1 is contr>y to ! app>5t diurnal motion & !reby ea* ev5+ f9ds h] f>!r to ! ea/w>d & consequ5tly ris+ lat]4 ,z a result ( ?is *ange 9 ! "t ( ris+1 ! moon mu/ ( necessity rise 9 e h\r ( bo? day & night 9 ! c\rse ( a mon?--! "t %e requires to revolve ar\nd ! e>?4 ,! onw>d movem5t ( ! e>? 9 its orbit z we face ! sun 9 latitudes nor? ( ! tropics1 is t[>d our "r1 & ?is causes ! sun to app>5tly move sl[ly ea/w>d or to ! left among ! />s1 correspond+ exactly to our movem5t we/w>d4 ,?is movem5t is opposite to 8 daily c\rse across ! heav5s4 ,z a ye> is requir$ = ! e>? to accompli% our revolution ar\nd ! sun1 x foll[s t ?is same l5g? ( "t is consum$ by ! sun 9 mak+ its app>5t ea/w>d revolution ( ! heav5s4 ,! movem5ts ( ! planets are m complex4 ,!y all revolve ar\nd ! sun 9 ! same direction z ! e>?1 b z _! orbits are ( va/ly diff]5t sizes1 !y w be f\nd 9 v>i\s positions relative to ! sun2 !y ov]haul & pass ea* o!r1 b ow+ to _! uni=m direction ( revolution !y nev] meet4 ,! planet>y sy/em is l ! horse race at a c\nty fair2 ! pole horse has ! advantage1 b ! v>y+ spe$s ( ! conte/ants soon place !m at v>i\s p>ts ( ! track4 ,f ! e>? ! movem5ts ( ! planets1 aside f ! diurnal movem5t1 are compos$ ( _! own actual movem5t ar\nd ! sun1 comb9$ ) an app>5t motion1 due to ! e>?'s onw>d movem5t precisely z describ$ above 9 ! case ( ! sun4 ,! comb9$ movem5t ( a planet may be not$ by ref]5ce to ! fix$ />s beyond x4 ,! positions ( heav5ly bodies are det]m9$ by two measurem5ts--coord9ates--! di/ance nor? or s\? ( ! cele/ial equator1 call$ ! decl9ation1 & ! di/ance ea/ f ! prime cele/ial m]idian tak5 z a ref]5ce1 call$ ! "r asc5sion1 ea* ( :i* w be subsequ5tly treat$ at l5g? "u its individual head+4 ,! movem5t ( ! planets ea/w>d or we/w>d z describ$1 con/antly *anges _! "r asc5sion2 & z _! orbits are incl9$ at diff]5t angles to ! cele/ial equator1 !y are always *ang+ _! decl9ation4 ,! planets ^: orbits are small] ?an t ( ! e>? are call$ inf]ior1 :ile ^? ^: orbits are ( great] dim5sions are kn[n z sup]ior planets4 ,m]cury & ,v5us are inf]ior planets & consequ5tly are always ne>] ! sun2 _! comp>atively close proximity mak+ !m appe> to u z morn+ & ev5+ />s4 ,9 fact1 ,m]cury is s close t x is unavailable1 ow+ to ! brilliancy ( ! sun1 = obs]vation ) a sextant2 :ile ,v5us1 on ! o!r h&1 a little m remote1 is an excell5t body to obs]ve1 & is always f\nd 9 ! ea/ or we/1 conv5i5tly ne> ! prime v]tical1 ! mo/ favorable place = a "t sight = longitude4 ,! twilight or dawn :i* usually prevails at ! "t ( a ,v5us sight gives ! navigator a good horizon to obs]ve ^u4 ,m>s1 ,jupit] & ,saturn are sup]ior planets & _! travels are s ext5d$ t !y may be f\nd almo/ any:]e 9 ! heav5s )9 ! limits ( _! decl9ations4 ,! e>?'s orbit is slightly elliptical1 ) ! sun locat$ a little out ( c5t]--a little ne>] "o end4 ,%\ld a l9e or axis be drawn ?r\gh ! long diamet]1 its int]section ) t "p ( ! orbit ne>e/ ! sun is call$ ! ,p]ihelion :ile ! opposite po9t is kn[n z ! ,aphelion4 ,! =m] is us$ z a po9t ( ref]5ce f :i* ! e>?'s position c be locat$ 9 t]ms ( angul> measurem5t f "t to "t4 ,?is angle1 kn[n z ! anomaly1 is =m$ by ! l9e f ! sun to ! ,p]ihelion & t drawn f ! sun to ! e>?4 ,! latt] di/ance is call$ ! radius vector ( ! e>?4 ,we 7! e>?71 are at ! ,p]ihelion ab\t ,janu>y #a1 & consequ5tly ?is angle at t date is #j1 b f ?is "t on1 ! angle increases approximately "o degree a day ?r\gh\t ! ye>4 ,! plane ( ! e>?'s equator makes at all times an angle ( ab\t #bc #bh ) ! plane ( its orbit4 ,?is is a highly important angle to mank9d1 = ^u x dep5ds ! climate ( ! _w4 ,! axis ( ! e>?1 if we c conceive x z repres5t$ by a sl5d] imag9>y /aff1 ext5ds ?r\gh ! unlimit$ di/ance to a po9t 9 ! heav5s--! cele/ial pole2 ?is po9t is 9 ! z5i? = a p]son at our nor? pole4 ,s9ce ! di/ance betwe5 ^! po9ts is ma!matically inf9ite1 any numb] ( l9es p>allel to ?is 8/aff0 w appe> to p5etrate ! sky at ! s+le po9t ( ! cele/ial pole4 ,?us ! p>allel positions ( ! axis correspond+ to ! e>?'s v>i\s positions1 ev5 ^? at opposite sides ( ! orbit1 conv]ge into ?is common po9t4 ,to be cle>]1 ! p>allel l9es repres5t+ ! diff]5t positions ( ! axis dur+ ! ye> accord+ to our geometry =m a gr\p ( sep>ate po9ts on ! heav5s1 b ! di/ance be+ beyond all reckon+1 our limit$ conceptions fail to id5tify ! gr\p ( po9ts & x resolves into "o po9t4 ,by ! same l9e ( reason+ ! plane ( ! e>?'s equator rema9s p>allel 9 all its positions ?r\gh\t ! ye>ly cruise ar\nd ! sun1 & its projection m>ks b "o cele/ial equator ^u ! sky4 ,:ile ! direction ( ! axis & correspond+ position ( ! equator are con/ant = all practical purposes1 !re is1 nev]!less1 an extremely sl[ circul> movem5t ( ! axis1 call$ ! precession ( ! equ9oxes1 a subject :i* is res]v$ = subsequ5t discussion4 ,,coord9ates ,9 nautical a/ronomy ! e>? is assum$ to be ! c5t] ( space ) ! heav5s =m+ a globul> %ell ar\nd x1 kn[n z ! cele/ial sph]e4 ,all fix$ />s are assum$ to lie on its concave surface f ! e>? reg>dless ( _! actual di/ances4 ,! tracks ( all o!r bodies mov+1 or appe>+ to move1 across ! sky are consid]$ to be on ! surface ( ?is sph]e4 ,x is necess>y1 9 ord] to conv5i5tly def9e ! position ( heav5ly bodies to m>k ?is cele/ial sph]e ) imag9>y circles to s]ve z coord9ates1 z we m>k ! e>? ) m]idians ( longitude & p>allels ( latitude4 ,be=e go+ into ! explanation ( ^! coord9ates1 x may be well to consid] a few facts conc]n+ circles4 ,a great circle is ( c\rse und]/ood to be "o ^: plane passes ?r\gh ! c5t] ( a sph]e1 divid+ x into two equal p>ts4 ,!re c be an inf9ite numb] ( ^! circles ^: planes cut ! sph]e at e possible incl9ation z long z !y pass ?r\gh its c5t]4 ,a circle may be a great circle ( ei!r ! cele/ial sph]e1 ! e>?1 or ev5 ( a baseball4 ,! poles ( a great circle are ! po9ts on ! surface ( its sph]e1 p5etrat$ by ! diamet] p]p5dicul> to ! plane ( ! great circle4 ,z = example1 ! poles ( ! e>? are connect$ by ! diamet] t is p]p5dicul> to ! plane ( ! equator4 ,an angle at any pole is measur$ on ! great circle :i* subt5ds x4 ,= in/ance1 angles at ! poles ( ! e>? are measur$ on ! equator2 angles at ! z5i? on ! horizon4 ,) ^! facts well 9 m9d we w proce$1 %[+ ! s*eme ( circles employ$ 9 lay+ (f ! surface ( ! heav5s4 ,!re are ?ree sy/ems ( circles1 ea* design$ to fulfil a diff]5t requirem5t4 ,! fir/ sy/em dep5ds ^u ! position ( ! obs]v] & *anges its :ole imag9>y /ructure to correspond ) 8 movem5ts4 ,! plumb-l9e1 if ext5d$ to ! heav5s ov]head1 w det]m9e ! z5i?1 ! po9t ( orig9 ( ?is sy/em on ! cele/ial sph]e4 ,! correspond+ po9t directly b5ea? u is kn[n z ! nadir4 ,! great circle ( ! cele/ial sph]e ev]y:]e equally di/ant f bo? ! z5i? & ! nadir is ! horizon4 ,x is pla9 t a new z5i? & new horizon are creat$ ) e movem5t ( ! obs]v]4 ,! facts t man is on ! surface & n at ! c5t] ( ! e>?1 & t 8 eye is elevat$ above its surface1 ea* creates ano!r horizon4 ,! rational horizon is m>k$ by a plane1 p]p5dicul> to a plumb-l9e & pass+ ?r\gh ! e>?'s c5t]2 :ile ! s5sible horizon is det]m9$ by a plane1 also p]p5dicul> to ! plumb-l9e1 b pass+ ?r\gh ! eye ( ! obs]v]4 ,x w !re=e be se5 t ^! two p>allel horizons are "s #djjj miles ap>t1 ! semi-diamet] ( ! e>?2 b ?is di/ance :5 project$ on ! cele/ial sph]e becomes insignificant :5 comp>$ ) ! inf9ite di/ance ( ?is sph]e f ! e>?1 & ! rational & s5sible horizons %r9k into a s+le l9e s f> z we c p]ceive4 ,:ile ?is /atem5t is true :5 deal+ ) ! />s1 x ne$s modify+ :5 deal+ ) ! sun & moon1 & 9 v accurate obs]vations ( planets1 z _! di/ances are insuffici5t to elim9ate ! angle =m$ betwe5 ! l9e f ! body to ! c5t] ( ! e>?1 & t f ! body to ! obs]v]4 ,?is is all[$ = :5 obs]v+ ^! bodies by apply+ ! correction ( p>allax to ! obs]v$ altitude4 ,! visible horizon is ! b\nd>y se5 betwe5 ! sea & sky4 ,if ! obs]v]'s eye 7 at ! level ( ! sea1 8 visible horizon w\ld co9cide ) ! s5sible horizon1 def9$ above2 b ! elevation above ! surface f :i* sights are tak5 causes ! l9e ( vision1 tang5t to ! sea1 to be depress$ bel[ ! plane ( ! s5sible horizon mak+ an angle ) x call$ ! dip ( ! horizon4 ,9 practice all altitudes ( heav5ly bodies tak5 f a vessel are measur$ to ! visible horizon & correct$ = ! dip to r$uce !m to ! s5sible horizon1 !n aga9 correct$ = p>allax to obta9 ! true altitude ( ! body above ! rational horizon2 or :at is ! same ?+1 ! altitude z obs]v$ at ! c5t] ( ! e>?4 ,f ! z5i?1 an inf9ite numb] ( great circles1 kn[n z v]tical circles1 sweep ar\nd ! cele/ial sph]e1 cutt+ ! horizon at "r angles & pass+ ?r\gh ! nadir4 ,! "o :i* cuts ! nor? & s\? po9ts is call$ ! cele/ial m]idian1 & is evid5tly a projection ( ! t]re/rial m]idian4 ,! v]tical circle pass+ ?r\gh ! ea/ & we/ po9ts is call$ ! prime v]tical1 & has a di/9ction above o!r v]tical circles by virtue ( its be+ ! mo/ favorable position = a body 9 obs]vations = longitude4 ,! heav5s are fur!r swept by an inf9ite numb] ( p>allels ( altitude :i* are1 z _! "n implies1 p>allel to ! horizon4 ,! azimu? ( a body is its angul> di/ance f ! nor? or s\? po9ts ( ! horizon1 det]m9$ by ! angle =m$ at ! z5i?1 or by ! arc ( ! horizon betwe5 ! m]idian ( ! obs]v] & ! v]tical circle pass+ ?r\gh ! body4 ,amplitude is ! angle at ! z5i? =m$ by ! prime v]tical & ! v]tical circle pass+ ?r\gh ! body or x is ! angul> di/ance f ! ea/ or we/ po9ts1 measur$ on ! horizon1 & is measur$ simil>ly to ! azimu?4 ,! sy/em ( lay+ (f ! heav5s j describ$ is well en\gh = ! mom5t>y locat+ ( a body1 :i* is a v important feature 9 navigation1 b = "s purposes a m /able po9t ?an ! z5i?1 :i* on %ipbo>d is ev] *ang+1 is ne$$1 f :i* to =m a sy/em t is con/ant ! _w ov]4 ,to meet ?is dem& we take ! po9t 9 ! sky p5etrat$ by ! prolongation ( ! e>?'s nor!rn axis--! cele/ial pole--& f ?is po9t m]idians & p>allels are develop$ ^u ! cele/ial sph]e z has be5 done on ! e>?4 ,9 fact1 x is z ?\gh ^! t]re/rial coord9ates 7 project$ to ! heav5s :]e !y hold ! same relative positions z ^u ! e>?4 ,! nor!rn cele/ial pole is 9 ! z5i? at our nor? pole4 ,! same is true ( ! s\? pole4 ,! cele/ial equator1 or equ9octial1 is a great circle1 :i* is midway betwe5 ! poles & ev]y:]e #ij f !m4 ,x m>ks ! t]m9ation ( ! plane ( our equator ext5d$ to ! cele/ial sph]e1 or 9 o!r words1 x is always directly ov] our equator4 ,! p>allels ( ! cele/ial sph]e evolv$ by ?is sy/em1 correspond+ to ^? ( latitude ^u ! e>? are call$ p>allels ( decl9ation1 :ile ! cele/ial m]idians hav+ z _! po9t ( orig9 ! prolongation ( ! e>?'s axis1 are kn[n z h\r circles4 ,! p>ticul> h\r circle pass+ ?r\gh ! z5i? is "o & ! same ) ! cele/ial m]idian4 ,x w be se5 t ?is circle mu/ pass ?r\gh ! z5i?1 nadir & ! poles4 ,! angle =m$ at ! pole by ! h\r circle pass+ ?r\gh a body & a local m]idian is ! h\r angle ( t body1 & is measur$ we/w>d ?r\gh #bd h\rs1 al?\gh ,a4,m4 h\r angles ( ! sun are reckon$ ea/w>d ?r\gh #ab h\rs4 ,at ! nor? pole :]e ! z5i? is id5tical ) ! cele/ial pole1 ! v]tical circles1 p>allels ( altitude & rational horizon are co9cid5t ) ! h\r circles1 p>allels ( decl9ation & ! equator1 respectively2 b dep>t+ f ?is po9t !y =m angles ) ea* o!r correspond+ to ! degrees ( latitude f ! pole2 at ! equator ! angle rea*es #ij4 ,! sy/em ( circles describ$ above is by f> ! mo/ ext5sively us$1 & positions det]m9$ by its coord9ates are comp>atively con/ant1 b !re is /ill a ?ird sy/em ( circles :i* 0 us$ & h&$ d[n to u by ! anci5ts4 ,9 ! place ( ! cele/ial equator1 a simil> great circle is us$1 kn[n z ! ecliptic4 ,?is circle is det]m9$ by ! ext5sion ( ! plane ( ! e>?'s orbit to ! cele/ial sph]e4 ,! poles ( ! ecliptic ev]y:]e #ij f ?is circle are ! po9ts f :i* m]idians dep>t z ^u ! e>?4 ,! prime m]idian ( ?is sy/em passes ?r\gh ! int]section ( ! cele/ial equator1 & ! ecliptic--! v]nal equ9ox or ,fir/ ,po9t ( ,aries4 ,cele/ial latitude & longitude are ! coord9ates us$ ) ?is sy/em1 b navigators univ]sally pref] to use ! well-kn[n decl9ation & "r asc5sion4 ,h5ce ! pa? ( usefulness ( ! =m] seldom leads beyond ! obs]vatories4 ,,*apt] ,,iii ,decl9ation & ,"r ,asc5sion ,ow+ to ! important place t decl9ation holds 9 nautical a/ronomy1 a detail$ explanation w appropriately foll[ closely 9 ! wake ( ! prec$+ rem>ks4 ,x mu/ be made cle>1 be=e gett+ "u way1 t decl9ation is ! di/ance1 9 degrees1 m9utes & seconds1 ( a body nor? 77 or s\? 7-7 ( ! cele/ial equator measur$ on ! h\r circle pass+ ?r\gh ! body4 ,?is di/ance is id5tical ) ! latitude ( ! place 9 ! z5i? ( :i* ! body happ5s to be4 ,:at decl9ation is to a body 9 ! heav5s1 latitude is to ! place on ! e>? directly b5ea? x4 ,! decl9ation ( fix$ />s *anges v sl[ly f mon? to mon?1 b ! planets me&] ab\t on ! cele/ial sph]e 9 a way t is liable to puzzle anyone o!r ?an an a/ronom]4 ,?is elem5t1 h[ev]1 is work$ out 9 ! obs]vatory & giv5 9 ! nautical almanac 9 a way t relieves ! navigator ( worry conc]n+ ! complex movem5ts ( ^! latt] bodies4 ,! same may be said ( ! moon1 b ! subject w be treat$1 some:at sup]ficially ?\gh suffici5tly = ! ne$s & desires ( ! practical m>9]1 9 a special talk on ! moon4 ,?is elim9ates all ! cele/ial bodies except ! sun1 ! mo/ important2 & = ?is reason ! facts relative to its decl9ation w be consid]$ at "s l5g?4 ,z has already be5 /at$1 ! sun is /ation>y1 b our movem5ts ar\nd x to ! "r causes x to appe> to move to ! left2 precisely z y see1 :5 "u way1 an an*or$ vessel's ma/s move to ! left along ! l& beh9d h]1 :ile y move on to ! "r4 ,we h no l&m>ks beh9d ! sun by :i* to obs]ve 8 app>5t movem5ts1 s 9 lieu ( su* ranges1 we resort to ! fix$ />s1 :i* s]ve z excell5t m>ks to get a be>+ on ,old ,sol & keep tab on him z he moves ea/w>d among !m4 ,?is movem5t mu/ 9 no way be conf\nd$ ) 8 app>5t daily motion we/w>d4 ,z an illu/ration1 we may see ,orion--a famili> fri5d--sw++ high 9 ! we/]n sky 9 ! e>ly ev5+2 "s weeks lat] he is rid+ l[1 & yet a little lat] /ill1 he is swall[$ up 9 ! brilliancy ( ! sett+ sun4 ,9 o!r words1 ! sun & ,orion h approa*$ & pass$ ea* o!r4 ,we "k ,orion does n move1 = he is compos$ ( fix$ />s1 & ?is seem+ we/w>d movem5t ( 8 is 9 reality ! app>5t ea/w>d m>*+ ( ! sun1 :i* is due to ! e>?'s movem5t ( revolution4 ,! sun 9 ?is app>5t movem5t ea/w>d foll[s a c\rse at a rate equal to t ( ! e>?1 along a great circle ( ! cele/ial sph]e call$ ! ecliptic1 a circle t plays an important "p 9 ! explanation ( decl9ation1 p>ticul>ly t ( ! sun4 ,! ecliptic is m>k$ by ! ext5sion ( ! e>?'s orbit to ! cele/ial sph]e4 ,a few m words conc]n+ great circles w be introduc$ "h1 & ! foll[+ /atem5ts1 :ile !y apply to great circles 9 g5]al1 especially fit ! relation%ip ( ! equ9octial or cele/ial equator to ! ecliptic4 ,^! two great circles cut ea* o!r at an angle ( #bc #bh4 ,great circles always bisect ea* o!r1 & h5ce any two great circles ( ! cele/ial sph]e1 reg>dless ( ! angle !y may take ) ! cele/ial equator1 mu/ int]sect ea* o!r at exactly opposite po9ts1 #ahj ap>t4 ,:at is true 9 ?is reg>d ( ! cele/ial sph]e is equally true ( ! great circles ( ! e>?4 ,a v]tex ( a great circle is ! po9t :i* dep>ts ! greate/ di/ance f ! equator--! highe/ po9t ( ! circle rea*$ 9 decl9ation4 ,!re are two v]tices #ahj ap>t ) ! two po9ts ( int]section #ij 9 ei!r direction4 ,! decl9ation or latitude ( ei!r v]tex is equal to ! angle at :i* ! circles int]sect ea* o!r4 ,! int]sections are call$ ! equ9oxes1 & x may be well to say "h t ! ^w equ9ox has sev]al mean+s 9 navigation1 (t5 r5d]+ x necess>y to judge by ! text :i* is int5d$4 ,! v]nal equ9ox1 = in/ance1 ref]s to a c]ta9 "t ( ye>--,m>* #ba/4 ,! sun is t day directly ov]head at ! int]section ( ! equator & ! t]re/rial ecliptic & ?is po9t is sometimes call$ ! v]nal equ9ox4 ,aga91 ! sun at ! same "t occupies a po9t on ! heav5s also kn[n z ! v]nal equ9ox1 :i* is at ! int]section ( ! cele/ial equator & ! ecliptic4 ,! po9t 9 ! orbit occupi$ by ! e>? at ?is "t is also spok5 ( z ! v]nal equ9ox4 ,! read] is n[ ask$ to ar\se 8 imag9ation & if possible to conceive himself a pass5g] 9 an a]oplane equipp$ ) "s rem>kable p[] capable ( c>ry+ him to a position 9 space1 above1 yet a little outside1 ! e>?'s orbit1 ne> ! ,p]ihelion1 & !re to heave to & view a:ile an a/ronomical picture4 ,spread out be=e 8 unre/rict$ vision w be ! e>?1 its orbit1 & ! sun4 ,x is to be hop$ t ! imag9ation ( ! read] is /ill suffici5tly supple to suppose ! plane ( ! orbit to be ! surface ( an inf9ite ocean /ret*+ away beyond human conception ( di/ance & 8break+0 aga9/ ! cele/ial sph]e2 ! 8surfl9e0 !re m>ks ! ecliptic2 ! 8ocean's0 surface repres5t+ ! great plane ( ! ecliptic4 ,! sun w be se5 z if at an*or 9 8 prop] place )9 ! orbit4 ,! e>? is 8und]way10 half subm]g$1 & li/$ #bc #bh t[>d our po9t ( vantage4 ,?is incl9ation1 or direction ( ! axis1 is 9 a g5]al way t[>d ! p]ihelion1 & )9 a few degrees ( be+ p>allel ) ! long diamet] ( ! orbit4 ,! e>? ma9ta9s ?is ne>ly p>allel position ( its axis ) ! long diamet] ?r\gh\t ! p]iod ( its revolution2 a fact ( importance to rememb]4 ,x w be readily se5 t dur+ ! encircl+ ( ! sun !re mu/ be "o position :]e ! nor!rn axis is incl9$ directly t[>d t body1 ano!r opposite :]e x is head$ away f him1 & two positions midway :]e ! be>+ ( ! axis 7project$ on ! plane ( ! orbit7 is at "r angles to ! be>+ ( ! sun f ! e>?2 ano!r feature to be 8salt$ d[n0 9 ! memory4 ,if ! e>? revolv$ on an ev5 keel1 ! equator & ! 8wat]l9e0 w\ld be co9cid5t1 b =tunately ?is is n ! case1 & ow+ to ! incl9ation ( ! axis ano!r great circle is def9$ by ! 8wat]l9e10 call$ ! t]re/rial ecliptic1 be+ directly b5ea? its cele/ial namesake4 ,! incl9ation ( ! nor!rn pole be+ 9 a g5]al way t[>d ! p]ihelion1 correspond+ly depresses or 8subm]ges0 t half ( ! equator bel[ ! plane ( ! ecliptic1 repres5t$ by ! 8wat] surface10 & at ! same "t ! opposite side rolls ! equator above x4 ,at two po9ts 7! equ9oxes7 on opposite sides ( ! e>?1 & at "r angles to ! direction ( its incl9ation1 ! equator & t]re/rial ecliptic cross ea* o!r at ! 8wat]'s edge40 ,! sun is always exactly ov]head = t po9t ( ! e>? :i* is ne>e/ to x4 ,?is is an ess5tial fact to rememb] 9 navigation4 ,be>+ 9 m9d t ! sun is /ation>y & ignor+ = a "t ! rotation ( ! e>?1 ea* advance 9 its orbit br+s ab\t a *ange ( be>+ ( ! sun & a new position becomes ! ne>e/ po9t1 & !reby directly b5ea? ! sun4 ,! con/ant *ang+ ( ! sun's be>+ cont9ues ?r\gh\t ! ye>1 or "o revolution1 & a circle ( ^! ov]head positions is m>k$ ^u ! e>?1 :i* is co9cid5t ) ! t]re/rial ecliptic--! vision>y 8wat]l9e40 ,x is obvi\s t ! v]tical rays ( ! sun mu/ app>5tly foll[ ?is l9e1 = x c only be ov]head = places t are 9 ! same plane1 & ?is aga9 is ! level ( ! 8ocean40 ,?is circle ( ov]head positions project$ on ! cele/ial sph]e m>ks ! ecliptic--! 8m>g90 ( ! inf9ite ocean1 & ! pa? t ! sun seems to foll[ ea/w>d among ! />s4 ,! above p>agraphs %[ u t ! sun 9 foll[+ ?is l9e ar\nd ! e>? crosses ! equator twice1 & twice he atta9s a di/ance ( #bc #bh f x1 & s mu/ be on ! equator twice & rea* a decl9ation ( #bc #bh nor? & #bc #bh s\? 9 ! c\rse ( "o ye>4 ,return+ to our imag9>y illu/ration1 we w n[ foll[ ! p]egr9ations ( ! e>? = a ye> & note ! effect ( its incl9ation 9 ! diff]5t p>ts ( ! orbit ^u ! decl9ation ( ! sun4 ,x w be assum$ t x is ! #ba/ ( ,m>* & f our airy position we see ! e>? away on our "r ne>ly #ij f ! ,p]ihelion4 ,z ?is is ! v]nal equ9ox1 !re are a numb] ( int]e/+ po9ts to be consid]$3 ,! direction ( ! e>?'s axis1 project$ on ! plane ( ! orbit1 is at "r angles to ! be>+ ( ! sun f ! e>?2 ! sun is directly ov] ! int]section ( ! equator & t]re/rial ecliptic1 & be+ ov]head = ?is po9t on ! equator1 ! decl9ation mu/ be #j4 ,moreov]1 a l9e drawn f ?is int]section1 or t]re/rial v]nal equ9ox1 ?r\gh ! c5t] ( ! sun & ext5d$ to ! cele/ial sph]e w\ld /rike ! correspond+ int]section ( ! ecliptic & ! equ9octial or cele/ial equator--! cele/ial v]nal equ9ox4 ,! arrival ( ! e>? at ?is position is ! signal ( spr+ = ! nor!rn hemisph]e1 likewise x ann\nces ! adv5t ( autumn to our s\!rn neighbors bel[ ! 8,l9e40 ,! sun ?is day rises 9 ! ea/ 7approximately7 & pass+ ?r\gh ! z5i?1 sets 9 ! we/ = ^? liv+ on ! equator4 ,! explor] at ! nor? pole is *e]$ by ! fir/ light z ! sun appe>s 9 ! horizon1 :ile ! s\? pole becomes en%r\d$ 9 ! long ,ant>ctic night4 ,)\t l+]+ = c]emonies ov] ! *ange ( seasons1 ! e>? cont9ues /eadily on its way t[>d ! aphelion2 ! sun's v]tical rays leave ! int]section ( ! equator & ! t]re/rial ecliptic1 & foll[ along ! latt]1 ?us wid5+ its di/ance f ! equator z ! e>? proce$s4 ,z ! ecliptic 9 ?is half ( ! orbit is above1 or nor?1 ( ! equator ! =m] is 9 nor? latitude & ! sun1 foll[+ along x1 is !reby also 9 nor? decl9ation4 ,a l9e f any place hav+ ! v]tical rays1 ?r\gh ! sun to ! cele/ial sph]e1 always t]m9ates on ! cele/ial ecliptic1 all be+ 9 ! same plane1 & %[s ! correspond+ cele/ial position ( ! sun on x4 ,its decl9ation di/ance f ! cele/ial equator1 9 degrees1 m9utes & seconds1 is id5tical ) t ( ! place on ! e>? directly b5ea? x relative to our equator4 ,s by %[+ ! c\rse ( ! sun's ov]head positions on ! e>? its cele/ial positions are1 at ! same "t1 indicat$4 ,! ov]head position ( ! sun on ! t]re/rial ecliptic gradually dep>ts f ! equator culm9at+ ab\t ,june #ba/1 ! summ] sol/ice1 9 a decl9ation ( #bc #bh at a po9t ne> ! aphelion 9 ! orbit1 #ij 7approximately7 f ! equ9ox4 ,! positions 9 ! orbit ( ! summ] & w9t] sol/ices are rea*$ by ! e>? sev]al days be=e ! po9ts ( ! aphelion & p]ihelion4 ,^! respective positions w\ld be 9 conjunction 7 x n = a sl[ & rem>kable motion ( ! e>?'s axis be=e spok5 (1 & lat] to be describ$1 call$ ! precession ( ! equ9oxes4 ,! summ] sol/ice is ! great half-way po9t ( ! e>?'s annual circumnavigation ( ! sun2 x is a matt] ( mom5t all ov] ! _w1 & ano!r great *ange ( seasons is at h&4 ,! sun is ov]head = places along ! p>allel ( #bc #bh ,n4 & be>s nor? #bc #bh f ! z5i? at noon f places on ! equator4 ,at ! nor? pole1 s9ce its appe>ance on ! horizon on ,m>* #ba/1 ! sun has m\nt$ to an altitude ( #bc #bh & to ne>ly #fg at places on ! ,arctic circle4 ,! e>?'s nor!rn axis is1 9 ?is position1 incl9$ #bc #bh directly t[>d ! sun1 :i* p\rs its rays cont9u\sly ^u ! nor!rn regions1 un9t]rupt$ ev5 by ! e>?'s daily rotation4 ,x is on ?is day t ! :ole ,arctic zone enjoys ! full glory ( ! midnight sun4 ,! e>?'s cont9u\s movem5t ( revolution does n all[ a delay ( ?is favorable season 9 nor!rn latitudes1 b cont9ues to make ! sun's v]tical rays foll[ ! t]re/rial ecliptic z be=e on its way t[>d ! int]section ) ! equator #ij away4 ,on ?is leg ( ! j\rney1 ! sun is travel+ on ! upp] "o ( two conv]g+ l9es & !reby gradually less5+ its di/ance f ! o!r--! equator--or1 9 o!r words1 r$uc+ its decl9ation4 ,?is cont9ues until ,septemb] #ba/ :5 ! autumnal equ9ox is rea*$ & ! sun's decl9ation becomes #j4 ,! sun n[ be+ ov]head at ! int]section ( ! equator & ! t]re/rial ecliptic1 is on ! opposite side ( ! e>? f ! int]section ( ,m>* #ba/4 ,9 fact ! conditions are simil>1 b n[ ! e>? is on ! opposite side ( ! sun1 & ! *ange ( seasons is ! entrance ( spr+ = ! dwell]s 9 s\!rn latitudes4 ,! sun has dropp$ l[] & l[] 9 ! sky at ! nor? pole s9ce ,june1 until on ?is day x is 9 ! horizon & x is "t = ! ,esquimos to seek _! igloos & prep>e to hib]nate dur+ ! long ,arctic night n[ u%]$ 94 ,! sun%9e at ! "t ( ! equ9oxes is equally di/ribut$ ov] ! nor!rn & s\!rn zones1 & ! z5i? di/ance ( ! sun at noon at any place is1 !oretically1 equal to ! latitude ( ! place 7except a small error due to *ange ( decl9ation accumulat$ subsequ5t1 or previ\s1 to ! in/ant ( ! equ9ox74 ,! conditions dur+ ! next six mon?s are rev]s$ z ! e>? proce$s into t half ( ! orbit conta9+ ! p]ihelion4 ,n[ ! sun foll[+ ! t]re/rial ecliptic ent]s s\!rn latitudes or s\? decl9ation1 = 9 ?is "p ( ! orbit ! equator is above 7or nor?7 ! plane ( ! ecliptic4 ,! sun's div]g+ c\rse f ! equator leads x f>!r & f>!r s\?w>d until on or ab\t ,decemb] #ba/ x arrives at ! w9t] sol/ice ) a culm9ation ( #bc #bh s\? decl9ation4 ,at ?is po9t ! e>? is b a few degrees f ! p]ihelion z x 0 f ! aphelion at ! summ] sol/ice4 ,! e>?'s nor? pole is n[ incl9$ directly away f ! sun & its rays h entirely =sak5 ! ,arctic = ! ,ant>ctic zone2 not)/&+ ! e>?'s daily rotation1 :i* br+s alt]nat+ light & d>kness to ! great] "p ( ! _w1 ! nor!rn pol> regions are 9 a cont9u\s %ad[1 & no sunlight rea*es ^! remote p>ts4 ,at ?is "t ( ! ye> ! nor!rn hemisph]e above ! tropic ( ,canc]1 is 9 an unfavorable position relative to ! sun1 & z a result places situat$ on p>allels less remote ?an ! ,arctic are hav+ long nights & %ort days 9 proportion to _! latitude nor?4 ,on ! o!r h&1 9 ! s\!rn hemisph]e ! days are long] & ! nights %ort]1 z ! s\!rn latitude increases until at ! ,ant>ctic circle night disappe>s & ! sun%9e is un9t]rupt$4 ,x is se5 t ?is is an exact rev]sal ( ! conditions at ! summ] sol/ice4 ,! e>? ent]s ! la/ quadrant ( ! great ellipse ( its orbit1 ! sun n[ approa*es ! equator z ! e>? ne>s ! v]nal equ9ox4 ,! s\? decl9ation dim9i%es until on ,m>* #ba/ x becomes #j & ! e>? has complet$ its revolution4 ,we w n[ g on ano!r tack & in/ead ( consid]+ only ! effects ( decl9ation due to ! e>?'s revolution1 w assume t ! e>? has be5 halt$ 9 its onw>d c\rse ( revolution & is mak+ its daily rotation 9 ! same position4 ,! e>? turn+ f we/ to ea/ causes ! sun to appe> to proce$ f ea/ to we/ 9 its diurnal motion4 ,ea* rotation1 requir+ #bd h\rs1 m>ks ^u ! e>? a circle ( ov]head positions p>allel to ! equator & h5ce )\t *ange ( decl9ation4 ,! result ( su* a rem>kable condition w\ld be1 no *ange ( seasons & no *ange 9 ! l5g? ( ! days & nights4 ,9 reality1 h[ev]1 we are sav$ f su* monotony1 = bo? ! motion ( rotation & revolution ( ! e>? are act+ toge!r & giv+ a comp\nd effect on ! app>5t movem5ts ( ! sun4 ,?is alt]s ! daily circles j m5tion$ to a f9e spiral ( ov]head positions1 ev] *ang+ 9 decl9ation4 ,! daily diff]5ce ( ! sun's decl9ation %[n 9 ! ,nautical ,almanac is equival5t to ! di/ance betwe5 two ?reads ( ?is spiral4 ,! *ange ( decl9ation is mo/ directly se5 & felt 9 ! pol> regions1 :]e ! activities ( ! d5iz5s are mo/ly limit$ to ! favorable phases ( ?is *ange4 ,at ! nor? pole1 aft] ! sun has appe>$ above ! horizon1 ?is spiral ( decl9ation c be cont9u\sly foll[$4 ,! sextant w disclose a con/ant increase 9 altitude z ! sun circles r\nd & r\nd ! sky1 w9d+ itself up & f9ally culm9at+ at #bc #bh4 ,! process is !n imm$iately rev]s$4 ,! />s "h make daily circles ( equal altitudes z _! *ange ( decl9ation is insignificant2 b ! circles ( ! planets & ! moon are conv]t$ into spirals1 ! f95ess ( :i* is 9 proportion to ! rate ( _! *ange ( decl9ation4 ,! fact t ! sun rea*es an altitude ( #bc #bh at ! pole at ! summ] sol/ice ) its decl9ation ( a l am\nt & t on ,m>* #ba/1 :5 ! sun is 9 ! horizon ) ! altitude #j1 x is directly ov] ! equator ) #j decl9ation1 %[s t at ?is place 7! pole7 ! altitude is equal to ! decl9ation4 ,%\ld an explor] travel s\?w>d #a1 8 sextant w\ld %[ an altitude #a great] ?an at ! pole1 yet mov+ ab\t does n affect ! decl9ation at a giv5 "t4 ,x foll[s by tak+ 8 altitude at noon ! explor] 9 ! pol> regions may readily le>n 8 di/ance f ! pole by subtract+ ! decl9ation 9 ! ,nautical ,almanac f 8 sextant read+4 ,x may n g5]ally be kn[n t ! s\!rn summ] is %ort] ?an ! summ] ( ! nor!rn hemisph]e1 b su* is ! case by approximately eight days4 ,! reason ( ?is inequality lies 9 ! fact t ! sun is ne>] "o end ( ! orbital ellipse1 & ! %ort diamet] pass+ ?r\gh ?is body divides ! orbit into unequal p>ts4 ,! small] "p be+ t travel$ by ! e>? dur+ ! s\!rn summ]4 ,fur!rmore ! ne>] proximity ( ! sun causes an accel]at$ motion :i* fur!r t5ds to less5 ! "t sp5t by ! e>? 9 ?is "p ( ! orbit4 ,,"r ,,asc5sion ,decl9ation & "r asc5sion be+ us$ toge!r z coord9ates1 we w n sep>ate !m4 ,x w be rememb]$ t ! equator & ! t]re/rial ecliptic cross ea* o!r on opposite sides ( ! e>?2 t on or ab\t ,m>* #ba1 ! sun is ov]head at ! int]section t is ! v]nal equ9ox4 ,n[ if at ?is int]section on ?is day a plumb-l9e 7 c>ri$ upw>d1 x w\ld at l5g? rea* ! sun1 & cont9u$ to inf9ity & project$ on ! cele/ial sph]e w\ld locate a po9t call$ ! cele/ial v]nal equ9ox1 kn[n by _m z ! ,fir/ ,po9t ( ,aries4 ,?is po9t is "o ( ! mo/ important cele/ial 8l&m>ks0 us$ 9 a/ronomy & navigation1 b1 un=tunately1 no heav5ly body m>ks its place4 ,h[ev]1 z its relative position among ! neighbor+ />s is well kn[n1 its exact location is easily asc]ta9$4 ,! h\r circle :i* passes ?r\gh ?is po9t is kn[n z ! equ9octial colure1 & may be consid]$ ! prime m]idian ( ! heav5s1 = f x is measur$ ! "r asc5sion ( all bodies4 ,"r asc5sion ( a body is ! angle at ! cele/ial pole betwe5 ?is m]idian ( ref]5ce & ! h\r circle pass+ ?r\gh ! body4 ,x is always measur$ ea/w>d ?r\gh #bd h\rs ( sid]eal "t 7#cfj74 ,! angle is measur$ by ! arc int]cept$ on ! cele/ial equator4 ,= example1 a /> #ae ea/ ( ! equ9octial colure has a "r asc5sion ( #a h\r or #ae1 b1 if ! /> is #ae we/1 its "r asc5sion is #bc h\rs or #cde4 ,! positions ( heav5ly bodies are def9$ by "r asc5sion & decl9ation exactly z positions ^u ! e>? are express$ by longitude & latitude1 "r asc5sion correspond+ to longitude & decl9ation to latitude4 ,9 ! discussion ( ,"t1 to foll[1 m facts conc]n+ "r asc5sion w be f\nd4 ,,precession ,,( ,,! ,,equ9oxes ,a comp>ison ( ! pres5t positions ( ! fix$ />s ) _! places z record$ 9 anci5t times %[s a great discrepancy4 ,! cele/ial latitudes1 :i* 7 reckon$ f ! ecliptic1 %[ no appreciable *ange2 b 9 ! decl9ations & "r asc5sions !re is a great dep>ture f ! old positions4 ,! error ( "r asc5sion 0 f\nd by ! old ,greek a/ronom]1 ,hipp>*us1 to appe> z a uni=m ea/w>d movem5t ( all ! />s1 :i* l$ him to reason t1 in/ead ( ! />s !mselves *ang+1 _! po9t ( ref]5ce 0 mov+ we/w>d1 ?us l5g!n+ all "r asc5sions4 ,! fam\s a/ronom] aft] fur!r reason+ decid$ t ! position ( ! cele/ial pole 0 *ang+1 9 fact t ! l9e ( ! e>?'s axis 0 describ+ a circle on ! heav5s1 :i* 0 left-h&$ or aga9/ ! h&s ( a wat* z view$ f ! nor? pole ( ! e>?4 ,?is movem5t 0 f\nd to be extremely sl[1 requir+ #be1hjj ye>s to complete ! circle :i* has z its radius ! am\nt ( ! incl9ation ( ! e>?'s axis--#bc #bh4 ,if a mat* is put ?r\gh a piece ( c>dbo>d ab\t ! size ( a half doll> to ! di/ance ( in*1 & spun1 ! motion ( ! c>dbo>d j z x /agg]s ?r\gh loss ( spe$1 gives "s idea1 al?\gh exagg]at$1 ( ! precession movem5t ( ! plane ( ! equator1 :i* is ( c\rse inf9itely sl[]4 ,! movem5t ( ! top ( ! mat* is a semblance ( ! correspond+ motion ( ! vani%+ po9t ( ! axis on ! cele/ial sph]e4 ,! e>?1 z already expla9$1 po9ts its axis at practically ! same spot 9 ! heav5s ?r\gh\t ! ye>1 & if x 7 n = ?is annual precession ( #ej x w\ld = all int5ts & purposes hold a p]man5t direction4 ,ab\t ,decemb] #ba1 ! w9t] sol/ice1 :ile ! e>? is /ill "s degrees f ! p]ihelion1 its nor!rn axis1 is incl9$ directly away f ! sun4 ,ea* ye> ?is di/ance f ! p]ihelion is becom+ great]1 wid5+ ?is angle betwe5 ! direction ( ! axis1 project$ on ! plane ( ! orbit1 & ! major diamet] ( ! orbit1 until 9 "t ! nor? pole w be head$ directly away f ! sun 9 t "p ( ! orbit :i* ! e>? n[ occupies 9 ,septemb]1 & s on4 ,illu/ration3 ,?is diagram %[s ! successive positions ( ! e>? at ! ,v]nal ,equ9ox 7,m>* #ba/7 due to ! revolution ( ! axis & ! consequ5t we/w>d movem5t ( ! ,fir/ ,po9t ( ,aries4 ,,fig4 #a4 ,9 ! ye> ,a4,d4 #abej ! w9t] sol/ice occurr$ at p]ihelion & 9 ! ye> #fdjj ,a4,d4 ! v]nal equ9ox w occur at ?is po9t ( ! orbit4 ,t is1 ! axis ( ! e>? 0 incl9$ directly away f ! sun at p]ihelion 9 ! =m] ye> b 9 ! latt] ye> ! incl9ation w h *ang$ ab\t #ij backw>d aga9/ ! e>?'s c\rse ab\t ! sun1 & x w be ! beg9n+ ( spr+ 7! v]nal equ9ox7 :5 ! e>? is at p]ihelion in/ead ( ! fir/ ( w9t] z 9 #abej ,a4,d4 ,s9ce #abej ,a4,d4 ! incl9ation has *ang$ an equival5t ( ab\t #aa days = n[ ! e>? is at p]ihelion ab\t ,janu>y #a/1 & ! sol/ice occurr+ ab\t ,decemb] #ba/1 %[s ! pres5t relative situation4 ,9 o!r words1 ! v]nal equ9ox is slipp+ back 9 ! orbit t[>ds ! p]ihelion1 & z ! sol/ices ma9ta9 _! positions at #ij f ! equ9oxes !y mu/ likewise be 8slipp+ a cog0 ea* ye>4 ,! v]nal equ9ox 0 situat$ _m c5turies ago 9 ! fir/ "p ( ! con/ellation ( ,aries1 & 0 kn[n z ! ,fir/ ,po9t ( ,aries1 b ow+ to ! movem5t ( precession x has dropp$ back or we/w>d 7z we face our s\!rn horizon7 #ej a ye> until x has left t con/ellation entirely & is n[ ab\t leav+ ! con/ellation ( ,pisces1 "s #cj f ! position us$ by ,hipp>*us 9 8 calculations4 ,! majority ( navigators /ill call ?is po9t ( ! cele/ial v]nal equ9ox ! ,fir/ ,po9t ( ,aries4 ,hold+ ^! facts 9 m9d1 x may be cle> t z ! e>? approa*es t "p ( ! orbit :]e ! v]nal equ9ox occurs x has turn$ its pole1 & correspond+ly po9ts on ! equator1 #ej to ! "r or we/ dur+ ! ye>2 ?us caus+ ! po9t ( ! t]re/rial equ9ox to meet 7or come "u7 ! sun t mu* soon]4 ,9 o!r words1 ref]r+ to ! effect z se5 on ! heav5s1 ! cele/ial equ9ox 0 advanc$ to ! we/w>d t mu* to meet ! sun 9 its ea/w>d movem5t among ! />s & w become ! ne>e/ po9t to ! sun1 #ej be=e ! position ( ! equ9ox ( la/ ye>4 ,z ! po9ts 9 ! orbit :]e ! v]nal equ9ox occurs ye> by ye> works back t[>d ! p]ihelion1 ! range l9e ?r\gh ! sun to ! heav5s beyond mu/ ea* ye> correspond+ly edge its way we/w>d along ! cele/ial ecliptic ?r\gh diff]5t con/ellations4 ,?is is :at is kn[n z ! precession ( ! equ9oxes4 ,! c\rse ( ! cele/ial pole 9 ! heav5s is %[n by a circle drawn ab\t ! pole ( ! ecliptic us+ #bc #bh z a radius4 ,?is pa? w pass #a f our pole /> & ?is position m>ks ! pres5t t]m9ation ( our ext5d$ axis2 half way ar\nd ! circle x passes ! fir/ magnitude /> ,vega close abo>d1 ?us mak+ ?is ! future pole /> "s #ab1jjj ye>s h5ce4 ,if !re be su* creatures z navigators 9 ^? f>-away days1 latitude by ,vega w no d\bt be a popul> sight among !m4 ,! cause ( ?is rem>kable movem5t ( ! e>? is due to ! fact t ! e>? is n a true sph]e1 & ! influ5ce ( ! sun is n ex]t$ equally ^u its mass4 ,its flatt5+ at ! poles is att5d$ by a correspond+ bulg+ along ! equatorial belt4 ,:5 ! e>? is 9 ! vic9ity ( ! p]ihelion1 lean+ away f ! sun1 ! half ( ?is r+ ( extra matt] on ! side t[>ds ! sun is above ! plane ( ! ecliptic or orbit4 ,! t5d5cy ( ! add$ attraction ex]t$ ^u x1 is to draw ! e>? to an upright position1 or 9 o!r words1 at ?is "t ! sun is pull+ /rong] on ! nor!rn or upp] side ?an on ! l[]4 ,aga91 :5 ne> ! aphelion & summ] sol/ice1 lean+ t[>ds ! sun1 t "p ( ! r+ ( extra matt] on ! side t[>ds ! sun is bel[ ! level ( ! orbit1 & ! attraction is aga9 t5d+ z be=e to pull ! e>? upright4 ,at ! equ9oxes !re is an equal am\nt ( ?is extra matt] above & bel[ ! plane ( ! orbit ev5ly di/ribut+ ! attraction4 ,! effect ( ?is influ5ce w\ld 9 "t br+ ! e>?'s equator & ! plane ( ! ecliptic into co9cid5ce & ! e>?'s pole w\ld be directly b5ea? ! pole ( ! ecliptic1 7 x n = its rotation4 ,! two =ces act+ ^u ! e>? result 9 ! sl[ revolution ( ! axis4 ,! exact effect ( ^! =ces is r complex b x is a demon/ration ( ! pr9ciple ( ! gyroscope4 ,! movem5t ( ! axis is affect$ v slightly by o!r influ5ces ?an t ( ! sun1 ! mo/ notable ( :i* is ! moon1 ^: mon?ly revolutions ar\nd ! e>? produce a simil> influ5ce 9 ! bulg+ mass )9 ! tropics1 b z its revolutions are s rapid1 x has b a slight effect on ! precession movem5t ( ! e>?4 ,x is suffici5t1 h[ev]1 to cause ! ext5d$ axis to nod slightly & make a wav$ circle ( precession on ! heav5s4 ,?is is call$ 8,nutation10 f ! ,lat9 ^w nuto1 mean+ to nod4 ,,*apt] ,,iv ,"t ,a ?or\gh und]/&+ ( "t1 "o ( ! mo/ important elem5ts 9 navigation1 cle>s ! way to a bett] idea ( ! !ory ( f9d+ "o's position at sea2 !re is1 9 ! m9ds ( _m1 consid]able fog hang+ ab\t c]ta9 portions ( ?is subject1 & x is hop$ t ?is explanation w cle> "s ( ?is away4 ,worce/]'s ,diction>y def9es "t z measur$ duration4 ,x is ! int]val betwe5 ev5ts4 ,x fl[s ceaselessly & ) uni=mity1 yet ! mortal m9d is unable to conceive its beg9n+ or its end4 ,man1 9 ord] to measure 8 activities1 has block$ x (f into diff]5t d5om9ations conv5i5t = 8 uses4 ,( ^!1 ! navigator uses ! foll[+ 9 8 det]m9ations & reckon+s3 ye>s1 mon?s1 days1 h\rs1 m9utes & seconds4 ,c]ta9 a/ronomical ph5om5a 7 naturally enli/$ by ! anci5t a/ronom]s to furni% /&>ds = "t measurem5ts2 ! value ( a ye> 0 det]m9$ by ! "t necess>y = a complete revolution ( ! e>? ar\nd ! sun1 :ile ! l5g? ( a day 0 fix$ by ! "t ( a rotation ( ! e>? on its axis4 ,! precision ) :i* ^! evolutions are accompli%$ gives ! requir$ accuracy4 ,! revolution ( ! e>? gov]ns ! *ange ( seasons1 :ile ! rotation is responsible = ! alt]nat+ p]iods ( day & night4 ,) ! exception ( ! mon?1 ! o!r measurem5ts ( "t m5tion$ above are d5om9ations ( ^! /&>ds4 ,! mon?1 "o-twelf? ( a ye>1 is measur$ by ! revolution ( ! moon ar\nd ! e>?4 ,sol> "t1 z its "n implies1 is measur$ by ! app>5t diurnal movem5t ( ! sun4 ,x is ! v>iety ( "t 9 univ]sal use by :i* is regulat$ ! daily activities ( life2 & ?is is inde$ q natural1 = ( necessity ! "w & play ( ! _w dep5d ^u ! light & d>kness t ?is body s]ves out to u4 ,:ile we are unconsci\s ( ! e>?'s rotation1 its effect is se5 9 ! app>5t daily c\rse ( ! sun across ! heav5s1 caus$ by our turn+ pa/ x1 yet 9 common practice ! sun is assum$ to revolve ar\nd ! e>?1 & is usually ?us spok5 ( = ! purpose ( simpl] explanation4 ,! "t at ea* m]idian is necess>ily diff]5t f t ( e o!r1 z only "o ( !m holds ! same position relative to ! sun at ! same "t or putt+ x 9 ano!r way1 only "o m]idian c cross ! sun at ! same "t1 det]m9+ local noon = ^? places locat$ ^u x4 ,x is =5oon = t "p ( ! _w we/w>d ( ! sun & aft]noon = t portion ea/w>d ( x4 ,z ! e>? turns f we/ to ea/1 ! places or m]idians to ! ea/w>d are fir/ favor$ ) ! sun's light1 & ^? m]idians cross ?is body be=e ^? to ! we/w>d4 ,! sun app>5tly moves f ! ea/w>d to ! we/w>d1 cross+ ea* m]idian 9 succession until 9 a few h\rs x is aft]noon = places to ! ea/w>d & noon ) u4 ,! sun is n[ 9 our m]idian1 & x is =5oon = p to ! we/w>d ( u4 ,= example1 at #g ,a4,m41 #ge? m]idian "t1 x is noon 9 ,engl& & dead ( night 9 our ,pacific ,coa/2 at our noon 7#ge?71 x is late aft]noon 9 ,engl& & breakfa/ "t 9 ,cali=nia4 ,x requires #bd h\rs1 sol> "t1 = ! sun to make its app>5t revolution ar\nd ! e>?1 ?is c\rse be+ a circle2 x conta9s #cfj ( arc4 ,x foll[s t 9 "o h\r x passes ov] #ae ( arc1 :ile #d m9utes are requir$ = #a to be travel$4 ,?us x is evid5t t any arc ( ! circumf]5ce ( ! e>?1 or diff]5ce ( longitude1 :i* is ! same ?+1 has an equival5t "t value & vice v]sa4 ,t is1 ! arc compris$ betwe5 ! m]idian ( ,gre5wi* & ! #fj? m]idian we/1 = in/ance1 besides be+ measur$ z #fj ,w41 is equal to #d h\rs ( "t4 ,aga9 #d h\rs ( ,gre5wi* "t indicates t ! sun has cross$ ! ,gre5wi* m]idian #d h\rs ago & is at t p>ticul> in/ant cross+ ! m]idian #fj we/ ( ,gre5wi*4 ,if ! arc 7 betwe5 ,gre5wi* & a place #fj ,e41 ! equival5t "t int]val w\ld also be #d h\rs1 because #fj ( arc is ev]y:]e equal to #d h\rs ( "t2 b ! "t at ,gre5wi*1 ) sun on ! #fj? m]idian ea/1 is #bj h\rs ( ! previ\s day1 or #h ,a4,m4 ( ! pres5t day4 ,?us3 ,may #ad1 #bj h\rs1 or ,may #ae1 #h ,a4,m4 ,! m]idians ext5d f pole to pole1 & x matt]s n :at p>allel y may be on1 :e!r nor? or s\? latitude1 y\r di/ance c always be measur$ to ! ,gre5wi* m]idian 9 arc or "t precisely z well z ?\gh y 7 on ! exact p>allel ( ,gre5wi* itself4 ,if ! "t at ,gre5wi* is c>ri$1 & ! local "t ( any o!r m]idian is desir$1 turn ! diff]5ce ( longitude into "t & apply x ) reg>d to signs3 - if we/ ( ,gre5wi* & if ea/4 ,! local "t at any place c ?us be calculat$2 or to g f>!r1 if ! "t ( any m]idian is at h&1 ! "t ( any o!r place c be readily f\nd4 ,e m]idian c>ries a "t ( its own1 & ! in/ant ( ! click ( a telegraph key may be record$ all ov] ! _w 9 ! local "t ( ea* locality1 yet ! int]val betwe5 ?is & a subsequ5t click has an absolute value :i* is ! same at e place1 reg>dless ( :e!r x is express$ 9 sol>1 sid]eal or lun> "t1 & its actual value is inv>iable4 ,= conv5i5ce1 on l&1 our c\ntry is block$ (f into belts ( /&>d "t1 #ae wide1 ea* c>ry+ ! "t ( its c5tral m]idian4 ,= in/ance1 #ge? m]idian "t is us$ by ! ea/]n /ates1 :ile j we/w>d ! clocks' faces %[ an h\r e>li] "t1 t ( ! #ij belt1 & s on4 ,x is a good rule to rememb] 9 reckon+ all k9ds ( "t t ! clock's face %[s e>li] "t to ! we/w>d1 & f ?is x is easy to d$uce ! prop] application ( a correction4 ,!re are two k9ds ( sol> "t us$ 9 navigation2 ! fir/ to be consid]$ is app>5t "t1 ! k9d %[n by ! sun dial1 or measur$ by ! sun z we see x4 ,x is noon ( ! app>5t day :5 ! sun is se5 ) ! sextant to dip :ile tak+ a m]idian altitude4 ,x is at ! mom5t ( dipp+ t ! navigator ann\nces #ab o'clock1 & ) ! /rik+ ( eight bells beg9s a new app>5t day on %ipbo>d4 ,! ,day ,lo/ & ! ,day ,ga9$4--,! fact t ! sun seems to travel f ea/ to we/1 det]m9+ ! local "t = successive m]idians or places along ! way1 causes an int]e/+ condition 9 reckon+ "t abo>d %ip4 ,a vessel /eam+ we/w>d on a p>allel sails ) ! sun2 9 ! =5oon %e is sail+ away f x1 at noon ! sun ov]hauls ! vessel & !y race toge!r1 b x becomes a hopeless *ase = ! /eam] dur+ ! aft]noon4 ,9 consequ5ce ( _! simil> c\rse1 h[ev]1 ! vessel w hold ! sun long]1 & ! l5g? ( daylight w be increas$ ov] t "t allott$ a /ation>y position 9 proportion to ! spe$ ( ! vessel4 ,on ! o!r h&1 a vessel /eam+ ea/w>d ea* h\r advances to meet ! sun2 at noon ! effect is z if !y pass ea* o!r1 & dur+ ! rema9d] ( ! day !y are mov+ 9 opposite directions1 h5ce ?is vessel has a %ort] t]m ( light & is depriv$ ( its full %>e ( sun%9e4 ,9 practice ^! facts require ! cont9u\s sett+ back ( ! %ip's clock1 keep+ app>5t "t on a we/b\nd vessel4 ,take a concrete case = illu/ration3 to-day assume we are at sea on ! #de? m]idian we/ & set ! clock at ! dipp+ ( ! sun1 app>5t noon2 ! vessel is we/b\nd1 /eam+ along ! equator1 & rolls along at a good #ae-knot clip4 ,9 #bd h\rs by ! clock we w cov] #cfj miles1 or #cfj ( arc on ! equator1 :i* is equal to #f diff]5ce ( longitude4 7,%\ld ! ea/+ or we/+ be made 9 high] latitudes1 ! diff]5ce ( longitude w be increas$ proportionately47 ,s :5 ! %ip's clock %[s noon we w be #f f>!r we/ ?an at ! prec$+ noon1 or 9 #ea we/4 ,! navigator1 %\ld he obs]ve ! sun1 w\ld f9d x _h n rea*$ its highe/ altitude 7! m]idian71 & he w\ld be oblig$ to wait 7approximately7 #bd m9utes1 ! equival5t 9 "t ( #f1 be=e ! sun w\ld dip4 ,! clock is c>ry+ #de? m]idian "t1 & we are n[ det]m9+ noon = ! #ea/ m]idian4 ,he s+s out #h bells1 b ! clock %[s #ab4bd ,p4,m4 ,! %ip has ga9$ #bd m9utes by sail+ ) ! sun1 & ! clock is set back & a fre% />t is made4 ,a vessel sail+ ea/ has ! opposite exp]i5ce4 ,! navigator1 if guid$ by ! %ip's clock1 w\ld f9d t ! sun _h dipp$ "s #bd m9utes be=e noon if a run simil> to ! above m5tion$ 0 made ea/w>d4 ,9 ?is case ! app>5t "t ( ! #ea/ m]idian is %[n by ! clock1 :ile ! %ip has mov$ on to ! #de?1 & ! "t ( noon is correspond+ly approximately #bd m9utes e>li] ?an ! clock admits4 ,9 ! above example1 ! clock 9 ! fir/ in/ance is #bd m9utes fa/ & is set back t am\nt to correct x = ! "t ( ! #ea m]idian ,w42 b ?is "t _c be ?us arbitr>ily ?r[n away )\t "s subsequ5t reckon+4 ,!re is j s mu* "t all ov] ! _w1 & !re are no gaps or extra int]vals2 x is absolute 9 its uni=m fl[4 ,!re=e1 !re mu/ be a way ( squ>+ ourselves ) ,old ,fa!r ,"t4 ,b let u foll[ ! voyage f>!r & see :at transpires3 ,cont9u+ ! c\rse we/w>d & ignor+ = conv5i5ce all int]v5+ l&1 ea* day x becomes necess>y to set ! clock back #bd m9utes until we h circumnavigat$ ! e>?4 ,suppose we took our dep>ture f ! ,gre5wi* m]idian & kept our log ?r\gh\t ! voyage ) great c>e1 expect+1 accord+ to our reckon+1 to arrive on a ,saturday1 we w\ld inde$ be my/ifi$ on arrival to he> ! r++ ( *ur* bells & f9d t x 0 ,sunday4 ,we h lo/ a :ole day accord+ to our log1 by ?r[+ away #bd m9utes at a "t4 ,! "t ( ! _w goes on j ! same1 reg>dless ( h[ we juggle ! h&s ( ! clock4 ,n[1 if we try a simil> voyage ea/w>d ar\nd ! e>?1 we w be sett+ ! clock ahead #bd m9utes ea* day1 & :5 ! an*or is dropp$ on our return1 we w discov] t x is ,friday in/ead ( ,saturday4 ,! %ip's clock has skipp$ ?is #bd m9utes ea* day1 & our log is a day ahead ( :at x %\ld be4 ,9 ord] to prev5t ?is diff]5ce ( date1 x 0 decid$ ye>s ago to e/abli% an int]national date l9e1 :i* %\ld correspond approximately1 ) ! #ahj? m]idian4 ,! logs ( vessels go+ we/ ar\nd ! e>? w be a day beh9d ! cal5d> :5 !y rea* ,gre5wi*1 s a day is dropp$ f ! reckon+ :5 cross+ ! #ahj? m]idian2 t is1 if x is ,monday1 ! next day 9 ! log w be ,w$nesday4 ,on ! contr>y vessels b\nd ea/w>d w be a day ahead :5 !y rea* _! de/9ation ( ,gre5wi*1 s ! date ( cross+ ! date l9e is ent]$ twice 9 ! log1 z = in/ance1 !re w appe> two ,mondays4 ,by ?is me?od ! accumulat$ errors ( *as+ local "t1 are 9 a measure /raight5$ out1 & %ip's logs are kept 9 agreem5t ) ! cal5d> ( ^? at home4 ,?us x w be se5 t x is ! accumulation ( "t ?us ga9$ or lo/ t obliges navigators to add or drop a day to or f _! logs :5 cross+ ! #ahj? m]idian4 ,9 sl[ c>go /eam]s & sail+ vessels1 p>ticul>ly :5 ! c\rse creates b little dep>ture1 ! *ange ( "t due to diff]5ce ( longitude is n suffici5tly l>ge to cause mu* inconv5i5ce & c be tak5 c>e ( by sett+ ! clock back or ahead at noon4 ,b ) ! developm5t ( ! mod]n /eam]1 spe$ has increas$ to su* an ext5t t ! ea/+ or we/+ ( c]ta9 day's runs correspond to a consid]able am\nt ( "t1 & to correct ! clock to local "t1 all at once1 w\ld be a s\rce ( inconv5i5ce & a bo!r4 ,?is is especially true :]e a fa/ /eam] cov]s mu* ea/+ & we/+ 9 high latitudes :]e ! conv]g5ce ( ! m]idians has %ort5$ ! degrees ( longitude1 !reby increas+ ! diff]5ce ( longitude ov] a simil> day's run 9 l[] latitudes4 ,h5ce1 9 ord] to m equally di/ribute its error1 ! longitude at noon is anticipat$ by ! navigator & ! clocks set at #h ,a4,m4 = ! local "t ( ! approa*+ noon m]idian4 ,:5 ! clocks are set at noon1 !y are correct only = ! mom5t & !n />t an accumulat+ error1 dep5d+ 9 am\nt ^u ! rapidity ( ! ea/+ or we/+ made4 ,b by anticipat+ ! longitude at noon1 ! =5oon wat* w exp]i5ce a decreas+ error in/ead ( "o accumulat$ = tw5ty h\rs1 & /ill increas+4 ,x s]ves to keep ! "t ( day m ne>ly correct4 ,9 ! transatlantic s]vice1 :]e high spe$ is ma9ta9$ & ! c\rses result 9 a l>ge am\nt ( ea/+ & we/+1 ano!r me?od is us$ = conv5i5ce4 ,! navigator e/imates ! noon position ( ! next day & accord+ly divides ! error into ?irds4 ,! am\nt ( ! fir/ ?ird is appli$ at #aa ,p4,m41 ! second at #c ,a4,m4 & ! la/ ?ird at #e ,a4,m4 ,by ?is me?od ! error is di/ribut$ betwe5 ! 8fir/10 8mid0 & 8morn+0 wat*es4 ,x is a matt] ( consid]able mom5t1 & no joke1 to ! h>d-work+ /ok]s to h ! clock set back on !m ! full am\nt ( ! day's run all at "o "t2 & likewise go+ ea/1 x w\ld be giv+ an unfair advantage to ^? on duty to set ! clock ahead ne>ly an h\r dur+ ! morn+ wat*4 ,! app>5t or real sun is n a v accurate timekeep] & its days are unequal 9 l5g?4 ,! aborig9es & ev5 our ance/ors 7 cont5t ) ! "t ( day indicat$ by ! sun dial1 b z ! g5]ations h pass$1 ea* br++ increas$ developm5t1 "t has become valuable2 ! crude timepieces h be5 =c$ aside by m reliable in/rum5ts until to-day we figure d[n at times to a "o hundr$? "p ( a second4 ,x is impossible to con/ruct a clock t w foll[ ! irregul>ities ( ! app>5t sun1 s an imag9>y sun has be5 devis$ :i* is assum$ to make its revolution at a uni=m spe$ along ! cele/ial equator ) exactly #bd h\rs betwe5 its transits ( ! same m]idian4 ,?is int]val is ! av]age ( all app>5t days 9 "o ye>4 ,! v>y+ rate ( ! sun's app>5t motion is due to sev]al causes :i* w be subsequ5tly discuss$ "u ! ,equation ( ,"t4 ,! "t measur$ by ! transit & progress ( ! mean sun is call$ mean "t2 if at ,gre5wi*1 x is ,gre5wi* mean noon & ,gre5wi* mean "t 7,g4 ,m4 ,t472 if x repres5ts ! "t ( ! obs]v]'s place or m]idian1 x is local mean "t 7,l4 ,m4 ,t474 ,x is mean "t t is %[n by all clocks & *ronomet]s us$ 9 e day life4 ,! di/ance betwe5 ! app>5t & mean suns1 express$ 9 "t1 is kn[n z ! ,equation ( ,"t1 & ! application ( ?is correction dep5ds ^u :i* sun is ahead4 ,x is tabulat$ 9 ! nautical almanac = e two h\rs ( ,gre5wi* mean "t1 ) h\rly diff]5ces1 s x c be r$uc$ = longitude 9 "t to any m]idian1 or correct$ to any int]m$iate ,gre5wi* "t4 ,x is appli$ accord+ to ! sign accompany+ x1 & c be us$ to *ange app>5t into mean1 or mean into app>5t "t4 ,! progress ( ! mean sun across ! sky ) ref]5ce to ! m]idian is measur$ by ! angle at ! pole 7express$ 9 "t71 betwe5 ! m]idian & ! h\r circle pass+ ?r\gh ! mean sun4 ,?is is ! h\r angle ( ! mean sun z well z ! local mean "t4 ,civil ,"t is a v>iety ( mean "t1 & is reckon$ ?r\gh #ab h\rs f midnight to noon1 & aga9 #ab h\rs f noon to midnight1 divid+ ! day into ! well-kn[n p]iods ( ,a4,m4 & ,p4,m4 ,) ?is k9d ( "t1 ! day beg9s at midnight & ! h\r angle until noon is measur$ ea/w>d ?r\gh #ahj ( ! revolution & we/w>d ?r\gh ! rema9+ half f noon to midnight4 ,9 o!r words1 #d3jj ,p4,m4 signifies t ! sun has a we/]ly h\r angle ( #d h\rs1 :ile #h3jj ,a4,m4 indicates t ! sun is #d h\rs ea/w>d ( ! m]idian4 ,a/ronomical "t is reckon$ we/w>d ?r\gh ! :ole #bd h\rs ( ! day1 #j h\rs be+ noon4 ,f noon to noon is an a/ronomic day4 ,?us #e ,p4,m4 civil is ! same z #e h\rs a/ronomical "t1 :ile #e ,a4,m41 ,may #ad? is ! same z ,may #ac?1 #ag h\rs4 ,9 e sol> obs]vation = "t ! real or app>5t sun is obs]v$ & h5ce ! "t d]iv$ f ! sight mu/ be local app>5t2 to :i* ! equation ( "t mu/ be appli$ to conv]t x into local mean "t4 ,x has already be5 made cle> t ! longitude is equal to ! diff]5ce betwe5 ! local mean "t & ,gre5wi* mean "t1 or betwe5 local app>5t "t & ,gre5wi* app>5t "t4 ,,sid]eal ,,"t ,sid]eal is d]iv$ f ! ,lat9 ^w sidus1 mean+ ( or belong+ to ! />s4 ,sid]eal "t is measur$ by ! app>5t diurnal revolution ( ! />s1 result+ f ! rotation ( ! e>?4 ,by _! use ! conditions :i* r5d] ! sun inaccurate z a timekeep] are elim9at$2 = ! p]iod ( rotation ( ! e>? is s regul> t ! passages ( ! />s across ! m]idian occur ) great precision4 ,?is exactness enables ! a/ronom] to keep ! obs]vatory clock *eck$ to a rem>kable degree ( accuracy4 ,^! obs]vatory clocks c>ry sid]eal "t1 & = conv5i5ce x is cu/om>y to divide _! faces into #bd in/ead ( #ab h\rs4 ,sid]eal "t is ! b$rock ( all "t2 = x is by conv]t+ x into sol> "t & s5d+ x ?r\gh\t ! c\ntry by telegraph & radio t ! p ( ! _w get ! /&>d by :i* to set _! clocks & *ronomet]s4 ,sid]eal "t is n practicable = e day use z its noon occurs1 )\t reg>d to light or d>kness1 at e h\r ( day or night dur+ a ye>4 ,9 ,m>*1 at ! "t ( ! v]nal equ9ox1 x agrees ) ! sol> clocks1 b 9 ,septemb] at ! autumnal equ9ox1 its noon occurs at ! sol> midnight4 ,:ile ! sun is employ$ z ! object ( ref]5ce 9 sol> "t1 x may appe> /range t no p>ticul> /> is ?us us$ 9 sid]eal2 b 9 lieu ( a def9ite /ell> object by :i* to measure ! sid]eal movem5t ( ! heav5s1 we ref] to ! cele/ial v]nal equ9ox4 ,?is po9t 0 locat$ 9 ! con/ellation ( ,aries c5turies ago1 & h5ce its popul> "n--,! ,fir/ ,po9t ( ,aries2 b ?is has become a misnom]1 = ! po9t has long ago mov$ we/w>d into ano!r con/ellation1 z discuss$ "u ! ,precession ( ! ,equ9oxes4 ,navigators /ill cl+ to ! "n1 h[ev]1 & ! equ9ox cont9ues to s]ve its purpose1 reg>dless ( its sl[ drift we/w>d4 ,?is imag9>y po9t ( ref]5ce crosses ! obs]v]'s m]idian mu* z ! />s d1 ) ! diff]5ce t x is always on ! cele/ial equator & acquires no decl9ation4 ,! value ( ?is po9t becomes fur!r enhanc$ by ! fact t x always lies 9 ! same direction reg>dless ( our position 9 ! orbit4 ,9 o!r words1 ! di/ance ( ! equ9ox be+ inf9ite1 l9es drawn f p]ihelion & aphelion1 respectively1 to x1 fail to produce an appreciable angle4 ,9 explanation ( ?is /atem5t1 x mu/ be und]/ood t = all uses on ! e>? ! t]re/rial sy/em ( direction 7t is1 us+ ! be>+ ( ! nor? pole z a /&>d1 ) ea/ to ! left & we/ to ! "r :5 ! back is t[>d ! pole7 is entirely adequate1 b :5 deal+ ) ! direction ( cele/ial bodies1 a broad] /&>d mu/ be consid]$4 ,nor? & ,s\? bo? h a def9ite place 9 ! heav5s1 be+ ! po9ts ( ! ext5d$ axis ( ! e>?1 b ea/ & we/ are only relative expressions4 ,to demon/rate ?is3 x is possible = a man1 travel+ we/w>d on ! ,trans ,sib]ian ,railroad1 to see f ! re> plat=m1 9 ! ev5+1 a c]ta9 /> be>+ ea/w>d4 ,at ! same mom5t x is possible = an (fic] ( a transpacific l9] 9 ! e>ly morn+1 to be tak+ a sight ( ?is same /> be>+ we/w>d4 ,9 t]ms ( absolute direction t /> bore ! same f bo? sides ( ! _w4 ,on ! #ba/ ( ,m>* ! e>?1 sun1 & cele/ial v]nal equ9ox are 9 range1 ) ! sun betwe5 ! e>? & ! equ9ox4 ,= a place 9 nor? latitude on ! m]idian ( ! t]re/rial equ9ox1 ! sun z usual be>s s\? at noon ?is day1 & h5ce ! range m5tion$ above be>s s\? at t "t4 ,?is co9cid5ce ( be>+ is only mom5t>y1 = ! e>? ) its onw>d motion imm$iately moves out ( range & =ms an angle betwe5 ! sun & ! cele/ial equ9ox4 ,at noon on ! day succe$+ ! equ9ox ! sun be>s to ! left ( ! s-call$ ,fir/ ,po9t ( ,aries 7cele/ial v]nal equ9ox74 ,! sun accord+ to t]re/rial direction always be>s s\? by true compass at noon1 yet ! ,fir/ ,po9t ( ,aries be+ at an inf9ite di/ance always be>s ! same by absolute direction4 ,if ?is po9t c\ld be se5 & a be>+ ( x tak5 by compass simultane\sly ) ! sun1 x w\ld be1 p]haps1 ,s4 #a ,w4 & s on wid5+ ! angle1 r\ghly speak+1 a degree ea* day4 ,illu/ration3 ,! accel]ation ( ,sid]eal ov] ,mean ,"t ,,fig4 #b4 ,! int]val betwe5 two successive transits ( ! sun across ! m]idian con/itutes a sol> day1 & likewise ! p]iod requir$ = a c]ta9 /> to return to ! same m]idian is a sid]eal day1 b ^! two days are n ( ! same l5g?4 ,! sol> day we "k is #bd h\rs long1 b its sid]eal contempor>y has a l5g? ( only #bc h\rs1 #ef m9utes 7approximately7 sol> "t4 ,! sid]eal clocks1 h[ev]1 are ge>$ to %[ #bd h\rs1 sid]eal "t1 9 #bc h\rs1 #ef m9utes1 sol> "t4 ,by ?is x w be se5 t 9 any giv5 p]iod ! face ( ! sid]eal clock w %[ m h\rs ?an ! sol> clock4 ,bo? ! sol> & sid]eal clocks />t ev5 at ! v]nal equ9ox1 ab\t ,m>* #ba/1 b f !n on1 ! sid]eal clock ga9s on ! sol> "t clock ab\t #d m9utes a day until 9 a ye> x is a full #bd h\rs ahead1 %[+ t !re is "o m day 9 a sid]eal ye> ?an 9 a sol> ye>4 ,! approximate relation ( ! times %[n by ^! clocks is readily calculat$ by all[+ a ga9 9 ! sid]eal clock ( "o h\r = ea* #ae days aft] ,m>* #ba/1 or two h\rs = ea* mon?4 ,9 ord] to aid 9 a simpl] explanation1 let u aga9 foll[ ! e>? ar\nd its orbit & note ! conditions t di/+ui% sid]eal f sol> "t4 ,let u once m assume x to be ! "t ( ! v]nal equ9ox1 ! clocks1 bo? sid]eal & sol>1 n[ %[ #j h\rs1 & ! sun1 ! e>? & ! ,fir/ ,po9t ( ,aries are 9 range4 ,! e>? imm$iately moves out ( l9e by virtue ( its onw>d motion1 & ! sun correspond+ly appe>s to move ea/w>d2 ?is is imp]ceptible at fir/1 h[ev]1 & n noticeable )\t a c>eful measurem5t1 z x seems to be swall[$ up 9 ! contr>y 7we/w>d7 diurnal movem5t4 ,aft] #bd h\rs ( rotation f ! in/ant ( ! equ9ox ! e>? turns ! m]idian until x causes ! ,fir/ ,po9t ( ,aries to transit1 m>k+ sid]eal noon ( ! fir/ day4 ,! sid]eal clock at ?is mom5t reads #bd h\rs1 b a glance at ! sol> clock %[s #aa h\rs #ef m9utes ,a4,m41 ab\t #d m9utes %ort ( 7sol>7 noon4 ,an obs]vation w %[ t ! sun has app>5tly mov$ ab\t a degree ea/w>d ( ! h\r circle pass+ ?r\gh ! ,fir/ ,po9t ( ,aries s9ce ! prec$+ noon1 & ! e>? mu/ turn ?is extra degree be=e ! sun w be br\ght to ! m]idian1 ?us occupy+ ! #d m9utes m5tion$ above4 ,9 o!r words1 ! e>? turns #cfj 9 a sid]eal day b mu/ turn ab\t #cfa 9 a sol> day4 ,?ree mon?s aft] ! v]nal equ9ox1 ! angle betwe5 ! ,fir/ ,po9t ( ,aries & ! sun becomes1 9 r\nd numb]s1 #ij1 & x requires #f h\rs = ! e>? to br+ ! sun to ! m]idian aft] ! passage ( ! ,fir/ ,po9t ( ,aries4 ,9 pla9] language1 :5 ! ,fir/ ,po9t ( ,aries crosses ! m]idian 7sid]eal noon7 ! sun is ab\t #ij to ! left--ab\t ris+ 9 ! ea/]n sky2 ! e>? mu/ make a qu>t] turn1 or #f h\rs1 be=e x w be sol> noon4 ,?us x w be se5 t at ?is po9t sid]eal "t is #f h\rs ahead ( sol> "t4 ,9 six mon?s1 :5 ! ,fir/ ,po9t ( ,aries is on ! m]idian ! noonday sun is %9+ on ! antipodes1 & x lacks #ab h\rs ( sol> noon4 ,! diff]5ce betwe5 ! sid]eal & sol> clocks has n[ rea*$ #ab h\rs & ?r\gh a cont9uation ( ! same process ! int]val betwe5 _! read+s1 wid5s ?r\gh\t ! rema9d] ( ! ye>4 ,:5 ! #ba/ ( ,m>* comes ar\nd aga91 & ! m]idian pres5ts itself to ! sun & ! ,fir/ ,po9t ( ,aries 9 range1 a c>eful c\nt ( ! numb] ( times ?is latt] po9t has cross$ ! m]idian dur+ ! ye>1 discloses #cff transits4 ,t is1 ! e>? has actually turn$ ab\t its axis #cff times4 ,! sun is f\nd to h pass$ ! m]idian only #cfe times4 ,c\nt+ ! rotations ( ! e>? by ! numb] ( ! sun's transits :ile we are revolv+ ar\nd him1 causes ! app>5t loss ( a day due to ! e>? unw9d+ itself once1 s to speak1 dur+ ! ye>4 ,! accumulat$ diff]5ce am\nts to "o sid]eal day4 ,h5ce x w be se5 t a ye> conta9s #cff sid]eal days ( #bc h\rs1 #ef m9utes ea*1 & #cfe sol> days ( #bd h\rs ea*4 ,n[ = a recapitulation ( ! subject ( "t4 ,! rotation ( ! e>? is ! real /&>d ( measur+ "t int]vals2 ! p]iod requir$ = ?is rotation does n v>y4 ,x has be5 sugge/$ t ! tide waves h a m9ute effect on ! regul>ity ( ?is movem5t1 b ! con/ruction ( our clocks is su*1 t if any v>iation exi/s we are unable to detect x4 ,:e!r we use ! passages ( ! />s1 or ! transits ( ! sun to reckon our "t1 x falls back 9 ei!r case ^u ! diurnal rotation ( ! e>?4 ,app>5t "t is measur$ by ! seem+ progress ( ! actual sun4 ,! "t ( its transit ( ! m]idian is irregul>1 b is always %[n by its 8dip10 culm9ation1 ) ! sextant4 ,mean "t is reckon$ by ! revolutions ( a fictiti\s sun1 call$ ! mean sun1 & ! l5g? ( "o ( ^! revolutions is ! av]age ( a ye> ( app>5t days4 ,?is1 ow+ to its uni=mity1 is ! "t us$ = ! ev]yday purposes ( life4 ,! diff]5ce betwe5 app>5t & mean "t is call$ ! equation ( "t1 &1 by apply+ x accord+ to signs giv5 9 ! ,nautical ,almanac1 "o c be conv]t$ to ! o!r z desir$4 ,sid]eal "t is indicat$ by ! position ( ! ,fir/ ,po9t ( ,aries relative to ! m]idian2 x is /> "t4 ,! />s make a complete revolution ( ! heav5s 9 #d m9utes less "t ?an is requir$ by ! mean sun4 ,!re=e ! sid]eal day is t am\nt %ort] ?an ! sol> day4 ,! po9t ( ! cele/ial v]nal equ9ox or ,fir/ ,po9t ( ,aries is a sort ( cele/ial 8b5* m>k20 besides indicat+ sid]eal "t1 x s]ves z a po9t f :i* "r asc5sion is measur$ ea/w>d4 ,?is subject has be5 discuss$ previ\sly1 b z x is intimately associat$ ) sid]eal "t1 p]haps x may be made cle>] s9ce ! latt] has be5 s fully expla9$4 ,"r asc5sion is measur$ on ! cele/ial equator1 precisely ! same z longitude on ! e>?1 except+ t x is always measur$ ea/w>d ?r\gh ! full #bd sid]eal h\rs1 contr>y to ! diurnal movem5t ( heav5ly bodies4 ,moreov]1 ! m]idian pass+ ?r\gh ! v]nal equ9ox is call$ ! cele/ial prime m]idian1 & sometimes ! ,gre5wi* ( ! heav5s4 ,!re is ano!r po9t ( di/9ction1 h[ev]1 betwe5 ?is prime m]idian ( ! sky & our m]idian ( ,gre5wi*1 :i*1 :ile x does n effect practical navigation1 has to receive consid]ation 9 ! long run2 our longitude values on ! e>? rema9 at all times con/ant1 b ow+ to ! precession ( ! equ9oxes ! cele/ial prime m]idian is sl[ly mov+ we/w>d1 ?us caus+ ! "r asc5sions measur$ f x to become v sl[ly 9 error 7#ej ye>ly74 ,! h\r angle ( a body is ! angle =m$ at ! pole betwe5 ! m]idian & ! h\r circle pass+ ?r\gh ! body measur$ we/w>d4 ,) all ^! important facts well 9 m9d we w g ahead "u a sl[ bell1 ?r\gh a few m /atem5ts :i* may be f\nd a little p]plex+4 ,h[ev]1 a c>eful /udy ( ! ,"t ,diagram w1 no d\bt1 drive away ! haz9ess s (t5 surr\nd+ ! subject ( "t4 ,illu/ration3 ,?is diagram repres5ts ! plane ( ! equator look+ d[n ^u ! ,nor? ,pole4 ,! #ge ,w m]idian is *os5 z t ( ! obs]v] & local "t reckon$ !refrom4 ,! arr[s on ! out] circumf]5ce indicate ! directions ( ! e>?'s rotation2 ! o!r small] arr[s indicate ! direction 9 :i* ea* elem5t is reckon$4 ,,fig4 #c4 ,! h\r angle ( ! mean sun is ! local mean "t1 & ! h\r angle ( ! ,fir/ ,po9t ( ,aries is ! local sid]eal "t4 ,! local mean "t & longitude 9 "t accel]at$ by ,table ,,iii ,nautical ,almanac plus "r asc5sion ( ! mean sun is equal to ! local sid]eal "t4 ,! "r asc5sion ( ! m]idian is ! same ?+1 exactly1 z ! h\r angle ( ! ,fir/ ,po9t ( ,aries1 & bo? ( ^! are id5tical ) ! local sid]eal "t4 ,! sid]eal "t ( ,gre5wi* mean noon is ! same z ! "r asc5sion ( ! mean sun at t "t4 ,! h\r angle ( a /> plus ! "r asc5sion ( ! same /> is equal to ! local sid]eal "t4 ,diff]5ce ( longitude c be repres5t$ by an int]val ( sid]eal "t or by a diff]5ce ( "r asc5sion1 precisely ! same z by a diff]5ce ( sol> "t4 ,?us ) ! local sid]eal "t calculat$ f an obs]vation ( a />1 & ! correspond+ ,gre5wi* sid]eal "t tak5 f ! ,nautical ,almanac1 ! longitude is at h&1 by turn+ _! diff]5ce into arc4 ,! fact t ! actual "t int]val is long] 9 ! case ( sol> "t ?an 9 an int]val ( ! same numb] ( h\rs ( sid]eal "t1 has no influ5ce on ! result+ diff]5ce ( longitude4 ,! numb] ( degrees 9 any arc c be ! same1 yet v>y 9 l9e> measurem5t1 b ! same numb] ( h\rs ( sol> & sid]eal "t repres5t ! same proportionate "p ( a circle4 ,x 0 j /at$ t ! h\r angle ( a /> plus its "r asc5sion is ! same z ! local sid]eal "t2 n[ ?is is also true ( ! sun4 ,! h\r angle ( ! mean sun plus ! "r asc5sion ( ! mean sun is equal to ! local sid]eal "t2 by means ( ?is equality we are able to f9d ! ,gre5wi* sid]eal "t on any occasion4 ,x is necess>y to h ?is elem5t 9 ord] to comp>e x ) ! local sid]eal "t1 :i* we f9d by obs]vation ( a />1 to obta9 diff]5ce ( longitude 79 "t74 ,9 page #b ( ! ,nautical ,almanac w be f\nd ! ,"r ,asc5sion ( ! ,mean ,sun at ,gre5wi* ,mean ,noon2 ?is mu/ always be tak5 out = ! prec$+ noon4 ,we n[ h a measure ( sid]eal "t to be add$ to a measure ( mean "t1 b x w be rememb]$ 9 e>ly ari?metic t an apple & a pea* c n be add$ toge!r any m ?an c be add$ to 4 ,! only c\rse to /e] is to r$uce ! quantities to a common d5om9ator1 or l quantities4 ,s 9 h&l+ ^! two v>ieties ( "t1 sol> "t mu/ be accel]at$ by add+ a correction to x1 or sid]eal "t ret>d$ by subtract+ an am\nt necess>y to make x equal to a correspond+ value ( sol> "t4 ,! tables = ! conv]sion ( "o ( ^! v>ieties ( "t to ! o!r are f\nd 9 ! ,am]ican ,ephem]is ,tables ,,ii & ,,iii1 ,b[dit* ,tables #h & #i1 & at ! foot ( pages #b & #c1 ,nautical ,almanac4 ,a practical illu/ration ( ?is may make a cle>] impression4 ,9 ! e>ly ev5+ ( ,april #h?1 secur$ a sight ( ,regulus2 ! *ronomet] %[$ #h days1 #i h\rs1 #ef m9utes1 & #j seconds 7correct$71 ) o!r necess>y elem5ts giv51 ! sight is work$ z usual to f9d ! />'s h\r angle1 :i* proves to be3 h4 m4 s4 ,h ,a ,regulus #a #ei #dg be>+ we/4 ,r ,a #aj #c #jb ,,rams #a h4 #f m4 #g s4 -- -- -- ,,gmt #i h4 #ef m4 #j s4 ,l4 ,s4 ,t4 #ab #jb #di ,accel4 #i h4 #a m4 #bi s4 ,g4 ,s4 ,t4 #aa #jc #de ,accel4 #ef m4 #i s4 -- -- -- ----- ----- ----- ,long4 9 "t #ei #jd ,g4 ,s4 ,t4 #aa h4 #c m4 #de s4 ,?is be+ a /> sight we obta9 f x ! sid]eal "t at place ( obs]vation & z ! *ronomet] c>ries ,gre5wi* mean "t we seek ! correspond+ sid]eal "t by add+ ?is & its accel]ation = a sid]eal int]val to ! "r asc5sion ( ! mean sun tak5 f ,nautical ,almanac4 ,! result is ! ,gre5wi* ,sid]eal ,"t4 ,x is occasionally requir$ to f9d ! sid]eal "t at ! %ip 9 :i* case x is only necess>y to apply ! longitude 9 "t to ! ,gre5wi* ,sid]eal ,"t4 ,z ,gre5wi* mean "t is ! mo/ us$ & is ! be/ und]/ood x is a v conv5i5t practice to c>ry ,g4 ,m4 ,t4 on ! navigator's wat*4 ,x is readily conv]t$ into any o!r "t ) ease b s]ves m purposes z x is )\t conv]sion4 ,a /op wat* is an excell5t in/rum5t = tak+ "t sights :]e great accuracy is ess5tial4 ,by sett+ x at #j m9utes a man c obs]ve alone />t+ ! wat* z he makes contact ) ! horizon & :5 subsequ5tly comp>+ ) ! *ronomet] subtract ! read+ ( ! wat* to get ! ,g4 ,t4 ( obs]vation4 ,! mo/ exp$iti\s way to conv]t "t into arc is to multiply ! h\rs by #ae & add ! numb] ( m9utes divid$ by #d to get ! degrees2 multiply ! rema9+ m9utes by #ae & add ! seconds divid$ by #d to get ! m9utes2 multiply ! rema9+ seconds by #ae to get ! seconds 9 arc3 ,?us3 ,long4 9 "t #b hrs4 #db m4 #bc s4 #cj #cj #de #aj #e -------------------- ,long4 9 arc #dj #ce #de ,to *ange arc into "t divide ! degrees by #ae to get ! h\rs2 multiply ! rema9d] by #d & divide ! m9utes by #ae & add to get ! numb] ( m9utes 7m472 multiply ! rema9d] ( m9utes 77 by #d & divide ! seconds 77 by #ae c>ry+ ! division ( t5?s if desir$1 add+ ! result to get ! seconds 7s473 ,?us3 ,long4 9 arc #dj #ce #de #b hrs4 #dj m4 #bj s4 #b #c ------------------- ,long4 9 "t #b hrs4 #db m4 #bc s4 ,?is may appe> complicat$ at fir/ b is mu* ! quicke/ way ( conv]sion4 ,h[ev]1 ,table ,no4 #g1 ,b[dit* is always available if desir$4 ,9 gett+ an und]/&+ ( any "t problem1 t is su* z *ang+ mean "t into sid]eal "t2 obta9+ ! h\r angle ( a /> or planet2 9 seek+ ! local "t f ! *ronomet]1 or any "t values t are f\nd p]plex+1 always draw a diagram4 ,make ! circle on ! plane ( ! equator1 ) ! pole z ! c5t]1 & m]idians radiat+ f x t[>ds ! circumf]5ce ( ! circle4 ,n[ imag9e = ! mom5t t y are at ! nor? pole1 & ! date is ! #ba/ ( ,septemb]4 ,! sun is travel+ 9 ! horizon1 & if ! direction ( ! ,gre5wi* m]idian is kn[n1 ?is body s]ves z a "t piece1 = ! angle betwe5 ?is m]idian 7direction7 & ! sun is ! ,gre5wi* "t4 ,?is angle corresponds ) twice ! angle betwe5 ,,xii h\rs on ! wat* & ! h\r h&2 or w\ld 7disreg>d+ equation ( "t7 co9cide ) x if ! wat*'s face 0 divid$ into #bd h\rs4 ,likewise :5 ! v]nal equ9ox or ,fir/ ,po9t ( ,aries lies 9 ! direction ( ,gre5wi* x is ,gre5wi* sid]eal noon1 & ! subsequ5t angle t appe>s ?r\gh ! rotation ( ! e>?1 %[s ! ,gre5wi* sid]eal "t4 ,,equation ,,( ,,"t ,x is necess>y 9 consid]+ ?is subject to reit]ate "s ( ! /atem5ts made 9 ! prec$+ talk on "t1 b1 z !y are v important1 no "t is wa/$ by fur!r impress+ !m on ! m9d4 ,let x be und]/ood t ! app>5t orbit ( ! sun is actually due to ! e>?'s revolution ar\nd him1 yet = simpl] explanation x is consid]$ to be ! sun's own revolution4 ,! app>5t movem5t ( ! real sun is n ( uni=m spe$ &1 9 consequ5ce1 x has become necess>y to devise a fictiti\s sun ^: assum$ revolutions ar\nd ! e>? are at all times regul> 9 _! rate4 ,! equation ( "t is ! diff]5ce betwe5 ^! two suns &1 z !y are at times 9 conjunction & at o!r times atta9 a di/ance f ea* o!r ( #af m9utes #bj seconds1 &1 moreov]1 z ! real sun is sometimes ahead & aga9 9 ! wake ( ! mean sun1 x becomes evid5t t ! equation ( "t is an ev] v>y+ quantity4 ,! irregul>ity ( ! sun's app>5t movem5t z comp>$ ) ! uni=mity ( ! mean sun1 is subject to two causes3 ,fir/1 ! e>? travels 9 an ellipse1 &1 z ! l5g? ( a degree v>ies 9 ! diff]5t p>ts ( ! circumf]5ce1 ! motion w\ld appe> to be irregul>1 t is1 if ! sun actually travel$ at a uni=m rate1 x w\ld1 f ! above fact1 appe> to u to be v>iable 9 its motion2 fur!rmore1 ! laws ( =ces only all[ a body travel+ 9 a circle ! privilege ( a uni=m spe$ s ! e>?1 ow+ to its v>y+ di/ance f ! sun1 exp]i5ces a correspond+ *ange 9 ! am\nt ( attraction ex]t$ ^u x by ! sun & its velocity1 actually becomes v>iable4 ,?us1 dur+ ! w9t]1 ,decemb] & ,janu>y1 :5 !y are ne>e/ ea* o!r1 ! attraction is /ronge/ & ! e>? increases its spe$ 9 revolution2 :ile 9 ,june & ,july ! e>? is at its greate/ di/ance f ! sun & ! attraction is less1 result+ 9 a sl[+ d[n 9 ! rate ( ! onw>d movem5t4 ,z ! sun appe>s to u to take on movem5ts correspond+ to ^? ( ! e>?1 ^! v>iable movem5ts ( ! latt] are se5 9 ! app>5t motion ( ! sun4 ,second1 ! plane ( ! e>?'s orbit is incl9$ at an angle to t ( ! equator1 :i* makes ! sun appe> to be travel+ at a v>iable spe$ along ! ecliptic4 ,) ^! two errors comb9$ influ5c+ ! app>5t sun1 he becomes unreliable = regulat+ timepieces4 ,! mean sun1 :i* 0 orig9at$ to obviate ^! irregul>ities1 is assum$ to travel 9 a circle ) ! e>? locat$ 9 ! c5tre1 :i* disposes ( ! fir/ reason = an app>5t v>iable motion2 & aga91 ! mean sun revolves 9 ! plane ( ! equator1 ?us elim9at+ ! second ob/acle 9 ! way ( uni=m "t4 ,n[ we w cont9ue a little f>!r into ! explanation ( ! reasons = ! irregul> movem5t ( ! real sun4 ,a law discov]$ by ,kepl]1 & nam$ = him1 provides t a radius f ! sun to ! e>? cov]s sectors ( equal areas 9 equal times2 a sector equal 9 area to any sector cov]$ 9 ! same "t4 ,t is1 :5 ! e>? is 9 t "p ( ! orbit ne> ! v]nal equ9ox1 ! radius ( ! orbit w 9 a giv5 "t1 say a week1 sweep ov] a c]ta9 area2 ! e>? proce$s t[>d aphelion & :5 9 ! vic9ity ( t po9t1 ! radius becomes greatly increas$ 9 l5g?4 ,n[ 9 a week ) ?is long] radius1 a f> great] area w\ld be cov]$ if ! e>? ma9ta9$ ! same rate ( spe$ z at ! equ9ox1 b ,kepl]'s law says1 8equal areas 9 equal times10 s 9 ord] to con=m ) ! law1 ! e>?'s spe$ ( revolution mu/ be r$uc$4 ,! e>? does n sl[ d[n j = ! sake ( obey+ ,kepl]1 b at ?is "p ( ! orbit x is at its greate/ di/ance f ! sun & h5ce ! r$uc$ attraction causes ! e>? to lag a little4 ,at ! "t ( ! autumnal equ9ox1 an area simil> to t ( ! v]nal equ9ox is cov]$4 ,z ! e>? approa*es p]ihelion1 ! radius is gradually %ort5$ by ! ecc5tricity ( ! sun 9 ?is "p ( ! orbit & ! increas$ attraction causes ! e>? to spe$ up correspond+ly4 ,at ! increas$ spe$1 ! %ort] radius sweeps ! same area 9 a week z at o!r p>ts ( ! orbit & ,kepl]'s law /ill holds good4 ,z ! app>5t motion ( ! real sun corresponds exactly ) ! real motion ( ! e>?1 x is evid5t f ! above t ! real sun app>5tly moves at diff]5t rates ( spe$ along ! ecliptic1 fa/] 9 w9t] & sl[] 9 summ] ?an ! mean sun4 ,! value ( a mean sol> day is ! av]age ( a ye> ( app>5t days1 or 9 o!r words1 !re is ! same numb] ( mean sol> days 9 a ye> z !re are app>5t days4 ,9 consid]+ ! effect ( ! v>iable motion ( ! e>? 9 its orbit1 we w recall ! conditions us$ :5 def9+ sid]eal & sol> days4 ,! =m] comprises ! int]val betwe5 two successive passages ( a c]ta9 /> across ! m]idian1 or p]haps bett]1 betwe5 two successive passages ( ! m]idian ov] a />4 ,?is is ! true l5g? ( ! e>?'s rotation & is ! /&>d to :i* we may ref] ! l5g? ( ! mean or app>5t sol> days4 ,n[ x requires ab\t #c m9utes #ef seconds long] = ! m]idian to sweep ar\nd f sun to sun ?an f /> to />1 ow+ to ! fact t ! mean sun moves uni=mly ea/w>d t am\nt daily1 !reby requir+ ! m]idian1 aft] rea*+ its position ( ye/]day noon1 to ov]haul ! mean sun ?is #c m9utes #ef seconds ( ea/w>d movem5t4 ,! mean sun ma9ta9s ?is uni=m diff]5ce betwe5 its days & ! l5g? ( ! sid]eal day4 ,)\t ?is daily ea/+ ( ! sun1 ! sid]eal & sol> day w\ld be ! same4 ,b1 9 consid]+ ! app>5t sun1 we f9d ! l5g? ( its days cont9ually v>ies f bo? t ( ! sid]eal & mean day4 ,?is is expla9$ by ! fact t ! ea/w>d movem5t ( ! app>5t sun is due to ! movem5t ( ! e>? 9 its orbit1 & z ?is movem5t becomes fa/] or sl[] ! ea/w>d movem5t ( ! sun becomes correspond+ly fa/] or sl[]4 ,?us1 we readily see t ) ! app>5t sun mov+ ea/w>d fa/] or sl[] at times1 ! l5g? ( ! app>5t day mu/ v>y accord+ly & we _c e/abli% a uni=m diff]5ce betwe5 x & ! sid]eal day1 z 9 ! case ( ! latt] & ! mean day4 ,! app>5t days exce$ ! mean days 9 l5g?1 betwe5 ,septemb] & ,m>*1 :ile ! e>? is travel+ fa/e/ 9 its orbit4 ,beg9n+ at ! autumnal equ9ox ) ! app>5t sun eight m9utes beh9d ! mean sun1 ! =m] ga9s sl[ly at fir/ b ) increas+ rapidity4 ,ab\t ! end ( ,decemb]1 at p]ihelion1 x ov]hauls ! mean sun & !y are co9cid5t z reg>ds ?is correction only4 ,leav+ p]ihelion1 ! app>5t sun rapidly takes ! lead b ) a gradually decreas+ am\nt until at ! equ9ox 9 ,m>*1 rea*es its maximum lead ( #h m9utes4 ,ent]+ t portion ( ! ye> ,m>* to ,septemb]1 we f9d ! e>? travel+ sl[] & ! mean sun ga9+ on ! app>5t sun2 betwe5 ! v]nal equ9ox & aphelion1 ! mean sun ga9s until bo? are toge!r at ! summ] sol/ice & !n =g+ ahead ! mean sun atta9s a lead ( #h m9utes 9 ,septemb]4 ,x mu/ be borne 9 m9d t ?is error is caus$ only by ! ecc5tricity ( ! orbit & is b a compon5t "p ( ! :ole correction ( ! equation ( "t4 ,! o!r portion is due to ! obliquity ( ! orbit1 or its incl9ation to ! equator4 ,?is error is introduc$ ?r\gh ! fact t ! app>5t sun moves 9 ! ecliptic & ! mean sun is assum$ to proce$ along ! cele/ial equator4 ,9 consid]+ ?is phase ( ! "q1 we w ignore entirely1 = ! "t be+1 ! error ( ecc5tricity describ$ above4 ,! error ( equation ( "t due to ! obliquity ( ! orbit is a simple "o to see1 b l _m simple ?+s x is easi] to %[ x by a diagram ?an to expla9 9 words1 s ! read] is ref]r$ to ! accompany+ figure1 t a /udy ( x may be made be=e proce$+4 ,illu/ration3 ,,fig4 #d4 ,at ! equ9oxes1 :]e ! ecliptic & equator cross & ! sol/ices--! v]tices ( ! ecliptic--t is1 f\r times a ye>1 ! true & mean sun are toge!r1 b dep>t+ f ^! po9ts !y d n travel ) ! same "r asc5sion1 rememb]+ t "r asc5sion is measur$ on ! equator4 ,tak+1 = example1 ! e>? 9 t quadrant ( ! orbit compris$ betwe5 ! v]nal equ9ox & summ] sol/ice1 ! app>5t sun 9 ! heav5s w\ld be by cause ( obliquity alone1 to ! "r or to ! we/w>d ( ! mean sun1 & ?us x w be se5 t ) ! e>? rotat+ f "r to left ! app>5t sun w cross ! m]idian fir/2 consequ5tly betwe5 ,m>* #ba/ & ,june #ba/ t "p ( ! equation ( "t due to ! obliquity ( ! orbit be>s a m9us sign :5 mean "t is desir$ f ! app>5t "t4 ,?is correction rea*es its maximum half-way or #de f ! equ9ox1 am\nt+ at t po9t to ne>ly #aj m9utes4 ,illu/ration3 ,,fig4 #e4 ,n[ ! reason = ?is diff]5ce betwe5 ! mean & app>5t sun :5 ea* 7s f> z ?is problem is conc]n$7 moves along its respective pa?--! equator & ! ecliptic--at ! same rate1 is ?is3 suppose ! equator betwe5 ! equ9ox & ! sol/ice is divid$ into an equal numb] ( p>ts & an h\r circle drawn ?r\gh ea* po9t ( division4 ,beg9n+ f ! equ9ox 7! common apex ( ! triangle7 ! arc ( ea* h\r circle betwe5 ! equator & ! ecliptic1 =ms ! altitude ( a "r-angl$ triangle1 :ile ! equator & ! ecliptic are base & hypo!nuse respectively4 ,?us x w be se5 t ea* portion ( ! equator 7base7 is %ort] ?an ! correspond+ "p ( ! ecliptic z def9$ ! h\r circle1 to ! ext5t ( ! ratio ( ! base to ! hypo!nuse4 ,?is am\nt increases ) ! increas+ size ( ! triangle1 b a new elem5t ent]s to c\nt]act its effect4 ,) ! increas+ div]g5ce ( ! ecliptic & equator1 ! div]g5ce ( ! h\r circles becomes a factor & z ! sol/ice is approa*$ ! divisions on ! equator1 are repres5t$ on ! ecliptic by gradually decreas+ spaces betwe5 ! h\r circles4 ,! comb9ation ( ^! effects produces ! error due to ! obliquity ( ! orbit4 ,! error has ! opposite effect 9 ! next quadrant1 t is1 f ,june to ,septemb]2 & 9 opposite quadrants x is ! same4 ,s x w be se5 t error due to ! ecc5tricity causes ! app>5t sun to lead ! mean sun f ,decemb] #ca/ to ,june #cj?1 rea*+ a maximum ( #h m9utes ab\t ,april #b;d4 ,?is sun !n falls a/]n until ,decemb]1 aga9 atta9+ a maximum ( -#h m9utes ab\t ,octob] #a/4 ,! error due to ! obliquity ( ! orbit accumulates betwe5 ! equ9oxes & sol/ices = at ^! po9ts ! two suns are toge!r & !re is no error1 b ab\t ! #f? ( ,may1 ,augu/1 ,novemb]1 & ,febru>y1 x rea*es a maximum ( #aj m9utes2 9 ,augu/ & ,febru>y1 ! mean sun takes ! lead4 ,^! two errors ( equation ( "t comb9$ algebraically w result 9 ! pla9 l9e ( ! diagram4 ,,cal5d> ,! anci5ts1 9 ord] to keep track ( pa/ ev5ts & to anticipate ! future1 devis$ a cal5d>1 :i*1 :ile n id5tical ) ! "o n[ 9 use1 0 ( itself a rem>kable production4 ,!y *ose ! revolutions ( ! moon z _! basis ( measur+ ! passage ( "t1 &1 z a lun> mon? conta9s only #bg days1 ! #ab mon?s us$ 9 ?is e>ly cal5d> compris$ a ye> ( ab\t #ced days4 ,x became app>5t z ! _w progress$ t use ( ! moon 0 v unsatisfactory = ?is purpose1 z ! cal5d> became complicat$ & confusion result$1 ow+ to ! diff]5ce betwe5 ! lun> & sol> ye>s4 ,?is condition rema9$ until ! reign ( ,caes>1 :5 t mon>* det]m9$ to e/abli% a m satisfactory me?od ( reckon+ "t4 ,) ! aid ( an em95t a/ronom]1 he completely revis$ ! cal5d>1 us+ ! revolution ( ! e>? ar\nd ! sun z ! /&>d = ! l5g? ( a ye>4 ,! "t requir$ = ?is is #cfe days1 approximately1 & z x 0 inconv5i5t to include ! day 9 ! ye>1 x 0 all[$ to accumulate = #d ye>s1 :5 z a :ole day1 x 0 add$ to ! end ( ,febru>y4 ,caes>1 evid5tly pr\d ( ?is accompli%m5t1 honor$ himself by nam+ 8 a/ronom]'s inv5tion ! ,julian ,cal5d> & 9 ord] to fur!r immortalize himself he *ang$ ! "n ( ! sev5? mon? to ,july4 ,augu/us1 8 successor1 app>5tly envi\s ( ! honor 8 pr$ecessor d]iv$ f ?is s\rce1 & det]m9$ n to be ?us outdone 9 p]petuat+ 8 "n1 *ang$ ! mon? ,sextilis to ,augu/4 ,! commonly accept$ #cfe days z ! l5g? ( ye> is only an approximation1 h[ev]1 & ! small diff]5ce betwe5 ?is & ! actual l5g? ( a ye> began to accumulate until ?is weak po9t 9 ! ,julian ,cal5d> became a matt] ( mom5t4 ,! exact l5g? ( a ye> f v]nal equ9ox to v]nal equ9ox is #cfe days #e h\rs #dh m9utes & #df seconds1 :i* lacks j #aa m9utes #ad seconds ( #cfe days4 ,?is caus$ ! dates ( ! equ9oxes & sol/ices to keep slipp+ back #aa m9utes ea* ye> & :5 consid]able "t _h pass$ ! diff]5ce became l>ge en\gh to cause inconv5i5ce2 ! date ( ! v]nal equ9ox hav+ dropp$ back to ,m>* #aa? 9 #aehb4 ,9 ?is ye> ,pope ,gregory1 act+ "u ! advice ( an a/ronom] by ! "n ( ,clavius1 modifi$ ! ,julian ,cal5d>4 ,he fir/ add$ #aj days to re/ore ! date1 & !n to =e/all a fur!r retrogress+ ( ! cal5d>1 provid$ t only ^? c5tury ye>s divisible by #djj %\ld be consid]$ leap ye>s4 ,9 ?is way ! #aa m9utes #ad seconds 0 prev5t$ f caus+ fur!r mis*ief4 ,?is cal5d> kn[n z ! ,gregorian ,cal5d> is n[ 9 almo/ univ]sal use1 ?\gh at fir/ x 0 adopt$ only by ,ca?olic c\ntries4 ,x is int]e/+ to note t ! "t consum$ by ! sun 9 mak+ 8 app>5t ye>ly revolution f a c]ta9 /> back to t /> aga9 is a sid]eal ye> ( #cfe days #f h\rs #i m9utes #i seconds4 ,! tropical ye>--! "o 9 common use--is %ort]1 be+ ! "t requir$ = ! sun to leave & return to ! v]nal equ9ox1 or ,fir/ ,po9t ( ,aries4 ,?is po9t1 x w be rememb]$1 is mov+ we/w>d ab\t #ej annually1 & x w be se5 t :ile ! sun />ts its ea/w>d revolution among ! />s1 ! equ9ox is v sl[ly mov+ we/w>d to meet him1 ?us mak+ ! tropical ye> ab\t #bj m9utes %ort] ?an ! sid]eal ye>4 ,:ile discuss+ ! cal5d> x is an opportune "t to expla9 a matt] conc]n+ ! dates ( ! equ9oxes & sol/ices4 ,x has ( c\rse be5 notic$ by ev]yone t ! v]nal equ9ox occurs "o ye> on ,m>* #bj? & ano!r on ,m>* #ba/1 or ! summ] sol/ice on ,june #bb;d & yet ano!r ye> on ,june #ba/ & s on4 ,aside f ! slight *ange due to ! dropp+ back ( ! seasons 9 ! orbit by ! precession ( ! equ9oxes1 ! actual "t ( ! equ9oxes & sol/ices may be consid]$ z con/ant1 yet ! dates v>y a few h\rs4 ,! ye> 9 common use--! tropical ye>--conta9s approximately #cfe days1 yet we take acc\nt ( only #cfe days1 ! extra day be+ laid aside = future reckon+4 ,dur+ ! next ye> ?is #f h\rs w be augm5t$ by #f m2 ! next by ano!r #f1 mak+ #ah h\rs ahead ( ! cal5d>4 ,! f\r? ye> ?is am\nt rea*es #bd h\rs1 & a full day1 ! #bi? ( ,febru>y1 is add$ to ! cal5d> = t ye>1 & we are squ>e aga94 ,b ! diff]5t equ9oxes & sol/ices occur at j #cfd days2 tak+ = example ! v]nal equ9ox1 x occurs on ! foll[+ 7approximate7 dates1 :i* x w be notic$ are #f h\rs lat] ea* ye>3 #aijh--,m>* #bj1 #ab h\rs 7leap ye>74 #aiji--,m>* #bj1 #ah h\rs4 #aiaj--,m>* #bj1 #bd h\rs or ,m>* #ba/ noon4 #aiaa--,m>* #ba1 #f h\rs4 #aiab--,m>* #bj1 #ab h\rs 7leap ye>74 ,x is evid5t by ! above t ! ins]tion ( ! extra day j previ\s to ! equ9ox 9 ! leap ye>s1 sets ! date ( ! equ9ox back a day by ! cal5d>4 ,juggl+ ! day z %[n above causes ! *ange 9 ! cal5d> dates ( ^! ph5om5a4 ,,*apt] ,v ,corrections = ,obs]v$ ,altitudes ,! obs]v$ altitude ( a heav5ly body1 z measur$ ) ! sextant1 requires treatm5t = num]\s errors to r$uce x to ! true altitude & make x ready = use 9 work+ any ( ! navigational obs]vations4 ,! am\nt ( error v>ies 9 diff]5t bodies1 ! moon requir+ ! maximum & ! fix$ /> ! m9imum correction4 ,all ! errors are n common to all bodies1 t is1 ) "s1 c]ta9 errors become s insignificant t !y are ca/ aside4 ,^! errors comprise ! index error ( ! sextant1 refraction1 dip1 semi-diamet]1 & p>allax4 ,9 ,table #df1 ,b[dit*1 w be f\nd ! comb9$ corrections 7index error except$7 to be appli$ to an obs]v$ altitude ( a /> or planet & to t ( ! sun's l[] limb4 ,a supplem5t>y table furni%es an additional correction to be appli$ to ! semi-diamet] ( ! sun :5 accuracy is desir$4 ,^! corrections w n[ be discuss$ 9 ! ord] nam$3 ,,index ,,correction ,! index & horizon glasses ( a sextant are suppos$ to be p>allel :5 ! z]o ( ! v]ni] & ! z]o ( ! limb are 9 "o1 & ) ?is ! case1 ! true & reflect$ images se5 9 ! horizon glass %\ld exactly co9cide4 ,any diff]5ce betwe5 !m is ! index error4 ,x is seldom t a sextant is s well adju/$ t no index error exi/s1 b x is n desirable to keep tamp]+ ) ! in/rum5t ) an attempt to elim9ate ?is error1 = x w 9 "t injure its accuracy4 ,by te/+ ! sextant at ea* sight1 ! error c be closely wat*$ & all[ance made = x 9 correct+ altitude4 ,! easie/ & mo/ accurate me?od ( asc]ta9+ ?is error is by us+ a /> 9 ! foll[+ mann]3 ,set ! z]o ( ! v]ni] a little to ei!r side ( ! z]o ( ! limb1 & obs]ve a #b;d or #c;d magnitude />--move ! reflect$ image pa/ ! real & note if !y pass directly ov] "o ano!r4 ,if n1 ! horizon glass is n p]p5dicul> & ne$s adju/m5t4 ,br+ ! reflect$ /> 9 exact conjunction ) ! real />1 & read (f ! index correction--if ! z]o ( ! v]ni] is to ! left ( ! z]o ( ! limb--on ! arc--! diff]5ce is m9us 7-7 & subtract$ f ! obs]v$ altitude2 & if to ! "r--(f ! arc--x is plus 77 & add$4 ,a well-kn[n rule ( ?umb expresses x ?us3 if x's on x's (f1 & if x's (f x's on4 ,! sea horizon is also available = det]m9+ ?is correction & s]ves ! purpose ) fairly accurate results4 ,,semi-,,diamet] ,9 measur+ ! altitude ( c]ta9 bodies = navigational purposes1 x is necess>y to det]m9e ! di/ance ( ! c5t] ( ! body above ! horizon4 ,to accompli% ?is 9 an accurate mann] ! l[] edge or limb is br\ght d[n to ! horizon & ! semi-diamet] appli$ to ?is measur$ altitude4 ,:5 ! l[] limb is us$1 z is ! usual practice1 ! correction = semi-diamet] is obvi\sly plus 774 ,! upp] limb c be resort$ to1 h[ev]1 %\ld ! l[] side ( ! body become veil$ by cl\d1 & 9 ?is case ! correction is m9us 7-74 ,semi-diamet] ( ! sun is obta9$ readily f ! ,nautical ,almanac = ea* t5-day p]iod1 = x mu/ be rememb]$ t ! sun is cont9ually *ang+ its di/ance f ! e>?1 & consequ5tly ! diamet] ( ! =m] is increas$ & less5$ slightly at diff]5t times ( ! ye>4 ,= in/ance3 ,on ,janu>y #b;d1 :5 ! e>? is ne> p]ihelion & we are at our ne>e/ po9t to ! sun1 ! semi-diamet] is #af #ag4ij1 :ile on ,july #b;d1 :5 we are 9 ! remote p>ts ( ! orbit1 ! semi-diamet] is only #ae #de4fi1 mak+ a diff]5ce ( ov] #cb4 ,! moon be+ su* a ne> neighbor ( ours gives m tr\ble 9 det]m9+ h] diamet]4 ,besides be+ greatly affect$ by h] rapidly *ang+ di/ance f ! e>?1 a fur!r correction is occasion$ by ! fact t our position on ! surface is ne>] ! moon at times ?an is ! c5t] ( ! e>?4 ,t is1 :5 ! moon is 9 ! z5i? we are #djjj miles1 ! e>?'s radius1 ne>] t body ?an :5 %e is 9 our horizon4 ,x is evid5t t ! direction ( ! moon 9 our s5sible horizon is at "r angles to a p]p5dicul> erect$ at our place ( obs]vation & pass+ ?r\gh ! e>?'s c5t]1 & ?is aga9 makes x evid5t t ! moon is ab\t equally di/ant f ! e>?'s c5t] & our position on ! surface2 b z %e asc5ds ! heav5s %e comes ne>] our position until 9 ! z5i? ! di/ance has be5 r$uc$ by #djjj miles & ! diamet] appe>s correspond+ly l>g]4 ,draw a diagram & see = y\rself4 ,?is ,augm5tation ( ! ,semi-diamet]1 due to ! altitude1 is f\nd tabulat$ 9 ,b[dit*1 ,table #ah4 ,! semi-diamet] becomes too small to consid] 9 ord9>y navigation :5 obs]v+ any ( ! planets1 & ( c\rse fix$ />s are beyond its scope4 ,,refraction ,ev]yone kn[s t ! blade ( an o> :5 dipp$ 9 ! wat] appe>s to be b5t 9 a rem>kable mann] at ! surface4 ,?is is a cle> case ( refraction4 ,%\ld ! o>1 h[ev]1 be held "u ev]y:]e at an equal dep?1 a squ>e look d[nw>d at x w\ld fail to %[ any refraction4 ,s x becomes evid5t t refraction is caus$ by ! rays ( light pass+ obliquely f a r>] to a d5s] m$ium or vice v]sa4 ,a ray ( light com+ f a heav5ly body to ! e>? passes ?r\gh a m$ium ( gradually increas+ d5sity1 f ! ?9 out] air to ! d5s] atmosph]e at ! surface ( ! e>?4 ,! ray ( light consequ5tly becomes curv$ d[nw>d & rea*es ! e>? at a po9t ne>] ! heav5ly body ?an w\ld be ! case if ! light ray travel$ 9 a /raight l9e4 ,! effect ( ?is to ! obs]v] is t ! body appe>s high] ?an x really is4 ,! diff]5ce betwe5 ! actual direction ( ! ray ( light unaffect$ by ! air1 & our l9e ( vision z we see ! body1 is ! refraction4 ,! am\nt ( refraction ord9>ily affect+ an obs]v$ altitude dep5ds ^u ! di/ance ( ! body above ! horizon4 ,at ! z5i?1 ! rays ( light1 ent]+ our atmosph]e p]p5dicul>ly1 are n deflect$ & refraction is nil4 ,b1 on ! o!r h&1 :5 ! body is ne> ! horizon1 ! rays ( light pass ?r\gh ! atmosph]e at a %>p angle & are consequ5tly subject to ! greate/ b5d+1 ?us giv+ u our maximum refraction4 ,9 fact1 ?is elem5t becomes s unreliable 9 l[ altitudes t x is n advisable to obs]ve a body :5 less ?an #aj or #ac above ! horizon4 ,?is 9 no way conc]ns be>+s tak5 ( bodies 9 ! horizon = amplitude1 z refraction affects ! altitude & n ! azimu? ( a body4 ,,dip ,x is a well-kn[n fact to e seaman t by go+ al(t1 he c pick up a light soon] ?an on deck2 t is1 ! high] 8 elevation ! wid] 8 horizon becomes4 ,! horizon ( a man 9 a small boat is only ab\t #c miles away1 b1 if he climbs to ! bridge ( a /eam] "s #fj feet above ! wat]1 he f9ds t ! horizon has rec$$ until he has a range ( ab\t #i miles4 ,! fact t ! horizon c be alt]$ by *ang+ ! altitude %\ld appeal to e navigator z a possible means ( gett+ a horizon 9 foggy wea!r1 by go+ al(t or gett+ z l[ z possible1 provid$ ! fog bank is ly+ above or close to ! wat]4 ,! altitude ( a body is measur$ to ! visible horizon1 yet ! measurem5t mu/ be adju/$ to ! s5sible horizon be=e ! true altitude c be obta9$4 ,?is correction is accompli%$ by apply+ to ! obs]v$ altitude ! am\nt ( ! angle =m$ at ! obs]v]s eye by ! planes ( ! s5sible & visible horizons4 ,! angle is kn[n z ! dip ( ! horizon4 ,x is readily se5 t ?is angle always makes ! obs]v$ altitude too l>ge1 = ! eye if locat$ at ! exact surface ( ! sea1 !oretically sees ! s5sible & visible horizons 9 "o1 :ile at e elevation above ! surface x depresses ! visible horizon correspond+ly4 ,x is1 !re=e1 always necess>y to apply ! dip z f\nd 9 ,table #ad1 ,b[dit*1 ) a m9us 7-7 sign4 ,an inspection ( ! table ( dip w %[ t ! rate ( increase ( ?is error becomes m rapid z ! height ( ! eye is dim9i%$4 ,to illu/rate3 ,! read] w note t betwe5 an elevation ( #d feet & "o ( #i feet !re is a diff]5ce ( #a m9ute 9 ! dip1 :ile high] up1 say betwe5 #bf feet & #ch feet1 a diff]5ce ( #a m9ute is likewise f\nd1 yet 9 ! fir/ in/ance !re 0 a range ( #e feet & 9 ! second a range ( #ab feet4 ,?is fact 9 itself is an argum5t 9 favor ( obs]v+ altitudes at a good height above ! wat]4 ,9 calculat+ a m]idian altitude1 an error 9 ! dip directly affects ! result by a correspond+ am\nt1 s extra c>e %\ld be ex]cis$ 9 ?is respect4 ,9 ?is in/ance1 we endeavor to locate ! body relative to our z5i? & any?+ t affects its altitude directly affects ! latitude4 ,9 a "t sight1 a diff]5t pr9ciple is involv$4 ,"h ! position ( ! body z def9$ by ! latitude locates ! apex ( "o angle ( ! a/ronomical triangle & h5ce a small error 9 ! altitude w v likely cause a great] effect on ! longitude4 ,an allusion 0 made "u ! caption ( ,refraction to ! displacem5t ( ! visible horizon by t]re/rial refraction to detect :i* requires wat*fulness on ! navigator's "p4 ,! famili> 8loom0 se5 along ! coa/ is an example ( ! work+s ( v>iable refraction4 ,n[ imag9e ?is di/ortion less aggravat$ ) no l& to %[ its exi/5ce & y h a good illu/ration ( ?is error4 ,refraction ( ?is nature is usually f\nd dur+ light airs & calms :5 ! diff]5t lay]s ( air arrange !mselves accord+ to _! temp]atures4 ,! heat$ air ov] l& bel[ ! horizon 9 hot wea!r w displace ! int]v5+ horizon2 moreov]1 :5 ! air is w>m] ?an ! sea1 ! horizon is elevat$ above ! normal &1 :5 ! conditions are rev]s$1 ! horizon is unduly depress$4 ,?us lights become visible a little soon] aft] a hot day a%ore4 ,! ,r$ ,sea1 ,gulf ,/ream1 m\? ( ! ,amazon1 & o!r l>ge riv]s are places :]e ! horizon %\ld be especially di/ru/$4 ,capt4 ,lecky1 9 8 fam\s ,wr9kles 9 ,practical ,navigation1 ref]s to an exp]i5ce he once _h ) ?is error4 ,! latitude _h be5 f\nd 8by an excell5t m]idian altitude ( ! sun to be z mu* z #ad 9 error4 ,! "t 0 mid-w9t]--! day a cle> cl\dless "o--! sea smoo?1 & ! horizon clean-cut4 ,five obs]v]s at noon agre$ )9 ! usual m9ute or half m9ute ( arc1 nev]!less1 on mak+ ,long ,isl& 7,u4 ,s4 ,a47 9 less ?an two h\rs aft]w>ds1 ! latitude 0 f\nd wrong to ! am\nt /at$4 ,_m su* cases h come "u ! writ]'s notice1 b ?is "o alone is cit$ on acc\nt ( ! magnitude ( ! ph5om5on40 ,:at ,capta9 ,lecky said 9 8 "w on navigation is reliable & ?is %\ld s]ve to make an impression z to ! dang]s ( su* occurr5ces4 ,9 cle> wea!r ?is displacem5t ( ! horizon may be less5$ some:at by obs]v+ f al(t4 ,by ext5d+ ! horizon1 su* di/urb+ influ5ces z ! motion ( ! vessel & an irregul> horizon caus$ by r\gh sea are m9imiz$4 ,9 hazy wea!r1 h[ev]1 x is recomm5d$ to obs]ve l[1 br++ ! horizon z close z possible4 ,,p>allax ,9 calculat+ ! true altitude ( a body ! di/ance ( its c5t] above ! horizon is suppos$ to be measur$ f ! c5t] ( ! e>?1 or :at is ! same ?+1 ! altitude above ! rational horizon4 ,! application ( semi-diamet] adju/s ! measur$ angle ) ! c5t] ( ! body1 :ile p>allax corrects ! error due to our obs]v+ f ! surface ( ! e>? to ! s5sible horizon1 in/ead ( f ! c5t] to ! rational horizon4 ,p>allax1 9 o!r words1 is ! angle =m$ at ! body by ! l9es drawn f ! obs]v]'s position1 & f ! c5t] ( ! e>?1 respectively4 ,?is angle is subt5d$ by ! radius ( ! e>?1 & x is obvi\s t ! f>!r away a body is1 ! small] ! angle1 & consequ5tly ! less ! p>allax4 ,s :5 deal+ ) planets or fix$ />s1 x becomes insignificant & no p>allax is consid]$4 ,! moon1 on ! contr>y1 is s close abo>d t ! angle ( p>allax rea*es a value ( ne>ly #a2 z a m9ute ( altitude means a m9ute ( latitude & 9 turn a mile1 s ) ?is body ! error due to p>allax mu/ be c>efully det]m9$4 ,9 ! case ( ! sun1 h[ev]1 x is some:at ( a wa/e ( "t to bo!r ) p>allax1 = x nev] exce$s #h or #i & su* f9e calculation is uncall$ = 9 ord9>y navigation :]e s _m great] errors mu/ be kept 9 sight4 ,h[ev]1 we desire to elim9ate e kn[n elem5t ( error )\t undue figures1 s x is recomm5d$ t ,table #bj;,b1 ,b[dit*1 be us$1 :]e )\t extra tr\ble ! p>allax may be f\nd conv5i5tly comb9$ ) ! refraction4 ,:5 a body is 9 ! s5sible horizon1 ! p>allax is greate/4 ,! angle ( p>allax subt5d$ by ! radius ( ! e>? is !n an acute angle ( a "r-angl$ triangle & is z l>ge z x c possibly be ) ! body at ! same di/ance4 ,z ! body obta9s altitude above ! horizon1 ! "r angle ( ! triangle 7at ! obs]v]7 becomes obtuse & our acute angle ( p>allax becomes small] & small] until ! body rea*es an altitude ( #ij--;9 our z5i?1 :5 ! obtuse-angl$ triangle has resolv$ itself into ! p]p5dicul> l9e t passes ?r\gh our position & ! e>?'s c5t]4 ,! angle ( p>allax "h disappe>s4 ,:5 a body is 9 ! horizon1 its p>allax is kn[n z ,horizontal ,p>allax 9 contra-di/9ction to ,p>allax ( ,altitude4 ,! latt] has become g5]ally kn[n among navigators m]ely z p>allax4 ,our position on ! surface causes a body to appe> l[] ?an if view$ f ! c5t] ( ! e>?1 s ! error ( p>allax is add$ to ! obs]v$ altitude2 :51 h[ev]1 x is comb9$ ) refraction x is subtract$ 9 an obs]vation ( ! sun1 b add$ :5 ! moon is us$4 ,! p>allax ( ! moon is excessive because ! radius ( ! e>? becomes a consid]able am\nt :5 comp>$ ) ! close proximity ( ! body1 & causes a consid]able angle at ! body betwe5 ! l9es drawn f ! obs]v] & t drawn f ! c5t] ( ! e>?4 ,! *ange 9 p>allax is s great t x becomes necess>y 9 ord] to pres]ve accuracy to correct ! obs]v$ altitude = index correction1 dip & semi-diamet]1 to secure an approximate correct$ altitude be=e attempt+ to correct = p>allax4 ,! horizontal p>allax1 :i* is ! angle subt5d$ by ! e>?'s radius :5 ! moon is 9 ! horizon1 is tak5 f ! ,nautical ,almanac1 & ) ?is & ! approximate altitude z argum5ts1 ent] ,table #ah1 ,b[dit*1 & pick out1 hav+ reg>d = correction tables at ! "r1 ! p>allax & refraction comb9$4 ,! usual corrections to ! obs]v$ altitude ( ! sun or />s c be pick$ out at once f ,table #df1 ,b[dit*1 :]e !y are all comb9$ = a quick correction4 ,,*apt] ,,vi ,latitude ,,m]idian ,,altitude ,x is surpris+ to u1 9 ^! advanc$ days ( nautical sci5ce1 to read ( our adv5tur\s ance/ors ( a c5tury ago navigat+ _! %ips to all p>ts ( ! kn[n & unkn[n _w ) no?+ to guide !m b _! dead reckon+ & ! latitude crudely obta9$ by ! me?od ( m]idian altitude4 ,_m ( our f9e/ %ips1 z late z ! fir/ decade ( ! n9ete5? c5tury1 sail$ to ,*9a & back ) no k ( _! longitude save :at ! ma/] guess$ x to be4 ,ev5 9 lat] days mu* navigat+ has be5 done 9 ! less lucrative trades by m>9]s :o _h no k ( ! me?od ( f9d+ longitude4 ,x requir$ m "t & di/ance to navigate by latitude & dead reckon+ only1 z x 0 n always safe to lay a c\rse f an indef9ite position directly = ! coa/4 ,x 0 ! cu/om 9 ! old days to keep (f s\nd+s until on ! latitude ( ! port ( de/9ation1 !n /e] due we/1 & :atev] ! longitude might turn out to h be5 ! ma/] w\ld soon] or lat] make ! l& 9 ! vic9ity ( 8 port4 ,! fir/ /ep 9 obta9+ ! latitude by m]idian altitude is ! measurem5t ) ! sextant ( ! sun's altitude4 ,?is is done :5 x rea*es its highe/ po9t 9 its c\rse across ! sky2 ?is occurs :5 x be>s due ,n4 or ,s4 true & ?is mom5t is local app>5t noon4 ,a few m9utes be=e ?is "t ! image ( ! sun %\ld be br\ght to ! horizon1 & by sw++ ! l[] "p ( ! in/rum5t ! image w be made to sw+ likewise 9 an arc2 ! l[e/ po9t ( its l[] edge 7limb7 %\ld !n be br\ght 9 contact ) ! horizon z closely z ! circum/ances w p]mit4 ,! image w keep ris+ f ! horizon1 b by us+ ! tang5t screw x c be cont9ually br\ght back to contact4 ,at noon x w hang1 & dip bel[2 ! read+ ( ! sextant at ?is mom5t is ! m]idian altitude4 ,9 work+ ! problem ?ree quantities are us$ & ! navigator mu/ be famili> ) !m3 ,! fir/ is ! z5i? di/ance 7z71 :i* z its "n implies is ! sun's 7or />s7 di/ance f ! z5i?4 ,z5i? is #ij f ! horizon1 s ! true altitude ( ! body subtract$ f #ij is z ! quantity desir$4 ,! second elem5t is ! decl9ation 7d71 :i* is ! di/ance 9 degrees1 m9utes1 seconds1 ( ! body ei!r nor? or s\? ( ! equator4 ,?is is tak5 f ! ,nautical ,almanac4 ,! ?ird & result+ quantity is ! latitude1 :i* is ! di/ance 9 degrees1 m9utes1 seconds1 ( ! %ip ei!r nor? or s\? ( ! ,equator4 ,! altitude obs]v$ tak5 ) ! sextant at noon is correct$ = semi-diamet]1 p>allax1 dip1 refraction & in/rum5t error 7if any exi/s74 ,^! corrections are expla9$ 9 detail 9 ,corrections = ,obs]v$ ,altitudes4 ,! decl9ation ( ! sun is con/antly *ang+ betwe5 #bc ,n4 & #bc ,s4 ,?is is giv5 9 ! ,nautical ,almanac = ea* two h\rs ( ,gre5wi* mean "t ) ! diff]5ce = ea* h\r giv5 = ea* day4 ,s x becomes necess>y to asc]ta9 ! decl9ation at ! mom5t ( obs]vation1 namely1 at local noon4 ,?is any:]e 9 ! ,atlantic w occur subsequ5t to ,gre5wi* noon1 z ! sun 7app>5tly7 passes ar\nd ! _w f ! ea/w>d to ! we/w>d once a day--#bd h\rs--:i* corresponds to #cfj ( longitude4 ,! rate ( travel is !re=e equival5t to #ae 9 an h\r4 ,h5ce if ! sun crosses ,gre5wi* m]idian & five h\rs lat] crosses ! m]idian ( ! %ip1 say 9 #ge ,w41 ! int]val is #ge divid$ by #ae1 or #e h\rs4 ,dur+ ?is int]val ! sun has *ang$ 9 decl9ation nor?w>d or s\?w>d & %\ld be pick$ out ( ! ,almanac = #e h\rs ,gre5wi* mean "t4 ,:5 ! z5i? di/ance & decl9ation are at h& ! latitude is obta9$ by a m]e algebraic addition1 :i* is1 z d latitude2 :]e1 if ! body be>s s\? ! z is m>k$ 1 if nor? x is m>k$ -2 if ! decl9ation is s\? x is m>k$ - & if nor? x is 4 ,! result ( ! addition if - indicates s\? latitude1 if nor? latitude4 ,! m]idian altitude ( a />1 planet or moon is f\nd 9 a simil> mann]4 ,! =mula ( z d latitude1 hav+ reg>d to signs nam$ z above1 is applicable to ea*4 ,! decl9ation & ! correction ( ! obs]v$ altitude are pick$ out ( ! ,almanac & ,b[dit* tables 9 a some:at diff]5t mann] peculi> to ea* body4 ,x is f\nd by _m navigators to be m conv5i5t to obs]ve a body = m]idian altitude by "t ?an 9 wait+ = ! 8dip40 ,! altitude is tak5 at exactly local app>5t noon 9 case ( ! sun & ! "t ( m]idian passage 9 ! cases ( o!r bodies4 ,?is exp$i5t is especially desirable 9 obs]v+ />s1 z ! horizon is n z di/9ct & ! 8dip0 n s easily detect$ z ) ! sun4 ,9 ord] to secure ! local mean "t 7,l4 ,m4 ,t47 ( a />'s transit1 ! ,g4 ,m4 ,t4 ( ! />'s transit ov] ! ,gre5wi* m]idian is f\nd 9 ! ,nautical ,almanac 7p4 #if7 = ! fir/ day ( ! mon? & correct = ! day by table on next page 7,n4 ,a474 ,! %ip's mean "t ( transit w be ! same1 z bo? sun & /> hold _! relative positions z ! /> moves f ,gre5wi* to ! %ip's m]idian except = ! small ret>dation ( ! sun's movem5t ov] ! />'s movem5t4 ,?is is be/ f\nd at ! foot ( page #b1 ,nautical ,almanac1 :]e ! longitude 9 "t gives ! correction to be subtract$ f 7,g4 ,m4 ,t47 ( transit :i* w give ! local mean "t ( transit at %ip--! "t to obs]ve ! />4 ,an obs]vation ( a planet is simil>ly h&l$4 ,! moon is some:at unreliable ow+ to its rapid *anges 9 position & ! l>ge corrections necess>y to correct ! altitude1 & is consequ5tly r an unpopul> body to obs]ve4 ,h[ev]1 !re are times :5 %e might prove valuable 9 giv+ position :5 mu* ne$$4 ,9 ! case ( ! sun ! "t ( transit is local app>5t noon1 by apply+ ! longitude 9 "t gives ,gre5wi* app>5t "t ( local noon1 & correct$ = equation ( "t gives ,gre5wi* mean "t ( transit4 ,x is (t5 necess>y to report ! latitude at noon v quickly to ! ma/]4 ,?is c be accompli%$ by calculat+ ! problem to a po9t :]e ! addition or subtraction ( ! obs]v$ altitude is all t is necess>y to give ! latitude4 ,! corrections are appli$ 9 advance by ! e/imat$ altitude1 & decl9ation correct$ by ! e/imat$ longitude4 ,art4 #cbe1 ,b[dit*1 gives ! con/ants to be us$ 9 f\r diff]5t situations4 ,,circum- ,,or ,,ex-,,m]idian ,,altitude ,x frequ5tly happ5s1 especially 9 ! high] latitudes1 t an aggravat+ mass ( cl\d drives ov] ! sun or o!r objects t y are *as+1 ) ! tang5t screw1 & x is lo/ f view toge!r ) all hope ( a m]idian altitude4 ,b su* an un=tunate occurr5ce z ! loss ( ! mid-day latitude may be av]t$ by employ+ ! ,circum-m]idian sight or ,ex-m]idian1 z our ,engli% c\s9s call x4 ,! m>9] accu/om$ to its use 8%oots0 ! sun & notes ! "t by *ronomet] or wat*4 ,or on cl\dy days1 he w\ld be /&+ by1 ne> app>5t noon wat*+ = a *ance to cat* a glimpse ( ! object ?r\gh a rift ( cl\d1 & !reby =e/all ! loss ( 8 latitude4 ,! !ory ( ?is obs]vation is extremely simple1 be+ m]ely to add to ! obs]v$ altitude1 tak5 be=e or aft] app>5t noon :5 ! sun is be+ consid]$1 ! am\nt ( rise or fall betwe5 ! "t ( sight & ! "t ( culm9ation1 & proce$ ) ?is am5d$ altitude z 9 an ord9>y m]idian altitude sight4 ,! use ( ?is me?od ( obta9+ ! latitude is re/rict$ to c]ta9 limits4 ,^? :o use ,b[dit* ,tables w f9d !mselves re/rict$ to #bf m9utes f ! "t ( transit & a decl9ation ( #fc1 :ile ,br5t's ,ex-m]idian ,tables all[ a great] scope & _! limit ( #gj ( decl9ation includes _m />s t w\ld be o!rwise unavailable4 ,a good guide is to nev] all[ ! numb] ( degrees 9 ! z5i? di/ance to be exce$$ by ! numb] ( m9utes f noon4 ,9 v high altitudes circum-m]idians are n to be recomm5d$1 & ! high] ! altitude1 ! m accurate mu/ be ! "t us$4 ,?is is pla9 :5 x is realiz$ t ! l[] ! sun's altitude at noon1 ! m ne>ly its diurnal pa? approa*es ! l9e ( ! horizon2 ) ! less5+ curve ( its c\rse1 comes a less5+ rise ne> noon1 h5ce less accuracy is ne$$ 9 ! exact "t ( sight f t ( transit4 ,9 ! tropics1 h[ev]1 :]e high altitudes ( ! sun prevail1 ! cl\ds d n (f] su* an elem5t ( bo!r z !y d f>!r nor? or s\?1 & !re ?is problem z appli$ to ! sun loses its popul>ity4 ,9 practice ! use ( ! tables ( ,b[dit* makes ?is problem an exce$+ly simple "o1 requir+ b few figures4 ,table #bg conta9s ! value ( rise ( ! body = "o m9ute1 b z ?is rise v>ies z ! squ>e ( ! int]val f noon1 x becomes necess>y to resort to ano!r table 7#bf7 ( con/ants = a multipli]1 9 lieu ( ! numb] ( m9utes f noon4 ,t is1 if we %\ld multiply ! am\nt ( rise or fall = #a m9ute by ! numb] ( m9utes f noon1 we w\ld n be tak+ into acc\nt ! decreas+ rapidity ( rise or ! increas+ rapidity ( fall z ! body approa*es or leaves ! m]idian4 ,b ,table #bf provides a multipli] :i* reconciles ?is inequality & gives ! prop] correction to apply to ! obs]v$ altitude4 ,?is quantity is add$ 9 e case :]e ! upp] transit is obs]v$ b subtract$ :5 a sight is tak5 bel[ ! pole :]e ! conditions are rev]s$4 ,!re are sev]al pamphlets & books on ! m>ket f :i* ! correction to ! obs]v$ altitude may be obta9$4 ,all are simple 9 =m & ) _! explanations are readily und]/ood4 ,notable among ^! ,ex-m]idian ,tables are ^? by ,capt4 ,armi/$ ,ru/1 ,u4 ,s4 ,n4 ,! circum-m]idian is a reliable me?od ( f9d+ ! latitude1 b ! "t us$ %\ld be accurate to produce satisfactory results4 ,if1 h[ev]1 ! conditions be favorable1 x is n necess>y to disc>d ?is obs]vation ev5 if ! correctness ( ! "t is some:at 9 d\bt1 = 9 ,t[son's ,ex-m]idian ,tables is f\nd ?is note3 8,if equal altitudes be tak5 be=e & aft] ! m]idian passage1 half ! elaps$ "t may be employ$ z ! h\r angle = det]m9+ ! r$uction4 ,or1 :5 ! altitudes be=e & aft] noon diff] by only a few m9utes1 ! mean ( ! two may be r$uc$ by employ+ half ! elaps$ "t z ! h\r angle = r$uc+ ! mean altitude40 ,9 practic+ ?is sugge/ion x is necess>y1 9 ord] to pres]ve accuracy1 to put ! vessel on ! ne>e/ ea/ or we/ c\rse dur+ ! run betwe5 ^! equal altitude obs]vations4 ,?is is imp]ative 9 a swift vessel4 ,! />s & planets (f] !mselves = use 9 ?is problem z 9 all o!rs1 & "h !y possess special advantages ( :i* ! m>9] may well avail himself4 ,inde$1 x may be said 9 tru? t :5 a horizon c be obta9$ ! latitude is always available ?r\gh ?is problem4 ,& "r "h %\ld be impress$ ^u ! navigator ! great advantage ( becom+ famili> ) ! />s1 n m]ely ^? ( greate/ brilliancy1 b ! 8less] lights0 t c be obs]v$4 ,among ! latt]1 especial acqua9tance %\ld be s\ght ) ^? ^: "r asc5sions place !m 9 ! gaps betwe5 ! l>g] />s1 ?us almo/ ! entire heav5s are includ$ 9 ! scope ( op]ations1 mak+ ! latitude & longitude practically always available1 provid$ aga9 !re is a horizon4 ,/> *>ts1 planisph]es1 & globes are = sale ev]y:]e & no /udy is m int]e/+ ?an t ( ! ways ( ^! cele/ial travel]s4 ,!y appe> & pass ea* day1 ye> aft] ye>1 until y consid] !m z old fri5ds1 &1 z y come on deck = ! mid-wat*1 y look = ,orion1 = in/ance1 ! same z y look = ! memb]s ( y\r wat* at _! prop] /ations4 ,b we are (f our c\rse4 ,! increas+ popul>ity ( ! circum-m]idian & its und\bt$ accuracy :5 us$ ) "t obta9$ f a c>efully rat$ *ronomet]1 is break+ ! hold ( ! "t-honor$ m]idian altitude4 ,!re is no wait+ ) cold f+]s1 p]haps1 = ! body to dip = ?is sight1 j %oot ! />1 note ! "t & duck = ! *>t room to "w x up4 ,! mo/ favorable position ( a body = a circum-m]idian altitude is "o 9 :i* ! rise & fall ne> ! m]idian are sl[4 ,9 ! case ( ! sun1 x 0 expla9$ t a l[ altitude prov$ ! be/1 b1 9 ! case ( ! />s1 we f9d ano!r condition2 ^? ne> ! pole1 or 9 o!r words1 ( l>ge decl9ations1 describe su* small diurnal circles t "h also ! *ange 9 altitude is correspond+ly small1 ?us fulfill+ a desir$ condition = ! successful work+ ( ?is problem4 ,to illu/rate ?is po9t ! read] is ref]r$ to ,pol>is4 ,n[ ?is /> has an extremely small diurnal circle & x w be rememb]$ t ! altitude is = all practical purposes ! same = a half h\r ei!r side ( ! m]idian1 %[+ ! extreme sl[ness ( its movem5t ( revolution4 ,! />s are us$ 9 ! same way z ! sun except1 ( c\rse1 t ! di/ance f ! m]idian becomes ! />'s h\r angle in/ead ( local app>5t "t4 ,?is is readily obta9$ z foll[s3 ,add+ to ! ,gre5wi* mean "t ! sid]eal "t ( ! prec$+ ,gre5wi* mean noon 7,nautical ,almanac71 toge!r ) ! accel]ation ( ,gre5wi* mean "t 7,table #i ,b[dit*71 gives ! "r asc5sion ( ! m]idian4 ,tak+ ! diff]5ce betwe5 ?is latt] quantity & ! "r asc5sion ( ! />1 we h ! />'s h\r angle1 we/1 if ! "r asc5sion ( ! m]idian is great] ?an t ( ! />1 & ea/1 if contr>y conditions exi/4 ,! circum-m]idian1 z well z ! /raight m]idian altitude1 is available = use ( />s ne> ! m]idian bel[ ! pole1 &1 z "o proce$s into high] latitudes1 ! pole becomes m & m elevat$1 (f]+ !reby m opportunities = practic+ ?is phase ( ! problem4 ,! only feature to be rememb]$ 9 ?is case is t ! body is high] at ! "t ( a circum-m]idian ?an :5 x transits1 s ! correction to be appli$ to ! obs]v$ altitude mu/ be subtract$ 7-7 9 ord] to obta9 ! m]idian altitude4 ,! planets1 too1 are us$ by ! ex-m]idian altitude me?od1 b be+ w&]]s 9 ! heav5s _! "r asc5sions & decl9ations mu/ be det]m9$ = ! ,gre5wi* date f ! ,nautical ,almanac4 ,! am5d$ altitude ( any body is assum$ to be ! m]idian altitude & is us$ 9 ! famili> =mula z d latitude 7see ,latitude by m]idian altitude72 b x mu/ be borne 9 m9d t ! result is n ! latitude at noon b at ! "t ( sight4 ,if ! obs]vation 0 made say #i m9utes be=e noon & ! latitude consid]$ to be ! position at local app>5t noon z 9 an ord9>y m]idian altitude1 !re w\ld be an error ( #c miles f ! correct position = a #bj-knot /eam]4 ,ano!r po9t to be gu>d$ aga9/ is t :5 tak+ sev]al altitudes & _! correspond+ times _! mean _c be obta9$ 9 ! ord9>y way1 b ea* altitude mu/ be sep>ately r$uc$ & ! mean tak5 ( ! results4 ,x is aga9 necess>y to div]ge f ! subject to impress on ! m>9] an urg5t w>n+ aga9/ any?+ b ! mo/ untir+ vigilance 9 ! c>e ( 8 *ronomet]1 & ! keep+ ( accurate "t4 ,if ?is elem5t _c be dep5d$ ^u !re w be _m h\rs ( anxiety com+ to him & probably soon] or lat] d[nright disa/]4 ,! almo/ univ]sal e/abli%m5t ( "t signals 9 all good-siz$ sea ports ( ! _w toge!r ) radio "t signals s5t broadca/ all[s b little excuse = n obta9+ a good rate by ! "t a vessel is ready = sea4 ,e well-kn[n "w on navigation deals ) ! subject ( rat+ *ronomet]s & s no space w "h be giv5 to x4 ,aft] read+ ?is talk on "o ( ! mo/ important & up-to-date obs]vations :]e s mu* dep5ds ^u ! accuracy ( ! "t1 ! read] _c fail to appreciate ?is e>ne/ admoni%m5t4 ,,pol>is ,! process ( f9d+ ! latitude by means ( ,pol>is is valuable1 comp>atively %ort & ! result1 if ! conditions are favorable1 is accurate4 ,we w consid] x fir/ 9 a g5]al way4 ,! imag9>y l9e repres5t+ ! e>?'s axis1 if ext5d$ indef9itely1 is presum$ to pi]ce ! cele/ial sph]e at ! cele/ial pole1 !re=e = an obs]v] /&+ at our nor? pole ?is imag9>y po9t w\ld be exactly 9 ! z5i? & h5ce #ij f ! horizon j z ! pole is #ij f ! equator1 ^! am\nts evid5tly be> a relation to "o ano!r4 ,%\ld ! p]son at ! pole leave 8 frigid surr\nd+s & proce$ t[>d ! equator1 he w\ld note t ! pole _h dropp$ l[] & l[] 9 ! heav5s1 precisely 9 proportion to 8 progress s\?w>d1 until at l5g?1 :5 ! equator 7latitude #j7 0 rea*$1 ! pole w\ld be obs]v$ to be exactly 9 ! horizon 7altitude #j74 ,f ?is x is easy to d$uce ! /atem5t t ! altitude ( ! cele/ial pole is equal to ! latitude ( ! place ( obs]vation4 ,! object ( ?is problem !n is to obta9 ! altitude ( ! cele/ial pole4 ,?is po9t1 un=tunately1 is m>k$ by no /> ( :i* a direct altitude may be obs]v$ to aid ! navigator 9 rea*+ ?is desir$ result4 ,!re is1 h[ev]1 a /> ( ! #b;d magnitude1 call$ ,pol>is 7because ( its proximity to ! pole7 ) a pol> di/ance ( only #a4 ,z all fix$ />s are app>5tly revolv+ 9 circles ar\nd ! cele/ial pole1 ?is /> jo9s ! gr& procession ) its little radius ( #a4 ,x is pla9 t at no "t c ?is /> be m ?an ! am\nt ( ?is radius 7#a7 f ! pole1 & :5 on ! m]idian ei!r above or bel[ ! pole ! full am\nt ( ! radius is subtract$ f or add$ to ! correct$ altitude ( ! /> to obta9 ! true altitude ( ! pole4 ,:5 ! /> is on a l9e pass+ ?r\gh ! pole & p>allel to ! horizon at its elongations z x is call$1 ! altitude is !n equal to ! latitude1 = its elevation is ! same z t ( ! pole4 ,x requires #bd h\rs = ?is /> to complete ! small circle ( revolution1 ! same "t requir$ by e />2 its movem5t is necess>ily v sl[4 ,by comput+ its h\r angle1 we c locate its position on ?is circle1 & h5ce by apply+ a correction to its altitude1 subtract+ or add+ accord+ to ! position ( ! /> above or bel[ ! pole1 we w obta9 ! altitude ( ! pole4 ,a r\gh e/imate ( ! position ( ! pole may be secur$ by not+ ! position ( ! ,big ,dipp]1 ! second /> 9 ! h&le1 call$ ,miz>1 is approximately 9 l9e ) ,pol>is & ! pole4 ,we w n[ proce$ to %[ ! me?od by :i* ! h\r angle is obta9$3 ,9 ! talk on ,"t1 x 0 /at$ t ! local 7a/ronomical7 mean "t plus ! "r asc5sion ( ! mean sun is equal to ! local sid]eal "t2 & aga91 t ! "r asc5sion ( a /> plus its h\r angle equals local sid]eal "t4 ,) ^! facts z a basis1 ! =mula = latitude by ,pol>is giv5 9 ! ,nautical ,almanac w be foll[$ 9 explanation4 ,illu/ration3 ,,fig4 #f4 ,! "t ( obs]vation mu/ be not$ by *ronomet] & conv]t$ into local 7a/ronomical7 mean "t2 ?is mu/ be correct$ by ,table ,,iii 7,nautical ,almanac7 9 ord] to *ange ?is sol> int]val into a sid]eal "t int]val2 to ?is conv]t$ "t mu/ be add$ ! ,gre5wi* sid]eal "t ( mean noon 7page #b72 t is1 ! h\r angle ( ! ,fir/ ,po9t ( ,aries1 or :at is ! same ?+1 ! "r asc5sion ( ! mean sun2 to ?is sum mu/ be appli$ a correction = longitude1 9 "t1 tak5 f ! foot ( page #b1 ,n4 ,a4 ,! sum is ! local sid]eal "t4 ,! reason = ! correction ( longitude is ?is3 ,! diff]5ce betwe5 ! "r asc5sion ( ! mean sun at noon on two successive days is #c m4 #ef s41 ! same z ! accumulat$ diff]5ce betwe5 sol> & sid]eal "t 9 #a day4 ,n[ we take f ! ,nautical ,almanac ?is elem5t = ,gre5wi* mean noon1 yet ! sun has s9ce cov]$ ! di/ance equal to ! longitude1 & dur+ ! int]val requir$ to d ?is1 ! sid]eal "t has accel]at$ ov] ! sol> an am\nt :i* be>s ! same ratio to ! #c m4 #ef s41 t ! longitude 9 "t be>s to #bd h\rs4 ,! ,nautical ,almanac h&les ! t]ms ( ?is proportion 9 tabul> =m at ! foot ( page #b4 ,x is /at$ t ! sun has travel$ f ! m]idian ( ,gre5wi* to ! local m]idian1 & x might be sugge/$ t at ! "t ( obs]vation ! sun has cov]$ ?is am\nt plus ! local h\r angle or ! local a/ronomical mean "t4 ,?is is true b ! am\nt ( local h\r angle has be5 previ\sly accel]at$ to sid]eal "t by ! correction to local a/ronomical mean "t4 ,) ! local sid]eal "t ent] ,table ,i 7,nautical ,almanac7 & pick out ! correction to be appli$ accord+ to sign to ! altitude4 ,x is probably ne$less to say t ! obs]v$ altitude mu/ be correct$ = index error1 dip & refraction be=e apply+ ?is latt] correction1 :i* conv]ts x into latitude4 ,?is is call$ ! ,nautical ,almanac me?od & is suffici5tly accurate = navigational purposes1 b %\ld a great] ref9em5t be desir$ !re are tables ( fur!r corrections giv5 9 ! ,am]ican ,ephem]is & ,nautical ,almanac4 ,x is always advantage\s to get an obs]vation ( a /> ne> twilight or dawn1 9 ord] t a well-def9$ horizon may be available2 b1 9 tak+ a sight ( ,pol>is1 ano!r important feature is to be consid]$4 ,:5 ! />'s h\r angle is at or ne> #f or #ah h\rs1 t is1 ne> t "p ( its orbit cut by a l9e pass+ ?r\gh ! pole & p>allel to ! horizon1 x is ris+ or fall+ mo/ rapidly1 ) ! result t a small error 9 "t w produce a consid]able error 9 ! h\r angle1 an error ( #c m9utes introduc+ a diff]5ce ( #a 9 ! latitude4 ,x is q wor? :ile1 !re=e1 to select a "t = ! obs]vation ( ,pol>is :5 ?is /> is ne> ei!r ( its culm9ations1 its highe/ or l[e/ positions1 :]e ! "t ne$ n be especially accurate2 b by c>efully not+ ! "t x is possible to get good results at o!r times :5 ! horizon is def9$4 ,by us+ ! position ( ! /> ,miz>1 z sugge/$ above1 h[ev]1 ! navigator w be greatly aid$ 9 select+ ! mo/ propiti\s "t = obs]v+ ,pol>is4 ,,*apt] ,,vii ,azimu?s & ,amplitudes ,( all ! navigational in/rum5ts n[ 9 practical use1 !re are few1 if any1 t exce$ ! m>9]'s compass 9 usefulness to mank9d4 ,! "p x has play$ 9 ! developm5t ( ! _w has be5 mo/ important1 & its utility is no less to-day ?an 9 ! pa/1 = ! int]c\rse ( nations is /ill guid$ by ! compass ne$le4 ,) su* a responsibility dep5d+ on ?is in/rum5t1 x w\ld naturally be suppos$ t its indications mu/ be v accurate1 b1 on ! contr>y1 ! ne$le is sway$ by ! slighte/ magnetic influ5ce & po9ts ,nor? only on r>e occasions2 & 9 /eel vessels only by m]e *ance4 ,! ne$le is drawn f true nor? fir/ by ! direction ( ! e>?'s magnetic =ce :i* is n co9cid5t ) ! m]idian ow+ to ! position ( ! magnetic poles4 ,! nor? magnetic pole be+ 9 ! extreme nor!rn "p ( ,canada1 all ! l9es ( =ce 9 ! nor!rn hemisph]e conv]ge t[>d ?is locality4 ,! ne$le :5 o!rwise undi/urb$ lies 9 ! direction ( ^! l9es ( =ce & takes an angle ) ! m]idian dep5d+ on ! locality4 ,! am\nt ( div]g5ce f ! true nor?1 or v>iation1 z x is call$1 diff]s 9 diff]5t localities b is readily obta9$ by a glance at ! *>t :]e ea* compass rose %[s ! am\nt ( v>iation at t place4 ,f a magnetic c\rse1 or be>+1 ! true c\rse1 or be>+1 is readily f\nd by ! prop] application ( ?is v>iation1 :i* may be ei!r ea/]ly or we/]ly4 ,! true c\rse is to ! "r ( ! magnetic c\rse1 :5 consid]$ f ! c5t] ( ! compass1 9 ea/]ly v>iation2 ,t4 ,r4 ,e4--,true-,"r-,ea/]ly4 ,rememb] ^! ?ree words & ! :ole lesson is le>n$1 = if true is to ! "r 9 ea/]ly v>iation x mu/ be to ! left 9 we/]ly2 & if true is to ! "r 9 ea/]ly1 ! magnetic c\rse mu/ be to ! left ( true c\rse 9 ea/]ly & to ! "r 9 we/]ly4 ,9 ?is way ! true & magnetic c\rses are conv]t$ "o to ! o!r at w4 ,if we 7 to sail always 9 an entirely wood5 %ip1 our compass tr\bles w\ld be v few1 = ! above w\ld include e phase ( ! situation4 ,z wood is non-magnetic ! compass w\ld be un9flu5c$ by outside di/urbances4 ,wood1 z a %ip-build+ mat]ial1 hav+ be5 s mu* displac$ by iron & /eel1 ! use ( ^! metals has br\ght _m problems to solve 9 connection ) ! deflection ( ! compass ne$le4 ,! effect on ! compass ne$le ( ! magnetism 9 a vessel & h] c>go is kn[n z deviation & is v complicat$1 ow+ to _m influ5ces :i* are at "w at all times giv+ an ev]-v>y+ value to ?is elem5t ( error4 ,! causes ( deviation & its treatm5t 9 ! way ( comp5sat+ ! compass are subjects mu* too ext5sive = ?is little book2 fur!rmore1 !y are c>efully dealt ) 9 a half doz5 ( ! well-kn[n works on navigation1 s we w t\* only on ! e-day side ( compass "w4 ,! deviation *anges ) e alt]ation ( ! vessel's head1 ow+ to ! *ange 9 position ( prom95t p>ts ( ! vessel's hull relative to ea* o!r1 to ! compass1 & to ! t]re/rial l9es ( =ce 7magnetism74 ,z a result ( ^! influ5ces on ! compass ne$le1 ! m>9] has ?ree c\rses to deal )4 ,! fir/ is ! true c\rse1 :i* is bas$ on a compass ^: ne$le po9ts true nor?4 ,! second1 ! magnetic c\rse1 is tak5 f a compass affect$ by v>iation alone & !re=e po9t+ to ! magnetic pole4 ,! ?ird is ! compass c\rse1 or t c\rse actually %[n by an ord9>y /&>d compass 9 a /eel %ip1 affect$ by ! error ( v>iation comb9$ ) ! error ( deviation4 ,! comb9ation ( ! deviation & ! v>iation is ! compass error & is obta9$ by add+ ! deviation & v>iation if bo? are ( ! same "n1 ! compass error tak+ t "n2 = in/ance suppose we h a v>iation ( #b ,w4 & deviation ( #aj ,w41 ! comb9$ error is #ab ,w4 ,if1 h[ev]1 ! v>iation & deviation are ( diff]5t names1 x becomes necess>y to f9d ! diff]5ce betwe5 ! two & "n ! result aft] ! great] quantity2 ?us1 ) a deviation ( #d ,e4 & a v>iation ( #aj ,w41 ! error is #f ,w4 ,! compass error is appli$ to compass c\rse to obta9 true c\rse & vice v]sa by ! same rule z = v>iation4 ,! navigator 9 plann+ 8 c\rse betwe5 two positions lays ! p>allel rul]s on ^! positions on ! *>t & c>ries ?is direction to ! ne>e/ compass rose4 ,?is may be a true rose1 9 :i* ev5t he rememb]s 8 ,t4 ,r4 ,e4 rule1 rev]s+ x 9 ?is case1 & ) ! v>iation giv5 on ! *>t secures ! magnetic c\rse4 ,9 an iron or /eel vessel1 ! deviation = t c\rse mu/ be asc]ta9$ f ! deviation c>d by trial or f a ,napi] ,diagram direct & appli$ to ! magnetic c\rse 9 ord] to obta9 ! compass c\rse4 ,?is is accompli%$ precisely z 9 f9d+ ! magnetic f ! true c\rse 7to ! left if deviation is ea/]ly & to ! "r if we/]ly74 ,! c\rse by /&>d compass is n[ at h& by :i* we c /eam f "o select$ po9t to ! o!r4 ,! deviation z has be5 said is an ev]-v>y+ error1 & consequ5tly x is q impracticable to dep5d :olly on a fix$ deviation c>d4 ,we may take abo>d "s magnetic c>go or *ange our latitude to a great ext5t1 ! vessel may be p\nd$ excessively by heavy seas1 a /roke ( lightn+ or by /r&+2 all ^! are causes liable to affect ! deviation m or less4 ,9 ord] to =e/all ! s]i\s consequ5ces t are liable to att5d su* a d]angem5t ( ! normal & expect$ deviation1 ! c>eful navigator takes azimu?s or amplitudes on e c\rse :5 practicable4 ,azimu?s & amplitudes are no?+ m nor less ?an a/ronomical be>+s ( heav5ly bodies2 !y indicate ! true be>+ ( ! body1 & ! diff]5ce betwe5 ?is be>+ & ! be>+ tak5 simultane\sly by /&>d compass is ! compass error4 ,! azimu? ( a body is ! angle at ! z5i? betwe5 ! m]idian & ! v]tical circle pass+ ?r\gh ! body4 ,x is cu/om>y1 h[ev]1 to consid] ! azimu? z measur$ by ! arc ( ! horizon r ?an by ! angle at ! z5i?4 ,x is measur$ f ! nor? or s\? po9t accord+ to ! latitude1 t[>d ei!r ! ea/ or we/ po9t1 ?r\gh #ahj4 ,an amplitude1 unlike an azimu?1 is re/rict$ z to "t ( obs]vation1 = ! body mu/ be on ! horizon ei!r ris+ or sett+2 & %\ld be obs]v$ :5 ! sun is ab\t its own diamet] above ! horizon & ) a n excessive height ( eye4 ,! amplitude is measur$ f ! ea/ or we/ po9t ?r\gh #ij to ! nor? or s\? po9t4 ,if ! body obs]v$ has a s\? decl9ation & is ris+1 ! amplitude w be ,ea/ s mu* ,s\?2 if decl9ation is nor?1 ,ea/ s mu* ,nor?1 = a body rises 9 ! ,ea/ po9t :5 its decl9ation is #j--on ! equator4 ,! pr9ciple ( ! amplitude lies 9 ! solution ( a "r-angl$ sph]ical triangle1 ^: sides are ! body's pol> di/ance1 ! co-latitude1 & ! z5i? di/ance :i* is #ij4 ,we desire ! complem5t ( ! angle at ! z5i?4 ,x is unnecess>y to compute an amplitude1 = 9 ,table #ci1 ,b[dit*1 w be f\nd ! desir$ be>+s = diff]5t latitudes & decl9ations4 ,! sun w be f\nd ! mo/ satisfactory ( ! heav5ly bodies to utilize = amplitudes4 ,!re are two me?ods ( calculat+ an azimu?1 "o kn[n z ! "t azimu? & ! o!r z ! altitude azimu?4 ,! =m] is ! mo/ popul> ow+ to ! tables t h be5 compil$1 an inspection ( :i* facilitates ! navigator 9 quickly obta9+ ! true azimu? ( a body4 ,be=e ent]+ ! tables1 x is necess>y to h z argum5ts ! latitude & decl9ation1 &1 if us+ ! sun1 ! local app>5t "t1 or = /ell> "w ! h\r angle4 ,%\ld ! />'s h\r angle exce$ #ab h\rs1 #ab h\rs %\ld be subtract$ f x1 & ! rema9d] us$ z ,p4,m4 "t4 ,a planet may be employ$ precisely 9 ! same mann] z a />4 ,"o ( ! simple/ & mo/ exp$iti\s me?ods ( secur+ ! azimu? is by means ( a diagram4 ,^u ?is conv5i5t inv5tion ! be>+ ( a body c v quickly be tak5 (f ) a pair ( rul]s4 ,weir's ,azimu? ,diagram is sold by ! ,hydrographic ,(fice = a v small sum4 ,! only argum5t t c be us$ aga9/ its use is t x requires a small table to lay x ^u4 ,simple & complete directions are pr9t$ on ! diagram4 ,! altitude azimu? is (t5 comput$ at ! same "t z ! ord9>y ,a4,m4 & ,p4,m4 "t sights1 utiliz+ ! altitude ( ! body = bo? op]ations4 ,! pr9ciple involv$ 9 comput+ bo? an altitude azimu? & a "t azimu? is ! solution ( ! same a/ronomical triangle = ! same angle1 b 9 ! case ( ! altitude azimu? ?ree sides are giv5 7! co-latitude1 ! z5i? di/ance1 & pol> di/ance7 to f9d ! angle at ! z5i?4 ,9 ! "t azimu?1 two sides & ! includ$ angle are giv5 7! pol> di/ance1 co-latitude & local app>5t "t or h\r angle7 to f9d also1 ! angle at ! z5i?4 ,! azimu? f\nd by computation %\ld be nam$ ,nor? if 9 nor? latitude1 or ,s\? if 9 s\? latitude4 ,x has be5 cu/om>y to add up ! logs1 divide by #b & ! cos9e w be half ! azimu? nam$ f ! elevat$ pole1 b a m exp$iti\s way is aft] add+ ! logs seek 9 ! log hav]s9es & f9d ! azimu? directly b nam$ f ! opposite pole to ! latitude4 ,) ! correct be>+ ( ! sun1 & its simultane\s be>+ by /&>d compass at h&1 ! compass error is f\nd by m]ely tak+ _! diff]5ce4 ,n[ ?is error1 z said be=e1 is compos$ ( ! sum or diff]5ce ( ! deviation & ! v>iation1 s1 if ei!r is subtract$ f _! sum1 or add$ to _! diff]5ce ! rema9d] is ! o!r quantity4 ,! v>iation be+ always kn[n is subtract$ f or add$ to ! compass error to obta9 ! deviation1 ?us *eck+ ! deviation c>d = t p>ticul> c\rse ! vessel 0 /e]+ at ! "t ( obs]vation4 ,) ! compass error at h&1 _m /ud5ts become p]plex$ z to ! prop] mann] ( deal+ ) ?is error1 & f9d+ f x ! deviation4 ,! compass error is fir/ nam$1 by consid]+ ! two be>+s 7compass & true7 f ! c5t] ( ! compass2 if ! true is to ! "r ( ! compass be>+1 ! error is ea/]ly1 if to ! left1 we/]ly4 ,n[ %\ld ! v>iation happ5 to be id5tical ) ! compass error1 bo? 9 am\nt & 9 "n1 !re is no deviation2 if ! v>iation is #j1 !n ! :ole error is deviation4 ,if by *ance ! compass error is #j1 x indicates t ! v>iation & deviation are equal 9 am\nt & oppos$ to ea* o!r 9 _! influ5ce on ! ne$le4 ,! deviation1 9 su* a case1 naturally takes ! opposite "n f ! v>iation4 ,9 sep>at+ ! v>iation f ! compass error1 x is necess>y to ex]cise a little ?\ght & to consid] :at deviation appli$ to ! giv5 v>iation w produce t compass error4 ,?is w be readily se5 aft] a little practice4 ,!re are1 h[ev]1 "s rules :i* are "h giv51 by :i* ! deviation c be obta9$ me*anically4 ,! deviation is ! diff]5ce betwe5 ! v>iation & ! compass error if !y are ( ! same "n or add+ !m if ( diff]5t names4 ,x is giv5 ! same "n z ! compass error unless ! compass error is subtract$ f ! v>iation1 :5 ! deviation takes ! opposite "n4 ,or a diagram 9 :i* ! error is %[n by its p>ticul> numb] ( degrees ea/ or we/ ( ! true nor? l9e may be drawn & ! v>iation likewise prop]ly %[n ea/ or we/ ( true nor?4 ,if ! error is to ! left ( ! v>iation ! deviation is we/ & if to ! "r ! deviation is ea/4 ,,*apt] ,,viii ,longitude ,! longitude ( any position on ! e>? is its di/ance ea/ or we/ f ! m]idian ( ,gre5wi*1 :i* has be5 *os5 z ! m]idian ( orig94 ,longitude is measur$ on ! equator ea/w>d & we/w>d ?r\gh #ahj1 complet+ 9 ?is way ! :ole circumf]5ce ( ! e>?4 ,! circumf]5ce ( e circle comprises #cfj1 :e!r x is a great circle ( ! e>? or any ( ! p>allels :i* range 9 size f a po9t at ! poles to a great circle at ! equator4 ,!re are always #cfj b ! l5g? ( ea* degree is det]m9$ by ! size ( ! circle4 ,?us a degree ( longitude on ! equator is #fj miles1 :ile on ! #ej? p>allel ( latitude x is only ab\t #ci miles1 ow+ to ! decreas+ size ( ! p>allels ( latitude4 ,a m9ute ( longitude on ! equator1 l a m9ute ( latitude1 is equal to "o mile1 b ! diff]5ce betwe5 ! m]idians 9 actual di/ance decreases t[>d ! poles gradually less5+ ! l9e> value ( a degree ( longitude4 ,?us x w be se5 t :5 x is desir$ to repres5t a diff]5ce ( longitude 9 di/ance1 x mu/ be done 9 t]ms ( dep>ture 7miles7 correspond+ to ! p>ticul> p>allel ( latitude ( ! position4 ,! sun app>5tly moves ar\nd ! e>? 9 its diurnal motion1 cov]+ #cfj 9 #bd h\rs1 :e!r ! decl9ation is nor? or s\?1 & a little simple division %[s t 9 "o h\r he passes ov] #ae ( longitude1 :atev] ! latitude4 ,?is r$uc$ %[s t #a is pass$ ov] e #d m9utes4 ,z ! /&>d "t1 ! _w ov]1 is reckon$ by ! movem5ts ( ! sun1 x is pla9ly se5 t :5 consid]+ longitude1 a def9ite relation exi/s betwe5 "t & arc 7--74 ,ow+ to ?is relation1 "t & arc become int]*angeable by a simple process ( conv]sion4 ,s x foll[s t if we h ! "t at ,gre5wi* by a *ronomet]1 & ?r\gh a trigonometrical calculation we det]m9e ! local mean "t at ! %ip1 ! diff]5ce 9 "t betwe5 ,gre5wi* & ! %ip's m]idian repres5ts ! longitude 9 "t1 :i* is readily conv]t$ into arc4 ,! calculation involv$ 9 det]m9+ ! local mean "t is ! solution ( ! a/ronomical triangle1 or 9 o!r words x is a problem 9 sph]ical trigonometry4 ,?is triangle has its apex at ! pole ) "o side z ! pol> di/ance 7#ij - decl9ation ( ! obs]v$ body71 ano!r side ! co-latitude 7#ij - dead reckon+ latitude7 & ! ?ird side ! z5i? di/ance 7#ij - ! correct$ altitude ( ! body74 ,x is "o ( ! pr9ciples ( trigonometry t ) any ?ree elem5ts giv5 9 a triangle any ( ! rema9+ elem5ts may be comput$2 t is1 any angle or side is obta9able4 ,! solution ( ! a/ronomical triangle = v>i\s elem5ts includes ! f9d+ ( ! z5i? di/ance & f ?is ! altitude1 :i* =ms ! ma9 feature ( ! problem involv$ 9 ! ,new ,navigation4 ,x also provides u ) ! angle betwe5 co-latitude & ! z5i? di/ance1 :i* is ! azimu? ( ! body1 by :i* ! m>9] is able to asc]ta9 ! error ( 8 compass4 ,! mo/ important feature ( ! a/ronomical triangle is ! angle at ! pole1 kn[n z ! h\r angle1 :i* :5 f\nd secures = ! navigator 8 local "t4 ,! problem pres5ts itself 9 ! =m ( ?ree sides be+ giv5 to f9d "o angle4 ,x is f\nd by ! "t sight =mula1 :i* is too well-kn[n to ne$ any discussion "h4 ,! %ape ( ! triangle is det]m9$ by ! decl9ation ( ! body1 its altitude & ! latitude ( ! vessel1 & ! pol> or h\r angle2 & x /&s to reason t a =mula w n produce ! same accuracy 9 ! h\r angle ) e %ape ( ! triangle4 ,= in/ance1 9 high latitudes or :5 ! body has a decl9ation approa*+ #ij1 ! accuracy ( ! "t sight =mula becomes effect$4 ,ano!r v important po9t to be> 9 m9d :5 obs]v+ a body ) ! view ( comput+ its h\r angle1 is its azimu?4 ,:5 ! be>+ is ne>ly ea/ or we/1 on ! prime v]tical1 ! body is ris+ or fall+ fa/] ?an at any o!r "t1 & an error 9 altitude or latitude w produce ! lea/ error 9 ! result+ longitude4 ,! necessity = close att5tion to ?is po9t is increas$ ) ! latitude4 ,obs]vations = "t tak5 :5 ! body has an azimu? ( less ?an #de or ov] #ace are :olly unreliable4 ,! sun does n always cross ! prime v]tical 9 8 daily track across ! heav5s1 = "u c]ta9 conditions1 say dur+ ! nor!rn w9t]1 he w rise s\?w>d ( ea/ & set s\?w>d ( we/4 ,"u ^! adv]se conditions1 ! calculation ( longitude is n dep5dable1 & ! be/ a navigator c d :5 us+ ! sun is to obs]ve z soon z he has an altitude suffici5t to cle> ! excess refraction exi/+ ne> ! horizon4 ,x is "u su* circum/ances t /> sights are ( incalculable value1 = a /> c always be f\nd 9 a suitable position ) b little wait+1 or we may employ ! ,new ,navigation me?od1 :]e ! azimu? ( ! sun is z good "o place z ano!r4 ,9 ord] t a body w cross ! prime v]tical1 ! latitude mu/ be ( ! same "n & great] ?an ! decl9ation4 ,9 conditions cit$ above ! decl9ation ( ! sun is s\? & ! latitude is nor?1 h5ce ! body w nev] be on ! prime v]tical4 ,if ! latitude is less ?an ! decl9ation1 ! sun's diurnal track is tilt$ t[>d ! z5i?1 in/ead ( away f x z :5 ! latitude is great]1 & ! result is t ! sun1 :ile nev] on ! prime v]tical1 approa*es x = a "t aft] ris+1 !n rec$es aga94 ,x %\ld be obs]v$ :5 at its ne>e/ po9t to ! be>+ ( ea/ ( we/4 ,! be>+ ( v>i\s bodies c be readily f\nd by an inspection ( ,hydrographic ,(fice ,azimu? ,tables ,nos4 #ga & #abj1 ! decl9ation & latitude be+ us$ z argum5ts4 ,!re is a me?od ( f9d+ ! longitude kn[n z ! equal altitude me?od1 b x is n valuable4 ,! conditions are exact+ :]e accurate results are requir$ & :5 ^! conditions exi/ ! ord9>y "t sight is available & at its be/ advantage1 s longitude by equal altitudes is n popul>4 ,to secure good results1 ! body mu/ h an altitude above #gj & ne> ! prime v]tical2 &1 fur!rmore1 ! %ip mu/ be kept on an ea/ or we/ c\rse or rema9 /ation>y4 ,! !ory ( ! problem is simplicity itself1 & = ?is reason is v allur+1 b ! be/ use t equal altitudes c be put to is ! det]m9ation ( *ronomet] error a%ore1 & 9 ^! days ( radio "t signals ev5 ?is use is almo/ obsolete4 ,! rule is z foll[s3 ,obs]ve ! sun's altitude1 simultane\sly notic+ ! "t by *ronomet] & clamp ! sextant to prev5t any *ance ( ! altitude becom+ di/urb$4 ,:5 ! sun has fall5 to ! same altitude z ( ! =5oon sight1 note ! "t aga9 by ! *ronomet]4 ,! mean ( ! two times1 correct$ = *ronomet] error1 equation ( "t1 & ! equation ( equal altitudes due to *ange 9 decl9ation1 9 case ( ! sun1 is ! ,gre5wi* app>5t "t correspond+ to our local noon or our longitude 9 "t1 :i* %\ld !n be conv]t$ into arc4 ,! />s & planets are available z well z ! sun = ! f9d+ ( longitude & :5 !re is a di/9ct horizon1 /ell> sights h _m advantages4 ,! problem dep5ds ^u ! solution ( ! a/ronomical triangle by ! same =mula z ) ! sun4 ,!re are a few po9ts ( diff]5ce betwe5 a "t sight ( ! sun & "o ( a /> or planet ne$+ explanation4 ,9 ! case ( ! =m] body1 we naturally comp>e ! sol> "t ( ,gre5wi* ) ! sol> "t ( ! local m]idian1 b 9 /ell> "w we employ = ?is comp>ison /ell> "t1 or1 z x is m popul>ly call$1 sid]eal "t4 ,s x becomes necess>y to turn ! ,gre5wi* mean "t ( ! *ronomet] into ,gre5wi* sid]eal "t & comp>e x ) local sid]eal "t4 ,! diff]5ce1 z 9 mean "t1 is ! longitude 9 "t1 :i* is conv]t$ into arc 9 precisely ! same way4 ,! ,gre5wi* mean "t is turn$ into sid]eal "t by add+ to x ! "r asc5sion ( ! mean sun1 tak5 f ! ,nautical ,almanac & ! accel]ation = ! ,gre5wi* mean "t 7,table #i1 ,b[dit*74 ,! local sid]eal "t is ! result ( an addition ( ! />'s "r asc5sion & ! />'s h\r angle1 ! "r asc5sion is tak5 f ! ,nautical ,almanac )\t correction if a fix$ /> is be+ consid]$ & ! computation ( a "t sight gives ! />'s h\r angle4 ,! local sid]eal "t be+ ! "r asc5sion ( ! m]idian1 x foll[s t ! angle f ! v]nal equ9ox to ! /> plus ! angle f ! /> to ! m]idian is :at we desire2 h5ce ! above rule = obta9+ ! local sid]eal "t4 ,%\ld ! /> be> ea/ ( ! m]idian1 ! local sid]eal "t may be f\nd by subtract+ ! 7ea/]ly7 h\r angle f ! />'s "r asc5sion or add+ !m z above & subtract+ #bd h\rs4 ,ref]5ce to ! ,"t ,diagram1 ,fig4 #c1 w make ^! po9ts cle> also4 ,x is cu/om>y to add up ! famili> logs ( "t sight--sec4 lat41 cosec4 p4 d41 cos sum1 s91 rema9d]--divide by #b & seek ! ,h4 ,a4 7h\r angle7 9 ! ,a4,m4 or ,p4,m4 column ( ,table #dd1 ,b[dit*1 us+ ! log z a s92 b a m exp$iti\s way is to use ! sum ( ! logs z ! log hav]s9e 9 ,table #de & pick out ! h\r angle directly4 ,,*apt] ,,ix ,sumn] ,me?od ,e m>9] :o has rea*$ a position 9 ! pr(ession :]e he is intru/$ ) ! responsibilities ( navigat+ a vessel is "u obligation to ! late ,capt4 ,?omas ,h4 ,sumn]1 ( ,bo/on4 ,?is %ipma/] discov]$ & develop$ ! pr9ciple ( ! s-call$ ,sumn] or ,position ,l9es1 a pr9ciple :i* has prov$ ( ine/imable value & :i*1 ) its subsequ5t improvem5ts1 has well-nigh revolutioniz$ ! me?ods ( navigation4 ,! discov]y 0 purely accid5tal & = t reason is int]e/+4 ,"h1 9 ,capt4 ,sumn]'s own words1 is h[ x occurr$3 8,hav+ sail$ f ,*>le/on1 ,s4 ,c41 #be? ,novemb]1 #ahcg1 b\nd = ,gre5ock1 a s]ies ( heavy gales f ! we/w>d promis$ a quick passage4 ,aft] pass+ ! ,azores1 ! w9d prevail$ f ! s\?w>d1 ) ?ick wea!r1 aft] pass+ longitude #ba ,w41 no obs]vation 0 _h until ne> ! l&1 b s\nd+s 7 _h n f>1 z 0 suppos$1 f ! edge ( ! bank4 ,! wea!r 0 n[ m boi/]\s1 & v ?ick1 & ! w9d /ill s\!rly4 8,arriv+ ab\t midnight1 #ag? ,decemb]1 )9 #dj by dead reckon+1 ( ,tusk> light1 ! w9d haul$ ,s4,e4 7true71 mak+ ! ,iri% coa/ a lee %ore4 ,! %ip 0 !n kept close to ! w9d & sev]al tacks made to pres]ve h] position z ne>ly z possible until daylight1 :51 no?+ be+ 9 sight1 %e 0 kept on ,e4,n4,e4 "u %ort sail1 ) heavy gales4 ,at ab\t #aj ,a4,m4 an altitude ( ! sun 0 obs]v$1 & *ronomet] "t not$2 b hav+ run s f> )\t any obs]vation1 x 0 evid5t t ! latitude by dead reckon+ 0 liable to error & c\ld n be entirely reli$ ^u4 8,h[ev]1 ! longitude by *ronomet] 0 det]m9$1 us+ ! unc]ta9 ,d4 ,r4 latitude1 & ! %ip's position fix$ 9 accordance4 ,a second latitude 0 !n assum$ #aj to ! nor? ( ! la/ & work+ ) ?is latitude a second position ( ! %ip 0 obta9$ & aga9 a ?ird position by means ( a ?ird latitude /ill #aj fur!r nor?4 8,on pick+ (f ^! ?ree positions on ! *>t x 0 discov]$ t ! ?ree po9ts 7 all dispos$ 9 a /raight l9e ly+ ,e4,n4,e4 & ,w4,s4,w41 & t :5 ?is l9e 0 produc$ on ! fir/-nam$ direction x also pass$ ?r\gh ! ,smalls ,light4 ,! conclusion arriv$ at 0 t ! obs]v$ altitude mu/ h happ5$ at all ?ree po9ts1 at ! ,smalls ,light1 & at ! %ip at ! same in/ant ( "t4 ,! d$uction foll[$ t1 ?\gh ! absolute position ( ! %ip 0 d\btful1 yet ! true be>+ ( ! ,smalls ,light 0 c]ta91 provid$ ! *ronomet] 0 correct4 ,! %ip 0 !re=e kept on h] c\rse1 ,e4,n4,e4 & 9 less ?an an h\r ! ,smalls ,light 0 made be>+ ,e4 by ,n4 ,n4 & close abo>d4 ,! latitude by ,d4 ,r4 turn$ out to be #h 9 error40 ,if ! capta9 _h work$ m "t sights us+ diff]5t latitudes1 he w\ld h add$ new positions on ! l9e to :i* he ref]s1 ea* plac$ ^u x accord+ to ! latitude us$4 ,_h he c>$ to pursue 8 exp]im5ts f>!r1 & us$ latitudes v wide ( 8 dead reckon+ position1 he w\ld h discov]$ t ! result+ positions in/ead ( ly+ 9 a /raight l9e1 7 9 a curve & an arc ( a circle4 ,! pr9ciple involv$ is v crudely illu/rat$ 9 ! foll[+ exp]im5t3 ,let ! read] consid] himself abo>d %ip ly+ at an*or--say a full-rigg$ %ip1 s z to insure a =ema/ ( good height4 ,l[] ! d+hy & take along a sextant4 ,we />t ) a s]ies ( measurem5ts to det]m9e ! angle1 z read f ! sextant 9 ! d+hy1 betwe5 ! truck & ! wat]l9e ab\t ! vessel4 ,z a result ( ^! measurem5ts1 we discov] t ?is angle becomes small] z ! di/ance f ! vessel increases4 ,c>ry+ our te/s f>!r1 suppose :5 ! sextant %[s ! altitude ( ! =e truck above ! wat]l9e to be #gj1 t ! di/ance to ! vessel be det]m9$4 ,) ?is di/ance z a radius & ! =ema/ z ! c5t]1 we r[ 9 a circle ar\nd ! vessel1 ! sextant w cont9ue to read #gj all ar\nd ! circle4 ,x is ?us demon/rat$ t a circle surr\nds t =ema/ ^u :i* ! altitude ( its truck is ev]y:]e #gj--;a circle ( equal altitudes4 ,n be+ q sure ( ?is int]e/+ fact1 p]haps1 ano!r angle is select$ by mov+ a little f>!r f ! %ip4 ,! sextant %[s ! =e truck to h an altitude ( #ej2 ! di/ance to ! vessel is e/abli%$1 :]eupon ! d+hy is r[$ ar\nd ! vessel ) ?is di/ance z a radius4 ,aga9 ! sextant reveals no *ange f #ej & x is cle>ly %[n t we h mov$ ab\t on a circle ( #ej elevation ( ! truck4 ,we c cont9ue exp]im5t+ 9 ?is way until ! di/ance f ! %ip becomes s great t "s physical condition prev5ts our read+ ! angle ( ! truck's altitude4 ,^! inve/igations %[ t !re is a sy/em ( conc5tric circles ( equal altitude ab\t e elevat$ object l ! little undulations we h se5 s _m times produc$ by ! spla% ( a /one ?r[n into a pool4 ,^! circles ( equal altitudes surr\nd n only elevat$ t]re/rial objects b also cele/ial bodies1 z w n[ be %[n4 ,z ! sun is ! mo/ conv5i5t body = ?is illu/ration1 let u sub/itute x = ! =e truck ( ! =ego+ exp]im5ts1 :ile = ! wat]l9e ( ! vessel we w use ! po9t on ! e>? t\*$ by a plumb-bob susp5d$ f ! c5t] ( ! sun4 ,?is po9t w fall on ! equator on ! #ba/ ( ,m>* or !reab\ts1 z ! sun com+ up f 8 s\!rn decl9ation crosses ! equator into nor? decl9ation at ?is "t4 ,! in/ant ( ! transit is ! v]nal equ9ox4 ,n[ ?is po9t w be f\nd an excell5t "o f :i* to /udy ?is problem1 b1 z ?is takes "s "t & ! sun is ev] on ! move1 we w imag9e ourselves end[$ ) ! p[] ( ,jo%ua to comm& ! sun & moon1 :i* w enable u to /udy ?is ph5om5on :ile free f ! re/lessness ( ! ,univ]se4 ,fir/ ( all1 x mu/ be und]/ood t ! sun %9es on "o hemisph]e ( ! e>? at all times2 x matt]s n h[ ! e>? is tipp$ 9 relation to him1 "o half ( ! _w is always enjoy+ sun%9e4 ,! c5t] ( ! light$ area is ! spot directly b5ea? ! sun :]e ! plumb-bob t\*es & ab\t ?is po9t lies ! sy/em ( conc5tric circles ( equal altitudes ( ! sun4 ,"u ! conditions %[n above1 ! sun is 9 ! z5i? ( ! t]re/rial v]nal equ9ox1 %9+ on ! e>? = a di/ance ( #ij 9 e direction2 b its altitude dim9i%es 9 direct proportion ) ! di/ance ( ! obs]v] f ! po9t ( ! equ9ox4 ,on ! great circle ev]y:]e #ij f ! equ9ox ! sun is 9 ! horizon ) an altitude ( #j 7provid$ we disreg>d dip & refraction74 ,suppose ! memb]s ( "s intrepid exp$ition h rea*$ ! nor!rn or s\!rn pole2 !y w\ld1 at ! "t be+ consid]$1 see ! sun 9 ! horizon & 9 ! direction ( ! m]idian pass+ ?r\gh ! v]nal equ9ox4 ,ea/w>d along ! equator #ij ( longitude f ! v]nal equ9ox1 ! inhabitants are j re/+ f ! toils ( ! day1 = ) !m ! sun is sett+ 9 _! we/]n horizon1 :ile away to ! we/w>d #ij ! p are %[+ signs ( activity1 = x is j sun-up 9 _! ea/]n horizon4 ,s all ar\nd ! _w j #ij f ?is select$ position & at ?is appo9t$ "t is a circle ( equal altitudes1 namely #j1 = is n ! sun se5 9 ! horizon at all po9ts on ?is circle8 ,! altitude ( ! sun is #ij at ! po9t ( obs]vation & #j on its out] circle ( altitude2 ^! are ! two extremes & betwe5 !m lies an inf9ite numb] ( conc5tric circles ( equal altitude = navigators to utilize4 ,! z5i? di/ance1 d]iv$ by subtract+ ! altitude f #ij1 indicates ! di/ance ( ea* circle f ! c5t] or sun's position4 ,?us if an obs]vation 0 tak5 by "s bewild]$ m>9] 9 :i* ! altitude 0 f\nd to be #hj1 ! correspond+ z5i? di/ance ( #aj multipli$ by #fj w\ld indicate t ! altitude 0 tak5 #fjj miles f ! sun's position1 or to put x 9 ano!r way1 ! circle ( equal altitudes ^u :i* ! obs]v] 0 locat$ 9 ?is case _h a radius ( #fjj miles4 ,:at is true ( ! sun on ! equator reg>d+ ! pr9ciple ( ! circles ( equal altitudes holds good ?r\gh\t its range ( decl9ation1 ! :ole sy/em mov+ nor? & s\? ) ! cont9u\s *ange ( decl9ation & f ea/ to we/ ) its app>5t diurnal motion4 ,9 ! quot$ article1 ,capt4 ,sumn] %[s a me?od by :i* ! position ( a vessel may be e/abli%$ on "s p>ticul> circle ( equal altitude2 x matt]s n :]e ! obs]v$ body happ5s to be at ! "t1 = ) ! ,nautical ,almanac & *ronomet] x c be locat$ %\ld we c>e to "k4 ,! navigator1 h[ev]1 c>es to deal ord9>ily only ) a v small arc ( ! circle embrac$ )9 8 imm$iate :]eab\ts4 ,%\ld he be some:at unc]ta9 ( ^! he w\ld simply require ! use ( a long] l9e to ext5d beyond ! limits ( 8 possible position4 ,except :5 9 a latitude t diff]s b little f ! decl9ation ( ! obs]v$ body1 ! circle ( equal altitude w be suffici5tly l>ge to all[ ! m>9] to repres5t its arc 9 8 vic9ity by a /raight l9e4 ,?us ! l9es ( position us$ to plot a vessel's position on ! *>t are 9 reality *ords or tang5ts ( ! circle ( equal altitude4 ,9 geometry x w be rememb]$ t we us$ to /udy ab\t circumscrib$ & inscrib$ polygons & "h we h a practical application ( _! use4 ,if we consid] ! l9e ( position to be a tang5t1 x is "o side ( a great polygon ) a va/ numb] ( sides circumscrib$ ab\t ! circle ( equal altitude2 & if we consid] x to be a *ord1 x is likewise a side ( a great polygon inscrib$ )9 ! circle ( equal altitude4 ,x matt]s n1 h[ev]1 if ! l9e or curve ( position is consid]$ a /raight l9e1 except 9 ! ill-*os5 condition ( ! body ne> ! z5i? :5 ! radius ( ! circle w be proportionately small4 ,if exactly 9 ! z5i? !re w be no circle ( equal altitude at all & ! sextant w measure an altitude ( #ij4 ,x is comp>atively r>e1 h[ev]1 t su* a condition w emb>rass ! use ( ?is me?od4 ,ano!r po9t to be rememb]$ 9 connection ) ! inscrib$ & circumscrib$ polygon propositions & "o :i* has a practical application 9 ! use ( position l9es1 is t ! tang5t or *ord ( a circle is at "r angles to ! radius pass+ ?r\gh ! po9t ( tang5cy or c5t] ( ! *ord4 ,x foll[s t ! sub-cele/ial or t]re/rial position ( ! obs]v$ body1 be+ at ! c5t] ( ! circle1 is always at "r angles to a l9e ( position4 ,?is important fact gives ! navigator an opportunity to *eck 8 compass error ea* "t he e/abli%es a position l9e1 by comp>+ a compass be>+ ( ! body tak5 simultane\sly ) ! measurem5t ( ! altitude1 ) ! true be>+4 ,to e/abli% a position l9e z ,capt4 ,sumn] did & z x 0 done = ye>s aft]w>ds1 by assum+ two latitudes usually #aj ea* side ( ! dead reckon+ latitude1 & draw+ ! l9e ?r\gh ! two result+ longitudes1 is kn[n z ! *ord me?od4 ,! two longitudes be+ positions on ! circle a l9e drawn betwe5 !m is a *ord ( ! circle4 ,! "w ( comput+ a "t sight is m or less labori\s to ev]yone & ) "s seaf>]s =ms _! mo/ ardu\s m5tal ex]cise4 ,at any rate no "o wants to "w any m ?an is necess>y to insure accurate results4 ,s :5 e/abli%+ a position l9e x w (t5 be f\nd conv5i5t to use ! %ort cut kn[n z ! tang5t me?od4 ,) ! latitude by acc\nt "w ! obs]v$ altitude z 9 ! ord9>y "t sight1 in/ead ( assum+ two latitudes4 ,seek ! true azimu? 9 ! tables or on diagram1 us+ ! latitude & decl9ation employ$ 9 ! "t sight & ! local app>5t "t ga9$ f x1 z ! argum5ts4 ,! true azimu?1 x w be rememb]$1 always be>s at "r angles to ! position l9e4 ,h5ce if ! azimu? is laid d[n ?r\gh ! position furni%$ by ! "t sight1 ! position l9e may also be readily plott$ at "r angles to ! l9e ( azimu? at ! "t sight position4 ,! navigator n[-a-days is expect$ to ?9k 9 position l9es :5 he is cle> ( ! l&1 z a pilot ?9ks 9 %ore be>+s & m>ks4 ,t is1 he mu/ see ^! imag9>y l9es ( ! diff]5t visible bodies1 & keep track ( _! availibility = 8 p>ticul> use4 ,x is easy to get into ! habit ( ?is1 = !y are simply a/ronomical be>+s in/ead ( be>+s on di/ant t]re/rial objects1 ) ! di/9ction t ! cele/ial be>+ all[s ( a #ij correction to produce a position l9e4 ,! morn+ sun on ! prime v]tical ) a suffici5t altitude to avoid any dang]\s refraction1 w produce a nor? & s\? l9e ( position4 ,dur+ ! =5oon z ! sun passes t[>d ! m]idian1 ! nor!rn end ( ! position l9e w move 9 direct proportion ) ! body's *ange 9 azimu? to ! ea/w>d & ! s\!rn end to ! we/w>d1 until at noon ) ! sun on ! m]idian we h an ea/ & we/ position l9e4 ,x w be se5 t at "o mom5t ( ! day x is a v easy matt] to e/abli% a l9e ( position2 ! m]e work+ ( a m]idian altitude does ?is4 ,?is simple exp$i5t ( f9d+ a position l9e 0 utiliz$ a great deal z a means ( mak+ a l&fall 9 ! days be=e *ronomet]s 7 p]fect$4 ,9 ^? good old days1 be=e ! clipp] %ip era1 "t 0 n held at su* a premium z 9 ! pres5t hu/l+ p]iod1 & a few days m or less at sea matt]$ b little4 ,! %rewd %ipma/]s !n w\ld keep well (f%ore until 9 ! latitude ( ,bo/on or ! ,virg9ia capes1 z ! case might be1 :5 !y w\ld haul due we/ & let h] g1 mak+1 no d\bt1 fir/ rate l&falls1 if ! old pig yoke 0 9 good work+ ord]4 ,! value ( a position l9e 0 demon/rat$ to ! writ] "s ye>s ago :5 b\nd 9 f ! ea/w>d & runn+ into a heavy & v ext5sive fog bank some:]e s\!a/w>d ( ,halifax4 ,dur+ a break 9 ! prevail+ conditions ! navigator succe$$ 9 secur+ an ex-m]idian sight & =tunately got a fairly good idea ( ! latitude4 ,! vessel 0 "u sail & mak+ b sl[ progress1 & z a result ( ! protract$ p]iod ( ov]ca/ sky ! longitude became consid]ably a matt] ( guess "w4 ,! vessel1 h[ev]1 0 kept on a we/ c\rse ) a c>eful all[ance made = ! set4 8,sir ,william ,?ompson0 0 kept go+ at regul> int]vals & x 0 surpris+ to see ! s\nd+s *eck up ) ! *>t z ! vessel approa*$1 cross$1 & left a/]n ! ,roseway ,bank1 s\?w>d ( ,cape ,sable4 ,"o felt z sure ( ! position z did ! old ,nantucket sailor 9 cross+ 8,m>m ,hackett's g>d540 ,9 cases :]e ! s\nd+s d n *eck s precisely z 9 ?is in/ance1 x w sometimes be f\nd a great help to lay (f to scale ! dep?s obta9$ on ! edge ( a piece ( draftman's transp>5t l954 ,place x on ! *>t 9 ! l9e ( ! c\rse1 &1 %\ld ! s\nd+s fail to agree1 move ! scale =w>d & back or to ei!r side1 always pres]v+ ! direction ( ! c\rse1 until a position is f\nd :]e ! s\nd+s on ! scale agree ) ! dep?s giv5 by ! *>t4 ,progress has be5 made 9 ! sci5ce ( navigation z 9 all o!r sci5ces1 & ! mod]n %ipma/] is n oblig$ to hold alo( f ,nantucket ,%oals & ,georges ,bank "u ord9>y conditions z our ance/ors 7 compell$ to d1 = ) a correct *ronomet] & a k ( ! position l9e su* outly+ dang]s h be5 robb$ ( _m ( _! anxiety-produc+ elem5ts4 ,be=e %[+ ! me?od ( work+ ar\nd su* places ano!r po9t ( value ( ! position l9e is call$ to ! read]'s att5tion4 ,a l9e ( position ext5d$ until x rea*es ! l& or "s dang] w indicate to ! m>9] ! be>+ ( t p>ticul> po9t ( ! coa/ or dang]4 ,if x s happ5s t ?is po9t is n ! place ( de/9ation1 ! navigator1 n be+ able to lay a c\rse direct = 8 objective port ?r\gh inability to det]m9e ! vessel's di/ance (f%ore1 ov]comes ! difficulty by sail+ a suffici5t di/ance at "r angles1 !n haul+ on to a new position l9e p>allel to ! orig9al "o4 ,?is is simil> to :at our ance/ors did 9 ! simple way cit$ above4 ,if ! l9e lies 9 ! direction ( an (f-ly+ or isolat$ %oal t is dang]\sly ne> ! c\rse1 an (fset l t %[n above w all[ a c\rse p>allel to ! position l9e to be sail$ 9 safety4 ,"h is an example to %[ its useful application3 ,a /eam] sail+ f ,/4 ,john1 ,n4 ,b41 = ,new ,york proce$$ b ab\t #aj h\rs on h] voyage1 :5 %e ran into a t]rific gale4 ,! ma/] 0 soon =c$ to heave 8 vessel to & ride x out z be/ he c\ld4 ,! driv+ sn[ & m\nta9\s seas occupi$ ! att5tion ( ! (fic]s 9 _! ef=ts to save ! /eam] & 9 ?is way ! dead reckon+ position became a matt] ( m]e guesswork4 ,! w9d aft] "s #bj h\rs 9 ! nor!a/ quadrant haul$ to ! nor?w>d1 at l5g? bl[+ out 9 ! nor?we/ ) cle>+ wea!r4 ,x 0 ! ma/]'s int5tion to pass ?r\gh ! ,s\? ,*annel1 betwe5 ,georges ,bank & ,nantucket ,%oals1 b z he _h lo/ 8 reckon+ to su* an ext5t he hesitat$ ab\t lay+ a c\rse ?r\gh su* a dang]-/rewn locality4 ,9 ! late twilight imm$iately foll[+ ! cle>+ sky1 ! ma/] succe$$ 9 cat*+ ! altitude ( a /> be>+ #cjj & e/abli%$ a l9e1 ! direction ( :i* l$ close we/w>d ( ,cultivator ,%oal 7a #f-;foot spot on ,georges ,bank74 ,s to be on ! side ( prud5ce & give ?is %oal a good b]?1 ! ma/] /eam$ #h miles at "r angles to ?is position l9e4 ,! c\rse or direction ( ! new position p>allel to ! fir/ 0 f\nd to lead directly into ! range ( visibility ( ,nantucket ,light%ip4 ,s ! ma/]'s m9d 0 put at re/ z he laid 8 c\rse along ! second position l9e1 kn[+ he w\ld at l5g? make ! light%ip4 ,x (t5 happ5s t a di/ant m\nta9 peak is visible & ! sun is 9 a suitable position to e/abli% a set ( cross be>+s1 us+ ! m\nta9 = "o object & ! sun = ! o!r4 ,n[ ) :at has previ\sly be5 /at$1 x is h>dly necess>y to rem9d ! read] t a 8l9e ( position0 obta9$ f obs]vations ( ! sun w be at "r angles to ! sun's true be>+2 !re=e1 9 ord] to judge :e!r ^! objects are prop]ly plac$ to give a good int]section1 due consid]ation mu/ be giv5 to ! relative be>+s ( ! objects4 ,x is evid5t t ! sun mu/ be> by compass ne>ly 9 ! direction ( ! m\nta9 or 9 ! opposite direction to h ! position l9e & ! l9e ( be>+ ( ! m\nta9 cut at ne>ly "r angles4 ,( c\rse1 z ) any set ( cross be>+s ! angle ( int]section may /ill be effectual if ! l9es cut at #ej to #fj1 b ! ne>] a #ij cut ! m accurate ! result+ position4 ,a position l9e is liable to displacem5t ?r\gh a v>iety ( causes among :i* is an inaccurate altitude & ?r\gh incorrect ,gre5wi* mean "t4 ,9 ! =m] in/ance1 an error ( #a w displace ! position "o mile2 if ! altitude is #a too l>ge1 ! correct position ( ! l9e w be #a mile directly away f ! be>+ ( ! body & vice v]sa4 ,! effect ( an error 9 "t ^u a position l9e is to displace x bodily ea/w>d or we/w>d ! am\nt ( arc correspond+ to ! error 9 ! *ronomet]2 ! direction ( ! l9e is1 h[ev]1 unalt]$4 ,! sun c>ries 8 sy/em ( circles ( equal altitude ) him f ea/ to we/ z he travels along a c]ta9 p>allel ( latitude correspond+ to 8 decl9ation 7neglect+ ! slight *ange 9 decl9ation74 ,x is q evid5t t any arc ( a select$ circle1 w1 if its position is plott$ on a small scale *>t--say e #bj m9utes--be f\nd cont9u\sly p>allel ) itself4 ,& ! int]vals betwe5 ea* two plott$ positions ( ! arc w be #e 7( arc7 ! correspond+ value ( #bj m9utes4 ,?us ! displacem5t ( ! position l9e due to an error ( "t is expla9$4 ,if ! "t 0 sl[1 ! l9e 0 too f> to ! ea/w>d1 if fa/1 x 0 too f> to ! we/w>d4 ,! value ( a position l9e has be5 demon/rat$1 yet ) all x does n positively e/abli% ! position ( a vessel4 ,! m>9] 9 locat+ 8 vessel 9 a h>bor does n usually /op aft] he has tak5 "o be>+1 b proce$s to f9d ano!r object ^: be>+ w make a favorable 8cut0 ) ! fir/1 & ?us at _! int]section det]m9es 8 position4 ,z a fur!r *eck aga9/ possible error a ?ird object may be *os5 &1 if ! ?ree be>+s plot )\t =m+ a triangle at _! int]section1 a v reliable fix w be obta9$4 ,:at applies to t]re/rial objects ?us employ$ may be us$ z an illu/ration to be foll[$ 9 tak+ cele/ial be>+s4 ,if ! m>9] e/abli%es a position l9e & kn[s 8 vessel is locat$ at a po9t some:]e along x1 let him look ab\t = ano!r body s plac$ t ! position l9e d]iv$ f x w make a good int]section ) ! fir/ l9e2 if all data are correct ?is po9t w indicate ! position ( ! vessel4 ,:5 ! sun is us$ ?is is seldom possible b 9 lieu ( ano!r body ! sun c aga9 be employ$ to e/abli% ! second position l9e aft] x has mov$ suffici5tly 9 azimu? to make a good cut4 ,! ?\ght no d\bt imm$iately arises z to ! effect ( ! vessel's *ange 9 position dur+ ! int]val4 ,?is is easily tak5 c>e ( by means ( ! c\rse & di/ance run dur+ ! int]val betwe5 ! sights4 ,! fir/ position l9e mu/ be consid]$ c>ri$ bodily by ! vessel )\t *ange ( be>+ f its fir/ position to ! position ( ! second obs]vation4 ,t is1 if at #i ,a4,m4 a position l9e 0 e/abli%$ be>+ 9 a #ae-aie direction1 & ! vessel !n /eam$ & made good a #dj-;c\rse = #f h\rs & #aj knots an h\r1 :5 ano!r position l9e 0 e/abli%$1 ! #ae-aie l9e ( #i ,a4,m4 w\ld be mov$ bodily 9 a #dj direction #fj miles2 :]e its int]section ) ! second l9e w\ld indicate ! position ( ! vessel at #c ,p4,m4 ,! det]m9ation ( position at sea by employ+ two position l9es ( a body ) ! run betwe5 sights is call$ ,sumn]'s d\ble altitude problem4 ,x has already be5 %[n t "o body1 notably ! sun1 c be us$ to get an int]section ( two ( its l9es ( position by wait+ a suffici5t "t betwe5 obs]vations = ! body to *ange its be>+ at lea/ #cj1 ! ne>] #ij ! bett]4 ,! relation%ip betwe5 ! int]val ( "t & ! am\nt ( *ange ( be>+ v>ies greatly1 dep5d+ ^u ! latitude ( ! obs]v] & decl9ation ( ! body4 ,= example1 let u consid] ! two extreme cases3 ,suppose a m>9] to be obs]v+ ! sun on ! equator on ,m>* #ba/1 he w note practically no *ange 9 azimu? dur+ ! :ole =5oon4 ,yet ano!r m>9] 9 ! ,pol> sea1 ^: latitude diff]s ab\t #ij f t ( ! =m]1 w h ! sun encircl+ 8 horizon mak+ ! :ole am\nt ( ! sun's movem5t a correspond+ *ange 9 azimu?4 ,!re=e x w be se5 t ) a l[-rid+ sun 7or o!r body7 ! *ange ( azimu? is great] 9 a giv5 "t1 & = ?is reason ! position l9es d]iv$ f ! sun are m advantage\sly practic$ 9 high] latitudes1 especially 9 w9t]4 ,?is is a po9t ( great value 9 view ( ! fact t ! sun's diurnal c\rse is su* t x is nev] on ! prime v]tical 9 nor!rn latitudes dur+ ! w9t] mon?s1 mak+ longitudes d]iv$ f *ronomet] sights v unreliable4 ,b to g back to ! m>9] on ! equator ^: latitude & sun's decl9ation s ne>ly agree4 ,he is 9 a pr$icam5t %\ld he p]si/ 9 ! plan to det]m9e 8 :]eab\ts by position l9es ( ! sun4 ,9 su* an unusual case1 x w\ld be well to resort to "s o!r me?od or wait until ev5+ & det]m9e ! %ip's position by e/abli%+ ! position l9e ( "s /> or />s4 ,x w be b a few days be=e ! %ip's progress w cause ! sun to leave 8 "r c\rse across ! sky & take ! h\r circles at an angle4 ,take a case :5 ! sun at noon has a z5i? di/ance ( #aj1 ! *ange ( azimu? dur+ ! =5oon is /ill small1 b suppose ! be>+ 0 not$ #a h\r1 or ev5 less1 be=e noon & aga9 9 simil> am\nt aft] noon1 a *ange w be f\nd ( p]haps #ij1 ! diff]5ce ( mov+ f ! s\!a/ quadrant 7if decl9ation is s\? ( latitude7 to ! s\?we/ quadrant4 ,9 ?is way1 a rem>kably good cut may be _h )9 a comp>atively %ort "t4 ,! =ego+ w conv9ce ! read] t he mu/ be gov]n$ by ! *ange ( be>+ & n by "t elaps$1 9 pr$ict+ ! value ( ! cut ( 8 position l9es4 ,9 ! use ( position l9es1 x is necess>y to be> 9 m9d1 t1 :5 ! body's altitude beg9s to approa* ! z5i?1 or1 :at is ! same ?+1 :5 ! %ip is gett+ close to ! body's sub-cele/ial position1 ! circle is gett+ proportionately small]4 ,"u su* conditions ! arcs ( ! circle ( equal altitudes c no long] be %[n z a /raight l9e4 ,! d\ble altitude z x is ord9>ily practic$ is "h impracticable4 ,& ev5 outside ?is impracticable area1 discretion mu/ be %[n4 ,! dead reckon+ position mu/ be proportionately accurate1 & ! assum$ latitudes mu/ be br\ght correspond+ly close toge!r1 9 ord] to h a %ort] l9e ( position1 because ! curvature ( ! circle is gett+ %>p] z ! sub-cele/ial po9t is approa*$4 ,to put x 9 ano!r way1 a small] arc mu/ be us$ 9 ord] to avoid ! error due to excessive curvature4 ,v good results c be obta9$ by not+ ! "t ( obs]vation by *ronomet] 7,g4 ,m4 ,t47 & correct+ x = equation ( "t 9 ord] to get ,gre5wi* app>5t "t4 ,?is1 if conv]t$ into arc1 is ! longitude ( ! sub-sol> position4 ,by us+ ! ,gre5wi* mean "t to correct ! decl9ation tak5 f ! ,nautical ,almanac = t day1 ! latitude ( ! sub-sol> position may be obta9$4 ,plot ?is position on ! *>t & use x z ! c5t] ( a circle2 !n ) ! z5i? di/ance 7#ij - altitude7 z a radius1 draw an arc 9 ! probable position ( ! vessel4 ,some:]e along ?is arc is ! %ip's position4 ,! be>+ ( ! sun 7r h>d to get s ne>ly ov]head7 correct$ = compass error1 rev]s$1 & laid (f f ! sub-sol> position w give a fair idea ( ! position ( ! vessel4 ,n[ by wait+ a suffici5t "t = ! sun to *ange its azimu? en\gh to make a good cut & us+ its new sub-sol> position z a c5t] ) ! z5i? di/ance ( a second obs]vation z a radius1 an arc may be drawn :i* w int]sect ! fir/ arc at ! position ( ! vessel4 ,! run betwe5 ! sights w1 ( c\rse1 require ! fir/ arc to be c>ri$ =w>d z ! fir/ position l9e 9 ! ord9>y d\ble altitude problem4 ,,johnson',s ,,me?od ,x is n always f\nd conv5i5t to plot ! position l9es ( a set ( obs]vations on a *>t2 p]haps = lack ( a *>t ( prop] scale or possibly = want ( ! *>t itself4 ,aga9 _m navigators d n take k9dly to ! graphic me?od1 b pref] to solve _! latitudes or longitudes by computation4 ,9 any ev5t ,johnson's ,me?od comes z a relief to su* p]sons1 sav+ !m f ! ardu\s duty ( e/abli%+ a set ( position l9es by ! *ord me?od ( assum+ two latitudes to get two longitudes4 ,johnson's ,me?od c be practic$ 9 bo? ! d\ble altitude problem ( ! sun1 :]e ! fir/ sight1 or position l9e1 is br\ght =w>d to ! second sight by correct+ x = ! int]v5+ run1 or :]e />s are us$ simultane\sly4 ,*ief among its m]its is ! sav+ ( figures4 ,x is only necess>y to compute two 7in/ead ( f\r7 *ronomet] sights 9 ord] to f9d ! %ip's position1 ?us obta9+ a ma!matically accurate result by a %ort cut4 ,b also a great advantage 9 ! ,johnson ,me?od is t ! result+ longitude is obta9$ by calculation & x is n necess>y to plot ! l9es ^u ! *>t to secure ! position4 ,9 us+ ,johnson's me?od x is n absolutely necess>y to obs]ve two />s simultane\sly z ! quick "w ( a good man is suffici5tly close = ! practical purposes ( navigation4 ,x becomes evid5t to anyone read+ ! =ego+ pages t e ord9>y "t sight places ! vessel on a circle ( equal altitude1 ! longitude result+ f ! computation1 dep5d+ on ! latitude1 by dead reckon+1 us$4 ,n[ r ?an "w two sights employ+ two assum$ latitudes on ei!r side ( ! suppos$ position1 make ! calculation only once1 us+ ! latitude by acc\nt4 ,suppose by way ( explanation t ! altitude ( a /> be>+ ,s4 #ee ,e4 is obs]v$ simultane\sly ) t ( ano!r /> be>+ ,s4 #be ,e4 ,! longitudes d]iv$ by work+ ! "t sight ( ea* %\ld be id5tical1 provid$ ! altitudes are ! true altitudes1 ! ,gre5wi* "t is )\t error1 & ! latitude us$ is correct4 ,a comb9ation ( accuracy1 inde$1 & "o n likely to be exp]i5c$ (t5 9 actual practice4 ,h[ev]1 a skillful navigator %\ld f9d no great difficulty ^! days 9 always hav+ ! correct ,gre5wi* "t at h&4 ,!re is always1 ( c\rse1 an opportunity = ! display ( skill 9 measur+ altitudes1 refraction p>ticul>ly be+ an illusive elem5t & n always easy to detect4 ,b if c>e has be5 tak5 to elim9ate ! errors z mu* z possible f ! "t & ! altitude1 x is safe to consid] any discrepancy betwe5 ! result+ longitudes z acc\ntable to an error 9 ! dead reckon+ latitude4 ,! me?od ( obta9+ ! %ip's position f ! diff]5ce 9 ! longitudes1 d]iv$ f d\ble or simultane\s obs]vations1 0 orig9at$ by ,a4 ,c4 ,johnson1 ,r4 ,n41 & its _m advantages h = ye>s made x ! mo/ popul> =m among progressive %ipma/]s4 ,! work+ ( ?is problem involves ! application ( a correction to ea* calculat$ longitude 9 su* a way z to br+ !m into agreem5t4 ,! tables 7,b[dit* ,tables #dg & #dh7 furni% ?is correction1 :i* is kn[n z ! longitude factor & is symboliz$ by ! lett] ,f4 ,x con/itutes ! *ange 9 longitude due to a *ange ( #a 9 latitude4 ,?is quantity *anges directly ) ! *ange ( azimu? ( ! body2 = example1 ! *ange 9 longitude is nil if ! *ange 9 latitude is made on a due nor? or s\? l9e1 & *ange 9 longitude increases z ! *ange 9 latitude is made on l9es be>+ m & m ea/w>d or we/w>d4 ,s x is necess>y 9 ord] to obta9 ^! corrections to h ! true azimu?s ( ! bodies at ! mom5t ( obs]vation to use z an argum5t 9 ! table ( longitude factors4 ,^! are readily tak5 f ! ,azimu? ,tables or diagram us+ ! data furni%$ by ! "t sight4 ,! two longitudes obta9$ f "t sights 9 :i* ! same dead reckon+ latitude is us$1 lie on ! p>allel ( ?is latitude1 b 7unless ! two longitudes happ5 to be co9cid5t7 ! %ip's position is ei!r nor? or s\? ( ?is p>allel accord+ to ! error exi/+ 9 ! dead reckon+ latitude4 ,if ! obs]v$ azimu? ( ! body 7or bodies7 fall )9 ! same quadrant or 9 opposite quadrants1 ! correct longitude w be f\nd to ! ea/w>d or ! we/w>d ( bo? calculat$ longitudes4 ,?is is cle>ly %[n 9 ,fig4 #g2 bo? azimu?s are betwe5 s\? & ea/4 ,if ! obs]v$ azimu? ( ! body 7or bodies7 fall 9 adjac5t quadrants say1 "o betwe5 s\? & ea/ & ! o!r betwe5 s\? & we/1 ! %ip's position w be f\nd betwe5 ! two calculat$ or errone\s longitudes4 ,! position ( ?is true longitude is det]m9$ by means ( ! be=e-m5tion$ factors4 ,! factor ( a longitude is ! di/ance ( ! true longitude ea/ or we/ ( ! m]idian pass+ ?r\gh ! calculat$ or errone\s longitude1 assum+ ! latitude to be 9 error #a4 ,! mom5t ( ?is factor1 x w be se51 dep5ds on ! azimu? ( ! body1 :i* 9 turn det]m9es ! direction ( ! position l9e4 ,illu/ration3 ,,fig4 #g4 ,! comb9ation ( ! two factors1 by add+ if ! bodies are 9 ! same or opposite quadrants or vice v]sa1 is ! comb9$ error 9 diff]5ce ( longitude due to #a ( error 9 latitude4 ,x n[ becomes a matt] ( proportion by :i* to obta9 ! error 9 ! dead-reckon+ latitude4 ,z ! comb9$ error 9 diff]5ce ( longitude = #a ( latitude1 is to #a ( latitude1 s is ! diff]5ce betwe5 ! two calculat$ longitudes1 to ! error 9 latitude4 ,! longitude factors are bas$ ^u an error ( #a1 s if ! error is m ?an #a x becomes necess>y to multiply ! factor by ! error 9 ord] to obta9 ! correction to ! calculat$ or errone\s longitude4 ,illu/ration3 ,,fig4 #h4 ,an altitude may be tak5 ( any body & aft] a suitable *ange 9 be>+ has tak5 place 7n less ?an #cj7 a second altitude may be tak5 & ! fir/ longitude advanc$ = ! run dur+ ! int]val to ! p>allel ( ! latitude by dead reckon+ at ! "t ( second sight4 ,9 ! usual ev5t ( a disagreem5t 9 ! calculat$ longitudes ! rule ( proc$ure is z foll[s3 ,) ! body's true azimu? at ea* obs]vation1 ! diff]5ce betwe5 ! longitudes & ! latitude by dead reckon+1 us$ at second sight1 ent] ,table #dg1 ,b[dit*1 & take out ! correspond+ numb]s4 ,if ! azimu?s are 9 adjac5t quadrants1 ^! quantities %\ld be add$1 b if 9 ! same or opposite quadrants1 !y mu/ be subtract$4 ,! result 9 ea* case gives ! comb9$ error 9 diff]5ce ( longitude = an error ( #a 9 latitude4 ,x is n[ only necess>y to divide ! diff]5ce betwe5 ! two longitudes by ?is comb9$ error & we h ! error betwe5 ! correct latitude & ! latitude by dead reckon+4 ,n[ multiply ! error 9 latitude by ! numb] tak5 f ,table #dg correspond+ to ! fir/ longitude1 to obta9 ! correction to t longitude1 & by multiply+ ! same error 9 latitude by ! numb] correspond+ to ! second longitude we h ! correction = t longitude4 ,! application ( ^! corrections %\ld br+ ! two calculat$ longitudes into agreem5t at ! position ( ! true longitude4 ,"s difficulty may be exp]i5c$ 9 le>n+ h[ to apply ^! corrections to ! calculat$ longitudes1 b x is always easy to make a r\gh diagram if at all 9 d\bt4 ,a horizontal l9e repres5t+ ! p>allel ( latitude by dead reckon+ at second sight may be drawn ) ! two longitudes plott$ ^u x2 e/abli% ! position l9es ?r\gh ^! longitudes by draw+ !m at "r angles to ! sun's 7or />'s7 azimu?4 ,! int]section ( ! two position l9es indicates ! true longitude & a glance %[s h[ to apply ! corrections to ea* calculat$ longitude to get ! true4 ,9 ,fig4 #h ! we/]ly longitude requires ! correction to be appli$ to ! ea/ & ! ea/]ly longitude correction to ! we/ 9 ord] to arrive at ! true longitude4 ,)\t ! use ( a diagram a rule easy to rememb] 9 decid+ :e!r to apply ! correction 9 longitude to ! ea/w>d or we/w>d is "h giv53 ,if ! error 9 latitude is ( ! same "n z ! fir/ lett] ( ! be>+1 ! *ange 9 longitude is contr>y 9 "n to t ( ! second lett] & vice v]sa4 ,= example take ! case j cit$4 ,:5 a body's azimu? is less ?an #de1 x is wis]1 & insures m accurate results to "w by ,new ,navigation1 or1 if suffici5tly close to ! m]idian1 z an ex-m]idian4 ,9 ! case ( ! latt] ! corrections 9 su* a case are tak5 f ! table ( latitude factors 7,b[dit*1 ,table #dh71 ! problem be+ ! same 9 pr9ciple & 9 solution z t describ$ above4 ,good results are ev5 obta9$ by us+ two ex-m]idians1 "o on ea* side ( ! m]idian4 ,! corrections 9 ! latitude may be appli$ accord+ to ! foll[+ rule1 if x is pref]r$ to ! r\gh diagram me?od3 if ! error ( longitude is ( ! same "n z ! second lett] ( ! be>+1 ! *ange 9 latitude is ( ! contr>y "n to ! fir/ lett]1 & vice v]sa4 ,,! ,,new ,,navigation ,9 e bran* ( sci5ce & indu/ry s9ce "t immemorial a cont9u\s process ( simplification & increas$ accuracy has be5 tak+ place1 & amid ?is g5]al evolution ( work+ sy/ems ! sci5ce ( navigation w n be f\nd an exception4 ,ev5 n[ !re is a t5d5cy to displace ! "t-honor$ *ronomet] sight1 toge!r ) a long li/ ( m or less bewild]+ ways ( obta9+ latitude & longitude4 ,! advance me?od is popul>ly kn[n z ! ,new ,navigation1 yet its pr9ciples 7 orig9ally br\ght =w>d by ,m>cq ,/4 ,hilaire1 a ,fr5* admiral1 ne>ly #dj ye>s ago4 ,x is n a new me?od ( f9d+ position1 b r an improv$ way ( e/abli%+ a ,sumn] l9e4 ,l _m innovations x has tak5 all ^! ye>s = navigators to become reconcil$ to ! *ange & break away f ! m famili> =ms4 ,9 ord] to facilitate a simple explanation ( ,new ,navigation x w be br\ght to m9d t e heav5ly body has a correspond+ po9t on ! e>? directly b5ea? x1 :i* be>s ! same relation 9 latitude & longitude to ! e>?1 t ! body does 9 decl9ation & "r asc5sion to ! cele/ial sph]e4 ,to an obs]v] at su* a sub-cele/ial po9t ! body is 9 ! z5i? ) an altitude ( #ij2 & ab\t him lies a sy/em ( conc5tric circles ( equal altitude1 :i* ext5ds ov] a hemisph]e ( ! e>? #ij 9 e direction f ! po9t ( orig94 ,?is po9t1 ?r\gh ! app>5t diurnal revolution ( ! body1 c>ries ?is :ole sy/em ( circles ar\nd ! e>? ea* day & nor?w>d & s\?w>d ) ! body's *ange 9 decl9ation4 ,on ! out] limit ( ?is sy/em ( circles1 ! altitude ( ! body is #j4 ,?us x is se5 t ! altitude ( ! body decreases & its z5i? di/ance 7#ij - altitude7 correspond+ly increases 9 direct proportion z ! obs]v] dep>ts f ! sub-cele/ial po9t1 & vice v]sa4 ,if1 = in/ance1 an obs]v] is #ajj miles 7nautical7 f ?is po9t1 ! z5i? di/ance is #ajj or #a #dj & ! altitude ( ! body is #hh #bj2 at #bgjj miles #bgjj_/fj #de ( z5i? di/ance1 & #ij - #de ( altitude4 ,a feature is n[ introduc$ t has a close be>+ ^u ! pr9ciple "u discussion1 to s]ve z an op5+ view ( ! subject3 ,a navigator =tunate en\gh to h a body reasonably ne> 8 z5i?1 say #e1 has at h& an extremely simple way ( graphically f9d+ 8 %ip's position4 ,?is situation has previ\sly be5 describ$1 b is repeat$ to make cle> ! pr9ciple ( ,new ,navigation4 ,! sub-cele/ial position ( ! body at ! mom5t ( obs]vation is readily asc]ta9$ by not+ ! "t by *ronomet] & rec\rse to ! ,nautical ,almanac = its decl9ation4 ,) ! po9t ?us e/abli%$ z a c5t]1 & ! z5i? di/ance d]iv$ f ! obs]v$ altitude z a radius1 sw+ a circle ^u ! *>t4 ,! %ip's position is some:]e on ! circumf]5ce ( ?is circle ( equal altitudes4 ,?is circle is n[ c>ri$ =w>d ! am\nt & direction ( ! run ( ! vessel betwe5 ?is obs]vation & a subsequ5t "o simil>ly tak54 ,dur+ ?is int]val ! be>+ ( ! body %\ld h *ang$ suffici5tly to make a good int]section ( ! circles4 ,! %ip be+ on bo? circles mu/ be at "o ( ! two int]sections1 betwe5 :i* ! m>9] c readily decide4 ,! conditions cit$ are comp>atively unusual b %[ ! practical use ( a circle ( equal altitude 9 its simple/ =m4 ,! z5i? di/ance is ord9>ily too l>ge to become a radius = su* use on ! *>t4 ,! circles ( equal altitude are 9 practice s l>ge t #aj to #dj mile arcs 9 ! vic9ity ( ! vessel are treat$ by h] navigator z /raight l9es1 kn[n z ,sumn] or position l9es4 ,^! l9es are1 !oretically1 *ords or tang5ts accord+ to ! me?od employ$ 9 e/abli%+ ! l9e1 b 9 practice ! div]g5ce f ! circle is negligible1 except+ always :5 ! body is too close to ! z5i?4 ,! e/abli%m5t ( ! position l9e has be5 done 9 sev]al ways = _m ye>s until ! adv5t ( ?is new & m exp$iti\s me?od4 ,! altitude ( a body at any select$ "t = an assum$ position c be readily calculat$4 ,if ?is altitude does n agree 7& x seldom does7 ) ! altitude measur$ simultane\sly ) ! sextant1 correct$ = ! usual errors1 ! assum$ position is n co9cid5t ) ! actual position ( ! vessel4 ,! navigator n[ proce$s to lay (f f ! assum$ position1 ! l9e ( azimu? ( ! body tak5 f ! azimu? tables1 ,weir's ,azimu? ,diagram1 or det]m9$ by obs]vation4 ,on ?is l9e ! di/ance betwe5 ! obs]v$ & comput$ altitude1 express$ 9 m9utes ( arc1 is measur$1 t[>ds ! body if ! obs]v$ altitude is great]1 & away f x if less1 ?an ! comput$ altitude4 ,! po9t ?us indicat$ is a position on a circle ( equal altitudes1 ! arc 9 ! imm$iate vic9ity ( ! comput$ po9t be+1 approximately1 ! position l9e4 ,?is l9e is at "r angles to ! azimu? = ! reason t a tang5t is at "r angles to ! radius ( a circle at a giv5 po9t4 ,x is n[ kn[n t ! %ip is some:]e on ?is l9e ( position1 & x is necess>y to cut x ) ano!r su* l9e to det]m9e def9itely h] position4 ,if ! sun is ! body be+ obs]v$1 x becomes necess>y1 9 ord] to provide a good angle ( int]section1 to wait until ! azimu? *anges at lea/ #cj1 :5 ! obs]vation is repeat$1 a second l9e e/abli%$1 & ! fir/ l9e br\ght =w>d 9 exact accordance ) ! %ip's run4 ,! int]val requir$ naturally dep5ds ^u ! latitude ( ! %ip & ! decl9ation ( ! sun4 ,! int]section ( ! l9es w be ! position ( ! %ip at ! "t ( ! second sight4 ,! use ( />s has a decid$ advantage 9 t !re are always "s ( ^! bodies available = obs]vation ly+ 9 v>i\s azimu?s2 x is practicable1 ) a well-def9$ horizon1 to obs]ve simultane\sly two or m ( ^! bodies ^: be>+s %[ t !y w\ld produce desirable position l9es4 ,f ! result+ int]sections ! position ( ! %ip is secur$4 ,?is obviates wait+ = ! second l9e1 a feature t is always inconv5i5t & sometimes1 p]haps1 dang]\s4 ,! calculation ( ! altitude is accompli%$ by ! solution ( ! sph]ical triangle 9 :i* we h giv5 ! co-latitude 7#ij - assum$ latitude71 ! pol> di/ance & ! h\r angle ( ! m]idian ( ! assum$ position4 ,?us ) two sides & ! includ$ angle1 ! ?ird side or ! z5i? di/ance 7#ij - altitude7 is easily det]m9$ by ei!r ( sev]al =mulas4 ,) ! use ( ?is me?od all ! =mulas t =m]ly1 & /ill1 (t5 puzzle ! navigator to rememb] c be r$uc$ to ?is "o sight4 ,"o ( ! mo/ important features x possesses is t x c be utiliz$ reg>dless ( ! altitude ( ! body 7except :5 v high71 its azimu?1 or its h\r angle1 all ( :i* are elem5ts t h to be us$ "u c]ta9 favorable circum/ances 9 ord] to get accurate results f ! old] =ms4 ,! navigator is n[ giv5 a great] fre$om 9 *oos+ bodies to obs]ve ?an is f\nd 9 any o!r me?od4 ,! m>9] to-day has be5 almo/ entirely reliev$ f ! labor ( comput+ position at sea1 %\ld he c>e to avail himself ( a set ( altitude tables1 sev]al excell5t ones h made _! appe>ance on ! m>ket1 among !m ,hydrographic ,(fice ,publication ,no4 #bjj4 ,f !m ! altitude c be select$ correspond+ to ! conditions ( any p>ticul> obs]vation4 ,) a set ( ^! tables a navigator is no long] requir$ to be a ma!matician or to rememb] ! =ms ( a half doz5 sights4 ,?us 9 ?is wond]ful age ! m>9]'s utopian dream ( obta9+ position at sea by inspection1 is1 9 a way1 realiz$4 99 99 99 99 99 ,9 ord] to illu/rate ! practical work+ ( a problem by ?is me?od1 ! foll[+ example is tak5 up po9t by po9t3 ,e>ly on ! morn+ ( ,may #ba1 #ahii1 :ile 9 ! assum$ position ( latitude #ee #jj ,n41 longitude #aab #jh ,e4 obs]v$ ! true altitude ( ! /> ,arcturus to be #cg #ad #ej1 be>+ we/ ( ! m]idian4 ,! *ronomet] c>ry+ ,gre5wi* mean "t read #bj d4 #f h4 #bj m4 #jc s4 ,! obs]v] desir$ 8 position4 ,! problem by ! ,/4 ,hilaire me?od resolves itself into ! solution ( ! sph]ical triangle %[n 9 ,fig4 #aj1 :]e two sides & an includ$ angle are giv53 ,pol> di/ance #ij - decl9ation 7,nautical ,almanac74 ,co-latitude #ij - latitude 7by dead reckon+74 ,h\r angle ( />4 ,see figure & solution bel[4 ,! h\r angle ( ! sun is m readily f\nd ?an t ( a />4 ,x is accompli%$ by apply+ ! longitude 79 "t7 ( ! assum$ position to ! ,gre5wi* "t %[n by ! *ronomet] at ! "t ( sight4 ,?is h\r angle ( ! mean sun mu/ be correct$ by ! equation ( "t to obta9 ! h\r angle ( ! actual sun4 ,illu/ration3 ,,fig4 #i4 ,illu/ration3 ,,fig4 #aj4 ,! cos9e-hav]s9e =mula s]ves ! purposes ( ?is problem v satisfactorily3 ,hav z hav 7,l d7 cos ,l cos d hav h :i* is d]iv$ f ! well-kn[n expression3 ,cos z s9 ,l s9 d cos ,l cos d cos h :]e z z5i? di/ance2 ,l ! latitude2 & h ! h\r angle4 ,,solution ,dec4 ,arcturus #ai #db #bi4 ,lat4 #ee #jj ,n4 7,assum$74 ,g4 ,m4 ,t4 #bj d4 #f h4 #bj m4 #jc s4 ,r4 ,a4 ,m4 #c #ea #db ,accel]ation #a #jb -------------------------------------- ,lat4 #ee #jj #jj4 ,g4 ,s4 ,t4 #aj #ab #dg ,dec4 #ai #db #bi ,long4 #g #bh #cb ------------------------ -------------------------------------- ,l d #ce #ag #ca ,l4 ,s4 ,t4 #ag #da #ai ,r4 ,a4 #ad #aa #jc -------------------------------------- ,h4 ,a4 #c #cj #af ,w4 7,obs]v]7 #eb #cd #jj ,lat4 #ee #jj #jj cos4 #i4gehei ,dec4 #ai #db #bi cos4 #i4igcgh ,h4 ,a4 #eb #cd #jj hav4 #i4bibdd -------------------- #i4jbdha nat4 hav4 4#ajehh nat4 hav4 #ce #ag #ca 4#jiahi -------- z #eb #dh #ce nat4 hav4 4#aiggg #ij #jj #jj ------------ ,comput$ altitude #cg #aa #be ,obs]v$ altitude #cg #ad #ej ------------ ,altitude diff]5ce #c #be4 ,illu/ration3 ,,fig4 #aa4 ,a %ip's position is usually obta9$ by plott+ ! l9es ( azimu? & ! position l9es mu* 9 ! mann] %[n 9 ! *>tlet4 ,! azimu? ( ! body at ! mom5t ( obs]vation is readily tak5 by inspection f ! azimu? tables or bett] /ill f ,weir's ,azimu? ,diagram1 bo? publi%$ by ! ,u4 ,s4 ,hydrographic ,(fice4 ,9 ord] to get an int]section ( two l9es ( position & !reby asc]ta9 ! latitude & longitude at once x is assum$ t ! obs]v] took an obs]vation ( ano!r /> be>+ ,s4 #de ,e41 simultane\sly ) ,arcturus4 ,:5 ord9>y ,a4,m4 "t sights are tak5 ! result+ longitude e/abli%es a nor? & s\? sumn] l9e b ! latitude is by ,d4 ,r42 at noon ! latitude by m]idian altitude e/abli%es an ea/ & we/ l9e b ! longitude is by ,d4 ,r4 s x is ) a sumn] l9e a position is e/abli%$ ^u x b ! position along x is by ,d4 ,r4 ! latitude & longitude1 h[ev]1 c be obta9$ by a slight calculation )\t draw+ ! l9es on ! *>t2 t is1 ! mo/ probable position4 ! altitude diff]5ce hav+ be5 det]m9$ ent] table #b1 b[dit*1 us+ ! azimu?1 or its reciprocal z ! case may be1 z ! c\rse1 & ) ! altitude diff]5ce z ! di/ance1 pick out ! diff]5ce ( latitude & ! dep>ture & apply !m to ! dead reckon+ latitude & longitude z is ! usual practice4 ! result is ! mo/ probable position 7accord+ to ! ,d4 ,r47 on ! sumn] l9e4 ,,*apt] ,x ,,! ,,moon ,! moon is ! mo/ int]e/+ ( ! heav5ly bodies n only f a romantic viewpo9t1 b f ! a/ronomical z well4 ,look+ at ! practical side1 x is due mo/ly to ! moon's influ5ce ( attraction on ! wat]s ( ! e>? t we h ! highly important ph5om5a ( ! tides4 ,! moon is our ne>e/ neighbor 9 ! heav5s2 9 fact1 %e is a satellite1 t is1 revolves ar\nd ! e>?4 ,?is movem5t is f we/ to ea/ at an av]age rate ( #ea m9utes ea* day4 ,! moon's orbit is elliptical ) ! e>? ly+ a little out ( c5t]1 n unlike ! situation ( ! sun 9 ! e>?'s orbital ellipse b m pron\nc$4 ,:5 ! moon is at ! ne>e/ po9t to ! e>? %e is said to be at 8p]igee0 & ! po9t :]e %e is mo/ remote is call$ ! 8apogee40 ,! moon is a non-lum9\s body & gives (f no?+ b reflect$ sunlight4 ,! lun> hemisph]e fac+ ! sun is !re=e ! only illum9at$ portion ( ! body1 & z %e turns on h] axis precisely z ! e>? does1 ! same side is always t[>ds u4 ,! a/ronom]s h se5 b "o side ( our satellite4 ,?is sol> illum9ation acc\nts = ! v>i\s int]e/+ phases ( ! moon :i* we see ea* mon?4 ,:5 ?is body 9 h] mon?ly revolution ar\nd ! e>? passes betwe5 u & ! sun1 ! illum9at$ side is t[>ds ! sun & ! d>k side t[>ds u4 ,we see no moon at ?is "t & call x new moon4 ,two weeks lat]1 %e has complet$ "o-half ( h] revolution & is n[ on ! o!r side ( ! e>? & we are betwe5 ! moon & ! sun4 ,! illum9at$ face ( ! moon is n[ directly t[>ds u & we call x full moon4 ,at ! "t ( new moon1 ! ea/w>d movem5t quickly br+s h] out ( range ) ! sun & 9 a c\ple ( days we are able to see a f9e cresc5t 9 ! we/]n sky4 ,?is is ! v edge ( ! illum9at$ face--we c see ar\nd ! corn] j t mu*4 ,day aft] day ! moon's light$ surface becomes l>g] & l>g] until 9 ab\t a week %e is ne> our m]idian at sunset & !re=e at1 r\ghly 7dep5d+ on ! "t ( ! ye>71 #ij f ! be>+ ( ! sun4 ,! moon n[ pres5ts to u a face "o-half d>k & "o-half light4 ,?is is call$ ! quadrature4 ,?is t]m also applies to ! simil> condition occurr+ a week aft] full moon :5 %e is aga9 be>+ at "r angles to ! sun4 ,^! occasions are also call$ ! fir/ & la/ qu>t]1 respectively4 ,! movem5ts ( ! moon are v rapid4 ,%e makes h] revolution ar\nd ! e>? 9 #bg days1 mak+ a *ange 9 "r asc5sion ( #cfj or #bd h\rs 9 ?is int]val1 a *ange ( ov] two m9utes ea* h\r4 ,! decl9ation passes ?r\gh its :ole cycle ( *ange f nor? to s\? & return also 9 #bg days2 ! sun requires a ye> to pass ?r\gh its extremes ( decl9ation & return4 ,! *ange ( ! moon's decl9ation av]ages ab\t #i p] h\r4 ,^! facts dem& c>eful att5tion :5 employ+ ! moon 9 navigation4 ,x is a v curi\s & happy circum/ance t 9 ! high] latitudes :5 ! %ort days ( ! w9t] sun occur1 ! moon at full rides its highe/ decl9ations1 & consequ5tly gives extra long nights ( moonlight2 & t 9 ! summ]1 :5 ! sun is 9 high] decl9ation & ! days are long1 ! moon at full is 9 l[ decl9ation & !re is less moonlight :5 x is lea/ ne$$4 ,! reason ( ^! conditions is t ! full moon occurs :5 on ! opposite side ( ! e>? f ! sun & at ! w9t] sol/ice :5 ! e>?'s nor? pole is incl9$ away f ! sun %e mu/ be incl9$ t[>ds ! moon pass+ t body 9 high decl9ation4 ,! rev]se conditions exi/ at ! summ] sol/ice4 ,ano!r =tunate provision = lov]s ( moonlight nights is ! fact t ! plane ( ! moon's orbit is n 9 ! same plane z t ( ! e>?'s orbit1 = if su* 7 ! case ea* "t ! ?ree bodies1 ! e>?1 sun & moon1 came 9 range !re w\ld be an eclipse4 ,! new moon com+ 9 betwe5 ! e>? & ! sun w\ld cause an eclipse ( ! sun1 & at full moon :5 ! e>? is betwe5 ! sun & moon1 !re w\ld be an eclipse ( ! moon4 ,!re=e1 !re w\ld be an eclipse twice a mon?4 ,?is =tunately is avoid$ by ! angle ( #e t ! plane ( ! moon's orbit takes ) t ( ! e>?4 ,z a result !y only come 9 exact range occasionally :5 ! moon at new & full happ5s to be on ! ecliptic--! e>?'s orbit4 ,if1 to repeat1 ?is occurs at full !re is an eclipse ( ! moon1 if x occurs at new1 !re is an eclipse ( ! sun4 ! moon moves ea/w>d ?r\gh ! heav5s on h] mon?ly c\rse ( revolution2 x !n becomes app>5t t %e mu/ return to ! m]idian lat] & lat] ea* day ! am\nt ( 8ret>dation10 z x is call$4 ,?is ret>dation is a v>iable quantity dep5d5t ^u ! moon's irregul> *ange 9 "r asc5sion4 ,x is caus$ by ! moon's motion 9 h] elliptical orbit & at ! incl9ation :i* h] orbit takes ) ! cele/ial equator4 ,^! causes are precisely ! same 9 "* z ^? produc+ ! equation ( "t 9 ! conditions relative to ! sun & ! e>?'s orbit1 b ^? ( ! moon are mu* great]4 ,! errors caus+ a v>iation 9 ! "r asc5sion ( ! sun requir+ a ye> :]e ! simil> conditions 9 ! moon are br\ght ab\t 9 a mon?1 :i* acc\nts = ! m>k$ *anges 9 ! moon's rate ( ea/w>d motion4 ,! av]age daily ret>dation1 or av]age lat] "t 9 arriv+ at ! m]idian1 is v close to #ea m9utes4 ,yet ! extremes ( ret>dation range f #ch to #ff m9utes4 ,! av]age ( #ea m9utes daily ret>dation is also notic$ 9 ! lat] ris+ & sett+ ( ! moon4 ,! extreme times betwe5 successive ris+s or sett+s dur+ ! ye>1 :ile !y av]age #ea m9utes l ! cross+ ( ! m]idian1 !y d n ma9ta9 ! same extremes1 *ang+ on acc\nt ( ! latitude ( ! obs]v] z well z ^u h] own motions4 ,at #da nor? ! ret>dation on successive ris+s & sett+s ranges betwe5 #bc m9utes & #a h\r & #ag m9utes4 ,z ! vessel proce$s f>!r nor? ! range is great] until ne> #ff nor? :5 ! moon is 9 h] av]age greate/ decl9ation nor? %e does n set at all becom+ circumpol> = a c]ta9 "t ea* mon?4 ,9 ! duration ( a mon? ! moon *anges h] "r asc5sion #bd h\rs1 :]e ! sun takes a ye> to accompli% ?is am\nt z x 7app>5tly = navigational purposes7 moves ea/w>d ar\nd ! e>?4 ,?is %[s ! mu* m rapidly increas+ *ange 9 "r asc5sion 9 ! case ( our satellite4 ,?us aga9 ! moon's rapid motions are acc\nt$ =4 ,! moon's orbit ar\nd ! e>? is n co9cid5t--does n lie 9 ! same plane z ! e>?'s orbit 7! ecliptic7 b takes an angle ( ab\t #e #h ) x4 ,! po9t ( int]section betwe5 ! moon's orbit & ! ecliptic are call$ nodes 7correspond+ ) ! equ9oxes74 ,! po9t cross$ by ! moon z x passes f s\!rn to ! nor!rn side ( ! ecliptic is call$ ! asc5d+ & ! o!r ! desc5d+ node4 ,! moon's axis is v sl[ly describ+ a circle 9 ! heav5s simil> to t ( ! e>?2 & 9 consequ5ce ! nodes are sl[ly mov+ we/w>d along ! ecliptic ye> by ye>4 ,j z is ! equ9ox by ! movem5t ( precession1 b at a mu* great] rate 7see rem>ks on precession else:]e74 ,! moon's axis completes its revolution 9 ab\t #ai ye>s1 :ile ! e>? requires #bf1jjj ye>s4 ,?is is call$ ! lun> cycle4 ,at ! "t 9 ! lun> cycle :5 ! asc5d+ node ( ! moon's orbit is 9 range ) ! v]nal equ9ox ! moon has h] greate/ range ( decl9ation--ab\t #eg f extreme nor? to extreme s\?4 ,%e is !n #bc nor?1 ! am\nt t ! ecliptic is f ! equator & #e m1 ! am\nt t ! moon's orbit is above ! ecliptic4 ,ab\t #i ye>s lat] :5 ! moon's axis has li/$ 9 ! opposite direction & ! desc5d+ node co9cides ) ! v]nal equ9ox1 ! moon's maximum decl9ation equals #bc m9us #e or #ah nor? or s\?1 a range ( only ab\t #bf4 ,illu/ration3 ,?is figure is view$ f ! sun look+ t[>ds ! e>? on m>* #ba/--! v]nal equ9ox4 ,,fig4 #ab4 ,9 ! autumn1 !re occurs an int]e/+ ph5om5on reg>d+ ! moon call$ ! ,h>ve/ ,moon4 ,?is is ! "t ( unusually f9e moonlight nights 9 :i* ! moon rises = ?ree or f\r ev5+s at ab\t ! same "t in/ead ( ! usual rapid ret>dation4 ,! "t ! sun or moon is above our horizon dep5ds ^u its decl9ation & our latitude4 ,z ! sun moves nor?w>d 9 decl9ation f ,m>* to ,june1 our days l5g!n by ! sun ris+ e>li] & f>!r 9 ! nor!a/1 & sett+ lat] & f>!r to ! nor?we/4 ,simil>ly ! moon 9 ,septemb] is mov+ nor?w>d 9 decl9ation v rapidly & w\ld be ris+ e>li] ea* ev5+ 7 x n = its own ea/w>d movem5t ( revolution :i* causes h] to slip ea/w>d an av]age ( #ea m9utes daily & causes h] lat] ris+ at night4 ,! result is t ^! two influ5ces at "w almo/ c\nt]act ea* o!r & cause ! moon to rise at ab\t ! same "t = sev]al days giv+ u ?ree or f\r glori\s moonlight nights call$ ! ,h>ve/ ,moon4 ,x w be se5 by ! =ego+ t great c>e mu/ be ex]cis$ 9 hav+ ! "t ( obs]vation accurately det]m9$ ow+ to ^? rapid movem5ts ( ! moon4 ,x is also a matt] ( great difficulty to correct ! obs]v$ altitude ( ?is body on acc\nt ( num]\s errors t become consid]able 9 am\nts due to h] proximity to ! e>?4 ,& = ^! reasons ?is body is n popul> = obs]vations ) ! g5]al run ( navigators4 ,9 ! case ( ! semi-diamet]1 consid]able error is app>5t & is fully describ$1 ) p>allax1 :i* is excessive1 "u 8,corrections = ,obs]v$ ,altitudes40 ,,*apt] ,,xi ,*>ts ,a difficulty 0 enc\nt]$ :5 ! e>ly c>tograph]s attempt$ to repres5t ! e>?'s sph]ical surface on a flat %eet4 ,x c n be done1 ( c\rse1 )\t di/ortion be+ introduc$ 9 "s mann]4 ,!re are v>i\s me?ods ( tak+ c>e ( ?is error & "o is adopt$ = "o c]ta9 purpose :ile ano!r s*eme is us$ 9 "s o!r "w4 ,^! me?ods ( c>+ = ! error or di/ortion are kn[n z projections1 ! pr9cipal be+ ! ,m]cator1 ! gnomonic & polyconic4 ,! ,m]cator projection is almo/ univ]sally us$ = navigational purposes2 ! gnomonic projection facilitates ! use ( great circle sail+1 & ! polyconic is us$ = survey+ %eets4 ,! ,m]cator *>t repres5ts ! e>? z ?\gh x 7 a cyl9d] in/ead ( a sph]e4 ,if we take ! sk9 ( "o-half an orange1 & assume x to repres5t ! nor!rn hemisph]e ( ! e>?1 an attempt to =cibly br+ x flat ^u a table w result 9 ! te>+ or /ret*+ ( ! sk94 ,x c1 h[ev]1 be br\ght flat to ! table 9 a regul> uni=m way by cutt+ x 9 a saw too? fa%ion f ! /em 7pole7 to ! edge 7equator71 z %[n 9 ! diagram4 ,illu/ration3 ,,fig4 #ac4 ,! %ad$ portions repres5t actual e>?'s surface & ! blank p>ts %[ ! error introduc$ by us+ ?is me?od4 ,9 ?is =m x is useless z a *>t1 s ! real p>ts are /ret*$ or ext5d$ ea* way to ! dott$ l9es mak+ a complete *>t4 ,x is n[1 h[ev]1 )\t a ve/ige ( accuracy 9 repres5t+ ! bodies ( l& & wat] z !y really exi/4 ,! result w\ld be t if a r\nd isl& %\ld be 9 ! latitude ( ! top ( ! *>t x w\ld be /ret*$ into an elongat$ isl& ly+ ea/ & we/ giv+ a v errone\s inaccurate idea ( x1 z %[n by ! ea/ & we/ %ad+4 ,if1 h[ev]1 ! isl& _h be5 on ! equator :]e no ea/ & we/ /ret*+ w\ld h occurr$ ! isl& w\ld appe> 9 its natural %ape1 b ! f>!r nor? or s\? x lies j 9 proportion to ! latitude w x be /ret*$ 9 an ea/ & we/ direction4 ,su* a condition w n s]ve ! purposes ( navigation & x becomes necess>y to ext5d ! degrees ( latitude1 mak+ !m appe> long] & long] z ! equator is dep>t$ f4 ,?is /ret*es ! elongat$ ea/ & we/ isl& 9 a nor? & s\? direction & br+s x back approximately to its actual %ape ( a r\nd isl&4 ,if !re 0 a r\nd isl& 9 #aj ,n4 & a simil>-siz$ simil>-%ap$ isl& 9 #ej ,n4 ! ,m]cator *>t w\ld %[ ! nor!rn "o to be almo/ twice z l>ge ow+ to ?is artificial di/ortion4 ,b its relative %ape w\ld rema9 practically correct4 ,x w be se5 t ! latitude scale on ! sides ( ! *>t c>ries an increas+ value t[>ds ! nor?--on a *>t :]e a degree is ab\t long at ! equator x w\ld be ab\t long 9 #fj ,n4 or ,s4 ,a m9ute ( latitude is equal to a mile on ?is scale1 b x becomes necess>y to use x 9 ! latitude 9 :i* ! measurem5t is tak54 ,if a c\rse runs ,n4 #fj ,e4 f latitude #cj ,n4 to #dj ,n4 & ! di/ance is desir$1 take at ! middle latitude at ! side ( ! *>t a conv5i5t multiple ( di/ance1 say #cj1 on ! divid]s & /ep (f ! di/ance4 ,or ! :ole c\rse c be tak5 (f at once & ) ! po9ts ( ! divid]s at equal di/ances nor? & s\? ( ! middle latitude read (f ! numb] ( m9utes ( latitude ly+ betwe5 !m4 ,9 v high latitudes ! ,m]cator *>t is n reliable4 ,! di/ortion becomes excessive & be>+s tak5 w n plot correctly4 ,all ! m]idians on a ,m]cator *>t are p>allel & cut ! equator at "r angles4 ,!y all lie 9 a true nor? & s\? direction4 ,! p>allels ( latitude all lie ea/ & we/ & are p>allel to ea* o!r & at "r angles to ! m]idians4 ,! degrees ( longitude on ! globe gr[ small] & small] z ! pole is approa*$ due to ! actual conv]g5ce ( ! m]idians1 b z all m]idians are p>allel on ! ,m]cator *>t ! l5g? ( a degree mu/ be %[n ! same l5g? at ! top z well z at ! bottom ( ! *>t4 ,9 j ! proportion t ! degrees ( longitude h be5 l5g!n$ artificially beyond _! true l5g? mu/ ! degrees ( latitude be l5g!n$ 9 ea* latitude4 ,?is am\nt is %[n 9 ,table #c1 ,b[dit*1 reckon$ z ! di/ance 9 miles ea* p>allel is f ! equator by ! ,m]cator projection4 ,?us 9 latitude #dj ,n4 ! di/ance is #bdjj or miles1 ! table %[s t 9 ! con/ruction ( a ,m]cator *>t ?is p>allel %\ld be increas$ artificially to #bfjg4f4 ,^! are call$ ! m]idional p>ts4 ,on a ,m]cator *>t ! %ip's c\rse is repres5t$ by a /raight l9e & cuts ea* m]idian at ! same angle & is call$ a rhumb l9e4 ,= all practical purposes on %ort runs ?is rhumb l9e is ! be/ to use1 b x is n ! %orte/ di/ance betwe5 two po9ts4 ,%\ld y be able 9 a c\rse a ?\s& miles long1 to see y\r port ( de/9ation y\r rhumb l9e c\rse at ! outset w\ld n head y\r %ip = x1 b 79 nor!rn latitude7 to ! s\?w>d ( x4 ,h[ev]1 z y proce$$ ! %ip's head w\ld gradually draw t[>ds ! port & y w\ld ev5tually arrive4 ,:at appe>s to be a /raight l9e on ?is *>t is really a curve on ! sph]e ( ! e>?4 ,y\r l9e ( actual vision is a great circle1 & 9 ord] to foll[ su* a bee l9e y mu/ con/antly *ange y\r compass c\rse 7on a long run7 & describe a curve on ! ,m]cator *>t unless ! %ip is head$ nor? or s\? or ea/ or we/ along ! equator1 9 :i* cases %e is sail+ on a great circle4 ,! well-kn[n ,hydrographic ,(fice ,pilot ,*>ts are on ! ,m]cator projection & %[ all /eam%ip tracks z curves1 = !y are great circles4 ,! gnomonic *>t is bas$ on a projection ( ! e>?'s surface ^u a plane tang5t to any *os5 po9t :i* is to be ! c5t] ( ! *>t4 ,! eye is assum$ to be at ! c5t] ( ! e>? look+ outw>d to ! po9t ( tang5cy4 ,x w be se5 t ! surface ( ! e>? adjac5t to ! po9t ( tang5cy w be v accurately %[n on ! *>t1 b becomes di/ort$ gradually f ! c5t]1 ! sides ( :i* %[ ! l& 9 su* an unnatural %ape t x is h>dly recognizable4 ,) a *>t on ?is projection great circle sail+ is mu* simplifi$4 ,! /raight l9e betwe5 two po9ts indicates ! great circle to foll[1 & ! c\rse & di/ance is obta9$ by foll[+ ! directions & illu/rat$ example giv5 on ea* *>t4 ,!y are con/ruct$ = ! diff]5t oceans & are = sale by ! ,hydrographic ,(fice4 ,! c\rse c be transf]r$ to a ,m]cator *>t by tak+ successive positions f ! gnomonic *>t & plott+ !m accord+ to latitude & longitude1 & jo9+ by /raight or curv$ l9es4 ,9 sett+ out on a voyage ! port ( de/9ation c\ld x be se5 ahead w\ld indicate ! great circle c\rse1 & 9 ord] to cont9ue to head directly = x1 ! c\rse mu/ be cont9ually *ang$4 ,:ile 9 ! ,nor? ,atlantic b\nd = ,europe ! c\rse mu/ be *ang$ con/antly to ! ea/ 7"r7 9 ord] to rema9 on ! great circle--! /raight & %orte/ di/ance4 ,! c\rse & di/ance c be comput$ by ! =m giv5 9 ,b[dit*1 9 :i* two sides & an includ$ angle are giv5 to f9d ! o!r side & ! 7c\rse7 angle at ! po9t ( dep>ture4 ,! co-latitudes ( ! po9ts ( dep>ture & de/9ation & ! angle betwe5 !m at ! pole1 are respectively ! sides & ! includ$ angle4 ,h[ev]1 ! gnomonic *>t gives ! c\rse & di/ance graphically4 99 99 99 99 99 ,:5 a *>t is pur*as$ or receiv$ f ! ,gov]nm5t (fices ! date ( issue /amp$ ^u x %\ld be c>efully not$4 ,x c safely be tak5 = grant$ t ! *>t has be5 correct$ up to t date & x is incumb5t ^u ! navigator or ma/] to seek 9 all ,notices to ,m>9]s subsequ5t to ?is date = any t affect ! *>t4 ,if a ,notice conta9s in=mation requir+ a correction ! numb] ( ! *>t appe>s 9 boldface type4 ,! alt]ations %\ld be made neatly ) ,india wat]pro( ink1 & if by ! nature ( ! in=mation x is impracticable to make ! *anges a note %\ld be made 9 a conspicu\s place4 ,*>ts are pr9t$ f copp]1 z9c or alum9um plates & small *anges easily made by h& are n *ang$ on ! plate until an accumulation ( errata make x necess>y1 or sweep+ *anges ( a m ext5sive nature takes place su* z a new survey1 dr$g$ *annels1 etc4 ,a *>t "u ext5sive correction is br\ght up to date 9 e p>ticul>1 includ+ ! late/ geographic spell+1 new docks & public works4 ,! date is not$ on ! "r ( ! c5t] m>g9 & ! dates ( small] h& corrections are indicat$ at ! l[] left corn]2 ! figures d5ote ! numb] ( ! weekly ,notice to ,m>9]s1 9 :i* ! in=mation is f\nd1 & ! ye>4 ,! diff]5t scales ( *>ts range f ^? ( ! _w to a h>bor plan4 ,!re are *>ts ( oceans2 g5]al coa/s1 su* z f ! ,/4 ,lawr5ce to bel[ ,new ,york2 int]m$iate coa/s1 z f ,ea/port1 ,ma9e to ,cape ,ann2 & approa*es to ports1 say f ,cape ,ann to ,cape ,cod = ! port ( ,bo/on2 & la/ly !re are h>bor plans4 ,^? cov]+ l>ge areas are kn[n z small-scale *>ts :ile h>bor *>ts are call$ l>ge-scale *>ts4 ,a *>t dep5ds on ! surveys t furni%$ its data1 & its accuracy & reliability re/s ^u t survey4 ,ev5 ) ! mo/ c>eful surveys1 :]e ! lead is us$ to asc]ta9 dep?s1 !re are _m in/ances :]e p9nacle rocks h escap$ detection by com+ betwe5 ! ca/s ( ! lead tak5 by ! survey+ p>ty4 ,^! isolat$ rocks become po9ts ( great dang] to vessels ( deep draft1 & x becomes a measure ( safety to avoid rocky coa/s & (f%ore pat*es by giv+ !m a wide b]?4 ,spaces devoid ( s\nd+s may well be view$ ) suspicion if 9 reasonably %all[ wat]1 = x w\ld appe> to indicate a lack ( ?or\ghness 9 ! survey1 at lea/ a lack ( s\nd+s4 ,! wire drag1 a device us$ to sweep important areas to a c]ta9 dep?1 is ! only sure way ( discov]+ all ! dang]s ( ! bottom4 ,! aids to navigation %[n on ! *>ts are describ$ by symbols & abbreviations z fully z possible ) ! limit$ space4 ,all symbols are plac$ 9 ! location ( ! aid1 b 9 "s cases ! actual position may be 9 d\bt by ! nature ( ! symbol1 = in/ance a buoy's location is d5ot$ by ! r+ t accompanies ! symbol & n ! triangle2 a light vessel by ! position ( ! dot ( ! light1 or betwe5 !m if !re are two dots 7lights74 ,buoys & light vessels (t5 drag _! moor+s or g adrift entirely1 especially 9 ! w9t] season4 ,x is !re=e ! "p ( wisdom to *eck a %ip's position by %ore m>ks :5 possible & be prep>$ to f9d buoys out ( position4 ,! me*anism ( a light buoy is (t5 dis>rang$ ?r\gh v>i\s causes4 ,! *>act]i/ics ( all lights are briefly giv5 ) ! visibility & height above ! sea4 ,! *>t$ visibility is ! di/ance !y %\ld be se5 f a vessel's deck on :i* ! height ( ! eye is fifte5 feet above ! sea1 s1 f ! deck ( an ord9>y p[] boat a light w n be se5 until well )9 ! range ( visibility z publi%$1 :ile f ! deck ( a l>ge /eam] ! light w be se5 outside its *>t$ visibility4 ,?is ref]s to high-p[]$ lights :]e ! curvature ( ! e>? has to be giv5 consid]ation4 ,a fla%+ light is "o 9 :i* ! fla% is ( less duration ?an ! eclipse1 :ile an occult+ light has an eclipse equal to or less ?an ! p]iod ( light4 ,fla%es & eclipses are (t5 gr\p$ & receive ! "n ( gr\p fla%+ or gr\p occult+4 ,an alt]nat+ light is "o 9 :i* two colors are %[n ea* = an equal int]val ) no int]v5+ eclipse1 b if an eclipse sep>ates ! color fla% f a :ite fla%1 = in/ance1 x becomes a fla%+ :ite light v>i$ by a r$ fla%4 ,x is a v common practice to ins]t sectors ( diff]5t colors into ! arc ( visibility ( a light 9 ord] to cov] a dang]\s %oal or to indicate a *annel4 ,be>+s def9+ ^! sectors are tak5 f seaw>d & n f ! light4 ,! t]m lum9\s range w be met )1 & indicates ! di/ance ! p[] ( ! light c c>ry ! visibility irrespective ( an int]v5+ horizon4 ,a light may h a lum9\s range mu* 9 excess ( its visibility :i* is limit$ by ! horizon b 9 a haze or fog its p5etrat+ p[] w greatly exce$ t ( a light ( simil> visibility b less lum9\s range4 ,! p[] ( a light is m commonly %[n by units ( a ?\s& c&le p[]1 ?us1 #e4f indicates a p[] ( fifty-six hundr$ c&les4 ,! catoptric 7,c47 light employs ! reflect+1 & ! dioptric 7,d47 ! refract+ pr9ciple4 ,!re is a l>ge am\nt ( useful in=mation giv5 on e *>t t ! av]age m>9] all[s to escape 8 notice4 ,?is failure on 8 "p is mo/ly due to famili>ity1 or reliance on pilots ) local k4 ,! fir/ important feature ( a *>t to be consid]$ is ! %orel9e1 :i* is %[n z a cont9u\s l9e repres5t+ ! high-wat] m>k4 ,?is1 x mu/ be borne 9 m9d1 is mu* *ang$ at l[ wat]1 & :]e ! range ( tide is l>ge ! %orel9e is proportionately 9 error4 ,aga91 :]e ! wat] is %all[ ! *ange is m m>k$ ?an :]e ! %ores are /eep-to4 ,if acc\nt is n tak5 ( ! /age ( ! tide x is easy to be v mu* deceiv$4 ,9 approa*+ a /range h>bor ! *>t %\ld be scrut9iz$ = prom95t m>ks1 & ^! id5tifi$ z soon z possible1 !n ! less] objects c be pick$ up by _! relative positions ) ! already id5tifi$ l&m>ks4 ,among ! less] m>ks may be f\nd cliffs1 b\ld]s1 s&y bea*es1 vegetation1 build+s 7p>ticul>ly *ur* spires & h\ses ) cupolas74 ,prom95t elevations ( l& always s]ve to id5tify a locality4 ,! *>t %[s ^! elevations cle>ly by cont\r l9es4 ,a tw5ty-foot cont\r l9e1 = in/ance1 %[s ! l9e ( ! cut1 %\ld ! hill be saw$ (f tw5ty feet above ! sea4 ,:5 cont\r l9es are wide ap>t ! l& has a gradual slope1 & z ! grade becomes /eep] ! cont\r l9es come clos] proportionately4 ,! *>t1 :]ev] possible1 repres5ts ! e>? z se5 f ov]head1 b 9 ! case ( v]tical objects1 !y are ( necessity %[n horizontally4 ,"o ( ! notable cases ( ?is is 9 ! repres5tation ( cliffs1 :i* 9 ord] to %[ _! height are drawn ) ! side view z se5 f ! wat]4 ,numb]s se5 on ! l& %[ ! height above ! high wat]4 ,f ! topographical features ( a *>t we turn to ^? ( hydrography4 ,all ! dep?s indicat$ on a *>t are ^? exi/+ at mean l[ wat]1 on ! ,atlantic ,coa/1 & mean l[] l[ wat] on ! ,pacific ,coa/4 ,all ! ,briti% ,admiralty & mo/ ( ! ,hydrographic ,(fice *>ts are r$uc$ to ! level ( l[ wat] at ord9>y spr+ tides4 ,:ile !re is usually m wat] to be expect$ ?an %[n1 x mu/ be rememb]$ t :5 ! plane ( mean l[ wat] is us$1 ! l[ wat]s t1 r\ghly speak+1 come betwe5 ! moon's fir/ & la/ qu>t]s1 w fall bel[ ! s\nd+s on ! *>ts4 ,illu/ration ,illu/ration ,! effect ( an abnormal b>omet] & high w9ds mu/ at times be borne 9 m9d1 = a cont9u\s nor?we/ w9d w make a vital diff]5ce 9 ! dep?s along ! ,atlantic seabo>d1 especially 9 ! ,delaw>e & ,*esapeake ,bays4 ,v (t5 !re is in=mation t c n be symboliz$ on ! *>t & is plac$ 9 italics 9 ! =m ( a note4 ,^! are always important & %\ld be read c>efully4 ,sail+ directions are writt5 to supplem5t ! *>ts & pres]ve = ! m>9] a mass ( in=mation :i* o!rwise w\ld n rea* him4 ,x is always well to pay att5tion to ! curr5t arr[s1 z !y are a means by :i* ! /r5g? & direction ( ! tidal /ream may be asc]ta9$4 ,! symbol ( a tide rip %\ld n be ignor$ by "o 9 a small boat1 z ! conditions might be "r to make !m dang]\s4 ,on ! wat] areas ( ! *>t we f9d cont\rs ( dep?s z on ! l& are cont\rs ( height4 ,x is a good s*eme1 if "o want$ to take ! tr\ble to run a cont\r l9e indicat+ a dep? a few feet great] ?an ! draft ( 8 boat1 & t9t ! %all[ wat] ) a bru%4 ,l>ge vessels ( deep draft ^u approa*+ ! coa/ are guid$ by ! t5-fa?om curve unless ! %ore is v /eep-to & ! wat] v deep4 ,! ma/]s ( su* vessels w\ld rema9 outside t curve until _! position 0 well e/abli%$4 ,light] draft vessels are guid$ by ! five-fa?om curve 9 a simil> mann]4 ,:5 approa*+ ! l& & ! l&m>ks are n available1 ! "* ( ! bottom fur!r assi/s ! m>9] z he s\nds sl[ly t[>ds ! l&4 ,! k9d ( bottom is indicat$ by abbreviations :i* are obvi\s on almo/ e portion ( ! *>ts4 ,! ?ree-fa?om curve is ! mo/ important to ! greate/ numb] ( navigators & = ?is reason is made ! mo/ pron\nc$4 ,9 ! majority ( *>ts x is %[n by a 8s&$0 area )9 x1 b 9 _m new *>ts x is heavily t9t$4 ,9 *ang+ f "o *>t to ano!r :ile work+ 9 an unfamili> locality1 take especial note :e!r ! s\nd+s are 9 feet or fa?oms4 ,x is an excell5t practice :5 a vessel is br\ght to an*or & cross be>+s tak51 to e/imate ! radius ( h] sw++ circle by add+ ! am\nt ( *a9 out to ! l5g? ( ! vessel & ) ?is describe a circle on ! *>t & note if !re is any dang] ( tail+ into %oal wat] at any qu>t]4 99 99 99 99 99 ,?is has be5 a long voyage & ,i am glad to tie up & let ! pr9t]s take *>ge4 ,if any ( my read]s see places :]e ,i h /ood into ! %all[ wat] ( inaccuracy1 ,i w be grateful = a pass+ hail t ,i may %ift helm & get out ) z little damage z possible4 ,,index ,a ,accel]ation = longitude1 #ia ,amplitude1 #ab1 #ig ,aphelion1 #h ,apogee1 #aci ,a/ronomical triangle1 #ajb ,azimu?1 #ab1 #if altitude1 #ih ,weir's diagram (1 #ih ,azimu?s & amplitudes1 #ic ,c ,cal5d>1 #fd ,cele/ial latitude1 #ad longitude1 #ad ,*>t1 cont\rs1 #aee corrections1 #aea scales1 #aeb ,*>ts1 #adf datum1 #aee diagrams ( symbols1 #aef fa?om curves1 #aeh in=mation on1 #aed symbols1 #aeb ,*ronomet] "t1 necessity ( accuracy 91 #hg ,circles ( equal altitudes1 #aaj ,circum-m]idian altitude1 #hb ,compass1 #ic deviation (1 #id error (1 #id nam+ (1 #ii ,coord9ates1 #i ,corrections = obs]v$ altitudes1 #fh ,d ,day lo/ & day ga9$1 #cg ,dead reckon+1 #a ,decl9ation1 #ae daily *ange (1 #bd ,deviation1 nam+ (1 #ajj ,dip1 #gb ,d\ble altitude problem1 #abj ,e ,e>?'s orbit1 #h revolution ar\nd ! sun1 #bj ,eclipses1 #ada ,ecliptic1 #ad ,equal altitude circle1 #aji ,equal altitude me?od1 #ajd ,equation ( ,"t1 #ef diagram (1 #fb error due to obliquity1 #fj ,equ9octial colure1 #bf ,ex-m]idian altitude1 #hb bodies bel[ ! pole1 #hf planets1 #hf />s1 #hf ,f ,fir/ po9t ( ,aries1 #ad1 #bf ,g ,gnomonic *>t1 #aej ,great circles1 #aj1 #ag ,great-circle sail+1 #aej ,gre5wi* mean "t on navigator's wat*1 #ed ,h ,horizon1 rational1 #aa1 #ge s5sible1 #ab1 #gc visible1 #aa1 #gc ,h\r circles1 #ac ,i ,index correction1 #fh ,j ,johnson's me?od1 #abc diagrams1 #abf ,k ,kepl]'s ,law1 #ef ,l ,latitude1 #gh by ,pol>is1 #hh factor1 #abi =mula = f9d+1 #hj ,lay+ a c\rse1 #if ,lights1 *>act]i/ics1 etc41 #aec ,longitude1 #aja & "t1 #ajb by equal altitudes1 #ajd factor1 #abe prime v]tical1 #ajc />s & planets1 #aje ,lun> cycle1 #adc ,m ,mean "t into sid]eal1 #ajf ,m]cator ,projection1 #adf diagram1 #adg ,m]idian altitude1 #gh "t to obs]ve a />1 #ha to report at noon1 #ha ,m]idional p>ts1 #adi ,middle latitude sail+1 #d ,miz>1 #hi ,moon1 #aci full1 #adj h>ve/1 #adc new1 #adj ,moon's decl9ation1 #adc diagram1 #add nodes1 #adc ret>dation1 #adb revolution1 #adj "r asc5sion1 #adb ,n ,nadir1 #aa ,napi]'s diagram1 #if ,nautical a/ronomy1 #e ,new navigation1 #ajb1 #abi advantages (1 #acc diagrams (1 #ace1 #acg f9d+ position )\t plott+ on *>t1 #ach illu/rat$ examples1 #acd ,notices to m>9]s1 #aea ,nutation1 #cb ,p ,p>allax1 #ge horizontal1 #gf moon1 #gg ,p>allel sail+1 #c ,p]igee1 #aci ,p]ihelion1 #h ,plane sail+1 #b ,planets1 #f-g ,pol>is1 #hh diagram1 #ij "t to take sight1 #ib ,precession ( ! equ9oxes1 #bg causes (1 #ca ,prime v]tical1 #ab obs]vations on1 #ajc ,q ,quadrature1 #adj ,r ,refraction1 #ga ,rhumb l9e1 #adi ,"r asc5sion1 #bf1 #ej ,s ,sail+s1 #c ,seasons1 !1 #bj ,semi-diamet]1 #fi ,%ip's "t1 #dj ,sid]eal "t1 #dc 7local7 h[ to obta91 #eb longitude f1 #ec ye>1 #ff ,sol> sy/em1 #e ,summ]1 l5g? ( nor!rn & s\!rn1 #be l9es1 z *ords & tang5ts1 #aab :5 "u ! sun1 #aba ,sumn]1 ,capt41 8 exp]i5ce1 #ajg l9e1 displacem5t (1 #aah tang5t me?od1 #aad value (1 #aae me?od1 #ajg ,sun's *ange 9 azimu?1 #abj ea/w>d movem5t1 #af ,t ,"t diagram1 #ea ,tropical ye>1 #ff ,v ,vega z a pole />1 #ca ,v]nal equ9ox1 #bj dates (1 #fg ,v]tical circles1 #ab ,w ,weir's azimu? diagram1 #ih ,z ,z5i?1 #aj ,,! ,,lit]ature ( ,,naval ,,& ,,m>9e ,,sci5ce ,on our %elves is ! mo/ complete /ock ( te*nical1 indu/rial1 eng9e]+ & sci5tific books 9 ! ,unit$ ,/ates4 ,! te*nical lit]ature ( e bran* ( naval ar*itecture1 con/ruction1 ordnance1 m>9e eng9e]+1 seaman%ip & navigation is well repres5t$1 z well z are ! v>i\s o!r relat$ subjects4 ,a l>ge numb] ( ^! we publi% & = an ev] increas+ numb] we are ! sole ag5ts4 ,illu/ration3 ,pr9t]'s logo ,all ,our ,inquiries are ,*e]fully & ,c>efully ,answ]$ & ,complete ,catalogs z well z ,special ,li/s are ,s5t ,free on ,reque/ 33 33 ,d4 ,,van ,,no/r& ,,company ,publi%]s & ,booksell]s #be ,,p>k ,,place ,,new ,,york ,,van ,,no/r&',s ,,nautical ,,manuals #cej ,pages #e #g ,po/paid1 #c4jj ,! ,m5 on ,deck ,,ma/]1 ,,mates ,,& ,,crew ,_! ,duties & ,responsibilities ,a ,manual = ! ,am]ican ,m]*ant ,s]vice ,by ,,felix ,,ries5b]g ,comm&+ ,s*ool%ip ,newport ,new ,york ,/ate ,nautical ,s*ool ,,ma/] ,*ief ,,mate ,second ,,mate ,concise /atem5t ,?ird ,,mate ( ,,wat* ,,(fic] _! duties & ,junior ,(fic] responsibilities ,cadet & ! laws "u ,qu>t]ma/] :i* !y "w ,c>p5t] & live ,boatswa9 ,=ema/ ,h&s ,,discipl9e--on bo>d %ip ,! ,books ( ! ,sea ,po9ts out ! ?+s ! v>i\s memb]s ( ! deck dep>tm5t ( an ocean or ,great ,lakes /eam vessel may reasonably be expect$ to "k1 & ! ?+s !y may be requir$ to d4 ,! book does n pret5d to tell ,,h[1 b %[s ,,:at a mod]n ,am]ican seaman ought to "k1 & to d4 ,,van ,,no/r&',s ,,naval ,,books #gcj ,pages #f #i ,po/paid #f4ej #aei ,full ,page ,plates #aj ,color ,plates ,mod]n ,seaman%ip ,by ,admiral ,au/9 ,m4 ,knight1 ,u4,s4,n4 ,,sev5? ,,edition ,,revis$ ,,& ,,enl>g$ ,,cont5ts--,! ,hull & ,fitt+s ( a ,%ip4 ,rope4 ,knott+ & ,splic+4 ,me*anical ,appliances on ,%ipbo>d4 ,blocks & ,tackles4 ,h&l+ ,heavy ,weights4 ,compass4 ,log & ,lead4 ,subm>9e ,signals4 ,boats4 ,h&l+ ,boats 9 a ,surf4 ,gr\nd ,tackle4 ,c>ry+ ,out ,an*ors4 ,! ,/e]+ ( ,/eam]s4 ,! ,rules ( ! ,road4 ,manoeuv]+ to ,avoid ,collision4 ,pilot+4 ,h&l+ a ,/eam] ,alongside a ,dock4 ,plac+ a ,%ip 9 a ,dry ,dock4 ,wea!r & ! ,laws ( ,/orms4 ,h&l+ ,/eam]s 9 ,heavy ,wea!r4 ,! ,h&l+ ( ,torp$o ,vessels4 ,keep+ ,/ations & ,manoeuv]+ 9 ,squadron4 ,t[+4 ,rescu+ ! ,crew ( a ,wreck4 ,man ,ov]bo>d4 ,/r&+4 ,h9ts = ,junior ,(fic]s ,do+ ,l9e ,duty4 ,app5dix4 ,! (ficial text book at ! ,u4 ,s4 ,naval ,academy & 9 use ?r\gh\t ! s]vice4 ,describes ! h&l+ ( all vessels1 m5-(-w>1 m]*antm51 naval auxili>ies & small boats4 ,transcrib]'s ,note3 ,words may h multiple spell+ v>iations or inconsi/5t hyph5ation 9 ! text4 ,^! h be5 left un*ang$ unless indicat$ bel[4 ,obsolete & alt]native spell+s 7 left un*ang$4 ,words & phrases 9 italics are surr\nd$ by und]scores1 l ?is4 ,^? 9 bold are surr\nd$ by equal signs1 l ?is4 ,obvi\s pr9t+ errors1 su* z duplicate words1 backw>ds1 upside d[n1 or p>tially pr9t$ lett]s & punctuation1 7 correct$4 ,f9al /ops miss+ at ! end ( s5t5ces & abbreviations 7 add$4 ,! foll[+ items 7 *ang$3 8access0 to 8excess0 8,manoeuvr+0 to 8manoeuv]+0 8effect0 to 8affect0