,transcrib]'s ,note3- ,words & phrases surr\nd$ by und]scores are italicis$4 ,!re are f\r symbols :i* are d5ot$ by 3- 747 ,circle surr\nd+ a c5tr$ dot - ,"r ,asc5sion ( ! ,m]idian2 77 ,circle surr\nd+ a cross - ,e>?'s ,c5tral ,progress2 77 ,circle ) c5tre dot & l9e "u - ,obs]v$ altitude ( sun's l[] limb2 -7-7- ,circle ) l9e ?r\gh - ,true ,altitude4 ,,lectures ,,9 ,,navigation ,prep>$ = ,use z a ,text ,book at ! ,,(fic]s' ,,mat]ial ,,s*ool ,,naval ,,auxili>y ,,res]ve by ,lieut5ant ,,erne/ ,g4 ,,drap]1 ,u4,s4,n4,r4,f4 ,head ( ! ,dep>tm5t ( ,navigation ,(fic]s' ,mat]ial ,s*ool1 ,naval ,auxili>y ,res]ve ,,copyright ,,by ,,erne/ ,g4 ,,drap] ,,=eword ,^! ,lectures h be5 compil$ z spe$ily z possible to meet ! dem& = "s quick b fairly compreh5sive me?od :]eby l>ge bodies ( m51 divid$ into small classes1 might le>n ! elem5ts ( ,navigation & ?us assume1 )\t delay1 _! responsibilities z ,junior ,(fic]s ( ! deck1 ,navigators & ,assi/ant ,navigators 9 ! ,unit$ ,/ates ,naval ,auxili>y ,res]ve4 ,i realize t ! ha/e ) :i* ! book has be5 writt5 is app>5t 9 _m places1 & x is hop$ t _m evid5ces ( ?is ha/e w disappe> 9 case fur!r editions are pr9t$4 ,besides ackn[l$g+ ! help & in=mation :i* 0 secur$ f ! li/ ( navigational works1 m5tion$ on ano!r page1 ,i wi% to m5tion p>ticul>ly ,pr(4 ,*>les ,lane ,poor's book1 entitl$ ,nautical ,sci5ce1 f :i* 0 secur$ practically all ( ! in=mation 9 ! ,lecture on ,planets & ,/>s 7,tuesday--,week ,v72 ,comm&] ,w4 ,c4 ,p4 ,muir's book1 ,navigation & ,compass ,deviations1 & ,lieut5ant ,w4 ,j4 ,h5d]son's book1 ,elem5ts ( ,navigation1 ! text ( :i* 0 foll[$ closely 9 discuss+ ,v>iation & ,deviation & ,trav]se ,sail+4 ,i desire to express my gratitude to ,lieut5ant ,comm&] ,r4 ,t4 ,m]rill1 #bnd1 ,u4 ,s4 ,n41 = sugge/+ a detail$ outl9e ( ! :ole c\rse2 to ,lieut5ant ,comm&] ,b4 ,o4 ,wills1 ,u4 ,s4 ,n41 = 8 valuable criticisms & almo/ daily help dur+ ! prep>ation ( ^! ,lectures2 to ,lieut5ant 7j4 g47 ,c4 ,d4 ,drap]1 ,u4 ,s4 ,n4 ,r4 ,f42 ,lieut5ant 7j4 g47 ,r4 ,bru%1 ,u4 ,s4 ,n4 ,r4 ,f41 & ,lieut5ant 7j4 g47 ,p4 ,c4 ,mc,pherson1 ,u4 ,s4 ,n4 ,r4 ,f41 = _m criticisms & sugge/ions2 & to ,capta9 ,hunt+ton1 ,seam5's ,*ur* ,in/itute1 = sugge/+ helpful diagrams1 p>ticul>ly ! "o on page #dd4 ,?is opportunity is also tak5 = ?ank+ ! _m ,in/ructors 9 ! ,s*ool = _! op9ions on v>i\s que/ions t h come up 9 connection ) ! c\rse & = assi/ance 9 elim9at+ errors f ! text4 ,e4 ,g4 ,d4 ,,li/ ,,( ,,books ,,consult$ ,,am]ican ,,practical ,,navigator1 ,,b[dit* ,,navigation ,,& ,,compass ,,deviations1 ,,muir ,,nautical ,,sci5ce1 ,,poor ,,elem5ts ,,( ,,navigation1 ,,h5d]son ,,wr9kles ,,9 ,,practical ,,navigation1 ,,lecky ,,:ys ,,& ,,:]e=es ,,( ,,navigation1 ,,brad=d ,,epitome ,,( ,,navigation1 ,,norie ,,navigation1 ,,hosm] ,,f9d+ ,a ,,%ip',s ,,position ,,at ,,sea1 ,,sumn] ,,g5]al ,,a/ronomy1 ,,"y ,,preface ,,to ,,^? ,,tak+ ,,?is ,,c\rse ,,9 ,,navigation3 ,^! lectures h be5 writt5 ) ! idea ( expla9+1 9 z simple language z possible1 ! fundam5tal elem5ts ( ,navigation z set =? 9 ,b[dit*'s ,am]ican ,practical ,navigator4 ,!y w be giv5 y dur+ ! "t at ! ,tra9+ ,s*ool devot$ to ?is subject4 ,at pres5t ?is "t includes two morn+ p]iods ( "o & a half h\rs ea*1 sep>at$ by a recess ( fifte5 m9utes4 ,9 g5]al ! plan is to devote ! fir/ p]iod to ! lecture & ! second p]iod to practical "w4 ,n _m examples = practical "w h be5 includ$ 9 ?is book1 b "o example1 illu/rat+ ea* new me?od1 has be5 work$ out4 ,if y und]/& ^! examples y %\ld be able to und]/& o!rs simil> to !m4 ,t[>d ! end ( ! c\rse a portion ( ea* second p]iod w be devot$ to h&l+ ! sextant1 "w ) *>ts1 tak+ sights1 etc4 ,9 %ort1 e ef=t w be made to duplicate1 z ne>ly z possible1 navigat+ conditions on bo>d a mod]n m]*ant %ip4 ,,dep>tm5t ,,( ,,navigation1 ,(fic]s' ,mat]ial ,s*ool1 ,naval ,auxili>y ,res]ve ,,cont5ts ,,week ,i--,,pilot+ ,tuesday--,! ,compass #a ,w$nesday--,pelorus2 ,p>allel ,rul]s2 ,! ,lead1 ,s\nd+ ,ma*9e1 ,divid]s & ,log #f ,?ursday--,! ,*>t #aj ,friday--,! ,protractor & ,sextant #ac ,saturday--,fixes1 ,angles by ,be>+s & ,sextant #af ,,week ,,ii--,,dead ,,reckon+ ,tuesday--,latitude & ,longitude #bj ,w$nesday--,useful ,tables--,plane & ,trav]se ,sail+ #bc ,?ursday--,examples on ,plane & ,trav]se ,sail+ 7,cont9u$7 #bg ,friday--,m]cator ,sail+ #bh ,saturday--,great ,circle ,sail+--,! ,*ronomet] #cj ,,week ,,iii--,,cele/ial ,,navigation ,tuesday--,cele/ial ,co-ord9ates1 ,equ9octial ,sy/em1 etc4 #cd ,w$nesday--,"t by ! ,sun--,mean ,"t1 ,sol> ,"t1 ,conv]sion1 etc4 #cf ,?ursday--,sid]eal ,"t--,"r ,asc5sion #dc ,friday--,! ,nautical ,almanac #dg ,saturday--,correction ( ,obs]v$ ,altitudes #eb ,,week ,,iv--,,navigation ,tuesday--,! ,l9e ( ,position #ee ,w$nesday--,latitude by ,m]idian ,altitude #eh ,?ursday--,azimu?s ( ! ,sun #fa ,friday---,m>c ,/4 ,hilaire ,me?od by a ,sun ,sight #fc ,saturday--,examples on ,m>c ,/4 ,hilaire ,me?od by a ,sun ,sight #ff ,,week ,v--,,navigation ,tuesday--,a ,%ort ,talk on ! ,planets & ,/>s--,id5tification ( ,/>s--,"t ( ,m]idian ,passage ( a ,/> #ff ,w$nesday--,latitude by ,m]idian ,altitude ( a ,/>--,latitude by ,pol>is #gc ,?ursday--,m>c ,/4 ,hilaire ,me?od by a ,/> ,sight #gd ,friday--,examples3 ,latitude by ,m]idian ,altitude ( a ,/>2 ,latitude by ,pol>is2 ,m>c ,/4 ,hilaire ,me?od by a ,/> ,sight #ge ,saturday--,longitude by ,*ronomet] ,sight ( ! ,sun #gf ,,week ,,vi--,,navigation ,tuesday--,longitude by ,*ronomet] ,sight ( a ,/> #gi ,w$nesday--,examples on ,longitude by ,*ronomet] ,sight ( a ,/> #hj ,?ursday--,latitude by ,ex-,m]idian ,altitude ( ! ,sun #ha ,friday--,examples3 ,latitude by ,ex-,m]idian ,altitude ( ! ,sun #hc ,saturday--,f9d+ ! ,wat* ,"t ( ,local ,app>5t ,noon #hc ,,week ,,vii--,,navigation ,tuesday--,compass ,error by an ,azimu? #hh ,w$nesday--,correct+ ,longitude by a ,factor #hi ,?ursday--,! ,navigator's ,r\t9e--,a ,day's ,"w at ,sea #ia ,friday--,day's ,"w #aje ,saturday--,day's ,"w #aje ,,week ,,viii--,,navigation ,monday to ,?ursday--,day's ,"w #ajg-ajh ,additional ,lecture--,compass ,adju/m5t #aji ,,week ,i--,,pilot+ ,,tuesday ,,lecture ,,! ,,compass ,ev]yone is suppos$ to "k :at a compass looks l4 ,x is m>k$ 9 two ways--! old way & ! new way4 ,put 9 y\r ,note-,book ?is diagram3 ,illu/ration ,! new way m>k$ on ! outside ( ! diagram1 />ts at ,nor? ) #j deg41 increases t[>d ! "r ?r\gh ,ea/ at #ij deg41 ,s\? at #ahj deg41 ,we/ at #bgj deg4 & back to ,nor? aga9 at #cfj deg4 or #j deg44 ,! old way1 m>k$ on ! inside ( ! diagram1 />ts at ,nor? ) #j deg41 goes to ! "r to #ij deg4 at ,ea/ & to ! left to #ij deg4 at ,we/4 ,x also />ts at ,s\? ) #j deg41 goes to ! "r to ,ea/ at #ij deg4 & to ! left to ,we/ at #ij deg44 ,a ,compass ,c\rse c be nam$ 9 degrees1 accord+ to ei!r ! new or old way4 ,= in/ance1 ! new way is j #de deg44 ,! old way = ! same c\rse is ,n #de deg4 ,e4 ,new way--#ajj deg44 ,old way = same c\rse--,s #hj deg4 ,e4 ,!re is ano!r way to "n a compass c\rse4 ,x is by us+ ! "n ( ! po9t t[>d :i* ! %ip is head+4 ,on e %ip ! compass is plac$ ) ! lubb] l9e 7a v]tical black l9e on ! compass b[l7 v]tical & 9 ! keel l9e ( ! %ip4 ,! lubb] l9e1 !re=e1 w always repres5t ! b[ ( ! %ip1 & ! po9t on ! compass c>d ne>e/ ! lubb] l9e w be ! po9t t[>d :i* ! %ip is head+4 ,! compass c>d ( #cfj deg4 is divid$ into #cb po9ts4 ,ea* po9t1 !re=e1 repres5ts #aa-a_/d deg44 ,! f\r pr9cipal po9ts are call$ c>d9al po9ts4 ,!y are--,nor?1 ,ea/1 ,s\?1 ,we/4 ,ea* c>d9al po9t is #ij deg4 f ! "o imm$iately adjac5t to x4 ,x is also #h po9ts f ! "o adjac5t to x1 z #ij deg4 is #h po9ts1 i4e41 #aa-a_/d deg4 7"o po9t7 times #h4 ,midway betwe5 ! c>d9al po9ts are ! int]-c>d9al po9ts4 ,!y are--,n ,e1 ,s ,e1 ,s ,w1 ,n ,w1 & are #de deg4 or #d po9ts f ! ne>e/ c>d9al po9t4 ,midway betwe5 ea* c>d9al & int]-c>d9al po9t--at an angul> di/ance ( #bb-a_/b deg4 or #b po9ts1 is a po9t nam$ by comb9+ a c>d9al po9t ) an int]-c>d9al po9t4 ,= in/ance1 ,,nne1 ,,ene1 ,,ese1 ,,sse1 ,,ssw1 ,,wsw1 ,,wnw1 ,,nnw4 ,midway betwe5 ! la/ po9ts nam$ & a c>d9al or int]-c>d9al po9t1 at an angul> di/ance ( #aa-a_/d deg41 is a po9t :i* be>s ! "n ( t c>d9al or int]-c>d9al po9t jo9$ by ! ^w by to t ( ! c>d9al po9t ne>e/ to x4 ,z1 = in/ance1 ,n by ,e1 ,e by ,n1 ,e by ,s1 ,s by ,e1 ,s by ,w1 ,w by ,s1 ,w by ,n1 ,n by ,w4 ,also ,,ne x ,n1 ,,ne x ,e1 ,,se x ,e1 ,,se x ,s1 ,,sw x ,s1 ,,sw x ,w1 ,,nw x ,w1 ,,nw x ,n4 ,! angul> di/ance betwe5 ea* & e :ole po9t is divid$ into #d p>ts call$ half & qu>t] po9ts & ea* repres5t+ an angul> measure ( approximately #b deg4 #di'4 ,9 m5tion+ fractional po9ts1 ! ,u4 ,s4 ,navy regulations are to "n ea* po9t f ,nor? & ,s\? t[>d ,ea/ & ,we/ except t divisions adjac5t to a c>d9al or int]-c>d9al po9t are always ref]r$ to t po9t3 ,= in/ance1 ,n #a_/b ,e1 ,n x ,e #a_/b ,e1 ,,ne #a_/b ,n1 ,,nw #a_/b ,n1 ,,nw #a_/d ,w1 ,,nw #c_/d ,w1 ,,nw #a_/d ,n4 ,box+ ! compass is nam+ ea* po9t & qu>t]-po9t 9 rotation1 i4e41 />t+ at ,nor? & go+ ar\nd to ! "r back to ,nor? aga94 ,e man %\ld be able to id5tify & "n any po9t or qu>t]-po9t on ! compass c>d4 ,9 *ang+ a po9t c\rse into a degree c\rse1 = ei!r new or old compass1 a guide is h]e) furni%$ y4 ,?is %\ld be pa/$ into ! front ( y\r ,b[dit* ,epitome4 ,x %[s1 f left to "r1 ! "n ( ! po9t c\rse1 its angul> measure 9 ! new compass & its angul> measure 9 ! old compass4 ,x also %[s at ! bottom1 ! angul> measure ( ea* division ( "o po9t4 ,9 und]/&+ ?is guide1 rememb] t ea* c\rse is express$ 9 degrees or degrees & m9utes4 ,put 9 y\r ,note-,book3 ,9 ,navigation1 ea* degree is writt5 ?us deg44 ,ea* fraction ( a degree is express$ 9 m9utes & writt5 ?us '4 ,!re are #fj' 9 ea* degree4 ,ea* fraction ( a m9ute is express$ 9 seconds & is writt5 4 ,!re are #fj 9 ea* m9ute4 ,f\r degrees1 t5 m9utes & ?irty seconds w\ld be writt5 ?us3 #d deg4 #aj' #cj4 ,al?\gh ?is guide j giv5 y is giv5 z an aid to quickly transf] a po9t c\rse into a new or old compass c\rse--or vice v]sa--y %\ld le>n to d ?is y\rself1 aft] a:ile1 )\t ! guide4 ,put 9 y\r ,note-,book3 ---------------------------------------- ----------- ,%ip's ,head ,new ,old ,by ,po9t ---------------------------------------- ----------- ,,ne #de deg4 ,n #de deg4 ,e ,,ne #ij deg4 #ij deg4 ,n #ij deg4 ,e ,,ea/ ,,se x ,e #abc deg4 #de' ,s #ef deg4 ,e ,,se x ,e ,s #bj deg4 ,e #afj deg4 ,s #bj deg4 ,e ,s x ,e #c_/d ,e ,s #b pts4 ,e #aeg deg4 #cj' ,s #bb deg4 #cj' ,e ,,sse ,,nw #c_/d ,w #cjf deg4 #cd' ,n #ec deg4 ,w ,,nw #c_/d ,w #bhi deg4 #da' #bhi deg4 #da' ,n #gj deg4 ,w ,,wnw #a_/d ,w ---------------------------------------- ----------- ,i w %[ y j h[ ea* "o ( ^! c\rses is secur$ f ! guide j giv5 y4 ,note to ,in/ructor3 ,aft] expla9+ ^! c\rses 9 detail1 assign = read+ 9 ! class room ! foll[+ articles 9 ,b[dit*3 ,arts4 #be-bf-bg-bh-bi-cj-ca-cb1 #gd-ge-gf-gg-gh-gi-hj-ha-hb4 ,e compass1 if correct1 w\ld h its ne$le po9t directly to ! real or true ,nor?4 ,b practically no compass ) :i* y w become famili> w be correct4 ,x w h an error 9 x due to ! magnetism ( ! e>?4 ,?is is call$ ,v>iation4 ,x w also h an error 9 x due to ! magnetism ( ! iron 9 ! %ip4 ,?is is call$ ,deviation4 ,y are und\bt$ly famili> ) ! fact t ! e>? is a huge magnet & t ! magnets 9 a compass are affect$ !reby4 ,9 o!r words1 ! ,nor? & ,s\? magnetic poles1 runn+ ?r\gh ! c5t] ( ! e>?1 d n po9t true ,nor? & ,s\?4 ,!y po9t at an angle ei!r ,ea/ or ,we/ ( ! ,nor? & ,s\?4 ,! am\nt ( ?is angle 9 any "o spot on ! e>? is ! am\nt ( ,v>iation at t spot4 ,9 navigat+ a %ip y mu/ take into acc\nt ! am\nt ( ?is ,v>iation4 ,! am\nt ( all[ance to be made & ! direction 7i4e4 ei!r ,ea/ or ,we/7 9 :i* x is to be appli$ are usually indicat$ on ! *>t4 ,on l>ge *>ts1 su* z ^? ( ! ,nor? ,atlantic1 w be f\nd irregul> l9es runn+ ov] ! *>t1 & hav+ beside !m su* notations z #aj deg4 ,w1 #ae deg4 ,w1 etc4 ,"s l9es are m>k$ ,no ,v>iation4 ,9 su* cases no all[ance ne$ be made4 ,on h>bor *>ts or o!r small *>ts1 ! ,v>iation is %[n by ! compass-c>d pr9t$ on ! *>t4 ,! ,nor? po9t ( ?is c>d w be f\nd slew$ ar\nd f ! po9t m>k+ ,true ,nor? & 9 ! compass c>d w be "s su* inscription z ?is3 ,v>iation #i deg4 ,we/ 9 #aiad4 ,increas+ #f' p] ye>4 ,n[ let u see h[ we apply ?is ,v>iation s t al?\gh our compass ne$le does n po9t to true ,nor?1 we c make a correction :i* w give u our true c\rse 9 spite ( ! compass read+4 ,note ^! diagrams3 ,illu/ration ,! out] circle repres5ts ! sea horizon ) ! long arr[ po9t+ to true ,nor?4 ,! inn] circle repres5ts ! compass c>d4 ,9 ! diagram to ! left1 ! compass ne$le is po9t+ ?ree :ole po9ts to ! left or ,we/ ( ,true ,nor?4 ,9 o!r words1 if y\r compass said y 7 head+ ,,ne x ,n1 y w\ld n actually be head+ ,,ne x ,n4 ,y w\ld be head+ true ,nor?4 ,illu/ration ,9 o!r words1 /&+ 9 ! c5t] ( ! compass & look+ t[>d ! circumf]5ce1 y w\ld f9d t e true c\rse y sail$ w\ld be ?ree po9ts to ! left ( ! compass c\rse4 ,t is call$ ,we/]ly ,v>iation4 ,n[ look at ! diagram to ! "r4 ,! compass ne$le is po9t+ ?ree :ole po9ts to ! "r or ,ea/ ( ,true ,nor?4 ,9 o!r words1 /&+ 9 ! c5t] ( ! compass & look+ t[>d ! circumf]5ce1 y w\ld f9d t e true c\rse y sail$ w\ld be ?ree po9ts to ! "r ( ! compass c\rse4 ,t is call$ ,ea/]ly ,v>iation4 ,h5ce we h ^! rules1 :i* put 9 y\r ,note-,book3 ,to conv]t a compass c\rse into a true c\rse ,:5 ! ,v>iation is we/]ly1 ! true c\rse w be z _m po9ts to ! left ( ! compass c\rse z !re are po9ts or degrees ( ,v>iation4 ,:5 ! ,v>iation is ea/]ly1 ! true c\rse w be z _m po9ts or degrees to ! "r ( ! compass c\rse4 ,to conv]t a true c\rse into a compass c\rse ,! conv]se ( ! above rule is true4 ,9 o!r words1 ,v>iation we/]ly1 compass to ! "r ( true c\rse2 v>iation ea/]ly1 compass c\rse to ! left4 ,,deviation ,z /at$ be=e1 ,deviation causes an error 9 ! ,compass due to ! magnetism ( ! iron 9 ! %ip4 ,:5 a %ip turns1 ! compass c>d does n turn1 b ! relation ( ! iron's magnetism to ! magnets 9 ! compass is alt]$4 ,h5ce1 e *ange 9 c\rse causes a new am\nt ( ,deviation :i* mu/ be all[$ = 9 correct+ ! compass read+4 ,x is cu/om>y 9 m]*ant vessels to h ! compasses adju/$ :ile ! %ip is 9 port4 ,! adju/] tries to c\nt]act ! ,deviation all he c by magnets1 & !n gives ! ma/] ( ! %ip a table ( ! ,deviation errors rema9+4 ,^! tables are n to be dep5d$ ^u1 z !y are only accurate = a %ort "t4 ,ways w be taught y to f9d ! ,deviation y\rself1 & ^? ways are ! only ones y c dep5d ^u4 ,put 9 y\r ,note-,book3 ,we/]ly ,deviation is appli$ exactly z we/]ly ,v>iation4 ,ea/]ly ,deviation is appli$ exactly z ea/]ly ,v>iation4 ,! am\nt ( ,v>iation plus ! am\nt ( ,deviation is call$ ! ,compass ,error4 ,= in/ance1 a ,v>iation ( #aj deg4 ,w plus a ,deviation ( #e deg4 ,w equals a compass error ( #ae deg4 ,w1 or a ,v>iation ( #aj deg4 ,w plus a ,deviation ( #e deg4 ,e leaves a net compass error ( #e deg4 ,w4 ,,leeway ,leeway is n an error ( ! compass1 b x has to be comp5sat$ = 9 /eam+ any di/ance4 ,h5ce x is m5tion$ "h4 ,a %ip /eam+ ) a /rong w9d or curr5t abeam1 w slide (f to ! leew>d m or less4 ,h5ce1 h] c\rse w h to be correct$ = ,leeway z well z = ,v>iation & ,deviation4 ,put 9 y\r ,note-,book3 ,leeway on ! />bo>d tack is ! same z we/]ly ,v>iation4 ,leeway on ! port tack is ! same z ea/]ly ,v>iation4 ,?is is app>5t f ! foll[+ diagram3 ,illu/ration ,z ! w9d1 bl[+ f ! ,nor?1 hits ! left h& %ip1 = in/ance1 on h] />bo>d side1 x %oves ! %ip to ! left ( h] true c\rse by ! numb] ( po9ts or degrees ( leeway4 ,leave a space & put ! foll[+ head+ 9 y\r ,note-,book3 ,i4 ,complete rule = conv]t+ a compass c\rse into a true c\rse3 #a4 ,*ange ! compass c\rse into a new compass read+4 #b4 ,apply ,ea/]ly ,v>iation & ,deviation 4 #c4 ,apply ,we/]ly ,v>iation & ,deviation -4 #d4 ,apply port tack ,leeway 4 #e4 ,apply />bo>d tack ,leeway -4 ,,ii4 ,complete rule = conv]t+ a true c\rse into a compass c\rse3 #a4 ,rev]se ! above signs 9 apply+ ea* correction4 ,i w n[ correct a few c\rses1 & ^! are to be put into y\r ,note-,book3 ---------------------------------------- -------------------- ,c ,cos ,w9d ,leeway ,dev4 ,v>4 ,new ,old ---------------------------------------- -------------------- ,n x ,e ,,nw #a_/b pt4 #e deg4 ,e #aj deg4 ,w #ab deg4 ,n #ab deg4 ,e ,s #fg deg4 ,e ,s #a pt4 #c deg4 ,w #e deg4 ,e #ajd deg4 ,s #gf deg4 ,e ,e x ,n ,,se #a_/b pt4 #e deg4 ,w #aj deg4 ,e #gh deg4 ,n #gh deg4 ,e ,w x ,n ,,nw #a-a_/b pts4 #a deg4 ,e #ae deg4 ,e #bhj deg4 ,n #hj deg4 ,w ---------------------------------------- -------------------- ,assign = ,night ,"w ! foll[+ arts4 9 ,b[dit*3 #cf-h-aj-ac-ad-ae-af-ag-ah-ai-bj-ba-bb-b c-bd4 ,,w$nesday ,,lecture ,,pelorus1 ,,p>allel ,,rul]s1 ,,! ,,lead1 ,,s\nd+ ,,ma*9e1 ,,divid]s ,,& ,,log ,i4 ,! ,pelorus ,?is is an in/rum5t = tak+ be>+s ( di/ant objects1 & = tak+ be>+s ( cele/ial bodies su* z ! sun1 />s1 etc4 ,x consi/s ( a circul>1 flat metallic r+1 m\nt$ on gimbals1 ^u a v]tical /&>d4 ,! be/ po9t to m\nt x is 9 ! b[ or on ! bridge ( ! %ip1 :]e a cle> view = tak+ be>+s c be _h4 ,! c5t] l9e ( ! pelorus %\ld also be directly ov] ! keel l9e ( ! %ip4 ,! inn] edge ( ! metallic r+ is engrav$ 9 degrees--! #j deg4 or #cfj deg4 & ! #ahj deg4 m>ks indicat+ a =e-&-aft l9e p>allel to ! keel ( ! %ip4 ,)9 ?is r+ a gr\nd glass dial is pivot$4 ,?is gr\nd glass dial has pa9t$ ^u x a compass c>d divid$ into po9ts & sub-divisions & into #cfj deg44 ,?is dial is capable ( be+ mov$ ar\nd1 b c also be clamp$ to ! outside r+4 ,pivot$ ) ! glass dial & flat r+ is a horizontal b> c>ry+ at bo? ( its extremes a sight vane4 ,?is sight vane c be clamp$ 9 any position indep5d5tly ( ! gr\nd glass dial1 :i* c be mov$ freely b5ea? x4 ,an indicator %[+ ! direction ! sight vane po9ts c be read ^u ! compass c>d on ! glass dial4 ,if ! glass dial be revolv$ until ! degree ( dem>cation1 :i* is co9cid5t ) ! "r ahead m>k+ on ! flat r+1 is ! same z t :i* po9ts to ! lubb]'s l9e ( ! %ip's compass1 !n all directions indicat$ by ! glass dial w be p>allel to ! correspond+ directions ( ! %ip's compass1 & all be>+s tak5 w be compass be>+s1 i4e41 z ?\gh tak5 f ! compass itself4 ,9 o!r words1 x is j z ?\gh y took ! compass out ( its place 9 ! pilot h\se1 or :]ev] x is regul>ly situat$1 put x d[n :]e ! pelorus is1 & took a be>+ f x ( any object desir$4 ,9 tak+ a be>+ by pelorus1 two facts mu/ be kept 9 m9d4 ,fir/1 t :5 ! be>+ is tak51 ! exact head+1 z %[n by ! %ip's compass1 is ! head+ %[n by ! pelorus4 ,9 o!r words1 if ! %ip is head+ ,,nw1 ! pelorus mu/ be set ) ! ,,nw po9t on ! lubb] l9e :5 ! be>+ is tak5 ( any object4 ,second1 x mu/ be rememb]$ t ! be>+ ( any object obta9$ f ! pelorus is ! be>+ by compass4 ,to get ! true be>+ ( ! same object y mu/ make ! prop] corrections = ,v>iation & ,deviation4 ,?is c be comp5sat$ = by sett+ ! glass dial at a po9t to ! "r or left ( ! compass head+ to correspond ) ! compass error2 !n ! be>+ ( any object w be ! true be>+4 ,b naturally1 y w n be able to make comp5sation = ^! errors unless y h imm$iately be=e f\nd ! correct am\nt ( ! compass error4 ,p>allel ,rul]s ,! p>allel rul]s ne$ no explanation except = ! way 9 :i* !y are us$ on a *>t4 ,suppos+1 = in/ance1 y wi% to /eam f ,pelham ,bay to ! r$ buoy (f ! we/]ly end ( ,great ,capta9's ,isl&4 ,take y\r *>t1 m>k by a p5cil po9t ! place left & ! place to g to & draw a /raight l9e int]sect+ ^! two po9ts4 ,n[ place ! p>allel rul]s along t l9e & slide !m ov] until ! ne>e/ edge int]sects ! c5t] ( ! compass rose at ! bottom or side ( ! *>t4 ,look along ! rul]'s edge to f9d :]e x cuts ! circumf]5ce ( ! compass rose4 ,t po9t on ! compass rose w be ! true compass c\rse1 & c be express$ 9 ei!r ! new or old compass1 z1 = in/ance1 #fj deg4 or ,n #fj deg4 ,e4 ,rememb]1 h[ev]1 t ?is is ! true c\rse4 ,9 ord] to *ange x into ! compass c\rse ( y\r %ip1 y mu/ make ! prop] corrections = ! compass error1 i4e41 ,v>iation & ,deviation & = ,leeway1 if any4 ,! ,lead & ,s\nd+ ,ma*9e ,! lead1 z y "k1 is us$ to asc]ta9 ! dep? ( ! wat] &1 :5 necess>y1 ! "* ( ! bottom4 ,!re are two k9ds ( leads3 ! h& lead & deep-sea lead4 ,! fir/ weighs f #g to #ad p\nds & has m>k+s to #be fa?oms4 ,! second weighs f #cj to #ajj p\nds & is us$ 9 dep?s up to & ov] #ajj fa?oms4 ,put 9 y\r ,note-,book3 ,fa?oms :i* correspond ) ! dep?s m>k$ are call$ m>ks4 ,all o!r dep?s are call$ deeps4 ,! h& lead is m>k$ z foll[s3 #b fa?oms--#b /rips ( lea!r4 #c fa?oms--#c /rips ( lea!r or blue rag4 #e fa?oms--,a :ite rag4 #g fa?oms--,a r$ rag4 #aj fa?oms--,a piece ( lea!r ) "o hole 9 x4 #ac fa?oms--,same z at #c4 #ae fa?oms--,same z at #e4 #ag fa?oms--,same z at #g4 #bj fa?oms--#b knots or piece ( lea!r ) #b holes4 #be fa?oms--#a knot4 #cj fa?oms--#c knots4 #ce fa?oms--#a knot4 #dj fa?oms--#d knots4 ,& s on up to #ajj fa?oms4 ,! l>ge h& leads are holl[$ out on ! l[] end s t an arm+ ( tall[ c be put 94 ,?is w br+ up a specim5 ( ! bottom1 :i* %\ld be comp>$ ) ! description f\nd on ! *>t4 ,all up-to-date sea-go+ %ips %\ld be fitt$ ) ,sir ,william ,?ompson's ,s\nd+ ,ma*9e 7see picture 9 ,b4 ,j4 ,manual74 ,?is ma*9e consi/s ( a cyl9d] ar\nd :i* are w\nd ab\t #cjj fa?oms ( piano wire4 ,to ! end ( ?is is atta*$ a heavy lead4 ,an index on ! side ( ! in/rum5t records ! numb] ( fa?oms ( wire paid out4 ,above ! lead is a copp] cyl9drical case 9 :i* is plac$ a glass tube op5 only at ! bottom & *emically color$ inside4 ,! pressure ( ! sea =ces wat] up into ?is tube1 z x goes d[n1 a di/ance proportionate to ! dep?1 & ! color is remov$4 ,:5 hoi/$1 ! tube is laid ^u a prep>$ scale1 & ! height to :i* ! wat] has be5 =c$ inside %[s ! dep? 9 fa?oms on ! scale4 ,,divid]s ,! divid]s are no?+ b an in/rum5t = measur+ di/ances1 etc41 on ! *>t4 ,,! ,,log ,!re are two k9ds ( logs--! *ip log1 us$ = measur+ ! spe$ ( ! %ip1 & ! pat5t log1 us$ = measur+ di/ance run4 ,! *ip log consi/s ( a reel1 l9e1 toggle & *ip4 ,usually a second glass is us$ = measur+ "t4 ,! *ip is ! triangul> piece ( wood balla/$ ) lead to ride po9t up4 ,! toggle is a little wood5 case into :i* a peg1 jo9+ ! ends ( ! two l[] l9es ( ! bridle1 is set 9 su* a way t a j]k on ! l9e w free x1 caus+ ! log to lie flat s t x c be haul$ 94 ,! fir/ #aj or #ae fa?oms ( l9e f ! log-*ip are call$ /ray l9e1 & ! end ( ?is is di/+ui%$ by a m>k ( r$ bunt+4 ,its purpose is to let ! *ip get cle> ( ! vessel's wake4 ,! m>ks on ! l9e 7call$ knots7 are pieces ( fi% l9e runn+ ?r\gh ! /r&s ( ! reel l9e to ! numb] ( two1 ?ree1 f\r1 etc4 ,a piece ( :ite bunt+ m>ks e two-t5?s ( a knot4 ,?is is because ! run ( ! %ip is record$ 9 knots & t5?s4 ,! knots ( fi% l9e are #dg feet #d in*es f ea* o!r4 ,! log glass measures #bh seconds 9 "t4 ,= high rates ( spe$1 a #ad second glass is us$4 ,!n ! numb] ( knots %[n by ! log l9e mu/ be d\bl$4 ,! pr9ciple ( ! *ip log is t ea* division ( ! log l9e be>s ! same ratio to a nautical mile t ! log glass does to ! h\r4 ,9 o!r words1 if #aj knots or divisions ( ! log l9e run out :ile ! #bh second glass empties itself1 ! %ip's spe$ is #aj knots p] h\r4 ,if t5 knots or divisions run out :ile ! #ad second glass empties itself1 ! %ip's spe$ is #bj knots p] h\r4 ,! pat5t or t[+ log consi/s ( a dial1 l9e & rotator4 ,! l>ge circle ( ! dial records ! knots & ! small circle t5?s ( knots4 ,:5 *ang+ c\rse1 read ! log & ent] x 9 ! log book4 ,:5 *ang+ c\rse aga91 read ! log aga94 ,! diff]5ce betwe5 ! two read+s w be ! di/ance run4 ,bo? logs are liable to error4 ,a foll[+ sea makes !m "u-rate1 a head sea ov]-rate4 ,) bo? logs y mu/ all[ = curr5ts4 ,if a curr5t is aga9/ y--& y "k its rate--y mu/ d$uct its rate f t record$ 9 ! log & vice v]sa4 ,! reason = ?is is t y\r log measures y\r spe$ ?r\gh ! wat]4 ,:at y mu/ f9d is y\r actual di/ance made good ov] ! e>?'s surface4 ,put 9 y\r ,note-,book3 ,betwe5 ,s&y ,hook & ,=t ,hamilton1 b\nd due ,nor?1 spe$ by *ip-log 0 #aj knots1 tidal curr5t sett+ ,nor? #b knots p] h\r2 :at did ! %ip make p] h\r8 ,answ]3 #ab knots4 ,at sea 9 ,nor? ,sea %ip head+ ,s x ,w1 pat5t log bet4 #h ,a4,m4 & #ab ,m4 regi/]$ #cb miles1 curr5t runn+ ,n x ,e #b knots p] h\r2 :at 0 ! actual di/ance made good8 ,answ]3 #bd miles4 ,directions = all[+ = a curr5t sett+ diagonally across a %ip's c\rse w be giv5 9 ! prop] place4 ,assign = ,night ,"w ! foll[+ articles 9 ,b[dit*3 ,arts4 #afa-afb-afc-afd-afe4 ,,?ursday ,,lecture ,,! ,,*>t ,aids to ,navigation ,a *>t is a map ( an ocean1 bay1 s\nd or o!r navigable wat]4 ,x %[s ! "* ( ! coa/1 heights ( m\nta9s1 dep?s at l[ wat]1 direction & velocity ( tidal curr5ts1 location1 "*1 height & radius ( visibility ( all beacon lights1 location ( rocks1 %oals1 buoys1 & nature ( ! bottom :]ev] s\nd+s c be obta9$4 ,! top ( ! *>t is ,nor? unless o!rwise not$4 ,:5 9 d\bt z to :]e ,nor? is1 consult ! compass c>d pr9t$ some:]e on ! *>t4 ,on sea *>ts1 su* z ^? ( ! ,nor? ,atlantic1 only ! true compass is pr9t$1 ) ! am\nt & direction ( ,v>iation indicat$ by l9es on ! *>t4 ,p>allels ( latitude are %[n by /raight l9es runn+ p>allel to ea* o!r across ! *>t4 ,! degrees & m9utes ( ^! p>allels are giv5 on ! p]p5dicul> bord] ( ! *>t4 ,m]idians ( longitude are %[n by /raight l9es runn+ up & d[n1 p]p5dicul> to ! p>allels ( latitude1 & ! degrees & m9utes ( ^! m]idians are giv5 on ! horizontal bord] ( ! *>t4 ,put 9 y\r ,note-,book3 ,a m9ute ( latitude is always a mile1 because p>allels ( latitude are equidi/ant at all places4 ,a m9ute ( longitude is a mile only on ! equator1 = ! m]idians are com+ clos] to ea* o!r z !y conv]ge t[>d ei!r pole4 ,!y come toge!r at ! ,nor? & ,s\? poles1 & "h !re is no longitude4 99 99 99 99 99 ,i c expla9 ?is v easily by ref]5ce to ! foll[+ illu/ration3 ,illu/ration ,z e p>allel ( latitude is a circle ( #cfj deg4 ! di/ance f ,a to ,b w be ! same numb] ( degrees1 m9utes & seconds :e!r measur$ ^u p>allel ,,aa' or ,,ee'1 b x w n be ! same numb] ( miles z ! m]idians ( longitude are gradually conv]g+ t[>d ! poles4 ,on ! o!r h&1 ! di/ances f ,a to ,c1 ,c to ,d1 ,d to ,e1 etc41 mu/ be ! same because ! l9es ,,aa'1 ,,cc'1 ,,dd'1 ,,ee' are all p>allel4 ,t is :y ! di/ance is always measur$ on ! latitude scale 7i4e4 on ! v]tical bord] ( ! *>t71 & a m9ute ( latitude is always a mile on ! *>t1 no matt] 9 :at locality y\r %ip happ5s to be4 ,y %\ld be able to und]/& any k9d ( in=mation giv5 y on a *>t4 ,= in/ance1 :at are ! v>i\s k9ds ( buoys & h[ are !y m>k$8 ,put 9 y\r ,note-,book3 #a4 ,9 com+ f seaw>d1 r$ buoys m>k ! />bo>d side ( ! *annel1 & black buoys ! port side4 #b4 ,dang]s & ob/ructions :i* may be pass$ on ei!r h& are m>k$ by buoys ) r$ & black horizontal /ripes4 #c4 ,buoys indicat+ ! fairway are m>k$ ) black & :ite v]tical /ripes & %\ld be pass$ close to4 #d4 ,sunk5 wrecks are m>k$ by r$ & black /rip$ buoys describ$ 9 ,no4 #b4 ,9 =eign c\ntries gre5 buoys are frequ5tly us$ to m>k sunk5 wrecks4 #e4 ,qu>ant9e buoys are yell[4 #f4 ,z :ite buoys h no especial significance1 !y are frequ5tly us$ = special purposes n connect$ ) ,navigation4 #g4 ,/>bo>d & port buoys are numb]$ f ! seaw>d end ( ! *annel1 ! black be>+ ! odd & r$ be>+ ! ev5 numb]s4 #h4 ,p]*es ) balls1 cages1 etc41 w1 :5 plac$ on buoys1 be at turn+ po9ts1 ! color & numb] indicat+ on :i* side !y %all be pass$4 #i4 ,s\nd+s 9 pla9 :ite are 9 fa?oms2 ^? on %ad$ p>ts are 9 feet4 ,on l>ge ocean *>ts fa?om curves1 %[+ ! range ( s\nd+s ( #aj1 #bj1 #cj1 #dj1 etc41 fa?oms are %[n4 #aj4 ,a light is indicat$ by a r$ & yell[ spot4 ,f4 means fix$1 ,fl41 fla%+2 ,int41 int]mitt5t2 ,rev41 revolv+1 etc4 #aa4 ,an arr[ indicates a curr5t & its direction4 ,! spe$ is always giv54 #ab4 ,rocks j "u wat] are %[n by a cross surr\nd$ by a dott$ circle2 rocks above wat]1 by a dott$ circle ) dots inside x4 ,practically all *>ts y w use w be call$ ,m]cator *>ts4 ,j h[ !y are con/ruct$ is a difficult ma!matical affair b1 r\ghly1 ! idea ( _! con/ruction is bas$ ^u ! e>? be+ a cyl9d]1 in/ead ( a sph]e4 ,h5ce1 ! m]idians ( longitude1 in/ead ( conv]g+ at ! poles1 are p>allel l9es4 ,?is compels ! p>allels ( latitude to be adju/$ correspond+ly4 ,al?\gh su* a *>t 9 any "o locality is out ( proportion comp>$ ) "s di/ant "p ( ! e>?'s surface1 x is nev]!less 9 proportion = ! di/ance y c travel 9 a day or possibly a week--& t is all y desire4 ,! ,hydrographic ,(fice publi%es blank ,m]cator *>ts = all latitudes 9 :i* !y c be us$ = plott+ y\r position4 ,x makes no diff]5ce :at longitude y are 9 =1 on a ,m]cator *>t1 m]idians ( longitude are all m>k$ p>allel4 ,x makes a great diff]5ce1 h[ev]1 :at latitude y are 91 z 9 ea* a mile is ( diff]5t l5g? on ! *>t4 ,h5ce1 x w be impossible = y to correctly plot y\r c\rse & di/ance sail$ unless y h a *>t :i* %[s on x ! degrees ( latitude 9 :i* y are4 ,= in/ance1 if y\r ,m]cator *>t %[s p>allels ( latitude f #cj deg4 to #dj deg4 t *>t mu/ be us$ :5 y are 9 "o ( ^? latitudes4 ,:5 y move into #da deg4 or #bi deg41 y mu/ be sure to *ange y\r plott+ *>t accord+ly4 ,9 v high latitudes & ne> ! ,nor? pole1 ! ,m]cator *>t is wor?less4 ,h[ c y /e] = ! ,nor? pole :5 ! m]idians ( y\r *>t nev] come toge!r at any pole8 ,= ! same reason1 be>+s ( di/ant objects may be slightly (f :5 laid d[n on ?is *>t 9 a /raight l9e4 ,on ! :ole1 h[ev]1 ! ,m]cator *>t answ]s ! m>9]'s ne$s s f> z all practical purposes are conc]n$4 ,! in/rum5ts us$ 9 consult+ a *>t1 i4e41 p>allel rul]s1 divid]s1 etc4 h already be5 describ$4 ,! only way to lay d[n a c\rse & read x is by practice4 ,! "o important ?+ to rememb] 9 lay+ d[n a c\rse1 is t :at y lay d[n is a true c\rse4 ,to /eam ?is c\rse y\rself1 y mu/ make ! prop] correction = y\r compass error4 ,assign = ,night ,"w 9 ,b[dit*1 ,arts4 #i-bci-bdj-bda-bdc-bdd-bde-bdf-bdg-bdh-b di-bea-beb-bec-bed-bee-bef-beg-beh4 ,if any "t 9 class room is left1 sp5d x 9 lay+ d[n c\rses on ! *>t & read+ !m2 also 9 answ]+ su* que/ions z ^!3 #a4 ,i desire to sail a true c\rse ( ,,ne4 ,my compass error is #b po9ts ,we/]ly ,v>iation & #a po9t ,ea/]ly ,deviation4 ,:at compass c\rse %all ,i sail8 #b4 ,i desire to sail a true c\rse ( ,,sw x ,w4 ,my ,v>iation is #aa deg4 ,w1 ,deviation #b pts4 ,w & ,leeway #a pt4 />bo>d4 ,:at compass c\rse %all ,i sail8 #c4 ,i desire to sail a true c\rse ( #bce deg44 ,my compass error is #d pts4 ,e ,v>iation1 #bg deg4 ,w ,deviation1 ,leeway #a pt4 port4 ,:at compass c\rse %all ,i sail8 #d4 ,i desire to sail a true c\rse ( ,s #fe deg4 ,w4 ,my compass error is #aj deg4 ,e ,v>iation1 #c deg4 ,e ,deviation1 ,leeway #a_/d po9t />bo>d4 ,:at compass c\rse %all ,i sail8 ,,friday ,,lecture ,,! ,,protractor ,,& ,,sextant ,! protractor is an in/rum5t us$ to %ape long c\rses4 ,!re are _m k9ds4 ,! simple/ & ! "o mo/ 9 use is m]ely a piece ( transp>5t celluloid ) a compass c>d pr9t$ on x & a /r+ atta*$ to ! c5t] ( ! compass c>d4 ,to f9d y\r c\rse by protractor1 put ! protractor d[n on ! *>t s t ! ,nor? & ,s\? l9e on ! compass c>d ( ! protractor w be imm$iately ov] a m]idian ( longitude on ! *>t1 or be exactly p>allel to "o1 & w int]sect ! po9t f :i* y int5d to dep>t4 ,!n /ret* y\r /r+ along ! c\rse y desire to /eam4 ,:]e ?is /r+ cuts ! compass c>d1 w be ! direction ( y\r c\rse4 ,rememb]1 h[ev]1 t ?is w be ! true c\rse to sail4 ,9 ord] to conv]t ?is true c\rse into y\r compass c\rse1 all[ = ,v>iation & ,deviation accord+ to ! rules already giv5 y4 ,9 case y "k ! exact am\nt ( ,v>iation & ,deviation at ! "t y lay d[n ! c\rse--& y\r c\rse is n f>--y c get y\r compass c\rse 9 "o op]ation by sett+ ! ,nor? po9t ( y\r protractor z f> ,ea/ or ,we/ ( ! m]idian z ! am\nt ( y\r compass error is4 ,by !n proce$+ z be=e1 ! c\rse indicat$ on ! compass c>d w be ! compass c\rse to sail4 ,?is me?od %\ld n be us$ :]e y\r c\rse 9 "o direction is long or :]e y\r c\rse is %ort b 9 two or m directions4 ,! reason = ?is is t 9 bo? cases1 ei!r y\r ,v>iation or ,deviation may *ange & ?r[ y (f4 ,practically all navigation 9 /range wat]s 9 sight ( l& & 9 all wat]s out ( sight ( l& dep5ds ^u ! det]m9ation ( angles4 ,! angle at :i* a ligh?\se is se5 f y\r %ip w give y mu* in=mation t may be absolutely necess>y = y\r safety4 ,! angul> altitude ( ! sun1 /> or planet does ! same4 ,! v he>t ( ,navigation is bas$ ^u deal+ ) angles ( all k9ds4 ,! in/rum5t1 !re=e1 t measures ^! angles is ! mo/ important ( any us$ 9 ,navigation & y mu/ become ?or\ghly famili> ) x4 ,x is ! sextant or "s memb] ( ! sextant family--su* z ! quadrant1 octant1 etc4 ,! sextant is ! "o mo/ 9 use & s w be describ$ fir/4 ,put 9 y\r ,note-,book3 ,! sextant has ! foll[+ p>ts3 7,in/ructor po9ts to ea*47 #a4 ,mirror #b4 ,telescope #c4 ,horizon ,glass #d4 ,%ade ,glasses #e4 ,back ,%ade ,glasses #f4 ,h&le #g4 ,slid+ ,limb #h4 ,read+ ,glass #i4 ,tang5t ,screw #aj4 ,arc ,9 gett+ angles ( l&-m>ks or buoys1 ! sextant is held by ! h&le ,no4 #f 9 a horizontal position4 ,! v]ni] arr[ 9 ! slid+ limb is set on z]o4 ,n[1 suppose y wi% to get ! angul> di/ance betwe5 two ligh?\ses z se5 f ! bridge ( y\r %ip4 7,draw diagram47 ,illu/ration ,look at "o ligh?\se ?r\gh ! l9e ( sight & true horizon "p ( ! horizon glass4 ,n[1 move ! slid+ limb along ! arc gradually until y see ! o!r ligh?\se 9 ! reflect$ horizon ( ! horizon glass4 ,:5 "o ligh?\se 9 ! true horizon is directly on top ( ! o!r ligh?\se 9 ! reflect$ horizon1 clamp ! slid+ limb4 ,if any additional adju/m5t mu/ be made1 make x ) ! tang5t screw ,no4 #i4 ,n[ look ?r\gh ! read+ glass ,no4 #h4 ,y %\ld see t ! arc is divid$ into degrees & six?s ( degrees 9 ! foll[+ mann]3 #aa deg4 #aj deg4 ------------------------------ ---------------------- ---------------------- ,n[1 z e degree is divid$ into sixty m9utes1 "o-six? ( a degree is #aj m9utes4 ,9 o!r words1 ea* ( ! divisions ( a degree on ?is arc repres5ts #aj m9utes4 ,n[ on ! v]ni] 9 ! slid+ limb1 directly "u ! arc1 is ! same k9d ( a division4 ,b ^! divisions on ! v]ni] repres5t m9utes & six?s ( a m9ute1 or #aj seconds4 ,to read ! angle1 ! z]o po9t on ! v]ni] is us$ z a />t+ po9t4 ,if x exactly co9cides ) "o ( ! l9es on ! scale ( ! arc1 t l9e gives ! measurem5t ( ! angle4 ,9 ! foll[+ illu/ration ! angle is #aj-a_/b degrees or #aj deg4 #cj'3 #aj deg4 #i deg4 --------------------------------------- ------------------------------------ ---------------------------------- ---------- #j ,if h[ev]1 y f9d ! z]o on ! v]ni] has pass$ a l9e ( ! arc1 y\r angle is m ?an #aj deg4 #cj' z 9 ?is3 #aa deg4 #aj deg4 ----------------------------------- ------------------------------ ------------------------------ --------------------- #j ,y mu/ !n look along ! v]ni] to ! left until y f9d ! po9t :]e ! l9es d co9cide4 ,!n add ! numb] ( m9utes & six?s ( a m9ute %[n on ! v]ni] betwe5 z]o & ! po9t :]e ! l9es co9cide to ! numb] ( degrees & m9utes %[n on ! arc at ! l9e :i* ! v]ni] z]o has pass$1 & ! sum w be ! angle measur$ by ! in/rum5t4 ,n[ 9 measur+ ! altitude ( ! sun or o!r cele/ial body1 exactly ! same process is gone ?r\gh except t ! sextant is held v]tically in/ead ( horizontally4 ,y look ?r\gh ! telescope t[>d t "p ( ! sea directly b5ea? ! cele/ial body to be obs]v$4 ,y !n move ! slid+ limb until ! image ( ! cele/ial body appe>s 9 ! horizon glass1 & is made to kiss ! horizon1 i4e41 its l[e/ po9t j t\*+ ! horizon4 ,! slid+ limb is !n screw$ d[n & ! angle read4 ,m ab\t ?is w be m5tion$ :5 we come to ,cele/ial ,navigation4 ,e sextant is liable to be 9 error4 ,to detect ?is error !re are f\r adju/m5ts to be made4 ,^! adju/m5ts d n ne$ to be le>n$ by he>t1 b ,i w m5tion !m3 #a4 ,! mirror mu/ be p]p5dicul> to ! plane ( ! arc4 ,to prove :e!r x is or n1 set ! v]ni] on ab\t #fj deg41 & look slant+ly ?r\gh ! mirror4 ,if ! true & reflect$ images ( ! arc co9cide1 no adju/m5t is necess>y4 ,if n1 ! glass mu/ be /raight5$ by turn+ ! screws at ! back4 #b4 ,! horizon glass mu/ be p]p5dicul> to ! plane ( ! arc4 ,set ! v]ni] on z]o & look slant+ly ?r\gh ! horizon glass4 ,if ! true & reflect$ horizons %[ "o unbrok5 l9e1 no adju/m5t is necess>y4 ,if n1 turn ! screw at ! back until !y d4 #c4 ,horizon glass & mirror mu/ be p>allel4 ,set ! v]ni] on z]o4 ,hold ! in/rum5t v]tically & look ?r\gh ! l9e ( sight & horizon glass4 ,if ! true & reflect$ horizons co9cide1 no adju/m5t is necess>y4 ,if !y d n1 adju/ ! horizon glass4 #d4 ,! l9e ( sight 7telescope7 mu/ be p>allel to ! plane ( ! arc4 ,?is adju/m5t is v]ifi$ by obs]v+ two />s 9 a c]ta9 way & !n p]=m+ o!r op]ations t are describ$ 9 ,b[dit*1 ,art4 #bdg4 ,d n try to adju/ y\r sextant y\rself4 ,h x adju/$ by an exp]t on %ore4 ,!n1 if !re is any error1 all[ = x4 ,an error aft] adju/m5t is call$ ! ,index ,error4 ,put 9 y\r ,note-,book3 ,h[ to f9d & apply ! ,,ie 7,index ,error73 ,set ! slid+ limb at z]o on ! arc1 hold ! in/rum5t p]p5dicul>ly & look at ! horizon4 ,move ! slid+ limb =w>d or backw>d sl[ly until ! true horizon & reflect$ horizon =m "o unbrok5 l9e4 ,clamp ! limb & read ! angle4 ,?is is ! ,,ie4 ,if ! v]ni] z]o is to ! left ( ! z]o on ! arc1 ! ,,ie is m9us & x is to be subtract$ f any angle y read1 to get ! correct angle4 ,if ! v]ni] z]o is to ! "r ( ! z]o on ! arc1 ! ,,ie is plus & is to be add$ to any angle y read to get ! correct angle4 ,index error is express$ ?us3 ,,ie #b' #cj or ,,ie - #b' #cj4 ,quadrants1 octants & qu9tants "w on exactly ! same pr9ciples z ! sextant1 except t ! divisions on ! arc & ! v]ni] diff] 9 numb] f ! six? divisions on ! arc & v]ni] ( ! sextant4 ,if any "t is left1 sp5d x 9 m>k+ c\rses ) ! protractor & h&l+ ! sextant4 ,assign = ,night ,"w ! foll[+ ,arts4 9 ,b[dit*3 #acd-ace-acf-ach-adb-add-ade-aea-aeb-aeg -aeh-aei-afj-afa-afb-afc4 ,,saturday ,,lecture ,,fixes1 ,,angles ,,by ,,be>+s ,,& ,,sextant ,!re are five good ways ( fix+ y\r position 7obta9+ a fix1 z x is call$7 provid+ y are )9 sight ( l&m>ks :i* y c id5tify or 9 comp>atively %oal wat]4 ,put 9 y\r ,note-,book3 #a4 ,cross be>+s ( two kn[n objects4 #b4 ,be>+ & di/ance ( a kn[n object1 ! height ( :i* is kn[n4 #c4 ,two be>+s ( a kn[n object sep>at$ by an int]val ( "t1 ) a run dur+ t int]val4 #d4 ,sextant angles betwe5 ?ree kn[n objects4 #e4 ,us+ ! compass1 log & lead 9 a fog or 9 unfamili> wat]s4 #a4 ,cross be>+s ( two kn[n objects4 ,select two objects m>k$ on ! *>t1 s f> ap>t t ea* w be> ab\t #de deg4 (f y\r b[ b 9 opposite directions4 ,^! be>+s w be secur$ 9 ! be/ way by ! use ( y\r pelorus4 ,correct ea* be>+ = ,v>iation & ,deviation s t x w be a true be>+4 ,!n ) ! p>allel rul]s c>ry ! be>+ ( "o object f ! *>t compass c>d until y c int]sect ! object itself & draw a l9e ?r\gh x4 ,d exactly ! same ) ! o!r object4 ,:]e ! two l9es int]sect1 w be ! position ( ! %ip at ! "t ! be>+s 7 tak54 ,illu/ration ,n[ suppos+ y wi% to f9d ! latitude & longitude ( t position ( ! %ip4 ,= ! latitude1 measure ! di/ance ( ! place f ! ne>e/ p>allel ) ! divid]s4 ,take ! divid]s to ! latitude scale at ! side ( ! *>t & put "o po9t ( !m on ! same p>allel4 ,:]e ! o!r po9t t\*es on ! latitude scale1 w be ! latitude desir$4 ,= ! longitude1 d exactly ! same ?+1 b use a m]idian ( longitude in/ead ( a p>allel ( latitude & read f ! longitude scale at ! top or bottom ( ! *>t in/ead ( f ! side4 #b4 ,be>+ & di/ance ( a kn[n object1 ! height ( :i* is kn[n4 ,take a be>+ (1 say1 a ligh?\se ! height ( :i* is kn[n4 ,! height ( all ligh?\ses on ! ,atlantic ,coa/ c be f\nd 9 a book publi%$ by ! ,u4,s4 ,dept4 ( ,comm]ce4 ,correct ! be>+1 z m5tion$ 9 case ,no4 #a4 ,n[ read ! angle ( ! height ( t light by us+ y\r sextant4 ,d ?is by putt+ ! v]ni] #j on ! arc #j1 slid+ ! limb sl[ly =w>d until ! top ( ! ligh?\se 9 ! reflect$ horizon j t\*es ! bottom ( ! ligh?\se 9 ! true horizon4 ,) ?is angle & ! kn[n height ( ! light1 ent] ,table #cc 9 ,b[dit*4 ,at ! left ( ! ,table w be f\nd ! di/ance (f 9 knots4 ,?is me?od c be us$ ) any fairly p]p5dicul> object1 ! height ( :i* is kn[n & :i* is n m ?an #e knots away1 z ,table #cc is n made out = great] di/ances4 #c4 ,two be>+s ( ! same object1 sep>at$ by an int]val ( "t & ) a run dur+ t int]val4 ,take a compass be>+ ( "s prom95t object :5 x is ei!r #b1 #c or #d po9ts (f ! b[4 ,take ano!r be>+ ( ! same object :5 x is ei!r #d1 #f or #h po9ts (f ! b[4 ,! di/ance run by ! %ip betwe5 ! two be>+s w be h] di/ance f ! obs]v$ object at ! second be>+4 ,! di/ance run is ! di/ance (f4 ,a diagram w %[ cle>ly j :y ?is is s3 ,illu/ration ,! %ip at ,a f9ds ! light be>+ ,,nnw #b po9ts (f h] b[4 ,at ,b1 :5 ! light be>s ,,nw & #d po9ts (f1 ! log regi/]s ! di/ance f ,a to ,b #i miles4 #i miles1 !n1 w be ! di/ance f ! light itself :5 ! %ip is at ,b4 ,! ma!matical reason = ?is is t ! di/ance run is "o side ( an isosceles triangle4 ,su* triangles h _! two sides ( equal l5g?4 ,= t reason1 ! di/ance run is ! di/ance (f4 ,n[ ! same fact holds true 9 runn+ f ,b1 :i* is #d po9ts (f ! b[1 to ,c1 :i* is #h po9ts (f ! b[1 or directly abeam4 ,! log %[s ! di/ance run betwe5 ,b & ,c is #f4c miles4 ,h5ce1 ! %ip is #f4c miles f ! light :5 directly abeam ( x4 ,?is la/ #d & #h po9t be>+ is :at is kn[n z ! b[ & beam be>+1 & is ! /&>d me?od us$ 9 coa/wise navigation4 ,any "o ( ^! me?ods is ( great value 9 fix+ y\r position ) relation to ! l&1 :5 y are ab\t to g to sea4 #d4 ,sextant angles betwe5 ?ree kn[n objects4 ,?is me?od is ! mo/ accurate ( all4 ,because ( its precision x is ! "o us$ by ! ,gov]nm5t 9 plac+ buoys1 etc4 ,take ?ree kn[n objects su* z ,a1 ,b & ,c :i* are f #cj deg4 to #fj deg4 f ea* o!r4 ,illu/ration ,) a sextant1 read ! angle f ,a to ,b & f ,b to ,c4 ,place a piece ( transp>5t pap] ov] ! compass c>d & draw ?ree l9es f ! c5t] ( ! compass c>d to ! circumf]5ce 9 su* a way t ! angles secur$ by ! sextant w be =m$ by ! ?ree l9es drawn4 ,n[ take ?is pap] ) ! angles on x & fit x on ! *>t s t ! ?ree objects ( :i* angles 7 tak5 w be int]sect$ by ! ?ree l9es on ! pap]4 ,:]e ! po9t ,s is 79 my diagram7 w be ! po9t ( ! %ip's position at ! "t ( sight4 ,to secure great] accuracy ! two angles %\ld be tak5 at ! same "t by two obs]v]s4 #e4 ,us+ a compass1 log & lead :5 y are 9 a fog or unfamili> wat]s4 ,suppos+ t y are ne> l& & want to fix y\r position b h no l&m>ks :i* y c recognize4 ,"h is a me?od to help y out3 ,take a piece ( trac+ pap] & rule a v]tical l9e on x4 ,?is w repres5t a m]idian ( longitude4 ,take ca/s ( ! lead at regul> int]vals1 not+ ! "t at :i* ea* is tak51 & ! di/ance logg$ betwe5 ea* two4 ,! compass correct$ = ,v>iation & ,deviation w %[ y\r c\rse4 ,rule a l9e on ! trac+ pap] 9 ! direction ( y\r c\rse1 us+ ! v]tical l9e z a ,n & ,s m]idian4 ,measure (f on ! c\rse l9e by ! scale ( miles 9 y\r *>t1 ! di/ance run betwe5 ca/s & opposite ea* "o note ! "t1 dep? asc]ta9$ &1 if possible1 nature ( ! bottom4 ,n[ lay ?is pap] d[n on ! *>t :i* c be se5 "u x1 9 ab\t ! position y believe y\rself 9 :5 y made ! fir/ ca/4 ,if y\r *a9 ( s\nd+s agrees ) ^? on ! *>t1 y are all "r4 ,if n1 move ! pap] ab\t1 keep+ ! v]tical l9e due ,n & ,s1 till y f9d ! place on ! *>t t does agree ) y4 ,t is y\r l9e ( position4 ,y w nev] f9d 9 t locality any o!r place :]e ! *a9 ( s\nd+s are ! same on ! same c\rse y are /eam+4 ,?is is ! only me?od by s\nd+s t y c use 9 ?ick wea!r & x is an invaluable "o4 ,put 9 y\r ,note-,book ?is diagram3 #aj #h4cj;,a4,m4 #ab #i4jj;,a4,m4 #ac #aj;,a4,m4 #ac-a_/b #aj4cj;,a4,m4 #ad #aa;,a4,m4 #ad-c_/d #aa4cj;,a4,m4 ,assign = ,night ,"w1 ,review = ,weekly ,exam9ation to be held on ,monday4 ,add an explanation ( ! ,deviation ,c>d 9 ,b[dit*1 page #da4 ,put 9 y\r ,note-,book3 ,ent]+ ,new ,york ,h>bor1 %ip head+ ,w #c_/d ,n1 ,v>iation #i deg4 ,w4 ,obs]v$ by pelorus ! foll[+ objects3 ,buoy ,no4 #a--;,,ene #a_/d ,e #b--;,e #a_/b ,n #c--,,ne #a_/d ,e #d--,,nw #a_/d ,n ,requir$ true be>+s ( objects obs]v$4 ,answ]3 ,f ,deviation ,c>d 9 ,b[dit*1 p4 #da1 ,deviation on ,w #c_/d ,n c\rse is #e deg4 ,e4 ,h5ce1 ,compass ,error is #e deg4 ,e 7,dev47 #i deg4 ,w 7,v>47 #d deg4 ,w4 ,c4 ,b4 ,c4 ,e4 ,t4 ,b4 ,,ene #a_/d ,e #gj deg4 #d deg4 ,w #ff deg4 ,e #a_/b ,n #hd deg4 #d deg4 ,w #hj deg4 ,,ne #a_/d ,e #dh deg4 #d deg4 ,w #dd deg4 ,,nw #a_/d ,n #cah deg4 #d deg4 ,w #cad deg4 ,,week ,,ii--,,dead ,,reckon+ ,,tuesday ,,lecture ,,latitude ,,& ,,longitude ,illu/ration ,we h be5 us+ ! words ,latitude & ,longitude a good deal s9ce ?is c\rse began4 ,let u see j :at ! words mean4 ,be=e do+ t1 !re are a few facts to keep 9 m9d ab\t ! e>? itself4 ,! e>? is a sph]oid slightly flatt5$ at ! poles4 ,! axis ( ! e>? is a l9e runn+ ?r\gh ! c5t] ( ! e>? & int]sect+ ! surface ( ! e>? at ! poles4 ,! equator is ! great circle1 =m$ by ! int]section ( ! e>?'s surface ) a plane p]p5dicul> to ! e>?'s axis & equidi/ant f ! poles4 ,e po9t on ! equator is1 !re=e1 #ij deg4 f ea* pole4 ,m]idians are great circles =m$ by ! int]section ) ! e>?'s surface ( planes p]p5dicul> to ! equator4 ,p>allels ( latitude are small circles p>allel to ! equator4 ,! ,latitude ( a place on ! surface ( ! e>? is ! arc ( ! m]idian int]cept$ betwe5 ! equator & t place4 ,x is measur$ by ! angle runn+ f ! equator to ! c5t] ( ! e>? & back ?r\gh ! place 9 "q4 ,latitude is reckon$ f ! equator 7#j deg47 to ! ,nor? ,pole 7#ij deg47 & f ! equator 7#j deg47 to ! ,s\? ,pole 7#ij deg474 ,! diff]5ce ( ,latitude betwe5 any two places is ! arc ( ! m]idian int]cept$ betwe5 ! p>allels ( ,latitude ( ! places & is m>k$ ,n or ,s accord+ to ! direction 9 :i* y /eam 7,t n'74 ,! ,longitude ( a place on ! surface ( ! e>? is ! arc ( ! equator int]cept$ betwe5 ! m]idian ( ! place & ! m]idian at ,gre5wi*1 ,engl&1 call$ ! ,prime ,m]idian4 ,longitude is reckon$ ,ea/ or ,we/ ?r\gh #ahj deg4 f ! ,m]idian at ,gre5wi*4 ,diff]5ce ( ,longitude betwe5 any two places is ! arc ( ! equator int]cept$ betwe5 _! m]idians1 & is call$ ,ea/ or ,we/ accord+ to direction4 ,example3 ,diff4 ,lo4 ,t & ,t' ,e' ,m1 & ,e or ,w accord+ z to :i* way y g4 ,dep>ture is ! actual l9e> di/ance measur$ on a p>allel ( ,latitude betwe5 two m]idians4 ,diff]5ce ( ,latitude is reckon$ 9 m9utes because miles & m9utes ( ,latitude are always ! same4 ,dep>ture1 h[ev]1 is only reckon$ 9 miles1 because :ile a mile is equal to #a' ( longitude on ! equator1 x is equal to m ?an #a' z ! latitude increases2 ! reason be+1 ( c\rse1 t ! m]idians ( ,lo4 conv]ge t[>d ! pole1 & ! di/ance betwe5 ! same two m]idians gr[s less & less z y leave ! equator & g t[>d ei!r pole4 ,example3 ,,tn1 ,n'n'4 #aj mi4 dep>ture on ! equator #aj' diff]5ce 9 ,lo4 #aj mi4 dep>ture 9 ,lat4 #ee deg4 equals some?+ l #ah' diff]5ce 9 ,lo4 ,! curv$ l9e :i* jo9s any two places on ! e>?'s surface1 cutt+ all ! m]idians at ! same angle1 is call$ ! ,rhumb ,l9e4 ,! angle :i* ?is l9e makes ) ! m]idian ( ,lo4 int]sect+ any po9t 9 "q is ! ,c\rse1 & ! l5g? ( ! l9e betwe5 any two places is call$ ! di/ance betwe5 !m4 ,example3 ,t or ,t'4 ,*>t ,projections ,! e>? is project$1 s to speak1 ^u a *>t 9 ?ree diff]5t ways--! ,m]cator ,projection1 ! ,polyconic ,projection & ! ,gnomonic ,projection4 ,! ,m]cator ,projection ,y already "k some?+ ab\t ! ,m]cator ,projection & a ,m]cator *>t4 ,z expla9$ be=e1 x is con/ruct$ on ! !ory t ! e>? is a cyl9d] in/ead ( a sph]e4 ,! m]idians ( longitude1 !re=e1 run p>allel in/ead ( conv]g+1 & ! p>allels ( latitude are l5g!n$ out to correspond to ! wid5+ out ( ! ,lo4 m]idians4 ,j h[ ?is ,m]cator *>t is con/ruct$ is expla9$ 9 detail 9 ! ,arts4 9 ,b[dit* y 7 giv5 to read la/ night4 ,y d n h to actually con/ruct su* a *>t1 z ! ,gov]nm5t has = sale blank ,m]cator *>ts = e p>allel ( latitude 9 :i* !y c be us$4 ,x is well to rememb]1 h[ev]1 t s9ce a mile or m9ute ( latitude has a diff]5t value 9 e latitude1 !re is an appe>ance ( di/ortion 9 e ,m]cator *>t :i* cov]s any l>ge ext5t ( surface4 ,= in/ance1 an isl& ne> ! pole1 w be repres5t$ z be+ mu* l>g] ?an "o ( ! same size ne> ! equator1 due to ! diff]5t scale us$ to pres]ve ! accurate "* ( ! projection4 ,! ,polyconic ,projection ,! !ory ( ! ,polyconic ,projection is bas$ ^u conceiv+ ! e>?'s surface z a s]ies ( cones1 ea* "o hav+ ! p>allel z its base & its v]tex 9 ! po9t :]e a tang5t to ! e>? at t latitude int]sects ! e>?'s axis4 ,! degrees ( latitude & longitude on ?is *>t are project$ 9 _! true l5g? & ! g5]al di/ortion ( ! e>?'s surface is less ?an 9 any o!r me?od ( projection4 ,illu/ration ,a /raight l9e on ! polyconic *>t repres5ts a ne> approa* to a great circle1 mak+ a slightly diff]5t angle ) ea* m]idian ( longitude z !y conv]ge t[>d ! poles4 ,! p>allels ( latitude are also %[n z curv$ l9es1 ?is be+ app>5t on all b l>ge scale *>ts4 ,! ,polyconic ,projection is especially adapt$ to survey+1 b is also employ$ to "s ext5t 9 *>ts ( ! ,u4 ,s4 ,coa/ ,geodetic ,survey4 ,gnomonic ,projection ,! !ory ( ?is projection is to make a curv$ l9e appe> & be a /raight l9e on ! *>t1 i4e41 z ?\gh y 7 at ! c5t] ( ! e>? & look+ out t[>d ! circumf]5ce4 ,! ,gnomonic ,projection is ( p>ticul> value 9 sail+ long di/ance c\rses :]e foll[+ a curv$ l9e ov] ! e>?'s surface is ! %orte/ di/ance betwe5 two po9ts t are widely sep>at$4 ,?is is call$ ,great ,circle ,sail+ & w be talk$ ab\t 9 m detail lat] on4 ,! po9t to rememb] "h is t ! ,hydrographic ,(fice pr9ts ,great ,circle ,sail+ ,*>ts cov]+ all ! navigable wat]s ( ! globe4 ,s9ce all ^! *>ts are con/ruct$ on ! ,gnomonic ,projection1 x is only necess>y to jo9 any two po9ts by a /raight l9e to get ! curv$ l9e or great circle track :i* y\r %ip is to foll[4 ,! c\rses to sail & ! di/ance betwe5 ea* c\rse are easily asc]ta9$ f ! in=mation on ! *>t4 ,?is is ! way x is done3 7,note to ,in/ructor3 ,provide y\rself ) a *>t & expla9 f ! *>t explanation j h[ ^! c\rses are laid d[n47 ,sp5d ! re/ ( ! "t 9 hav+ pupils lay d[n c\rses on ! diff]5t k9ds ( *>ts4 ,if ^! *>ts are n available assign = night "w ! foll[+ articles 9 ,b[dit*1 "p ( :i* read+ c be done imm$iately 9 ! class room--s t z mu* "t z possible c be giv5 to ! read+ on ,dead ,reckon+3 #afg-afh-afi-agb-agc-agd-age-agf--;fir/ two s5t5ces #agh-bjb-bjc-bjd-bje-bjf-bjg-bjh4 ,note to pupils3 ,9 read+ articles #afg-agh1 disreg>d ! =mulae & ! examples work$ out by log>i?ms4 ,j try to get a cle> idea ( ! diff]5t sail+s m5tion$ & ! !ory ( ,dead ,reckon+ 9 ,arts4 #bjb-bji4 ,,w$nesday ,,lecture ,,useful ,,tables--,,plane ,,& ,,trav]se ,,sail+ ,! :ole subject ( ,navigation is divid$ into two p>ts1 i4e41 f9d+ y\r position by :at is call$ ,dead ,reckon+ & f9d+ y\r position by obs]vation ( cele/ial bodies su* z ! sun1 />s1 planets1 etc4 ,to f9d y\r position by dead reckon+1 y g on ! !ory t small sections ( ! e>? are flat4 ,! :ole affair !n simply resolves itself into solv+ ! l5g? ( "r-angl$ triangles except1 ( c\rse1 :5 y are go+ due ,ea/ & ,we/ or due ,nor? & ,s\?4 ,= in/ance1 any c\rses y sail l ^! w be ! hypot5uses ( a s]ies ( "r-angl$ triangles4 ,! problem y h to solve is1 hav+ left a po9t on l&1 ! latitude & longitude ( :i* y "k1 & sail$ s _m miles 9 a c]ta9 direction1 9 :at latitude & longitude h y arriv$8 ,illu/ration ,if y sail due ,nor? or ,s\?1 ! problem is m]ely "o ( ari?metic4 ,suppose y\r position at noon today is ,latitude #ci deg4 #ae' ,n1 ,longitude #dj deg4 ,w1 & up to noon tomorr[ y /eam due ,nor? #cjj miles4 ,n[ y h already le>n$ t a m9ute ( latitude is always equal to a nautical mile4 ,h5ce1 y h sail$ #cjj m9utes ( latitude or #e deg44 ,?is #e deg4 is call$ diff]5ce ( latitude1 & z y are 9 ,nor? latitude & go+ ,nor?1 ! diff]5ce ( latitude1 #e deg41 %\ld be add$ to ! latitude left1 mak+ y\r new position #dd deg4 #ae' ,n & y\r ,longitude ! same #dj deg4 ,w1 s9ce y h n *ang$ y\r longitude at all4 ,9 sail+ ,ea/ or ,we/1 h[ev]1 y\r problem is m difficult4 ,only on ! equator is a m9ute ( longitude & a nautical mile ( ! same l5g?4 ,z ! m]idians ( longitude conv]ge t[>d ! poles1 ! l5g?s betwe5 ea* less54 ,we n[ h to rely on tables to tell u ! numb] ( miles 9 a degree ( longitude at e di/ance ,nor? or ,s\? ( ! equator1 i4e41 9 e latitude4 ,longitude1 !n1 is reckon$ 9 miles4 ,! numb] ( miles a %ip makes ,ea/ or ,we/ is call$ ,dep>ture1 & x mu/ be conv]t$ into degrees1 m9utes & seconds to f9d ! diff]5ce ( longitude4 ,a %ip1 h[ev]1 seldom goes due ,nor? or ,s\? or due ,ea/ or ,we/4 ,%e usually /eams a diagonal c\rse4 ,suppose1 = in/ance1 a vessel 9 ,latitude #dj deg4 #cj' ,n1 ,longitude #gj deg4 #be' ,w1 sails ,,ssw #ej miles4 ,:at is ! new latitude & longitude %e arrives 98 ,%e sails a c\rse l ?is3 ,illu/ration ,n[ suppose we draw a p]p5dicul> l9e to repres5t a m]idian ( longitude & a horizontal "o to repres5t a p>allel ( latitude4 ,!n we h a "r-angl$ triangle 9 :i* ! l9e ,,ac repres5ts ! c\rse & di/ance sail$1 & ! angle at ,a is ! angle ( ! c\rse ) a m]idian ( longitude4 ,if we c asc]ta9 ! l5g? ( ,,ab1 or ! di/ance ,s\? ! %ip has sail$1 we %all h ! diff]5ce ( latitude1 & if we c get ! l5g? ( ! l9e ,,bc1 we %all h ! ,dep>ture & f x ! diff]5ce ( longitude4 ,?is is a simple problem 9 trigonometry1 i4e41 kn[+ ! angle & ! l5g? ( "o side ( a "r triangle1 :at is ! l5g? ( ! o!r two sides8 ,b y d n h to use trigonometry4 ,! :ole problem is work$ out = y 9 ,table #b ( ,b[dit*4 ,f9d ! angle ( ! c\rse ,,ssw1 i4e41 ,s #bb deg4 ,w 9 ! old or #bjb deg4 9 ! new compass read+4 ,look d[n ! di/ance column to ! left = ! di/ance sail$1 i4e41 #ej miles4 ,opposite ?is y f9d ! diff]5ce ( latitude #df-d_/aj 7#df4d7 & ! dep>ture #ah-g_/aj 7#ah4g74 ,n[ ! position we 7 9 at ! />t 0 ,lat4 #dj deg4 #cj' ,n1 ,longitude #gj deg4 #be' ,w4 ,9 sail+ ,,ssw #ej miles1 we made a diff]5ce ( latitude ( #df' #bd 7#df4d71 & z we w5t ,s\?--t[>d ! equator--we %\ld subtract ?is #df' #bd f our latitude left to give u our latitude 94 ,n[ we mu/ f9d our diff]5ce ( longitude & f x ! new or ,longitude 94 ,! fir/ ?+ to d is to f9d ! av]age or middle latitude 9 :i* y h be5 sail+4 ,d ?is by add+ ! latitude left & ! latitude 9 & divid+ by #b4 #dj deg4 #cj' #jj #ci #dc #cf ----------- #b7hj #ac #cf ----------- #dj deg4 #jf' #dh ,mid4 ,lat4 ,take ! ne>e/ degree1 i4e41 #dj deg41 z y\r answ]4 ,) ?is #dj deg4 ent] ! same ,table #b & look = y\r dep>ture1 i4e41 #ah4g 9 ! diff]5ce ( latitude column4 #ah4d is ! ne>e/ to x4 ,n[ look to ! left 9 ! di/ance column opposite #ah4d & y w f9d #bd1 :i* means t 9 ,lat4 #dj deg4 a dep>ture ( #ah4g miles is equival5t to #bd' ( diff]5ce ( ,longitude4 ,we 7 9 #gj deg4 #be' ,we/ ,longitude & we sail$ ,s\? & ,we/1 s ?is diff]5ce ( ,longitude %\ld be add$ to ! ,longitude left to get ! ,longitude 93 ,lo4 left #gj deg4 #be' ,w ,diff4 ,lo4 #bd ----------- ,lo4 9 #gj deg4 #di' ,w ,! :ole problem !re=e w\ld look l ?is3 ,lat4 left #dj deg4 #cj' ,n ,lo4 left #gj deg4 #be' ,w ,diff4 ,lat4 #df #bd ,diff4 ,lo4 #bd ------------- ---------- ,lat4 9 #ci deg4 #dc' #cf ,n ,lo4 9 #gj deg4 #di' ,w ,!re is "o m fact to expla94 ,:5 ! c\rse is #de deg4 or less 7old compass read+7 y read f ! top ( ! page ( ,table #b d[n4 ,:5 ! c\rse is m ?an #de deg4 7old compass read+7 y read f ! bottom ( ! page up4 ,! di/ance is tak5 out 9 exactly ! same way 9 bo? cases1 b ! diff]5ce ( ,latitude & ! ,dep>ture1 y w notice1 are rev]s$4 7,in/ructor3 ,read a few c\rses to ?or\ghly expla9 ?is47 ,f all ?is explanation we get ! foll[+ rules1 :i* put 9 y\r ,note-,book3 ,to f9d ! new or ,lat4 93 ,ent] ,table #b ) ! true c\rse at ! top or bottom ( ! page accord+ z to :e!r x is less or great] ?an #de deg4 7old compass read+74 ,take out ! diff]5ce ( ,latitude & ,dep>ture & m>k ! diff]5ce ( ,latitude m9utes 7'74 ,:5 ! ,latitude left & ! diff]5ce ( ,latitude are bo? ,nor? or bo? ,s\?1 add !m4 ,:5 "o is ,nor? & ! o!r ,s\?1 subtract ! less f ! great] & ! rema9d]1 nam$ ,nor? or ,s\? aft] ! great]1 w be ! new ,latitude1 kn[n z ! ,latitude 94 ,to f9d ! new or ,lo4 93 ,f9d ! middle latitude by add+ ! latitude left to ! latitude 9 & divid+ by #b4 ,) ?is middle latitude1 ent] ,table #b4 ,seek = ! dep>ture 9 ! diff]5ce ( latitude column4 ,opposite to x 9 ! di/ance column w be ! figures indicat+ ! numb] ( m9utes 9 ! diff]5ce ( longitude4 ,) ?is diff]5ce ( ,longitude1 apply x 9 ! same way to ! ,longitude left z y appli$ ! diff]5ce ( ,latitude to ! ,latitude left4 ,! result w be ! new or ,longitude 94 ,n[ if a %ip /eam$ a :ole day on ! same c\rse1 y w\ld be able to get h] ,dead ,reckon+ position )\t any fur!r "w1 b a %ip does n usually sail ! same c\rse #bd h\rs /raight4 ,%e usually *anges h] c\rse sev]al times1 & z a %ip's position by ,d4,r4 is only comput$ once a day--at noon--x becomes necess>y to h a me?od ( obta9+ ! result aft] sev]al c\rses h be5 sail$4 ,?is is call$ work+ a trav]se & sail+ on v>i\s c\rses 9 ?is fa%ion is call$ ,trav]se ,sail+4 ,put 9 y\r ,note-,book ! foll[+ example & ! way 9 :i* x is work$3 ,dep>ture tak5 f ,b>negat ,light 9 ,lat4 #ci deg4 #df' ,n1 ,lo4 #gd deg4 #jf' ,w1 be>+ by compass ,,nnw1 #ae knots away4 ,%ip head+ ,s\? ) a ,deviation ( #d deg4 ,w4 ,%e sail$ on ! foll[+ c\rses3 ---------------------------------------- -------------------------- ,c\rse ,w9d ,leeway,deviation,di/ance ,rem>ks ---------------------------------------- -------------------------- ,,se #c_/d ,e ,,ne #a pt4 #c deg4 ,e #cj ,v>iation ?r\gh\t day #h deg4 ,w4 ,s #aa deg4 ,w ,,ne #j #f deg4 ,e #ee ,a curr5t set ,,ne magnetic ,,nnw ,,ne #j #b deg4 ,w #ad #a_/b mi4 p] hr4 = ! day4 ,s #hg deg4,e ,,ne #j #c deg4 ,e #ej ,requir$ ,lat4 & ,lo4 9 & c\rse & di/ance made good4 ---------------------------------------- -------------------------- ---------------------------------------- ------------------------------------- ,c4 ,cos4 ,w9d,leeway ,dev4 ,v>4 ,,new ,,old ,di/4,diff4 ,lat4 ,dep>ture ,t4 ,cos4,t ,cos4 ------------------- ,n ,s ,e ,w ---------------------------------------- -------------------------- ,,sse 44 44 #d deg4 ,w #h deg4 ,w #ade deg4 ,s #ce deg4,e #ae 44 #ab4c #h4f 44 ,,se #c_/d ,e ,,ne #a pt4 #c deg4 ,e #h deg4 ,w #acc deg4 ,s #dg deg4,e #cj 44 #bj4e #ba4i 44 ,s #aa deg4 ,w ,,ne #j #f deg4 ,e #h deg4 ,w #ahi deg4 ,s #i deg4,w #ee 44 #ed4c 44 #h4f ,,nnw ,,ne #j #b deg4 ,w #h deg4 ,w #cbg deg4 ,n #cc deg4,w #ad #aa4g 44 44 #g4f ,s #hg deg4 ,e ,,ne #j #c deg4 ,e #h deg4 ,w #hh deg4 ,n #hh deg4,e #ej #a4g 44 #ej 44 ,,ne 44 44 mg #h deg4 ,w #c deg4 ,n #c deg4 ,e #ab #i4f 44 #g4b 44 ---------------------------------------- --------------------------- #bc4j #hg4a #hg4g #af4b 44 #bc4j #af4b 44 -------------- 44 44 44 44 44 #fd4a #ga4e 44 -------------- 44 ,s ,e ,lat4 left #ci deg4-#df'-jj ,n ,mid4 ,lat4 #ci deg4 ,diff4 ,lat4 #a -#jd -#jf ,s ,dep4 #ga4e ---------- ,lat4 94 #ch -#da -#ed ,n ,table #b--,"u #ci deg4 ,dep4 9 #ci -#df -#jj ,diff4 ,lat4 col4 #ib' #a deg4 #cb' ,diff4 ,lo4 ---------- #b7gh -#bg -#ed ---------- ,mid4 ,lat4 #ci -#ac -#eg ,lo4 left #gd deg4-#jf'-jj ,w ,diff4 ,lo4 #a -#cb -#jj ,e -------------- ,lo4 94 #gb deg4-#cd'-jj ,w ,table #b--;,diff4 ,lat4 #fd4a1 ,dep4 #ga4e4 ,c\rse ,s #dh deg4 ,e--,di/ance #if miles4 ,! rule cov]+ all ^! op]ations is z foll[s3 #a4 ,write out ! v>i\s c\rses ) _! corrections = ,leeway1 ,deviation1 ,v>iation & ! di/ance run on ea*4 #b4 ,9 f\r adjo9+ columns head$ ,n1 ,s1 ,e1 ,w respectively1 put d[n ! ,diff]5ce ( ,latitude & ,dep>ture = ea* c\rse4 #c4 ,add toge!r all ! nor?+s1 all ! s\?+s1 all ! ea/+s & all ! we/+s4 ,subtract to f9d ! diff]5ce betwe5 nor?+s & s\?+s & y w get ! :ole diff]5ce ( ,latitude4 ,! diff]5ce betwe5 ! ea/+s & we/+s w be ! :ole dep>ture4 #d4 ,f9d ! latitude 91 z already expla9$4 #e4 ,f9d ! ,lo4 91 z already expla9$4 #f4 ,) ! :ole diff]5ce ( ,latitude & :ole ,dep>ture1 seek 9 ,table #b = ! page :]e ! ne>e/ agreem5t ( ,diff]5ce ( ,latitude & ,dep>ture c be f\nd4 ,! numb] ( degrees at ! top or bottom ( ! page 7accord+ z to :e!r ! ,diff4 ( ,lat4 or ,dep4 is great]7 w give y ! true c\rse made good1 & ! numb] 9 ! di/ance column opposite ! prop] ,diff]5ce ( ,latitude & ,dep>ture w give y ! di/ance made4 ,x is (t5 conv5i5t to use ! rev]se ( ! above me?od1 i4e41 be+ giv5 ! latitude & longitude ( ! position left & ! latitude & longitude ( ! position arriv$ 91 to f9d ! c\rse & di/ance betwe5 !m by ,middle ,latitude ,sail+4 ,! full rule is z foll[s3 #a4 ,f9d ! algebraic diff]5ce betwe5 ! latitudes & longitudes respectively4 #b4 ,us+ ! middle 7or av]age7 latitude z a c\rse1 f9d 9 ,table #b ( ,b[dit* ! ,diff4 ( ,lo4 9 ! di/ance column4 ,opposite1 9 ! ,diff4 ( ,lat4 column1 w be ! correct ,dep>ture4 #c4 ,) ! ,diff4 ( ,lat4 betwe5 ! position left & ! position arriv$ 91 & ! ,dep>ture1 j secur$1 seek 9 ,table #b = ! page :]e ! ne>e/ agreem5t to ^! values c be f\nd4 ,on ?is page w be secur$ ! true c\rse & di/ance made1 z expla9$ 9 ! prec$+ me?od4 #d4 ,use ?is me?od only :5 /eam+ approximately an ,ea/ & ,we/ c\rse4 ,= an example ( ?is me?od1 see ,b[dit*1 p4 #gg1 example #c4 ,,?ursday ,,lecture ,,examples ,,on ,,plane ,,& ,,trav]se ,,sail+ 7,cont9u$7 #a4 ,dep>ture tak5 f ,cape ,horn4 ,lat4 #ee deg4 #eh' #da ,s1 ,lo4 #fg deg4 #af' #ae ,w1 be>+ by compass ,,ssw #bj knots4 ,%ip head+ ,,sw x ,s1 ,deviation #d deg4 ,e1 /eam$ ! foll[+ c\rses3 ---------------------------------------- ------------ ,c4 ,cos4 ,w9d ,leeway ,deviation ,di/ance ---------------------------------------- ------------ ,,sw x ,s ,,se #a pt4 #d deg4 ,e #dj ,,wnw ,n #b pts4 #e deg4 ,e #be ,s #dj deg4 ,e ,,ne #b pts4 #d deg4 ,w #bj ---------------------------------------- ------------ ,rem>ks ,v>iation #ah deg4 ,e ?r\gh\t4 ,curr5t set ,,nw magnetic #cj mi4 = ! day4 ,requir$ ,latitude & ,longitude 9 & c\rse & di/ance made good4 #b4 ,dep>ture tak5 f ,/4 ,agnes ,ligh?\se1 ,scilly ,isl&s1 ,lat4 #di deg4 #ec' ,s1 ,lo4 #f deg4 #bj' ,w1 be>+ by compass ,e x ,s1 di/ance #ah knots1 ,deviation #aj deg4 ,w1 ,v>iation #bc deg4 ,w4 ,%ip head$ ,n /eam$ on ! foll[+ c\rses3 ---------------------------------------- ----------------------- ,c4 ,cos4 ,w9d ,leeway ,devia- ,dis- ,rem>ks tion tance ---------------------------------------- ----------------------- ,n 44 #aj deg4 ,w #fj ,v>iation #bc deg4 ,w4 ,curr5t set ,s #a_/b ,e ,w #c pts4 #aj deg4 ,e #dj ,,se mg #a-a_/b miles = #bd hrs4 ,,nne ,,nnw #b pts4 #h deg4 ,w #de ,req4 ,lat4 & ,lo4 9 & c\rse & di/ance made good1 ---------------------------------------- ----------------------- ,assign = ,night ,"w ! foll[+ articles 9 ,b[dit*3 #agi-ahj-aha-ahb4 ,also additional problems 9 ,dead ,reckon+4 ,,friday ,,lecture ,,m]cator ,,sail+ ,?is is a me?od to f9d ! true c\rse & di/ance betwe5 two po9ts4 ,! me?od c be us$ 9 two ways1 i4e41 by ! use ( ,tables #b & #c 7call$ ! inspection me?od7 & by ! use ( log>i?ms4 ,! fir/ me?od is ! quick] & w d = %ort di/ances4 ,! second me?od1 h[ev]1 is m accurate 9 all cases1 & p>ticul>ly :]e ! di/ances are great4 ,! inspection me?od is z foll[s 7,put 9 y\r ,note-,book73 ,f9d ! algebraic diff]5ce betwe5 ! m]idional p>ts correspond+ to ! ,lat4 9 & ,lat4 s\ght by ,table #c4 ,call ?is ,m]idional diff]5ce ( ,latitude4 ,f9d ! algebraic diff]5ce betwe5 ,longitude 9 & ,longitude s\ght & call ?is diff]5ce ( ,longitude4 ,) ! ,m]idional diff]5ce ( ,latitude & ! diff]5ce ( ,longitude1 f9d ! c\rse by se>*+ 9 ,table #b = ! page :]e !y /& opposite ea* o!r 9 ! latitude & dep>ture columns4 ,n[ f9d ! real diff]5ce ( latitude4 ,"u ! c\rse j f\nd & opposite ! real diff]5ce ( ,latitude1 w be f\nd ! di/ance sail$ 9 ! di/ance column4 ,example3 ,:at is ! c\rse & di/ance f ,lat4 #dj deg4 #bh' ,n1 ,lo4 #gc deg4 #ej' ,w1 to ,lat4 #ci deg4 #ea' ,n1 ,lo4 #gb deg4 #de' ,w8 ,lat4 9 #dj deg4 #bh' ,n ,m]idional pts4 #bfdd4b ,lat4 s\ght #ci #ea ,n ,m]idional pts4 #beif4j --------- ------ #j deg4 #cg' ,m]4 diff4 ,lat4 #dh4b ,lo4 9 #gc deg4 #ej' ,w ,lo4 s\ght #gb #de ,w --------- #a deg4 #je' #fe' ,on page #fjd ,b[dit* y w f9d #dh4g & #fd4g opposite ea* o!r1 & z #dh4g is 9 ! ,lat4 column only :5 y read f ! bottom1 ! c\rse is ,s #ec deg4 ,e4 ,! real diff]5ce ( ,lat4 "u ?is c\rse is opposite #fb 9 ! di/ance column4 ,h5ce ! di/ance to be sail$ is #fb miles4 ,if di/ances are too great1 divide m]idional diff]5ce ( ,lat41 real diff]5ce ( ,latitude & diff]5ce ( ,longitude by #aj or any o!r numb] to br+ !m )9 ! scope ( ! di/ances 9 ,table #b4 ,:5 di/ance to be sail$ is f\nd1 x mu/ be multipli$ by ! same numb]4 ,= in/ance1 if ! diff]5ce ( ,lat41 diff]5ce ( ,lo41 etc41 are divid$ by #aj to br+ !m 9 ! scope ( ,table #b1 & ) ^! figures #bai is ! di/ance f\nd1 ! real di/ance w\ld be #aj times #bai or #baij4 ,n[ let u "w out ! same problem by log>i?ms4 ,?is w acqua9t u ) two new ,tables1 i4e41 ,tables #db & #dd4 ,put ?is 9 y\r ,note-,book3 ,lat4 9 #dj deg4 #bh' ,n ,m]4 pts4 #bfdd4b ,lo4 9 #gc deg4 #ej' ,lat4 s\ght #ci #ea ,m]4 pts4 #beif4j ,lo4 s\ght #gb #de --------- ------ ------- ,real diff4 #j deg4 #cg' #dh4b #a deg4 #je' #fj -- #fj #e -- 7,table #db7 log 7 #aj7 #fe #aa4habia ,log #dh4b #a4fhcje -------- ,log tan ,,tc 7,table #dd7 #aj4abihf ,,tc ,s #ec deg4 #bf' ,e ,log sec ,,tc 7#ec deg4 #bf'7 #aj4bbdic ,log real diff4 ,lat4 #a4efhbj -------- #aa4gicac - #aj4 -------- #a4gicac ,di/ance 7,table #db7 #fb4aa miles ,f9d algebraically ! real diff]5ce ( latitude1 m]idional diff]5ce ( latitude & ! diff]5ce ( longitude4 ,r$uce real diff]5ce ( latitude & diff]5ce ( longitude to m9utes4 ,take log ( ! diff]5ce ( longitude 7,table #db7 & add #aj4 ,f ?is log subtract ! log ( diff]5ce ( m]idional p>ts4 ,! result w be ! log tan ( ! ,true ,c\rse1 :i* f9d 9 ,table #dd4 ,on ! same page f9d ! log sec ( true c\rse4 ,add to ?is ! log ( ! real diff]5ce ( latitude1 & if ! result is m ?an #aj1 subtract #aj4 ,?is result w be ! log ( ! di/ance sail$4 ,?is me?od %\ld be us$ only :5 /eam+ approximately a ,nor? & ,s\? c\rse4 ,note4--,= detail$ explanation ( ,tables #db & #dd see ,b[dit*1 pp4 #bga-bgf4 ,assign = ,night ,read+ ,arts1 9 ,b[dit*3 #ahc-ahd-ahe-ahf-ahg-ahh-ahi-aid-bei-bfj -bfa-bfb-bfc-bfd-bfe-bff-bfg-bfh4 ,also1 "o ( ! examples ( ,m]cator sail+ to be done by bo? ! ,inspection & ,log>i?mic me?od4 ,,saturday ,,lecture ,,great ,,circle ,,sail+--,,! ,,*ronomet] ,9 ,tuesday's ,lecture ( ?is week1 ,i expla9$ h[ a ,great ,circle track 0 laid d[n on "o ( ! ,great ,circle ,sail+ ,*>ts :i* are prep>$ by ! ,hydrographic ,(fice4 ,suppos+1 h[ev]1 y d n h ^! *>ts on h&4 ,!re is an easy way to con/ruct a great circle track y\rself4 ,turn to ,art4 #aid1 page #hb1 9 ,b[dit*4 ,"h is a table ) an explanation z to h[ to use x4 ,take1 = in/ance1 ! same two po9ts betwe5 :i* y j drew a l9e on ! great circle track4 ,f9d ! c5t] ( ?is l9e & ! latitude ( t po9t4 ,at ?is po9t draw a l9e p]p5dicul> to ! c\rse to be sail$1 ! o!r end ( :i* mu/ int]sect ! correspond+ p>allel ( latitude giv5 9 ! table4 ,) ?is po9t z ! c5t] ( a circle1 sweep an arc :i* w int]sect ! po9t left & ! po9t s\ght4 ,?is arc w be ! great circle track to foll[4 ,to f9d ! c\rses to be sail$1 get ! diff]5ce betwe5 ! c\rse at />t+ & t at ! middle ( ! circle1 & f9d h[ _m qu>t] po9ts are conta9$ 9 x4 ,n[ divide ! di/ance f ! />t+ po9t to ! middle ( ! circle by ! numb] ( qu>t] po9ts4 ,t w give ! numb] ( miles to sail on ea* qu>t] po9t c\rse4 ,see ?is illu/ration3 ,illu/ration ,diff]5ce betwe5 ,,ene & ,e #b pts4 #h qu>t] po9ts4 ,say di/ance is #afjj miles measur$ by divid]s or secur$ by ,m]cator ,sail+ ,me?od4 ,divide #afjj by #h #bjj4 ,e #bjj miles y %\ld *ange y\r c\rse #a_/d po9t ,ea/4 ,! ,*ronomet] ,! *ronomet] is no?+ m ?an a v f9ely regulat$ clock4 ,) x we asc]ta9 ,gre5wi* ,mean ,"t1 i4e41 ! mean "t at ,gre5wi* ,obs]vatory1 ,engl&4 ,j :at ! words ,gre5wi* ,mean ,"t signify1 w be expla9$ 9 m detail lat] on4 ,:at y %\ld rememb] "h is t practically e me?od ( f9d+ y\r exact position at sea is dep5d5t ^u kn[+ ,gre5wi* ,mean ,"t1 & ! only way to f9d x is by means ( ! *ronomet]4 ,x is ess5tial to keep ! *ronomet] z quiet z possible4 ,= t reason1 :5 y take an obs]vation y w probably note ! "t by y\r wat*4 ,j be=e tak+ ! obs]vation1 y w comp>e y\r wat* ) ! *ronomet] to notice ! exact diff]5ce betwe5 ! two4 ,:5 y take y\r obs]vation1 note ! wat* "t1 apply ! diff]5ce betwe5 ! *ronomet] & wat*1 & ! result w be ! ,,ct4 ,= in/ance1 suppose ! *ronomet] read #c;h #bem #ajs1 & y\r wat*1 at ! same in/ant1 read #a;h #ajm #es4 ,c--,w w\ld be3 #c;h -- #bem -- #ajs -- #a -- #aj -- #je ---------------- #b;h -- #aem -- #jes ,n[ suppose y took an obs]vation :i*1 accord+ to y\r wat*1 0 at #b;h #ajm #jes4 ,:at w\ld be ! correspond+ ,c ,t8 ,x w\ld be ,,wt #b;h -- #ajm -- #jes ,c -- ,w #b -- #ae -- #je -------------------- ,,ct #d;h -- #bem -- #ajs ,if ! *ronomet] "t is less ?an ! ,w ,t add #ab h\rs to ! ,c ,t1 s t x w always be ! l>g] & s t ! am\nt to be add$ to ,w ,t w always be 4 ,= in/ance1 ,,ct #a;h--#bem--#des1 ,,wt #d;h--#acm--#bes1 :at is ! ,c-,w8 ,,ct #ac;h--#bem--#des ,,wt #d --#ac --#be ---------------- ,c--,w #i;h--#abm--#bjs ,n[1 suppose an obs]vation 0 tak5 at #f;h #acm #bes accord+ to wat* "t4 ,:at w\ld be ! correspond+ ,,ct8 ,,wt #f;h--#acm--#bes ,c--,w #i --#ab --#bj ---------------- #ae;h--#bem--#des --#ab ---------------- ,,ct #c;h--#bem--#des ,put 9 y\r ,note-,book3 ,,ct ,,wt ,c - ,w4 ,if1 9 f9d+ ,c-,w1 ,c is less ?an ,w1 add #ab h\rs to ,c1 subtract+ same aft] ,,ct is secur$4 ,example ,no4 #a3 ,,ct #c;h--#bem--#ajs ,,wt #a --#aj --#je ---------------- ,c--,w #b;h--#aem--#jes ,,wt #b;h--#ajm--#jes ,c--,w #b --#ae --#je ---------------- ,,ct #d;h--#bem--#ajs ,example ,no4 #b3 ,,ct #a;h--#bem--#des ,,wt #d;h--#acm--#bes 7#ab hrs47 ,,ct #ac;h--#bem--#des ,,wt #d --#ac --#be ---------------- ,c-,w #i;h--#abm--#bjs ,,wt #f;h--#acm--#bes ,c-,w #i --#ab --#bj ---------------- #ae;h--#bem--#des 7-#ab hrs47 #ab ---------------- ,,ct #c;h--#bem--#des ,!re is "o m v important fact to "k ab\t ! *ronomet]4 ,x is physically impossible to keep x absolutely accurate ov] a long p]iod ( "t4 ,in/ead ( cont9ually fuss+ ) its adju/m5t & h&s1 ! daily rate ( error is asc]ta9$1 & f ?is ! exact "t = any giv5 day4 ,x is an inv>iable practice among good m>9]s to leave ! *ronomet] alone4 ,:5 y are 9 port1 y c f9d out f a "t ball or f "s *ronomet] mak] :at y\r error is4 ,) ?is 9 m9d1 y c apply ! new correction f day to day4 ,"h is an example 7,put 9 y\r ,note-,book73 ,on ,june #a/1 ,,ct #g;h--#bjm--#aes1 ,,cc #bm--#djs fa/4 ,on ,june #af?1 7same ,,ct7 ,,cc #am--#cjs fa/4 ,:at 0 ! correspond+ ,g4,m4,t4 on ,june #aj?8 ,june #a/ #bm--#djs fa/ #af? #am--#cjs fa/ ---------------- #am--#ajs #fj -- #fj #aj -- #ae7 #gjs 7#d4f sec4 ,daily ,rate ( error los+ ,june #a/-#aj?1 #i days times #d4f sec4 #da sec4 los+ ,june #a/ #bm--#djs fa/ ,june #aj? #das los+ --------- ,june #aj? #am--#eis fa/ ,,ct #g;h--#bjm--#aes ,,cc -- #a --#ei ------------ ,g4,m4,t4 #g;h--#ahm--#afs on ,june #aj? ,if ,,cc is fa/1 subtract f ,,ct ,if ,,cc is sl[1 add to ,,ct ,,week ,,iii--,,cele/ial ,,navigation ,,tuesday ,,lecture ,,cele/ial ,,co-,,ord9ates1 ,,equ9octial ,,sy/em1 ,,etc4 ,we h already discuss$ ! way 9 :i* ! e>? is divid$ s z to aid u 9 f9d+ our position at sea1 i4e41 ) an equator1 p>allels ( latitude1 m]idians ( longitude />t+ at ! ,gre5wi* m]idian1 etc4 ,we n[ take up ! way 9 :i* ! cele/ial sph]e is correspond+ly divid$ & also simple explanations ( "s ( ! m important t]ms us$ 9 ,cele/ial ,navigation4 ,z y /& on any po9t ( ! e>? & look up1 ! heav5ly bodies appe> z ?\gh !y 7 situat$ ^u ! surface ( a va/ holl[ sph]e1 ( :i* y\r eye is ! c5t]4 ,( c\rse ?is app>5t concave vault has no exi/5ce & we _c accurately measure ! di/ance ( ! heav5ly bodies f u or f ea* o!r4 ,we c1 h[ev]1 measure ! direction ( "s ( ^! bodies & t in=mation is ( trem5d\s value to u 9 help+ u to fix our position4 ,n[ we c\ld use our eye z ! c5t] ( ! cele/ial sph]e b m accurate ?an t is to use ! c5t] ( ! e>?4 ,suppose we d use ! c5t] ( ! e>? z ! place f :i* to obs]ve ^! cele/ial bodies &1 9 imag9ation1 transf] our eye !re4 ,!n we w f9d project$ on ! cele/ial sph]e n only ! heav5ly bodies b ! imag9>y po9ts & circles ( ! e>?'s surface4 ,p>allels ( latitude1 m]idians ( longitude1 ! equator1 etc41 w h ! same imag9>y position on ! cele/ial sph]e t !y h on ! e>?4 ,y\r actual position on ! e>? w be project$ 9 a po9t call$ y\r z5i?1 i4e41 ! po9t directly ov]head4 ,illu/ration ,f ?is we get ! def9ition t ! ,z5i? ( an obs]v] on ! e>?'s surface is ! po9t 9 ! cele/ial sph]e directly ov]head4 ,x w\ld be a simple matt] to fix y\r position if y\r position nev] *ang$4 ,b x is always *ang+ ) relation to ^! cele/ial bodies4 ,fir/1 ! e>? is revolv+ on its own axis4 ,second1 ! e>? is mov+ 9 an elliptic track ar\nd ! sun1 & ?ird1 c]ta9 cele/ial bodies !mselves are mov+ 9 a track ( _! own4 ,! *anges produc$ by ! daily rotation ( ! e>? on its axis are diff]5t = obs]v]s at diff]5t po9ts on ! e>? &1 !re=e1 dep5d ^u ! latitude & longitude ( ! obs]v]4 ,b ! *anges aris+ f ! e>?'s motion 9 its orbit & ! motion ( v>i\s cele/ial bodies 9 _! orbits1 are true no matt] on :at po9t ( ! e>? y happ5 to be4 ,^! *anges1 !re=e1 9 _! relation to ! c5t] ( ! e>?1 may be accurately gaug$ at any in/ant4 ,to ?is end ! facts necess>y = any calculation h be5 collect$ & are available 9 ! ,nautical ,almanac1 :i* we w take up 9 m detail lat]4 ,n[ ) ^! facts 9 m9d1 let u expla9 9 simple words ! mean+ ( "s ( ! t]ms y w h to become acqua9t$ ) 9 ,cele/ial ,navigation4 ,9 ! illu/ration 7,b[dit* p4 #hh7 ! e>? is suppos$ to be project$ ^u ! cele/ial sph]e ,n ,e ,s ,w4 ,! ,z5i? ( ! obs]v] is project$ at ,z & ! pole ( ! e>? :i* is above ! horizon is project$ at ,p4 ,! o!r pole is n giv54 ,! ,cele/ial ,equator is m>k$ "h ,e ,q ,w & l all o!r po9ts & l9es previ\sly m5tion$1 x is ! projection ( ! ,equator until x int]sects ! cele/ial sph]e4 ,ano!r "n = ! ,cele/ial ,equator is ! ,equ9octial4 ,all cele/ial m]idians ( longitude correspond+ to longitude m]idians on ! e>? are p]p5dicul> to ! equ9octial & likewise ,p ,s1 ! m]idian ( ! obs]v]1 s9ce x passes ?r\gh ! obs]v]'s z5i? at ,z1 is =m$ by ! ext5sion ( ! e>?'s m]idian ( ! obs]v] & h5ce int]sects ! horizon at its ,n & ,s po9ts4 ,?is makes cle> aga9 j :at is ! m]idian ( ! obs]v]4 ,x is ! m]idian ( longitude :i* passes ?r\gh ! ,n & ,s poles & ! obs]v]'s z5i?4 ,9 o!r words1 :5 ! sun or any o!r heav5ly body is on y\r m]idian1 a l9e /ret*$ due ,n & ,s1 int]sect+ ! ,n & ,s poles1 w pass ?r\gh y\r z5i? & ! c5t] ( ! sun or o!r cele/ial body4 ,to und]/& ?is is important1 = no sight ) ! sextant is ( value except ) relation to y\r m]idian4 ,! ,decl9ation ( any po9t 9 ! cele/ial sph]e is its di/ance 9 arc1 ,nor? or ,s\? ( ! cele/ial equator1 i4e41 ,n or ,s ( ! ,equ9octial4 ,nor? decl9ations1 i4e41 decl9ations nor? ( ! equ9octial are always m>k$1 2 ^? s\? ( ! equ9octial1 -4 ,= in/ance1 9 ! ,nautical ,almanac1 y w nev] see a decl9ation ( ! sun or o!r cele/ial body m>k$1 ,n #ah deg4 #bh' #cj4 ,x w always be m>k$ #ah deg4 #bh' #cj & a s\? decl9ation w be m>k$ -#ah deg4 #bh' #cj4 ,ano!r fact to rememb] is t ,decl9ation on ! cele/ial sph]e corresponds to latitude on ! e>?4 ,if1 = in/ance1 ! ,sun's decl9ation is #ah deg4 #bh' #cj at noon1 ,gre5wi*1 !n at t in/ant1 i4e41 noon at ,gre5wi*1 ! sun w be directly ov]head a po9t on e>? :i* is 9 latitude ,n #ah deg4 #bh' #cj4 ,! ,pol> ,di/ance ( any po9t is its di/ance 9 arc f ei!r pole4 ,x mu/1 !re=e1 equal #ij deg4 m9us ! decl9ation1 if measur$ f ! pole ( ! same "n z ! decl9ation or #ij deg4 plus ! decl9ation if measur$ f ! pole ( ! opposite "n4 ,p ,m is ! pol> di/ance ( ,m f ,p1 or ,p ,b ! pol> di/ance ( ,b f ,p4 ,! true altitude ( a cele/ial body is its angul> height f ! true horizon4 ,! z5i? di/ance ( any po9t or cele/ial body is its angul> di/ance f ! z5i? ( ! obs]v]4 ,! ,ecliptic is ! great circle repres5t+ ! pa? 9 :i* ! sun appe>s to move 9 ! cele/ial sph]e4 ,z a matt] ( fact1 y "k t ! e>? moves ar\nd ! sun1 b z y obs]ve ! sun f "s spot on ! e>?1 x appe>s to move ar\nd ! e>?4 ,?is app>5t track is call$ ! ,ecliptic z /at$ be=e1 & 9 ! illu/ration ! ,ecliptic is repres5t$ by ! curv$ l9e1 ,c ,v ,t4 ,! plane ( ! ,ecliptic is incl9$ to t ( ! ,equ9octial at an angle ( #bc deg4 #bg-a_/b'1 & ?is incl9ation is call$ ! obliquity ( ! ,ecliptic4 ,! ,equ9oxes are ^? po9ts at :i* ! ,ecliptic & ,equ9octial int]sect1 & :5 ! sun occupies ei!r ( ^! two positions1 ! days & nights are ( equal l5g?4 ,! ,v]nal ,equ9ox is t "o :i* ! sun passes ?r\gh or int]sects 9 go+ f ,s to ,n decl9ation1 & ! ,autumnal ,equ9ox t :i* x passes ?r\gh or int]sects 9 go+ f ,n to ,s decl9ation4 ,! ,v]nal ,equ9ox 7,v 9 ! illu/ration7 is also designat$ z ! ,fir/ ,po9t ( ,aries :i* is ( use 9 reckon+ /> "t & w be m5tion$ 9 m detail lat]4 ,! ,sol/itial ,po9ts1 or ,sol/ices1 are po9ts ( ! ,ecliptic at a di/ance ( #ij deg4 f ! ,equ9oxes1 at :i* ! sun atta9s its highe/ decl9ation 9 ea* hemisph]e4 ,!y are call$ ! ,summ] & ,w9t] ,sol/ice accord+ to ! season 9 :i* ! sun appe>s to pass ^! po9ts 9 its pa?4 ,to sum up3 ,! way to f9d any po9t on ! e>? is to f9d ! di/ance ( ?is po9t ,n or ,s ( ! equator 7i4e41 its ,latitude7 & its di/ance ,e or ,w ( ! m]idian at ,gre5wi* 7i4e41 its longitude74 ,9 ! cele/ial sph]e1 ! way to f9d ! location ( a po9t or cele/ial body su* z ! sun is to f9d its decl9ation 7i4e41 di/ance 9 arc ,n or ,s ( ! equator7 & its h\r angle4 ,by h\r angle1 ,i mean ! di/ance 9 "t f y\r m]idian to ! m]idian ( ! po9t or cele/ial body 9 "q4 ,assign = ,night read+1 ,arts1 9 ,b[dit*3 #bgj-bga-bgb-bgc-bgd-bge-bgg-bgh-bgi-bhj -bhb-bhc-bhd4 ,,w$nesday ,,lecture ,,"t ,,by ,,! ,,sun--,,mean ,,"t1 ,,sol> ,,"t1 ,,conv]sion1 ,,etc4 ,!re is no?+ m important 9 all ,navigation ?an ! subject ( ,"t4 ,e calculation = det]m9+ ! position ( y\r %ip at sea mu/ take into consid]ation "s k9d ( "t4 ,put 9 y\r ,note-,book3 ,!re are ?ree k9ds ( "t3 #a4 ,app>5t or sol> "t1 i4e41 "t by ! sun4 #b4 ,mean ,"t1 i4e41 clock "t4 #c4 ,sid]eal ,"t1 or "t by ! />s4 ,s f> z ?is lecture is conc]n$1 we w omit any m5tion ( sid]eal "t1 i4e41 "t by ! />s4 ,we w devote ?is morn+ to sun "t1 i4e41 app>5t "t1 & mean "t4 ,app>5t or ,sol> ,"t is1 z /at$ be=e1 no?+ m ?an sun "t or "t by ! sun4 ,! h\r angle ( ! c5t] ( ! sun is ! measure ( app>5t or sol> "t4 ,an app>5t or sol> day is ! int]val ( "t x takes = ! e>? to revolve completely ar\nd on its axis e #bd h\rs4 ,x is app>5t noon at ! place :]e y are :5 ! c5t] ( ! sun is directly on y\r m]idian1 i4e41 on ! m]idian ( longitude :i* runs ?r\gh ! ,nor? & ,s\? poles & also int]sects y\r z5i?4 ,?is is ! mo/ natural & ! mo/ accurate measure ( "t = ! navigator at sea & ! unit ( "t adopt$ by ! m>9] is ! app>5t sol> day4 ,app>5t noon is ! "t :5 ! latitude ( y\r position c be mo/ easily & mo/ exactly det]m9$ & on ! latitude by obs]vation j secur$ we c get data :i* w be ( great value to u = longitude sights tak5 lat] 9 ! day4 ,n[ x w\ld be v easy = ! m>9] if he c\ld measure app>5t "t directly s t 8 clock or o!r in/rum5t w\ld always tell him j :at ! sun "t 04 ,x is impossible1 h[ev]1 to d ?is because ! e>? does n revolve at a uni=m rate ( spe$4 ,consequ5tly ! sun is sometimes a little ahead & sometimes a little beh9d any av]age "t4 ,y _c manufacture a clock :i* w run t way because ! h\rs ( a clock mu/ be all ( exactly ! same l5g? & x mu/ make noon at precisely #ab o'clock e day4 ,h5ce we di/+ui% clock "t f sun "t by call+ clock "t1 mean 7or av]age7 "t & sun "t1 app>5t or sol> "t4 ,f ?is explanation y are ready to und]/& su* expressions z ,local ,mean ,"t1 :i*1 9 unte*nical language1 signifies clock "t at ! place :]e y are2 ,gre5wi* ,mean ,"t :i* signifies clock "t at ,gre5wi*2 ,local ,app>5t ,"t1 :i* signifies sun "t at ! place :]e y are2 ,gre5wi* ,app>5t ,"t1 :i* signifies sun "t at ,gre5wi*4 ,n[ ! diff]5ce betwe5 app>5t "t & mean "t c be f\nd = any m9ute ( ! day by ref]5ce to ! ,nautical ,almanac :i* we w take up lat] 9 m detail4 ,?is diff]5ce is call$ ! ,equation ( ,"t4 ,!re is "o m fact to rememb] 9 reg>d to app>5t & mean "t4 ,x is ! relation ( ! sun's h\r angle to app>5t "t4 ,9 ! fir/ place1 :at is a def9ition ( ! sun's ,,ha8 ,x is ! angle at ! cele/ial pole betwe5 ! m]idian int]sect+ any giv5 po9t & ! m]idian int]sect+ ! c5t] ( ! sun4 ,x is measur$ by ! arc ( ! cele/ial equator int]sect$ betwe5 ! m]idian ( any po9t & ! m]idian int]sect+ ! c5t] ( ! sun4 ,illu/ration ,= in/ance1 9 ! above diagram1 suppose ,,pg is ! m]idian at ,gre5wi*1 & ,,ps ! m]idian int]sect+ ! sun4 ,!n ! angle at ! pole ,,gps1 measur$ by ! arc ,,gs w\ld be ! ,h\r ,angle ( ,gre5wi*1 or ! ,gre5wi* ,h\r ,angle4 ,& n[ y notice t ?is angul> measure is exactly ! same z app>5t "t at ,gre5wi* or ,gre5wi* ,app>5t ,"t1 = ,gre5wi* ,app>5t ,"t is no?+ m ?an ! di/ance 9 "t ,gre5wi*1 ,engl&1 or ! m]idian at ,gre5wi* is f ! sun1 i4e41 ! "t x takes ! e>? to revolve f ,gre5wi* to ! sun2 & t di/ance is exactly measur$ by ! ,gre5wi* ,h\r ,angle or ! arc on ! cele/ial equator1 ,,gs4 ,! same is correspond+ly true ( ,local ,app>5t ,"t & ! %ip's ,h\r ,angle4 ,suppose1 = in/ance1 ,,pl is ! m]idian int]sect+ ! place :]e y\r %ip is4 ,!n y\r %ip's h\r angle w\ld be ! angle at ! pole int]sect+ ! m]idian ( y\r %ip & ! m]idian ( ! sun or ,,lps & measur$ by ! arc ,,ls4 ,& y w note t ?is di/ance is exactly ! same z app>5t "t at ! %ip1 = ,app>5t ,"t at %ip is no?+ m ?an ! di/ance 9 "t :i* ! %ip is f ! sun4 ,we c sum up all ?is in=mation 9 a few simple rules1 :i* put 9 y\r ,note-,book3 ,mean ,"t ,clock ,"t4 ,g4,m4,t4 ,gre5wi* ,mean ,"t4 ,l4,m4,t4 ,local ,mean ,"t4 ,app>5t ,"t ,actual or ,sun ,"t4 ,g4,a4,t4 7,g4,h4,a47 ,gre5wi* ,app>5t ,"t or ,gre5wi* ,h\r ,angle4 ,l4,a4,t4 7,s4,h4,a47 ,local ,app>5t ,"t or ,%ip's ,h\r ,angle4 ,diff]5ce betwe5 app>5t & mean "t or mean & app>5t "t--,equation ( ,"t4 ,"r "u ?is 9 y\r ,note-,book put ! foll[+ diagram1 :i* ,i w expla93 ,illu/ration ,y w see f ?is diagram t civil "t comm5ces at midnight & runs ?r\gh #ab h\rs to noon4 ,x !n comm5ces aga9 & runs ?r\gh #ab h\rs to midnight4 ,! ,civil ,day1 !n1 is f midnight to midnight1 divid$ into two p]iods ( #ab h\rs ea*4 ,! a/ronomical day comm5ces at noon ( ! civil day ( ! same date4 ,x comprises #bd h\rs1 reckon$ f ,o to #bd1 f noon ( "o day to noon ( ! next4 ,a/ronomical "t1 ei!r app>5t or mean1 is ! h\r angle ( ! true or mean sun respectively1 measur$ to ! we/w>d ?r\gh\t its entire daily circuit4 ,s9ce ! civil day beg9s #ab h\rs be=e ! a/ronomical day & ends #ab h\rs be=e x1 ,a4,m4 ( a new civil day is ,p4,m4 ( ! a/ronomical day prec$+4 ,= in/ance1 #f h\rs ,a4,m41 ,april #ae? civil "t is equival5t to #ah h\rs ,april #ad?1 a/ronomical "t4 ,n[1 all a/ronomical calculations 9 :i* "t is a necess>y fact to be kn[n1 mu/ be express$ 9 a/ronomical "t4 ,z *ronomet]s h _! face m>k$ only f #j to #ab z 9 ! case ( an ord9>y wat*1 x is necess>y to transpose ?is wat* or *ronomet] "t into a/ronomical "t4 ,no transpos+ is necess>y if ! "t is ,p4,m41 z y c see f ! diagram t bo? civil & a/ronomical times up to #ab ,p4,m4 are ! same4 ,b 9 ,a4,m4 "t1 su* transpos+ is necess>y4 ,put 9 y\r ,note-,book3 ,:5ev] local or *ronomet] "t is ,a4,m41 d$uct #ab h\rs f su* "t to get ! correct a/ronomical "t3 ,,ct #ae;d-- #i;h--#ajm--#cjs ,a4,m4 --#ab ------------------------ ,,ct #ad;d--#ba;h--#ajm--#cjs ------ ,l4,m4,t4 #aj;d-- #d;h--#djm--#afs ,a4,m4 --#ab ------------------------ ,l4,m4,t4 #i;d--#af;h--#djm--#afs ,n[ we come to a v important application ( "t4 ,y w rememb] t 9 "o ( ! =m] lectures we /at$ t to f9d our latitude1 we _h to f9d h[ f> ,nor? or ,s\? ( ! equator we 71 & to f9d our longitude1 we _h to f9d h[ f> ,ea/ or ,we/ ( ! m]idian at ,gre5wi* we 74 ,nev] m9d ab\t latitude = ! pres5t4 ,we c f9d our longitude exactly if we "k our ,gre5wi* "t & our "t at %ip4 ,= in/ance1 9 ! accompany+ diagram3 ,illu/ration ,suppose ,,pg is ! m]idian at ,gre5wi*1 !n any?+ to ! we/ ( ,,pg is ,we/ longitude & any?+ to ! ,ea/ ( ,,pg is ,ea/ longitude4 ,n[ suppose ,,gps is ! ,h4,a4 ( ,g4 or ,g4,a4,t4--i4e41 ! di/ance 9 "t ,g4 is f ! sun4 ,& ,l ,p ,s is ! ,h4,a4 ( ! %ip or ,l4,a4,t4--i4e41 ! di/ance 9 "t ! %ip is f ! sun4 ,!n ! diff]5ce betwe5 ,g ,p ,s & ,l ,p ,s is ,g ,p ,l1 measur$ by ! arc ,l ,g1 & t is ! diff]5ce t ! %ip1 repres5t$ by its m]idian ,,pl1 is f ! ,gre5wi* m]idian ,,pg4 ,9 o!r words1 t is ! %ip's longitude =1 z m5tion$ be=e1 longitude is ! di/ance ,ea/ or ,we/ ( ,gre5wi* t any po9t is1 measur$ on ! arc ( ! cele/ial equator4 ,! longitude is ,we/1 = y c see ,,lpg or ! arc ,,lg is we/ ( ! m]idian ,,pg4 ,likewise if ,p ,e is ! m]idian ( y\r %ip1 ! ,longitude 9 "t is ! ,s4,h4,a4 or ,l4,a4,t41 ,e ,p ,s 7! di/ance y\r %ip is f ! sun7 less ! ,g4,h4,a4 or ,g4,a4,t41 ,g ,p ,s 7! di/ance ,gre5wi* is f ! sun7 :i* is ! angle ,g ,p ,e measur$ by ! arc ,g ,e4 ,& ?is ,longitude is ,ea/ = y c see ,g ,p ,e1 measur$ by ,g ,e1 is ea/ ( ! ,gre5wi* m]idian1 ,p ,g4 ,9 bo? ^! cases1 h[ev]1 ! longitude is express$ 9 "t1 i4e41 s _m h\rs1 m9utes & seconds f ! ,gre5wi* m]idian & we wi% to express ?is di/ance 9 degrees1 m9utes & seconds ( arc4 ,! e>? describes a circle ( #cfj deg4 e #bd h\rs4 ,!n if y are #a h\r f ,gre5wi*1 y are #a_/bd ( #cfj deg4 or #ae deg4 f ,gre5wi* & if y are #ab h\rs f ,gre5wi*1 y are #a_/b ( #cfj deg4 or #ahj deg4 f ,gre5wi*4 ,by keep+ ?is 9 m9d1 y %\ld be able to transpose "t into degrees1 m9utes & seconds ( arc = any fraction ( "t4 ,x is1 h[ev]1 all work$ out 9 ,table #g ( ,b[dit* :i* turn to4 7,note to ,in/ructor3 ,expla9 ?is table c>efully74 ,put 9 y\r ,note-,book3 #hi deg4 #bd' #bf 7#hi deg47 #e;h--#efm 7#bd'7 #am--#cfs 7#bf7 #a--dd_/fjs -------------------- #e;h--#egm--#cgs #dd_/fjs #chs #d;h--#dbm--#bfs #d;h--#djm #gj deg4 #bm--#bds #cf' #bs #cj ----------- #gj deg4 #cf' #cj ,also put 9 y\r ,note-,book ?is diagram & ^! =mulas3 7,= diagram use illu/ration on p4 #dj47 ,l4,m4,t4 ,we/ ,lo4 ,g4,m4,t4 ,l4,a4,t4 ,we/ ,lo4 ,g4,a4,t4 ,l4,m4,t4 - ,ea/ ,lo4 ,g4,m4,t4 ,l4,a4,t4 - ,ea/ ,lo4 ,g4,a4,t4 ,g4,m4,t4 - ,we/ ,lo4 ,l4,m4,t4 ,g4,a4,t4 - ,we/ ,lo4 ,l4,a4,t4 ,g4,m4,t4 ,ea/ ,lo4 ,l4,m4,t4 ,g4,a4,t4 ,ea/ ,lo4 ,l4,a4,t4 ,if ,g4,m4,t4 or ,g4,a4,t4 is great] ?an ,l4,m4,t4 or ,l4,a4,t4 respectively1 ,lo4 is ,we/4 ,if ,g4,m4,t4 or ,g4,a4,t4 is less ?an ,l4,m4,t4 or ,l4,a4,t4 respectively1 ,lo4 is ,ea/4 ,example3 ,9 longitude #ha deg4 #ae' ,w1 ,l4,m4,t4 is ,april #ae;d--#aj;h--#agm--#cjs ,a4,m4 ,:at is ,g4,m4,t48 ,l4,m4,t4 #ae;d--#aj;h--#agm--#cjs ,a4,m4 --#ab ------------------ ,l4,m4,t4 #ad;d--#bb;h--#agm--#cjs #e --#be ,w ------------------ ,g4,m4,t4 #ae;d-- #c;h--#dbm--#cjs -------- ,g4,m4,t4 ,april #ae;d-- #c;h--#dbm--#cjs ,l4,m4,t4 ,april #ae;d--#aj;h--#agm--#cjs ,a4,m4 ,9 :at ,lo4 is %ip8 ,g4,m4,t4 #ae;d #c;h--#dbm--#cjs ,l4,m4,t4 #ad;d #bb;h--#agm--#cjs ------------------ ,lo4 9 ,t #e;h--#bem--#jjs ,w ,lo4 #ha deg4 #ae',w ,assign also = ,night ,"w read+ ! foll[+ articles 9 ,b[dit*3 #bgf-bgh-bgi-bbf-bbh-bhf-bhg-bhh-bij-bia -bid 7omitt+ ev]y?+ on page #aad47 ,,?ursday ,,lecture ,,sid]eal ,,"t--,,"r ,,asc5sion ,our la/ lecture 0 devot$ to a discussion ( sun "t4 ,today we are go+ to talk ab\t /> "t1 or1 us+ ! m common words1 sid]eal "t4 ,n[1 j "o ^w ( review4 ,y rememb] t we h le>n$ t a/ronomical "t is reckon$ f noon ( "o day to noon ( ! next & h5ce ! a/ronomical day corresponds to ! #bd h\rs ( a %ip's run4 ,! h\rs are c\nt$ f #j to #bd1 s t #aj o'clock 9 ! morn+ ( ,octob] #be? is a/ronomically ,octob] #bd?1 #bb h\rs or #bb o'clock ( ,octob] #bd?4 ,n[ ,"r ,asc5sion is diff]5t f bo? a/ronomical & civil "t4 ,"r ,asc5sion is practically cele/ial longitude4 ,= in/ance1 ! position ( a place on ! e>? is fix$ by its latitude & longitude2 ! position ( a heav5ly body is fix$ by its decl9ation & "r asc5sion4 ,b ,"r ,asc5sion is n measur$ 9 degrees & m9utes nor is x measur$ ,ea/ & ,we/4 ,x is reckon$ 9 h\rs & m9utes all ! way ar\nd ! sky1 ea/w>d f a c]ta9 po9t1 ?r\gh ! approximate #bd h\rs4 ,! po9t f :i* ?is cele/ial longitude beg9s is n at ,gre5wi*1 b ! po9t :]e ! cele/ial equator int]sects ! ecliptic 9 ! spr+ ( ! ye>1 i4e41 ! po9t :]e ! sun1 com+ ,nor? 9 ! ,spr+1 crosses ! cele/ial equator4 ,?is po9t is call$ ! ,fir/ ,po9t ( ,aries4 ,y w frequ5tly he> me speak ( a /> hav+1 = in/ance1 a ,"r ,asc5sion ( #e;h #afm #cbs4 ,i mean by t1 t />t+ at ! cele/ial m]idian1 i4e41 ! m]idian pass+ ?r\gh ! ,fir/ ,po9t ( ,aries1 x w take a spot on ! e>? #e;h #afm #cbs to travel until x rea*es ! m]idian ( ! /> 9 "q4 ,r\ghly speak+ !n1 j z ,gre5wi* ,app>5t ,"t means ! di/ance ,ea/ or ,we/ ! ,gre5wi* m]idian is f ! sun & ,local ,app>5t ,"t means ! di/ance ,ea/ or ,we/ y\r %ip is f ! sun1 s ,r4,a4,m4,g4 means ! di/ance 9 "t ! ,m]idian ( ,gre5wi* is f ! ,fir/ ,po9t ( ,aries1 measur$ ea/w>d 9 a circle4 ,& ?is di/ance is ! same z ,gre5wi* ,sid]eal ,"t1 i4e41 ,sid]eal ,"t at ,gre5wi* or ! di/ance 9 "t ! m]idian ( ,gre5wi* is f ! ,fir/ ,po9t ( ,aries4 ,n[1 :at is ! /> "t t corresponds to local "t8 ,x is call$ ! ,"r ,asc5sion ( ! ,m]idian1 :i* means ! ,r4 ,a4 ( ! m]idian :i* int]sects y\r z5i?4 ,j z ,l4,a4,t4 is ! di/ance 9 "t y\r m]idian is f ! sun1 s ,local ,sid]eal ,"t is ! ,r4 ,a4 ( y\r m]idian1 i4e41 ! di/ance 9 "t y\r m]idian is f ! ,fir/ ,po9t ( ,aries4 ,put 9 y\r ,note-,book3 ,g4,s4,t4 & ,r4,a4,m4,g4 are "o & ! same ?+4 ,l4,s4,t4 & ,r4,a4,m4 are "o & ! same ?+4 ,g4,m4,t4 7474,r4,a4 774,c4,p4 ,g4,s4,t4 7,r4,a4,m4,g47 ,if ! result is m ?an #bd h\rs1 subtract #bd h\rs4 ,g4,s4,t4 - 7474,r4,a4 - 774,c4,p4 ,g4,m4,t4 ,g4,s4,t4 - ,w4,lo4 ,l4,s4,t4 ,e4,lo4 ,l4,s4,t4 ,w4,lo4 ,g4,s4,t4 - ,e4,lo4 ,i c expla9 all ^! =mulas v easily by ! foll[+ illu/ration :i* put 9 y\r ,note-,book3 7,note to ,in/ructor3 ,if possible h copies ( ?is illu/ration mimeograph$ & di/ribut$ to ea* /ud5t47 ,illu/ration3 ,,fir/ ,,po9t ,,( ,,aries4 ,!re is "o t]m ,i h us$ :i* does n appe> 9 ! illu/ration4 ,x is ! ,e>?'s ,c5tral ,progress 7774,c4,p474 ,! a/ronomical day bas$ on ! sun1 is #bd h\rs long1 z said be=e4 ,! sid]eal day1 h[ev]1 is only #bc;h #efm #jds long4 ,?is is due to ! fact t :]eas ! e>? is mov+ 9 its ecliptic track ar\nd ! sun :ile revolv+ on its own axis1 ! ,fir/ ,po9t ( ,aries is a fix$ po9t & h5ce nev] moves4 ,! correction1 !n1 = ! diff]5ce 9 ! l5g? ( "t betwe5 a sid]eal day & a mean sol> day is call$ ! ,e>?'s ,c5tral ,progress &1 ( c\rse1 has to be figur$ = all am\nts ( "t aft] mean noon at ,gre5wi*1 s9ce ! ,sun's ,"r ,asc5sion tables 9 ! ,nautical ,almanac are bas$ on "t at mean noon at ,gre5wi*4 ,n[ y h a =mula = practically all k9ds ( conv]sion except = conv]t+ ,l4,m4,t4 into ,l4,s4,t4 ,y c\ld d x by ! =mula ,l4,m4,t4 ,w4,lo4 ,g4,m4,t4 7474,r4,a4 774,c4,p4 ,g4,s4,t4 - ,w4,lo4 ,l4,s4,t4 - ,e4,lo4 ,e4,lo4 ,b t involves too _m op]ations4 ,a %ort] way1 ?\gh n s simple p]haps1 is z foll[s3 ,l4,m4,t4 ,r$uction page #b ,n4,a4 = "t aft] local mean noon 7474,r4,a4 ( ,gre5wi* mean noon - ,r$uction page #b ,n4,a4 = ,lo4 9 ,t4 7,w1 ,e-7 ,l4,s4,t4 ,note to ,in/ructor3 ,expla9 ?is =mula by turn+ to page #ajg ,n4,a4 & "w x out by ! =mula ,l4,m4,t4 ,lo4 9 ,t 7,w7 ,g4,m4,t4 7474,r4,a4 774,c4,p4 ,g4,s4,t4 - ,lo4 9 ,t 7,w7 ,l4,s4,t4 ,example3 ,l4,m4,t4 #aj;h--#djm--#cjs ,lo4 9 ,t #d --#ef ,w ------------- ,g4,m4,t4 #ae --#cf --#cj 7474,r4,a4 #e --#aa --#aj 774,c4,p4 -- #b --#cd ------------- ,g4,s4,t4 #bj --#ej --#ad ,lo4 ,w - #d --#ef ------------- ,l4,s4,t4 #ae;h--#edm--#ads ,n[ ,b[dit* gets ?is ,l4,s4,t4 9 /ill ano!r way4 ,turn to page #aaj1 ,article #bij4 ,!re ! =mula us$ is ,l4,m4,t4 7474,r4,a4 774,c4,p4 ,l4,s4,t1 & 9 ord] to get ! correct 7474,r4,a4 & 774,c4,p4 ! ,g4,m4,t4 has to be secur$ by ! =mula ,l4,m4,t4 ,w4,lo4 ,g4,m4,t4 - ,e4,lo4 ,let u "w ?is same example 9 ,b[dit* by ! o!r two me?ods4 ,fir/ by ! =mula ,l4,m4,t4 ,w4,lo4 ,g4,m4,t4 7474,r4,a4 774,c4,p4 ,g4,s4,t4 - ,w4,lo4 ,l4,s4,t4 - ,e4,lo4 ,e4,lo4 ,l4,m4,t4 #bb;d-- #b;h--#jjm--#jjs ,w4 ,lo4 #e --#be ---------------------- ,g4,m4,t4 #bb;d-- #g;h--#bem--#jjs 7474,r4,a4 #a --#eg --#ei 774,c4,p4 #a --#ac ---------------------- ,g4,s4,t4 #bb;d-- #i;h--#bdm--#abs - ,w4 ,lo4 #e --#be ---------------------- ,l4,s4,t4 #bb;d-- #c;h--#eim--#abs ,! small diff]5ce betwe5 ?is answ] & t ( ,b[dit*'s is t ! 7474,r4,a4 = #aiaf is slightly diff]5t f t ( #aiai4 ,b[dit* us$ ! #aiaf ,almanac1 :]eas we are work+ f ! #aiai ,almanac4 ,n[ turn to page #ajg ( ! ,n4,a4 & let u "w ! same example 9 ,b[dit* by ! me?od us$ "h3 ,l4,m4,t4 #b;h - #jjm - #jjs ,r$4 = #b;h #j - #bj 7474,r4,a4 #j;h #a - #eg - #ei ,r$4 ,lo4 #e;h - #bem #j - #ec --------------- ,l4,s4,t4 #c;h - #eim - #abs ,! reason ,i am go+ s mu* into detail 9 expla9+ me?ods ( f9d+ ,l4,s4,t4 is because1 by a v simple calculation :i* w be expla9$ lat]1 we c get our latitude at night if we "k ! altitude ( ,pol>is 7,! ,nor? ,/>7 & if we "k ! ,l4,s4,t4 at ! "t ( obs]vation4 ,"s ( y may ?9k t ! ,n4,a4 way is ! simple/4 ,x is giv5 9 ! ,n4,a41 & 9 an exam9ation x w\ld be p]missible = y to use ! ,n4,a4 z a guide because1 9 an exam9ation1 ,i propose to let y h at h& ! same books y w\ld h 9 ! *>t h\se ( a %ip4 ,on ! o!r h&1 ! me?od giv5 9 ! ,n4,a4 is n z cle> to my m9d z ! me?od :i* />ts ) ,l4,m4,t41 !n f9ds ) ! ,longitude ! ,g4,m4,t4 ,t gives y1 r\ghly speak+1 ! di/ance 9 "t ,gre5wi* is f ! sun4 ,add to t ! sun's ,r4,a4 or ! di/ance 9 "t ! sun is f ! ,fir/ ,po9t ( ,aries at ,gre5wi* ,mean ,noon4 ,add to t ! correction = ! "t pa/ noon4 ,! result is ,g4,s4,t4 ,n[ all y h to d is to apply ! longitude correctly to f9d ! ,l4,s4,t41 j z :5 y h ,g4,m4,t4 & apply ! longitude correctly y get ,l4,m4,t4 ,t is a me?od :i* does n seem easy to =get1 = x dep5ds m ^u simple reason+ :]e ! o!rs1 = a beg9n]1 dep5d m ^u memory4 ,h[ev]1 any ( ! ?ree me?ods is correct & c be us$ by y4 ,p]haps ! be/ way is to "w a problem by two ( ! ?ree t seem easie/4 ,9 ?is way y c *eck y\r figures4 ,:5 ,i give y a problem t involves f9d+ ! ,l4,s4,t4 ,i d n c>e h[ y get ! ,l4,s4,t4 provid+ x is correct :5 y get x4 ,assign = ,night ,read+ 9 ,b[dit* ! foll[+ ,arts43 #bhb-bhc-bhd-bhe4 ,also ! foll[+ que/ions3 #a4 ,giv5 ! ,g4,m4,t4 & ! longitude 9 ,t :i* is ,w1 :at is ! =mula = ,l4,s4,t48 #b4 ,giv5 ! ,l4,a4,t4 & longitude 9 ,t :i* is ,e1 :at is ! =mula = ,g4,s4,t48 #c4 ,giv5 ! ,l4,s4,t4 & longitude 9 ,t :i* is ,w4 ,requir$ ,g4,m4,t4 ,etc4 ,,friday ,,lecture ,,! ,,nautical ,,almanac ,= ! la/ two days we h be5 discuss+ ,"t--sun "t or sol> "t & /> "t or sid]eal "t4 ,n[ let u exam9e ! ,nautical ,almanac to see h[ t "t is regi/]$ & h[ we read ! v>i\s k9ds ( "t = any in/ant ( ! day or night4 ,be=e />t+ 91 put a l>ge cross on pages #d & #e4 ,= any calculations y are go+ to make1 ^! pages are unnecess>y & !y are liable to lead to confusion4 ,sun "t ( ! mean sun at ,gre5wi* is giv5 = e m9ute ( ! day 9 ! ye> #aiai 9 ! pages f #f to #cj4 ,?is is indicat$ by ! column to ! left head$ ,g4,m4,t4 ,turn to page #f "u ,w$nesday1 ,jan4 #a/4 ,y c see t ! ev5 h\rs are giv5 f #j to #bd4 ,rememb] t ^! are express$ 9 a/ronomical "t1 s t if y _h ,jan4 #bnd--#aj h\rs ,a4,m41 y w\ld n look 9 ! column "u ,jan4 #bnd b "u ! column = ,jan4 #a/1 #bb h\rs1 s9ce #aj ,a4,m4 ,jan4 #bnd is #bb o'clock ,jan4 #a/1 & no read+ is us$ 9 ?is ,almanac except a read+ express$ 9 a/ronomical "t4 ,n[ at ! bottom ( ! column "u ,jan4 #a/ y see ! lett]s ,h4,d4 ,t /&s = h\rly diff]5ce & repres5ts ! am\nt to be add$ or subtract$ = an odd h\r f ! ne>e/ ev5 h\r4 ,9 ?is in/ance x is 4#b4 ,y note t ev5 h\rs #b1 #d1 #f1 etc41 are giv54 ,to f9d an odd h\r dur+ ?is a/ronomical day1 subtract 4#b f ! prec$+ ev5 h\r4 ,= any fraction ( an h\r y simply take ! correspond+ fraction ( ! ,h4,d4 & subtract x f ! prec$+ ev5 h\r4 ,= in/ance1 ! decl9ation = ,jan4 #a/--#ab h\rs w\ld be #bc deg4 #a4h' or #bc deg4--#a'--dh1 #ac h\rs w\ld be #bc deg4 #a4f' or #bc deg4--#a'--cf1 #ab-a_/b h\rs w\ld be #bc deg4 #a4g' or #bc deg4--#a'--db1 & #ac-a_/b h\rs w\ld be #bc deg4 #a4e' or #bc deg4--#a'--cj4 ,n[ to ! "r ( ! h\rs y note !re is giv5 ! correspond+ am\nt ( ,decl9ation & ! ,equation ( ,"t4 ,be=e go+ fur!r1 let u review a few facts ab\t ,decl9ation4 ,! decl9ation ( a cele/ial body is its angul> di/ance ,n or ,s ( ! cele/ial equator or equ9octial4 ,n[ get cle>ly 9 y\r m9d h[ we measure ! angul> di/ance f ! cele/ial equator ( any heav5ly body4 ,x is measur$ by ! angle "o ( ^: sides is an imag9>y l9e drawn to ! c5t] ( ! e>? & ! o!r ( ^: sides is an imag9>y l9e pass+ f ! c5t] ( ! e>? into ! cele/ial sph]e ?r\gh ! c5t] ( ! heav5ly body ^: decl9ation y desire4 ,n[ z y /& on any "p ( ! e>?1 y are /&+ at "r angles to ! e>? itself4 ,h5ce if ?is imag9>y l9e pass$ ?r\gh y x w\ld int]sect ! cele/ial sph]e at y\r z5i?1 i4e41 ! po9t 9 ! cele/ial sph]e :i* is directly above y4 ,n[ suppose y happ5 to be /&+ at a c]ta9 po9t on ! e>? & suppose t po9t 0 9 #ae deg4 ,n latitude4 ,& suppose at noon ! c5t] ( ! sun 0 directly ov] y1 i4e41 ! c5t] ( ! sun & y\r z5i? 7 "o & ! same po9t4 ,!n ! decl9ation ( ! sun at t mom5t w\ld be #ae deg4 ,n4 ,9 o!r words1 y\r angul> di/ance f ! e>?'s equator 7:i* is ano!r way ( express+ y\r latitude7 w\ld be precisely ! same z ! angul> di/ance ( ! c5t] ( ! sun f ! cele/ial equator4 ,suppose y 7 /&+ directly on ! equator & ! c5t] ( ! sun 0 directly ov] y1 !n ! decl9ation ( ! sun w\ld be #j deg44 ,n[ if ! axis ( ! e>? 7 always p]p5dicul> to ! plane ( ! sun's orbit1 !n ! sun w\ld always be imm$iately ov] ! equator & ! sun's decl9ation w\ld always be #j deg44 ,b y "k t ! axis ( ! e>? is incl9$ to ! plane ( ! sun's orbit4 ,z ! e>?1 !n1 revolves ar\nd ! sun1 ! am\nt ( ! decl9ation increases & !n decreases accord+ to ! location ( ! e>? at any "o "t ) relation to ! sun4 ,on ,m>* #ba/ & ,sept4 #bcrd1 #aiai1 ! sun is directly ov] ! equator & ! decl9ation is #j deg44 ,f ,m>* #ba/ to ,june #ba/ ! sun is com+ ,nor? & ! decl9ation is increas+ until on ,june #ba/--#ab h\rs--x rea*es its highe/ decl9ation4 ,f !n on ! sun />ts to travel ,s\?1 crosses ! equator on ,sept4 #bc;d & rea*es its highe/ decl9ation 9 ,s\? latitude on ,dec4 #bbnd1 :5 x />ts to come ,nor? aga94 ,?is expla9s easily ! l5g? ( days4 ,:5 ! sun is 9 ,nor? latitude1 x is ne>] our z5i?1 i4e41 high] 9 ! heav5s4 ,x c1 !re=e1 be se5 = a long] "t dur+ ! #bd h\rs t x takes ! e>? to revolve on its axis4 ,h5ce1 :5 ! sun rea*es its highe/ decl9ation 9 ,nor? latitude--,june #ba/--i4e41 :5 x is f>!/ ,nor? f ! equator & ne>e/ our z5i? 7:i* is 9 #dj deg4 ,n latitude7 x c be se5 = ! longe/ l5g? ( "t4 ,9 o!r words1 t day is ! longe/ ( ! ye>4 ,= ! same reason1 ,dec4 #bbnd1 :5 ! sun rea*es its highe/ decl9ation 9 ,s\? latitude1 i4e41 :5 x is f>!/ away to ! ,s\?1 is ! %orte/ day 9 ! ye> = u2 = on t day1 ! sun be+ f>!/ away f our z5i? & h5ce l[e/ d[n t[>d ! horizon1 c be se5 = ! %orte/ l5g? ( "t4 ,put 9 y\r ,note-,book3 ,nor? ,decl9ation is express$ 4 ,s\? ,decl9ation is express$ ---4 ,n[ turn to page #f ( ! ,nautical ,almanac4 ,y w see opposite ,jan4 #a/ #j;h1 a decl9ation ( --#bc deg4 #d4b'4 ,e calculation 9 ?is ,almanac is bas$ on "t at ,gre5wi*1 i4e41 ,g4,m4,t4 ,s at #j;h ,jan4 #a/ at ,gre5wi*--t is at noon--! ,sun's decl9ation is ,s #bc deg4 #d4b'4 ,y le>n$ 9 ! lecture ! o!r day on sol> "t1 t ! diff]5ce betwe5 mean "t & app>5t "t 0 call$ ! equation ( "t4 ,?is equation ( "t1 ) ! sign %[+ 9 :i* way x is to be appli$1 is giv5 = any m9ute ( any day 9 ! column m>k$ ,equation ( ,"t4 ,y w also notice t !re is an ,h4,d4 = equations ( "t j z !re is = ea* decl9ation1 & ?is ,h4,d4 %\ld be us$ :5 f9d+ ! equation ( "t = an odd h\r4 ,put 9 y\r ,note-,book3 #a4 ,! equation ( "t is to be appli$ z giv5 9 ! ,nautical ,almanac :5 *ang+ ,mean ,"t into ,app>5t ,"t4 #b4 ,:5 *ang+ ,app>5t ,"t into ,mean ,"t1 rev]se ! sign z giv5 9 ! ,nautical ,almanac4 ,t is all !re is to f9d+ sun "t1 ei!r mean or app>5t1 = any in/ant ( any day 9 ! ye> #aiai4 ,d n =get1 h[ev]1 t all ?is data is bas$ ^u ,gre5wi* ,mean ,"t4 ,to f9d ,local ,mean ,"t y mu/ apply ! ,longitude y are 94 ,to f9d ,local ,app>5t ,"t y mu/ fir/ secure ,g4,a4,t4 f ,g4,m4,t4 & !n apply ! ,longitude4 7,note to ,in/ructor3 ,make ! class "w out conv]sions "h if y h "t to d s & c f9i% ! re/ ( ! lecture by ! end ( ! p]iod47 ,s mu* = "t by ! sun4 ,n[ let u exam9e "t by ! />s--sid]eal "t4 ,turn to pages #b-c4 ,!re y f9d ! ,"r ,asc5sion ( ! ,mean ,sun at ,gre5wi* ,mean ,noon = e day 9 ! ye>4 ,y rememb] t1 r\ghly speak+1 ! ,sun's ,"r ,asc5sion 0 ! di/ance 9 "t ! sun 0 f ! ,fir/ ,po9t ( ,aries4 ,s ^! tables give t di/ance 7express$ 9 "t7 = noon at ,gre5wi* ( e day4 ,= ! correction to be appli$ = all "t aft] noon at ,gre5wi* 7i4e41 774,c4,p471 use ! table at ! bottom ( ! page4 ,= in/ance1 ! 7474,r4,a4 at ,gre5wi* #i;h #bdm on ,jan4 #a/ w\ld be 7474,r4,a4 #ah;h--#djm--#bas 774,c4,p4 #a #cc -------------- #ah;h--#dam--#eds ,n[ we mu/ g back to "s ( ! =mulas we le>n$ :5 discuss+ /> "t & apply !m ) ! in=mation we n[ h f ! ,nautical ,almanac4 ,if ! ,g4,m4,t4 on ,april #bj? is #d;h--#afm--#cjs1 :at is ! ,g4,s4,t4 = ! same mom5t8 ,t is1 :5 ,gre5wi* is #d;h--#afm--#cjs f ! sun1 h[ f> is ,gre5wi* f ! ,fir/ ,po9t ( ,aries8 ,y rememb] ! =mula 0 ,g4,s4,t4 ,g4,m4,t4 7474,r4,a4 774,c4,p4 ,g4,m4,t4 #d;h--#afm--#cjs 7474,r4,a4 #a --#ej -- #f 774,c4,p4 #j--db -------------- ,g4,s4,t4 #f;h--#jgm--#ahs ,suppose y 7 9 ,lo4 #gd deg4 ,w4 ,:at w\ld be ! ,r4,a4,m4 7,l4,s4,t478 ,y rememb] ! =mula = ,l4,s4,t4 f ,g4,s4,t4 0 ! same relatively z ,l4,m4,t4 f ,g4,m4,t41 i4e41 ,l4,s4,t4 ,g4,s4,t4 - ,w4 ,lo4 ,e4 ,lo1 ,"h x w\ld be ,g4,s4,t4 #f;h--#jgm--#ahs 7#gd deg4 ,w7 - #d --#ef --#jj --------------- ,l4,s4,t4 #a;h--#aam--#ahs ,n[ ^! are n a collection ( ab/ruse =mulas t y are le>n+ j = ! sake ( practice4 ,!y are us$ e cle> night on bo>d %ip1 or %\ld be1 & are j z vital to "k z "t by ! sun4 ,suppose y are at sea 9 ,lo4 #gj deg4 ,w & y\r ,,ct is ,octob] #bj? #f;h--#dm--#cjs ,a4,m41 ,,cc #bm--#cjs fa/4 ,y wi% to get ! ,r4,a4 ( y\r ,m1 i4e41 ! ,l4,s4,t4 ,h[ w\ld y g ab\t x8 ,! fir/ ?+ to d w\ld be to get y\r ,g4,m4,t4 ,x is ,,ct--,,cc4 #bj;d--#jf;h--#jdm--#cjs ,a4,m4 --#ab ------------------ ,,ct #ai;d--#ah;h--#jdm--#cjs ,,cc --#jb --#cj ------------------ ,g4,m4,t4 #ai;d--#ah;h--#jbm--#jjs ,!n get y\r ,g4,s4,t4 ,oct4 #ai;d--#ah;h--#jbm--#jjs 7474,r4,a4 #ac --#dg --#ch4e 774,c4,p #b --#eg4g -------------------- #ai;d--#ca;h--#ebm--#cf4bs --#bd -------------------- ,g4,s4,t4 #ai;d-- #g;h--#ebm--#cf4bs ,!n get y\r ,l4,s4,t4 ,g4,s4,t4 #g;h--#ebm--#cf4bs ,w4,lo 7--7 #d --#dj -------------- ,l4,s4,t4 #c;h--#abm--#cf4bs ,! la/ fact to "k at ?is "t ab\t ! ,almanac is f\nd on pages #id-ie4 ,"h is giv5 a li/ ( ! bright] />s ) _! positions respectively 9 ! heav5s1 i4e41 _! cele/ial longitude or ,r4,a4 on page #id & _! cele/ial latitude or decl9ation on page #ie4 ,^! />s h v little app>5t motion4 ,!y are practically fix$4 ,h5ce1 _! position 9 ! heav5s is almo/ ! same f ,janu>y to ,decemb] ?\gh1 ( c\rse1 _! position ) relation to y is con/antly *ang+1 s9ce y on ! e>? are con/antly mov+4 ,! relation%ip betwe5 ^! v>i\s k9ds ( "t is cle>ly express$ by ! foll[+ diagram1 :i* put 9 y\r ,note ,book3 ,illu/ration3 ,go+ ) arr[1 add4 ,go+ aga9/ arr[1 subtract4 ,assign = read+ 9 ,b[dit*1 ,articles #bid-bie-bif-big-bii-cjj-cja-cjb-cjc-cjd -cje-cjf-cjg4 ,if any "t is left1 h ! class "w out su* examples z ^!3 #a4 ,g4,m4,t4 ,june #bj?1 #aiai1 #e;h--#adm--#cis4 ,9 ,lo4 #fh deg4 #di' ,w4 ,requir$ ,l4,s4,t41 ,g4,s4,t41 ,l4,m4,t41 ,l4,a4,t4 #b4 ,l4,m4,t4 ,oct4 #ae?1 #aiai1 #f;h--#cjm--#bjs ,a4,m4 ,9 ,lo4 #di deg4 #ce' #af ,e4 ,requir$ ,l4,s4,t4 #c4 ,l4,m4,t4 ,may #ad?1 #aiai1 #aj;h--#aem4--#bjs ,a4,m4 ,lo4 #ef deg4 #ba' #ci ,w4 ,requir$ ,l4,a4,t4 #d4 ,w4,t4 ,april #bj?1 #aiai1 #aa;h--#cjm--#ads ,c-,w #b;h--#adm--#eis ,,cc #dm--#cjs sl[4 ,9 ,lo4 #hi deg4 #dh' #cj ,w4 ,requir$ ,g4,m4,t41 ,g4,a4,t41 ,l4,m4,t41 ,l4,a4,t41 ,g4,s4,t41 ,l4,s4,t4 #e4 ,:at is ,decl9ation & ,r4,a4 on ,may #ae?1 #aiai1 ( ,pol>is1 ,arcturus1 ,capella1 ,regulus1 ,altair1 ,d5eb1 ,vega1 ,aldeb>an8 #f4 ,:at is ! sun's decl9ation & ,r4,a41 ,"t at ,gre5wi*1 ,july #cj?3 #g;h--#adm--#cis ,a4,m4 #d;h--#bim--#ads ,a4,m4 #c;h--#jdm--#jfs #aa;h--#dim--#eis #b;h--#adm--#cjs ,a4,m48 ,,saturday ,,lecture ,,correction ,,( ,,obs]v$ ,,altitudes ,! true altitude ( a heav5ly body is ! angul> di/ance ( its c5t] z measur$ f ! c5t] ( ! e>?4 ,! obs]v$ altitude ( a heav5ly body z se5 at sea by ! sextant may be conv]t$ to ! true altitude by ! application ( ! foll[+ f\r corrections3 ,dip1 ,refraction1 ,p>allax & ,semi-diamet]4 ,dip ( ! horizon means an increase 9 ! altitude caus$ by ! elevation ( ! eye above ! level ( ! sea4 ,! foll[+ diagram illu/rates ?is cle>ly3 ,illu/ration ,if ! eye is on ! level ( ! sea at ,a1 x is 9 ! plane ( ! horizon ,,cd1 & ! angles ,,eac & ,,ead are "r angles or #ij deg4 ea*4 ,if ! eye is elevat$ above ,a1 say to ,b1 x is pla9 t ! angles ,,ebc & ,,ebd are great] ?an "r angles1 or 9 o!r words1 t ! obs]v] sees m ?an a semi-circle ( sky4 ,h5ce all measurem5ts made by ! sextant are too l>ge4 ,9 o!r words1 ! elevation ( ! eye makes ! angle too great & !re=e ! correction = dip is always subtract$4 ,refraction is a curv+ ( ! rays ( light caus$ by _! ent]+ ! e>?'s atmosph]e1 :i* is a d5s] m$ium ?an ! v light e!r ( ! out] sky4 ,! effect ( refraction is se5 :5 an o> is ?ru/ into ! wat] & looks z if x 7 b5t4 ,refraction always causes a cele/ial object to appe> high] ?an x really is4 ,?is refraction is greate/ at ! horizon & dim9i%es t[>d ! z5i?1 :]e x disappe>s4 ,table #bj;,a 9 ,b[dit* gives ! correction = mean refraction4 ,x is always subtract$ f ! altitude4 ,9 ! high] altitudes1 select ! correction = ! ne>e/ degree4 ,y %\ld avoid tak+ l[ altitudes 7#ae deg4 or less7 :5 ! atmosph]e is n p]fectly cle>4 ,haz9ess increases refraction4 ,p>allax is simply ! diff]5ce 9 angul> altitude ( a heav5ly body z measur$ f ! c5t] ( ! e>? & z measur$ f ! correspond+ po9t on ! surface ( ! e>?4 ,p>allax is greate/ :5 ! body is 9 ! horizon1 & disappe>s :5 x is at ! z5i?4 ,illu/ration ,:5 ! angul> altitude ( ! sun 9 ?is diagram is #j1 ! p>allax ,,abc is greate/4 ,:5 ! altitude is highe/ !re is no p>allax4 ,! sun is s f> away t its p>allax nev] exce$s #i4 ,! />s h practically none at all f ! e>?'s surface4 ,p>allax is always to be add$ 9 ! case ( ! sun4 ,! semi-diamet] ( a heav5ly body is half ! angle subt5d$ by ! diamet] ( ! visible disk at ! eye ( ! obs]v]4 ,= ! same body1 ! ,,sd v>ies ) ! di/ance4 ,?us1 ! diff]5ce ( ! sun's ,,sd at diff]5t times ( ! ye> is due to ! *ange ( ! e>?'s di/ance f ! sun4 ,illu/ration ,! ,,sd is to be add$ to ! obs]v$ altitude 9 case ! l[] limb is br\ght 9 contact ) ! horizon1 & subtract$ if ! upp] limb is us$4 ,probably mo/ ( ! sights y take w be ( ! sun's l[] limb1 i4e41 :5 ! l[] limb is br\ght 9 contact ) ! horizon1 s all y ne$ to rememb] is t 9 t ev5t ! ,,sd is additive4 ,n[ at fir/ we w correct altitudes by apply+ ea* correction sep>ately1 b z soon z y get ! idea1 !re is a %ort way to apply all f\r corrections at once4 ,?is is done 9 ,table #df4 ,h[ev]1 disreg>d t = ! mom5t4 ,put ?is 9 y\r ,note-,book3 ,dip is -4 ,table #ad ,b[dit* ,refraction is -4 #bj ,a ,b[dit* ,p>allax is 4 #af ,b[dit* ,s4,d4 is 4 ,nautical ,almanac ,obs]v$ altitude ( ,sun's l[] limb is express$ 774 ,true altitude is express$ -7-7-4 ,rememb] t be=e an obs]vation is at all accurate1 x mu/ be correct$ to make x a true altitude4 ,rememb] also t ! ,,ie mu/ be appli$1 9 addition to ^! o!r corrections1 9 ord] to make ! obs]v$ altitude a -7-7- altitude4 ,s !re are really five corrections to make in/ead ( f\r1 provid+1 ( c\rse1 y\r sextant has an ,,ie4 ,examples3 #a4 ,june #bj?1 #aiai1 obs]v$ altitude ( 77 #fi deg4 #be' #cj4 ,,ie #b' #cj4 ,,he #af ft4 ,requir$ -7-7-4 #b4 ,april #ae?1 #aiai1 obs]v$ altitude ( 77 #eh deg4 #bi' #dj4 ,,ie - #b' #cj4 ,,he #ah ft4 ,requir$ -7-7-4 #c4 ,m>* #d?1 #aiai1 obs]v$ altitude ( 77 #dd deg4 #dd' #aj4 ,,ie - #d' #bj4 ,,he #bj ft4 ,requir$ -7-7-4 ,etc4 ,,week ,,iv--,,navigation ,,tuesday ,,lecture ,,! ,,l9e ,,( ,,position ,x is practically impossible to fix y\r position exactly by "o obs]vation ( any cele/ial body4 ,! mo/ y c expect f "o sight is to fix y\r l9e ( position1 i4e41 ! l9e some:]e along :i* y are4 ,if1 = in/ance1 y c get a sight by sextant ( ! sun1 y may be able to "w out f ?is sight a v accurate calculation ( :at y\r latitude is4 ,say x is #ej deg4 ,n4 ,y are practically c]ta91 !n1 t y are some:]e 9 latitude #ej deg4 ,n1 b j :]e y are y _c tell until y get ano!r sight = y\r longitude4 ,simil>ly1 y may be able to fix y\r longitude1 b n be able to fix y\r latitude until ano!r sight is made4 ,cele/ial ,navigation1 !n1 r$uces itself to secur+ l9es ( position & by manipulat+ ^! l9es ( position 9 a way to be describ$ lat]1 s t !y int]sect4 ,if1 = in/ance1 y "k y are on "o l9e runn+ ,nor? & ,s\? & on ano!r l9e runn+ ,ea/ & ,we/1 ! only spot :]e y c be on bo? l9es is :]e !y int]sect4 ,?is diagram w make t cle>3 ,illu/ration ,illu/ration ,j :at a l9e ( position is w n[ be expla9$4 ,:]ev] ! sun is1 x mu/ be p]p5dicul>ly above ! same spot on ! surface ( ! e>? m>k$ 9 ! accompany+ diagram by ,s & suppose a circle be drawn ar\nd ?is spot z ,,abcde4 ,!n if a man at ,a takes an altitude1 he w get precisely ! same "o z m5 at ,b1 ,c1 ,d1 & ,e1 because !y are all at equal di/ances f ! sun1 & h5ce on ! circumf]5ce ( a circle ^: c5t] is ,s4 ,conv]sely1 if sev]al obs]v]s situat$ at diff]5t p>ts ( ! e>?'s surface take simultane\s altitudes1 & ^! altitudes are all ! same1 !n ! obs]v]s mu/ all be on ! circumf]5ce ( a circle & only "o circle4 ,if !y are n on t circle1 ! altitude !y take w be great] or less ?an ! "o 9 "q4 ,illu/ration ,n[ su* a circle on ! surface ( ! e>? w\ld be v l>ge--s l>ge t a small arc ( its circumf]5ce1 say #be or #cj miles1 w\ld be practically a /raight l9e4 ,suppose ,s to be ! po9t ov] :i* ! sun is v]tical & ,,gf "p ( ! circumf]5ce ( a circle drawn ar\nd ! po9t4 ,suppose y 7 at ,b & f an altitude ( ! sun1 tak5 by sextant1 y work$ out y\r position4 ,y w\ld f9d y\rself on a little arc ,,abc :i*1 = all purposes 9 ,navigation1 is a /raight l9e at "r angles to ! true be>+ ( ! sun f ! po9t ,s4 ,y c readily see ?is f ! above diagram4 ,suppose y\r obs]v] is at ,h4 ,8 l9e is ,,ghi1 :i* is aga9 a /raight l9e at "r angles to ! true be>+ ( ! sun4 ,he is n c]ta9 he is at ,h4 ,he may be at ,g or ,i4 ,he kn[s1 h[ev]1 he is some:]e on ! l9e ,,ghi1 ?\gh :]e he is on t l9e he _c tell exactly4 ,t l9e ,,ghi or ,,abc or ,,def is ! l9e ( position & su* a l9e is call$ a ,sumn] ,l9e1 aft] ,capt4 ,?omas ,sumn]1 :o expla9$ ! !ory "s #de ye>s ago4 ,put 9 y\r ,note-,book3 ,any p]son tak+ an altitude ( a cele/ial body mu/ be1 = all practical purposes1 on a /raight l9e :i* is at "r angles to ! true be>+ ( ! body obs]v$4 ,x %\ld be p]fectly cle> n[ t if ! sun be>s due ,nor? or ,s\? ( ! obs]v]1 i4e41 if ! sun is on ! obs]v]'s m]idian1 ! result+ l9e ( position mu/ run due ,ea/ & ,we/4 ,9 o!r words x is a p>allel ( latitude4 ,& t expla9s :y a noon obs]vation is ! be/ ( ! day = gett+ y\r latitude accurately4 ,aga91 if ! sun be>s due ,ea/ or ,we/ ! l9e ( position mu/ be> due ,nor? & ,s\?4 ,& t expla9s :y a morn+ or aft]noon sight--ab\t #h-i ,a4,m4 or #c-d ,p4,m41 if ! sun be>s ei!r ,ea/ or ,we/ respectively1 is ! be/ "t = det]m9+ y\r ,nor? & ,s\? l9e1 or longitude4 ,n[ suppose y take an obs]vation at #h ,a4,m4 & y are n sure ( y\r ,d4,r4 latitude4 ,y\r #h ,a4,m4 position :5 ! sun 0 ne>ly due ,ea/1 w give1 y an almo/ accurate ,nor? & ,s\? l9e & longitude4 ,suppose t f #h ,a4,m4 to noon y sail$ ,,ne #fj miles4 ,suppose at noon y get ano!r obs]vation4 ,t w give y an ,ea/ & ,we/ l9e1 = !n ! sun be>s true ,nor? & ,s\?4 ,an ,ea/ & ,we/ l9e is y\r correct latitude4 ,n[ y h an #h ,a4,m4 obs]vation :i* is ne>ly correct = longitude & a noon position :i* is correct = latitude4 ,h[ c y comb9e ! two s z to get accurately bo? y\r latitude & longitude8 ,put 9 y\r ,note-,book3 ,?r\gh ! #h ,a4,m4 position1 draw a l9e on ! *>t at "r angles to ! sun's true be>+4 ,suppose ! sun bore true ,e #a_/b ,s4 ,!n y\r l9e ( position w\ld run ,n #a_/b ,e4 ,m>k x #a/ ,position ,l9e4 ,illu/ration ,n[ draw a l9e runn+ due ,ea/ & ,we/ at "r angles to ! ,n-,s noon be>+ ( ! sun & m>k ?is l9e ,second ,position ,l9e4 ,advance y\r ,fir/ ,position ,l9e ! true c\rse & di/ance sail$ f #h ,a4,m4 to noon1 & ?r\gh ! extremity draw a ?ird l9e exactly p>allel to ! fir/ l9e ( position4 ,:]e a ?ird l9e 7! ,fir/ ,position ,l9e advanc$7 int]sects ! ,second ,position ,l9e1 w be y\r position at noon4 ,x _c be any o!r if y\r calculations are correct4 ,y knew y 7 some:]e on y\r #h ,a4,m4 l9e1 y "k y are some:]e on y\r noon l9e1 & ! only spot :]e y c be on bo? at once is ! po9t :]e !y int]sect4 ,y don't necess>ily h to wait until noon to "w two l9es4 ,y c d x at any "t if a suffici5t int]val ( "t betwe5 sights is all[$4 ,! :ole matt] simply resolves itself into gett+ y\r two l9es ( position1 hav+ !m int]sect & tak+ ! po9t ( int]section z ! position ( y\r %ip4 ,!re is "o o!r way to get two l9es to int]sect & x is "o ( ! be/ ( all = fix+ y\r position accurately4 ,x is by gett+ l9es ( position by obs]vation ( two />s4 ,if1 = in/ance1 y c get two />s1 "o ,ea/ & ! o!r ,we/ ( y1 y c take obs]vations ( bo? s closely toge!r z to be practically simultane\s4 ,!n y\r ,ea/]ly /> w\ld give y a l9e l ,,aa' & ! we/]ly /> ! l9e ,,bb' & y w\ld be at ! int]section ,s4 ,illu/ration ,assign = read+3 ,articles 9 ,b[dit* #cba-cbb-cbc-cbd4 ,sp5d ! re/ ( ! p]iod 9 gett+ times f ! ,n4 ,a41 gett+ true altitudes f obs]v$ altitudes1 work+ examples 9 ,m]cator sail+1 etc4 ,,w$nesday ,,lecture ,,latitude ,,by ,,m]idian ,,altitude ,a m]idian altitude is an altitude tak5 :5 ! sun or o!r cele/ial body obs]v$ be>s true ,s\? or ,nor? ( ! obs]v] or directly ov]head4 ,9 o!r words1 :5 ! cele/ial body is on y\r m]idian & y take an altitude ( ! body by sextant at t in/ant1 ! altitude y get is call$ a m]idian altitude4 ,9 ! case ( ! sun1 su* a m]idian altitude is at app>5t noon4 ,n[ latitude is always secur$ mo/ accurately at noon by means ( y\r m]idian altitude4 ,! reason = ?is 0 expla9$ 9 ye/]day's lecture4 ,! g5]al =mula = latitude by m]idian altitude is 7,put 9 y\r ,note-,book73 ,latitude by m]idian altitude ,z5i? ,di/ance 7,,zd7 - ,decl9ation 7,dec74 ,z5i? di/ance is ! di/ance 9 degrees1 m9utes & seconds f y\r z5i? to ! c5t] ( ! obs]v$ body4 ,= simplicity's sake1 we w consid] ! sun only z ! obs]v$ body4 ,!n ! z5i? di/ance is ! di/ance f y\r z5i? to ! c5t] ( ! sun4 ,n[ suppose t y & ! sun are bo? ,nor? ( ! equator & y are ,nor? ( ! sun4 ,if y c det]m9e exactly h[ f> ,nor? y are ( ! sun & h[ f> ,nor? ! sun is ( ! equator1 y w1 by add+ ^! two measurem5ts toge!r1 "k h[ f> ,nor? ( ! equator y are1 i4e41 y\r latitude4 ,z already expla9$1 ! decl9ation ( ! sun is its di/ance 9 degrees1 m9utes & seconds f ! equator & ! exact am\nt ( decl9ation is1 ( c\rse1 correct$ to ! prop] ,g4,m4,t4 ,y\r z5i? di/ance is ! di/ance 9 ! cele/ial sph]e y are f ! sun4 ,y "k t x is #ij deg4 f y\r z5i? to ! horizon4 ,y\r z5i? di/ance1 !re=e1 is ! diff]5ce betwe5 ! true m]idian altitude ( ! sun1 obta9$ by y\r sextant1 & #ij deg44 ,h5ce1 hav+ secur$ ! true m]idian altitude ( ! sun1 y h only to subtract x f #ij deg4 to f9d y\r z5i? di/ance1 i4e41 h[ f> y are f ! sun4 ,?is diagram w make ! :ole matt] cle>3 ,illu/ration3 ,a ,b 7,sun7 _/ _/ _/ _/ -_/- _/ #ij deg4 _/ ------v---------------------- ,c ,a ,z5i?1 ,b ,sun1 ,c ,horizon4 ,! arc ,,abc measures #ij deg44 ,t is ! di/ance f y\r z5i? to ! horizon4 ,n[ if ,,bc is ! true m]idian altitude ( ! sun at noon1 #ij deg4-,,bc or ,,ab is y\r z5i? di/ance4 ,if ,,bc measures by sextant #fj deg41 ,,ab measures #ij deg4-#fj deg4 or #cj deg44 ,?is #cj deg4 is y\r ,z5i? ,di/ance4 ,n[ suppose t f ! ,nautical ,almanac we f9d t ! ,g4,m4,t4 correspond+ to ! "t at :i* we measur$ ! m]idian altitude ( ! sun %[s ! sun's decl9ation to be #aj deg4 ,n4 ,well1 if y are #cj deg4 ,nor? ( ! sun1 & ! sun is #aj deg4 ,nor? ( ! equator1 y mu/ be #dj deg4 ,nor? ( ! equator or 9 latitude #dj deg4 ,n4 ,= t is all latitude is1 namely1 ! di/ance 9 degrees1 m9utes & seconds y are due ,nor? or ,s\? ( ! equator4 ,t is ! fir/ & simple/ case4 ,ano!r case is :5 y are some:]e 9 ,nor? latitude & ! sun's decl9ation is ,s\?4 ,!n ! situation w\ld1 r\ghly1 look l ?is3 ,illu/ration3 ,,bc ,altitude ( ! sun1 ,,ab ,z5i? ,di/ance & ,,db ,sun's ,decl9ation4 ,9 ?is case1 y\r di/ance ,nor? ( ! equator ,,ad w\ld be y\r z5i? di/ance ,,ab m9us ! sun's decl9ation ,,db4 ,?is diagram is n /rictly correct1 = ! obs]v]'s position on ! e>? #j appe>s to be ,s\? ( ! equator in/ead ( ,nor? ( ! equator4 ,t is because ! diagram is on a flat piece ( pap] in/ead ( on a globe4 ,s f> z illu/rat+ ! ,z5i? ,di/ance m9us ! ,decl9ation1 h[ev]1 ! diagram is correct4 ,! la/ case is :]e y are1 say1 #aj deg4 ,n ( ! sun 7y\r z5i? ,di/ance is #aj deg47 & ! sun is 9 #bj deg4 ,s decl9ation4 ,9 t case y w\ld h to subtract y\r z5i? di/ance f ! sun's decl9ation to get y\r latitude1 = ! sun's latitude 7its decl9ation7 is great] ?an y\rs4 ,n[ f ^! ?ree cases we d$uce ! foll[+ directions1 :i* put 9 y\r ,note-,book3 ,beg9 to measure ! altitude ( ! sun %ortly be=e noon4 ,by br++ its image d[n to ! horizon1 y c detect :5 its altitude /ops increas+ & />ts to decrease4 ,at t in/ant ! sun is on y\r m]idian1 x is noon at ! %ip1 & ! angle y read f y\r sextant is ! m]idian altitude ( ! sun4 ,to "w out y\r latitude1 "n ! m]idian altitude ,s if ! sun is s\? ( y & ,n if nor? ( y4 ,correct ! obs]v$ altitude to a true altitude by ,table #df4 ,if ! altitude is ,s1 ! ,z5i? ,di/ance is ,n or vice v]sa4 7,note to ,in/ructor3 ,if ! sun is ,s\? ( y1 y are ,nor? ( ! sun & vice v]sa47 ,correct ! decl9ation = ! prop] ,g4,m4,t4 z %[n by *ronomet] 7correct$74 ,if z5i? di/ance & decl9ation are bo? ,nor? or bo? ,s\?1 add !m & ! sum w be ! latitude1 ,n or ,s z indicat$4 ,if "o is ,n1 & ! o!r ,s1 subtract ! less f ! great] & ! result w be ! latitude 91 nam$ ,n or ,s aft] ! great]4 ,example3 ,at sea ,june #ae?1 obs]v$ altitude ( 77 #ga deg4 #ae' ,s1 ,,ie--#dg'1 ,,he #be ft4 ,,ct #c;h--#cdm--#aes ,p4,m4 ,requir$ latitude ( %ip4 77 #ga deg4 #ae' #jj ,s ,,ie -- #dg' ,corr4 -- #cf #bd ,,he #aj #cf ------------------- --------- -7-7- #gj deg4 #ch' #cf ,s ,corr4 -- #cf' #bd -- #ij #jj #jj ------------------- ,,zd #ai deg4 #ba' #bd ,n ,dec4 #bc #ag #ae ,n 7,g4,m4,t4 ,june #ae--c;h #cdm #aes7 ------------------- ,lat4 #db deg4 #ch' #ci ,n ------------------- ,assign = ,night ,"w or to be work$ 9 class room su* examples z ! foll[+3 #a4 ,june #a/1 #aiai4 77 #cc deg4 #ej' #jj ,s4 ,g4,m4,t4 #h;h #eem #dds4 ,,he #bj ft4 ,,ie #d' #c4 ,requir$ latitude 9 at noon4 #b4 ,april #bnd1 #aiai4 77 #ab deg4 #dd' #cj ,n4 ,,ct 0 #b;d #e;h #adm #cis ,a4,m41 :i* 0 #am #djs sl[ on ,m>* #a/ 7same ,,ct7 & #dm #bis fa/ on ,m>* #ae? 7same ,,ct74 ,,ie -- #b' #bj4 ,,he #bb ft4 ,requir$ latitude 9 at noon4 ,assign = ,night ,"w read+ also1 ! foll[+ ,articles 9 ,b[dit*3 #cdd & #bbc4 ,,?ursday ,,lecture ,,azimu?s ,,( ,,! ,,sun ,?is is a peculi> ^w to spell & pron\nce b its def9ition is really v simple4 ,put 9 y\r ,note-,book3 ,! azimu? ( a heav5ly body is ! angle at ! z5i? ( ! obs]v] =m$ by ! obs]v]'s m]idian & a l9e drawn to ! c5t] ( ! body obs]v$4 ,azimu?s are nam$ f ! latitude 9 & t[>d ! ,e 9 ! ,a4,m4 & f ! latitude 9 & t[>d ! ,w 9 ! ,p4,m4 ,all ?is def9ition means is t1 no matt] :]e y are 9 ,n latitude1 = in/ance1 if y face ,n1 ! azimu? ( ! sun w be ! true be>+ ( ! sun f y4 ,! same holds true = moon1 /> or planet1 b 9 ?is lecture we w say no?+ ( ! /> azimu?s =1 9 "s o!r respects1 !y are f\nd some:at diff]5tly f ! sun azimu?s4 ,put ?is 9 y\r ,note-,book3 ,to f9d an azimu? ( ! sun3 ,note ! "t ( tak+ ! azimu? by *ronomet]4 ,apply *ronomet] correction1 if any1 to get ! ,g4,m4,t4 ,conv]t ,g4,m4,t4 into ,g4,a4,t4 by apply+ ! equation ( "t4 ,conv]t ,g4,a4,t4 into ,l4,a4,t4 by apply+ ! longitude 9 "t4 ,! result is ,l4,a4,t4 or ,s4,h4,a4 ,) ! correct ,l4,a4,t41 latitude & decl9ation1 ent] ! azimu? tables to get ! sun's true be>+1 i4e41 its azimu?4 ,example3 ,m>* #ae?1 #aiai4 ,,ct #aj;h -- #dm -- #cbs4 ,d4,r4 latitude #dj deg4 #aj' ,n1 longitude #gd deg4 ,w4 ,f9d ! ,,tz4 ,g4,m4,t4 #aj;h--#jdm--#cbs ,eq4 ,t4 --#ji --#aj ,g4,a4,t4 #i;h--#eem--#bbs ,g4,a4,t4 #i;h--#eem--#bbs ,lo4 9 ,t4 #d --#ef --#jj 7,w--7 ,l4,a4,t4 #d;h--#eim--#bbs ,latitude & ,decl9ation opp4 "n4 ,,tz ,n #aja deg4 #cj',w ,we w take up lat] a fur!r use ( azimu?s to f9d ! error ( y\r compass4 ,"r n[ all y h to keep 9 m9d is :at an azimu? is & h[ y apply ! =mulas already giv5 y to get ! in=mation necess>y to ent] ! ,azimu? ,tables = ! sun's true be>+ at any "t ( ! a/ronomical day :5 ! sun c be se54 ,9 consult+ ^! tables x mu/ be rememb]$ t if y\r ,l4,a4,t4 or ,s4,h4,a4 is1 a/ronomically1 #bj;h 7,a4,m471 y mu/ subtract #ab h\rs 9 ord] to br+ ! "t )9 ! scope ( ^! tables :i* are arrang$ f app>5t six o'clock ,a4,m4 to noon & f app>5t noon to #f ,p4,m4 respectively4 ,we are tak+ up sun azimu?s today 9 ord] to get a ?or\gh und]/&+ ( !m be=e beg9n+ a discussion ( ! ,m>c ,/4 ,hilaire ,me?od :i* we w h tomorr[4 ,y mu/ get cle>ly 9 y\r m9ds j :at a l9e ( position is & h[ x is f\nd4 ,ye/]day ,i tri$ to expla9 :at a l9e ( position 01 i4e41 a l9e at "r angles to ! sun's or o!r cele/ial body's true be>+--9 o!r words1 a l9e at "r angles to ! sun's or o!r cele/ial body's azimu?4 ,today ,i tri$ to %[ y h[ to f9d y\r azimu? f ! azimu? tables = any h\r ( ! day4 ,tomorr[ we w />t to use azimu?s 9 work+ out sights = l9es ( position by ! ,m>c ,/4 ,hilaire ,me?od4 ,note to ,in/ructor3 ,sp5d ! re/ ( ! "t 9 f9d+ sun azimu?s 9 ! tables by work+ out su* examples z ^!3 #a4 ,april #bi?1 #aiai4 ,d4,r4 latitude #dj deg4 #dj' ,n1 ,longitude #gd deg4 #ee' #ad ,w4 ,,ct #aj;h--#adm--#bds4 ,,cc #dm--#cjs sl[4 ,f9d ,,tz4 #b4 ,may #ae?1 #aiai4 ,d4,r4 latitude #ai deg4 #bj' ,s1 ,longitude #dj deg4 #ae' #dd ,e4 ,,ct #aj;h--#ddm--#ees ,a4,m4 ,,cc #cm--#ajs fa/4 ,f9d ,,tz4 ,note to ,in/ructor3 ,if possible1 give m examples to f9d ,,tz & also "s examples on latitude by m]idian altitude4 ,assign = ,night ,"w read+ ! foll[+ ,articles 9 ,b[dit*3 #cga-cgb-cgc-cgd-cge4 ,also1 examples to f9d ,,tz4 ,,friday ,,lecture ,,m>c ,,/4 ,,hilaire ,,me?od ,,by ,a ,,sun ,,sight ,y h le>n$ h[ to get y\r latitude by an obs]vation at noon4 ,by ! ,m>c ,/4 ,hilaire ,me?od1 :i* we are to take up today1 y w le>n h[ to get a l9e ( position1 at any h\r ( ! day4 ,by hav+ ?is l9e ( position int]sect y\r p>allel ( latitude1 y w be able to e/abli% ! position ( y\r %ip1 bo? z to its latitude & longitude4 ,n[ y h already le>n$ t 9 ord] to get y\r latitude accurately1 y mu/ wait until ! sun is on y\r m]idian1 i4e41 be>s due ,nor? or ,s\? ( y1 & !n y apply a c]ta9 =mula to get y\r latitude4 ,:5 ! sun is on or ne> ! prime v]tical 7i4e41 due ,ea/ or ,we/7 y might apply ano!r set ( rules1 :i* y h n yet le>n$1 to get y\r longitude4 ,by ! ,m>c ,/4 ,hilaire me?od1 ! same set ( rules apply = gett+ a l9e ( position at any "t ( ! day1 no matt] :at ! position ( ! obs]v$ body 9 ! heav5s may be4 ,j "o condition is necess>y1 & ?is condition is necess>y 9 all calculations ( ?is "*1 i4e41 an accurate measurem5t ( ! obs]v$ body's altitude is ess5tial4 ,:at we d 9 work+ out ! ,m>c ,/4 ,hilaire me?od1 is to assume our ,dead ,reckon+ position to be correct4 ,) ?is ,d4 ,r4 position z a basis1 we compute an altitude ( ! body obs]v$4 ,n[ ?is altitude w\ld be correct if our ,d4 ,r4 position 7 correct & vice v]sa4 ,at ! same "t we measure by sextant ! altitude ( ! cele/ial body obs]v$1 say1 ! sun4 ,if ! comput$ altitude & ! actual obs]v$ altitude co9cide1 ! ,d4 ,r4 position is correct4 ,if !y d n1 ! comput$ altitude mu/ be correct$ & ! ,d4 ,r4 position correct$ to co9cide ) ! obs]v$ altitude4 ,j h[ ?is is done w be expla9$ 9 a mom5t4 ,put 9 y\r ,note-,book3 ,=mula = obta9+ ,l9e ( ,position by ,m4 ,/4 ,h4 ,me?od4 ,i4 ,?ree quantities mu/ be kn[n ei!r f obs]vation or f ,dead ,reckon+4 #a4 ,! ,s4 ,h4 ,a41 m>k$ t4 ,note3 ,! me?od = f9d+ ,s4 ,h4 ,a4 7t7 diff]s :5 ! sun or /> is us$ z foll[s3 7a7 ,= ! ,sun3 ,get ,g4,m4,t4 f ! correct$ *ronomet] "t4 ,apply ! equation ( "t to f9d ! ,g4,a4,t4 ,apply ! ,d4,r4 ,lo4 7-,w7 7,e7 & ! result is ,l4,a4,t4 or ,s4,h4,a4 z requir$4 7b7 ,= a ,/>3 7,note to pupils3 ,leave ?is blank to be fill$ 9 :5 we take up />s 9 m detail47 #b4 ,! ,latitude1 m>k$ ,l4 #c4 ,! ,decl9ation ( ! obs]v$ body1 m>k$ ,d4 ,,ii4 ,add toge!r ! log hav]s9e ( ! ,s4,h4,a4 7,table #de71 ! log cos9e ( ! ,lat4 7,table #dd71 & ! log cos9e ( ! ,dec4 7,table #dd7 & call ! sum ,s4 ,s is a log hav]s9e & mu/ always be less ?an #aj4 ,if great] ?an #aj1 subtract #aj or #bj to br+ x less ?an #aj4 ,,iii4 ,) ! log hav]s9e ,s ent] table #de 9 ! adjac5t p>allel column1 take out ! correspond+ ,natural ,hav]s9e1 :i* m>k ,n,s4 ,,iv4 ,f9d ! algebraic diff]5ce ( ! ,latitude & ,decl9ation1 & f ,table #de take out ! ,natural ,hav]s9e ( ?is algebraic diff]5ce angle4 ,m>k x ,n,d-,l ,v4 ,add ! ,n,s to ! ,n,d-,l1 & ! result w be ! ,natural ,hav]s9e ( ! calculat$ z5i? di/ance4 ,=mula ,n,,zd ,n,s ,n,d-,l ,,vi4 ,subtract ?is calculat$ z5i? di/ance f #ij deg4 to get ! calculat$ altitude4 ,,vii4 ,f9d ! diff]5ce betwe5 ! calculat$ altitude & ! true altitude & call x ! altitude diff]5ce4 ,,viii4 ,9 y\r ,azimu? ,table1 f9d ! azimu? = ! prop] t1 ,l & ,d4 ,,ix4 ,lay (f ! altitude diff]5ce along ! azimu? ei!r away f or t[>d ! body obs]v$1 accord+ z to :e!r ! true altitude1 obs]v$ by sextant1 is less or great] ?an ! calculat$ altitude4 ,illu/ration ,x4 ,?r\gh ! po9t ?us rea*$1 draw a l9e at "r angles to ! azimu?4 ,?is l9e w be y\r ,l9e ( ,position1 & ! po9t ?us rea*$1 :i* may be read f ! *>t or obta9$ by use ( ,table #b f ! ,d4 ,r4 ,position1 is ! ne>e/ to ! actual position ( ! obs]v] :i* y c obta9 by ! use ( any me?od f "o sight only4 ,example3 ,at sea1 ,may #ah?1 #aiai1 ,a4,m4 77 #bi deg4 #da' #jj4 ,d4,r4 ,latitude #da deg4 #cj' ,n1 ,longitude #cc deg4 #ch' #de ,w4 ,,wt #g;h #bjm #des ,a4,m4 ,c-,w #b;h #agm #jfs ,,cc #dm #eis4 ,,ie--#cj4 ,,he #bc ft4 ,requir$ ,l9e ( ,position & mo/ probable position ( %ip4 ,,wt #ah;d -- #g;h -- #bjm -- #des ,a4,m4 -- #ab ------------------------ ,,wt #ag;d -- #ai;h -- #bjm -- #des ,c-,w #b -- #ag -- #jf ,corr4 #i' #cd ------------------------ ,,ie -- #cj ,,ct #ag;d -- #ba;h -- #cgm -- #eas ------------ ,,cc #d -- #ei #i' #jd ------------------------ ,g4,m4,t4 #ag;d -- #ba;h -- #dbm -- #ejs 77 #bi deg4 #da' #jj ,eq4 ,t4 #c -- #dg #i #jd ------------------------ ------------ ,g4,a4,t4 #ag;d -- #ba;h -- #dfm -- #cgs -7-7- #bi deg4 #ej' #jd ,lo4 9 ,t #b -- #ad -- #ce 7,w--7 ------------------------ log hav #i4dhcfh ,l4,a4,t47t7 #ag;d -- #ai;h -- #cbm -- #jbs log cos #i4hgddf ,lat4 #da deg4 #cj' ,n log cos #i4igdgc ,dec4 #ai deg4 #ba' #be ,n -------- log hav ,s #i4ccbhg ,n s 4#baeba ,l - ,d #bb deg4 #jh' #ce ,n ,d - ,l 4#jcfhg -------- ,calc4 ,,zd #fj deg4 #af' #cj ,n ,,zd 4#bebjh -- #ij deg4 #jj #jj ------------- ,,tz f\nd f table to be ,cal4 ,alt4 #bi deg4 #dc' #cj ,n #ij deg4 ,e4 -7-7- #bi deg4 #ej' #jd ------------- ,alt4 ,diff #f' #cd ,t[>d4 ,c\rse4 ,di/4 ,diff4 ,lat4 ,dep4 ,diff4 ,lo4 #ij deg4 #f' #cd #j #f4e #h4f ,d4,r4 ,lat4 #da deg4 #cj' ,n ,d4,r4 ,lo4 #cc deg4 #ch' #de ,w ,diff4 ,lat4 -- ,diff4 ,lo4 #h #cf ,e ---------- ------------- ,mo/ probable fix ,lat4 #da deg4 #cj' ,n ,lo4 #cc deg4 #cj' #ji ,w ,z azimu? is ,n #ij deg4 ,e1 ,l9e ( ,position runs due ,n ,s 7#cfj deg47 ?r\gh ,lat4 #da deg4 #cj' ,n4 ,lo4 #cc deg4 #cj' #ji ,w4 ,assign = "w 9 class & = ,night ,"w examples su* z ! foll[+3 #a4 ,july #aa?1 #aiai4 77 #de deg4 #ce' #cj1 ,lat4 by ,d4 ,r4 #ej deg4 #jj' ,n1 ,lo4 #dj deg4 #jd' ,w4 ,,he #ae ft4 ,,ie--#d'4 ,,ct 7correct$7 #e;h4 #chm #jjs ,p4,m4 ,requir$ ,l9e ( ,position by ,m>c ,/4 ,hilaire ,me?od & mo/ probable fix ( %ip4 #b4 ,may #af?1 #aiai1 ,a4,m4 77 #fd deg4 #ja' #ae1 ,d4 ,r4 ,lat4 #ci deg4 #de' ,n1 ,lo4 #fj deg4 #bi' ,w4 ,,he #cf ft4 ,,ie #b' #cj4 ,,ct #b;h #ddm #ais4 ,requir$ ,l9e ( ,position by ,m>c ,/4 ,hilaire ,me?od & mo/ probable fix ( %ip4 ,etc4 ,,saturday ,,lecture ,,examples ,,on ,,m>c ,,/4 ,,hilaire ,,me?od ,,by ,a ,,sun ,,sight #a4 ,nov4 #a/1 #aiai4 ,a4,m4 at %ip4 ,,wt #i;h #djm #aes4 ,c--,w #d;h #edm #jjs4 ,d4 ,r4 ,lat4 #dj deg4 #ej' ,n1 ,lo4 #gc deg4 #ej' ,w4 77 #bg deg4 #ei'4 ,,he #ad ft4 ,requir$ ,l9e ( ,position by ,m>c ,/4 ,hilaire ,me?od & mo/ probable position ( %ip4 #b4 ,may #cj?1 #aiai4 ,p4,m4 at %ip4 ,d4 ,r4 ,lat4 #ch #ad' #cc ,n1 ,lo4 #ae deg4 #ch' #di' ,w4 ,! mean ( a s]ies ( obs]vations ( 77 0 #ci deg4 #je' #dj deg44 ,,ie--#ja' #jj4 ,,he #bg ft4 ,,wt #c;h #dm #dis4 ,c--,w #a;h #cim #ees4 ,c4,c4 fa/1 #jam #ebs4 ,requir$ ,l9e ( ,position by ,m>c ,/4 ,hilaire ,me?od1 & mo/ probable position ( %ip4 #c4 ,oct4 #ba/1 #aiai1 ,a4,m4 ,d4 ,r4 ,lat4 #dj deg4 #ab' #ch ,n1 ,lo4 #fi deg4 #dh' #ed ,w4 ,! mean ( a s]ies ( obs]vations ( 77 0 #ai deg4 #ba' #bj4 ,,ie #jb' #aj4 ,,he #bf ft4 ,,wt #g;h #ehm #dis4 ,c--,w #d;h #eam #des4 ,c4 sl[1 #jcm #jcs4 ,requir$ ,l9e ( ,position by ,m>c ,/4 ,hilaire ,me?od & mo/ probable position ( %ip4 #d4 ,june #a/1 #aiai1 ,p4,m4 at %ip4 ,lat4 ,d4 ,r4 #ce deg4 #bf' #ae ,s1 ,lo4 #aj deg4 #ai' #ej ,w4 ,w4,t4 #c;h #cjm #jjs4 ,c--,w #j;h #bjm #chs4 ,,cc #am #afs sl[4 77 #af deg4 #ae' #dj4 ,,ie #b' #aj4 ,,he #bf ft4 ,requir$ ,l9e ( ,position & mo/ probable fix ( %ip4 #e4 ,jan4 #e?1 #aiai4 ,a4,m4 ,d4 ,r4 ,lat4 #cf deg4 #bi' #ch ,n1 ,lo4 #ea deg4 #jg' #dd ,w4 ,! mean ( a s]ies ( obs]vations ( 77 0 #bc deg4 #ag' #bj4 ,,ie #ja' #ej4 ,,he #ai ft4 ,,wt #g;h #aam #cgs4 ,c--,w #e;h #eim #dis4 ,c4 sl[ #ehs4 ,requir$ ,l9e ( ,position & mo/ probable fix ( %ip4 ,,week ,v--,,navigation ,,tuesday ,,lecture ,a ,,%ort ,,talk ,,on ,,! ,,planets ,,& ,,/>s ,,id5tification ,,( ,,/>s #a4 ,! ,planets ,y %\ld acqua9t y\rself ) ! names ( ! planets & _! symbols4 ,^! c be f\nd opposite ,page #a 9 ! ,nautical ,almanac4 ,all ! planets diff] greatly 9 size & 9 physical condition4 ,?ree ( !m--,m]cury1 ,v5us & ,m>s--are some:at l ! e>? 9 size & 9 g5]al *>act]i/ics4 ,s f> z we "k1 !y are solid1 cool bodies simil> to ! e>? & l ! e>?1 surr\nd$ by atmosph]es ( cool vapors4 ,! out] planets on ! o!r h&1 i4e41 ,jupit]1 ,saturn1 ,uranus1 & ,neptune1 are trem5d\sly l>ge--_m times ! size ( ! e>?1 & resemble ! sun m ?an ! e>? 9 _! physical appe>ance & condition4 ,!y are globes ( gases & vapors s hot z to be practically self lum9\s4 ,!y probably conta9 a small solid nucleus1 b ! great] "p ( !m is no?+ b an imm5se gase\s atmosph]e fill$ ) m9ute liquid p>ticles & heat$ to an almo/ unbelievably high temp]ature4 ,( ! actual surface conditions on ,v5us & ,m]cury1 little is def9itely kn[n4 ,m]cury is a v difficult object to obs]ve on acc\nt ( its proximity to ! sun4 ,x is nev] visible at night2 x mu/ be exam9$ 9 ! twilight j be=e sunrise or j aft] sunset1 or 9 ! full daylight4 ,9 ei!r case ! gl>e ( ! sun r5d]s ! planet indi/9ct1 & ! heat ( ! sun di/urbs our atmosph]e s z to make accurate visibility almo/ impossible4 ,! surface ( ,m]cury is probably r\gh & irregul> & mu* l ! moon4 ,l ! moon1 too1 x has practically no atmosph]e4 ,m]cury rotates on its axis once 9 #hh days4 ,its day & ye> are ( ! same l5g?4 ,?us ! planet always pres5ts ! same face t[>d ! sun & on t side !re is p]petual day :ile on ! o!r side is night--unbrok5 & cold beyond all imag9ation4 ,v5us resembles ! e>? m ne>ly ?an any o!r heav5ly body4 ,its diamet] is )9 #abj miles ( ! e>?'s diamet]4 ,! exasp]at+ fact ab\t ,v5us1 h[ev]1 is t x is %r\d$ 9 deep banks ( cl\ds & vapors :i* make x impossible = u to secure any def9ite facts ab\t x4 ,! atmosph]e ab\t ,v5us is s d5se t sunlight is reflect$ f ! upp] surface ( ! cl\ds ar\nd ! planet & s rea*es our telescopes )\t hav+ p5etrat$ to ! surface at all4 ,f "t to "t m>k+s h be5 discov]$ t at fir/ seem$ real b :e!r !y are j cl\ds or tops ( m\nta9s has nev] really be5 e/abli%$4 ,( all ! planets1 we "k m ab\t ,m>s ?an any o!r4 ,& yet practically no?+ is actually kn[n 9 reg>d to conditions on ! surface ( ?is planet4 ,we d "k1 h[ev]1 t ,m>s m ne>ly resembles a m9iature ( our e>? ?an any o!r cele/ial body4 ,! diamet] ( ,m>s is #d1baj miles--almo/ exactly half ! e>?'s diamet]4 ,! surface area ( ,m>s is j ab\t equal to ! total area ( dry l& on ! e>?4 ,l ! e>?1 ,m>s rotates ab\t an axis incl9$ to ! plane ( its orbit1 & ! l5g? ( a ,m>tian day is v ne>ly equal to our own4 ,! late/ det]m9ations give ! l5g? ( a ,m>tian sol> day z #bd;h #cim #ces4 ,=tunately = u1 ,m>s is surr\nd$ by a v light & transp>5t atmosph]e ?r\gh :i* we are able to discov] ) our telescopes1 _m p]man5t facts4 ,! mo/ noticeable ( ^! are ! dazzl+ :ite pol> caps fir/ id5tifi$ by ,sir ,william ,h]s*el 9 #aghd4 ,dur+ ! long w9t] 9 ! nor!rn hemisph]e1 ! cap at ! ,nor? pole /eadily increases 9 size1 only to dim9i% dur+ ! next summ] "u ! hot rays ( ! sun4 ,^! discov]ies e/abli% )\t d\bt ! pres5ce ( vapors 9 ! ,m>tian atmosph]e :i* precipitate ) cold & evaporate ) heat4 ,! pol> caps1 !n1 are "s =m ( sn[ & ice or possible ho> fro/4 ,outside ! pol> caps ! surface ( ,m>s is r\gh1 unev5 & ( diff]5t colors4 ,"s ( ! d>k] m>k+s appe> to be long1 /raight holl[s4 ,!y are ! s-call$ canals discov]$ by ,s*iap>elli 9 #ahgg4 ,! t]m canal is an un=tunate "o4 ,! ^w implies ! exi/5ce ( wat] & ! pres5ce ( be+s ( suffici5t intellig5ce & me*anical ability to con/ruct elaborate works4 ,flamm>ion 9 ,france & ,l[ell 9 ! ,unit$ ,/ates claim ! ^w is correctly us$1 i4e41 t ^! m>k+s are really canals & t ,m>s is actually inhabit$4 ,! cons5sus ( op9ion among ! mo/ celebrat$ a/ronom]s is contr>y to ?is view4 ,mo/ a/ronom]s agree t ^! canals may n exi/ z drawn--t !y are to great ext5t due to defective vision4 ,!re is no conclusive pro( ( man-made "w on ,m>s1 nor ( ! exi/5ce ( consci\s life ( any k9d4 ,x may be !re b conclusive pro( ( x is /ill lack+4 #b4 ,! ,/>s ,! planets are (t5 call$ w&]]s 9 ! sky because ( _! ev] *ang+ position4 ,%>ply di/+ui%$ f !m1 !re=e1 are ! fix$ />s4 ,^! appe> z m]e po9ts ( light & always ma9ta9 ! same relative positions 9 ! heav5s4 ,?\s&s ( ye>s ago ! ,great ,dipp] hung 9 ! nor!rn sky j z x w hang tonight & z x w hang = ?\s&s ( ye>s to come4 ,yet ^! bodies are n actually fix$ 9 space4 ,9 reality !y are all 9 rapid motion1 "s mov+ "o way & "s ano!r4 ,x is _! trem5d\s di/ance f u t makes ?is motion inappreciable4 ,! sun seems f> away f u1 b ! ne>e/ /> is #bjj1jjj times z f> away f u z is ! sun4 ,express$ 9 miles1 ! figure is s huge z to be incompreh5sible4 ,a special unit has1 !re=e1 be5 inv5t$--a unit repres5t$ by ! di/ance trav]s$ by light 9 "o ye>4 ,9 "o second1 light travels ov] #ahf1jjj miles4 ,9 #h-a_/c m9utes1 light rea*es u f ! sun &1 9 do+ s1 cov]s ! di/ance t w\ld take ! ,vat]l& ov] f\r c5turies to travel4 ,yet ! ne>e/ /> is ov] f\r light ye>s di/ant--x is s f> away t x requires ov] f\r ye>s = its light to rea* u4 ,:5 y look at ! />s tonight y see !m1 n z !y are1 b z !y 71 ev5 c5turies ago4 ,pol>is1 = in/ance1 is di/ant "s sixty light ye>s4 ,_h x disappe>$ f ! heav5s at ! "t ,lee surr5d]$ to ,grant1 we %\ld /ill be see+ x & entirely unaw>e ( its disappe>ance4 ,n[ ea* /> 9 ! heav5s is 9 reality a sun1 i4e41 a va/ globe ( gas & vapor1 int5sely hot & 9 a cont9u\s /ate ( viol5t agitation1 radiat+ =? heat & light1 e pulsation ( :i* is felt ?r\gh\t ! univ]se4 ,s closely inde$ d _m ( ! />s resemble ! sun1 t ! light :i* !y emit _c be di/+ui%$ f sunlight4 ,"s ( !m are l>g] & hott] ?an ! sun--"s small] & cool]4 ,yet ! sun we see c be reg>d$ z a typical /> & f our k ( x we c =m a fairly correct idea ( ! nature & *>act]i/ics ( ^! o!r />s4 ,anyone kn[s t ! />s v>y 9 brightness4 ,"s ( ?is v>iation is due p>tly to actual diff]5ces among ! />s !mselves & p>tly to v>y+ di/ances4 ,if all ! />s 7 alike1 !n ^? :i* 7 f>!/ away w\ld be fa9te/ & we c\ld judge a />'s di/ance by its brilliancy4 ,?is is n ! case1 h[ev]4 ,"s ( ! m brilliant />s are f> m di/ant ?an "s ( ! fa9t] ones4 ,!re are />s ne> & remote & an app>5tly fa9t /> may 9 reality be l>g] & m brilliant ?an a /> ( ! fir/ magnitude4 ,vega1 = in/ance1 is inf9itely f>!r away f u ?an ! sun1 yet its brightness is m ?an #ej times t ( ! sun4 ,pol>is1 /ill f>!r away1 has #ajj times ! light & heat ( ! sun4 ,9 fact ! sun1 consid]$ z a />1 is relatively small & feeble4 #c4 ,id5tification ( ,/>s ,only ! bright] />s c be us$ 9 navigation4 ,s mu* light is lo/ 9 ! d\ble reflection 9 ! mirrors ( ! sextant1 t />s fa9t] ?an ! ?ird magnitude c seldom be obs]v$4 ,?is r$uces ! numb] ( />s available = navigation to )9 v n>r[ limits1 = !re are only #adb />s all told :i* are ( ! ?ird magnitude or bright]4 ,! ,nautical ,almanac gives a li/ ( "s #aej />s :i* may be us$1 b z a matt] ( fact1 ! li/ might be r$uc$ to "s #ej or #fj )\t s]i\s detrim5t to ! practical navigator4 ,ab\t #cj ( ^! are ( ! second magnitude or great] & h5ce easily f\nd4 ,x is n difficult to le>n to "k #cj or #dj ( ! bright] />s1 s t !y c be recogniz$ at any "t4 ,to aid 9 locat+ ! />s1 _m diff]5t /> *>ts & atlases h be5 publi%$1 b mo/ ( !m are s elaborate t !y confuse z mu* z !y help4 ,! simpl] ! *>t1 ! few] />s x pret5ds to locate1 ! bett] = practical purposes4 ,also1 all *>ts are ( necessity pr9t$ on a flat surface & su* a surface c nev] repres5t 9 _! true values1 all p>ts ( a sph]e4 ,a *>t1 !re=e1 :i* cov]s a l>ge "p ( ! heav5s1 is b\nd to give a di/ort$ idea ( di/ances or directions 9 "s "p ( ! sky & mu/ be us$ ) caution4 ,!re are a few />s :i* =m /rik+ figures ( "o k9d or ano!r4 ,^! c always be easily locat$ & =m a />t+ po9t1 s to speak1 f :i* to beg9 a se>* = o!r />s4 ,( ^! gr\ps ! ,great ,dipp] is ! mo/ prom95t 9 ! nor!rn sky & beg9n+ ) ?is ! o!r con/ellations c be locat$ "o by "o4 ,:5 ! gr\ps or con/ellations are n kn[n1 !n any individual /> c be readily f\nd by means ( its ,"r ,asc5sion1 & ,decl9ation4 ,z y h already le>n$1 ,decl9ation is equival5t to latitude on ! e>? & ,"r ,asc5sion practically equival5t to longitude on ! e>?1 except t :]eas longitude on ! e>? is measur$ ,e4 & ,w4 f ,gre5wi*1 ,"r ,asc5sion is measur$ to ! ea/ all ! way ar\nd ! sky1 f ! ,fir/ ,po9t ( ,aries4 ,) ?is 9 m9d1 y c easily see t if a />'s ,r4,a4 is less ?an y\rs1 i4e41 less ?an ,l4,s4,t4 or ! ,r4,a4 ( y\r ,m]idian1 ! /> is n z f> ea/w>d 9 ! heav5s1 z is y\r z5i?4 ,9 o!r words x is to ! we/ ( y4 ,& vice v]sa1 if ! ,/>'s ,r4,a4 is great] ?an y\rs1 ! ,/> is m to ! ea/w>d ?an y & h5ce to ! ea/ ( y4 ,moreov]1 z ,r4,a4 is reckon$ all ar\nd a circle & 9 h\rs1 ea* h\r's diff]5ce betwe5 ! ,/>'s ,r4,a4 & y\rs is #a_/bd ( #cfj deg4 or #ae deg44 ,h5ce if a />'s ,r4,a4 is1 = in/ance1 #b h\rs great] ?an y\rs1 ! /> w be f\nd to ! ea/ ( y\r m]idian & approximately #cj deg4 f y\r m]idian1 provid+ ! /> is 9 approximately ! same v]tical ea/ & we/ plane z is y\r z5i?4 ,:5 ! g5]al ea/ or we/ direction ( any /> has be5 det]m9$1 its nor? or s\? position c at once be f\nd f its decl9ation4 ,if y are 9 ,latitude #dj deg4 ,n4 y\r cele/ial horizon to ! ,s\? w be #ij deg4 f #dj deg4 ,n4 or #ej deg4 ,s4 & to ! ,nor? x w be #ij deg4 #dj deg4 ,n4 #acj deg4 or #dj deg4 ,n4 7bel[ ! ,n4 pole74 ,! g5]al position ( ! equator 9 ! sky is always readily f\nd accord+ to ! latitude y are 94 ,if y are 9 #dj deg4 ,n4 latitude1 ! cele/ial equator w\ld int]sect ! cele/ial sph]e at a po9t #dj deg4 ,s\? ( y4 ,kn[+ ?is1 ! angul> di/ance ( a /> ,nor? or ,s\? ( ! equator 7:i* is its decl9ation7 %\ld be easily f\nd4 ,rememb]1 h[ev]1 t ! equator 9 ! sky is a curv$ l9e & h5ce a /> 9 ! ,ea/ or ,we/ :i* looks to be slightly ,nor? ( y may actually be ,s\? ( y4 ,put 9 y\r ,note-,book3 ,if ! /> is we/ ( y its ,r4,a4 is less ?an y\rs4 ,if ea/ ( y1 its ,r4,a4 is great] ?an y\rs4 ,/> w be f\nd approximately #ae deg4 to ea/ or we/ ( y = ea* h\rly diff]5ce betwe5 ! />'s ,r4,a4 & y\r ,r4,a4 7,l4,s4,t474 ,hav+ e/abli%$ ! />'s g5]al ea/ & we/ direction1 its nor? & s\? position c be f\nd f its decl9ation4 #d4 ,"t ( ,m]idian ,passage ( a ,/> ,x is (t5 invaluable to "k fir/1 :5 a c]ta9 /> w be on y\r m]idian or second1 :at /> w be on y\r m]idian at a c]ta9 specifi$ "t4 ,"h is ! =mula = ea* case1 :i* put 9 y\r ,note ,book3 #a4 ,to f9d :5 a c]ta9 /> w cross y\r m]idian1 take f ! ,nautical ,almanac1 ! ,r4,a4 ( ! ,mean ,sun = ,gre5wi* ,mean ,noon ( ! prop] a/ronomical day4 ,apply to x ! correction = longitude 9 "t 7,we/ 1 ,ea/ -7 z p] ,table at bottom ( page #b1 ,nautical ,almanac1 & ! result w be ! ,r4,a4 ( ! ,mean ,sun at local mean noon1 i4e41 ! di/ance 9 sid]eal "t ! mean sun is f ! ,fir/ ,po9t ( ,aries :5 x is on y\r m]idian4 ,subtract ?is f ! />'s ,r4,a41 i4e41 ! di/ance 9 sid]eal "t ! /> is f ! ,fir/ ,po9t ( ,aries 7add+ #bd h\rs to ! />'s ,r4,a41 if necess>y to make ! subtraction possible74 ,! result w be ! di/ance 9 sid]eal "t ! /> is f y\r m]idian i4e41 ! "t int]val f local mean noon express$ 9 units ( sid]eal "t4 ,conv]t ?is sid]eal "t int]val into a mean "t int]val by always subtract+ ! r$uction = ! prop] numb] ( h\rs1 m9utes & seconds z giv5 9 ,table #h1 ,b[dit*4 ,! result w be ! local mean "t ( ! />'s m]idian passage4 ,example3 ,april #bbnd1 #aiai1 ,a4,m4 at %ip4 ,9 ,lo4 #ge deg4 ,e4 ,:at is ! local mean "t ( ! ,/> ,etam9's m]idian passage8 ,r4,a4,m4,s4 ,gr4 #ba;d--#j;h #a;h--#edm--#jbs ,r$4 = #ge deg4 ,e 7--#e;h7 --#di4c ,r4,a4,m4,s4 local mean noon #a;h--#ecm--#ab4gs ,/>'s ,r4,a4 #ag;h--#edm--#dds -- #a --#ec --#ab4g ,sid]eal int]val f ,l4,m4 ,noon #af;h--#jam--#ca4cs ,r$4 = ,sid4 ,int4 7,table #h7 -- #b --#cg4c ,l4,m4,t4 #ba d #ae;h--#ehm--#eds ,h5ce1 /> w cross m]idian at #c;h--#ehm--#eds ,a4,m4 ,april #bbnd4 #b4 ,to f9d at any h\r desir$ :at /> w cross y\r m]idian1 take ! ,r4,a4 ( ! ,mean ,sun = ,gre5wi* ,mean ,noon ( ! prop] a/ronomical day4 ,apply to x ! correction = longitude 9 "t 7,we/ 1 ,ea/ -7 z p] table at bottom ( page #b1 ,nautical ,almanac1 & ! result w be ! ,r4,a4 ( ! ,mean ,sun at local mean noon2 i4e41 ! di/ance 9 sid]eal "t ! mean sun is f ! ,fir/ ,po9t ( ,aries :5 x is on y\r m]idian4 ,suppose y wi% to f9d ! /> at #aj ,p4,m4 ,add #aj sid]eal h\rs to ! sun's ,r4,a4 j f\nd4 ,! result w be ! ,r4,a4 ( y\r m]idian at approximately #aj ,p4,m4 ,select 9 ! table on p4 #id ! ,r4,a4 ( ! /> ne>e/ 9 "t to y\r ,r4,a4 j secur$4 ,subtract ! ,r4,a4 ( ! ,mean ,sun at local mean noon f ! />'s ,r4,a4 j f\nd on p4 #id ( ! ,n4,a4 & ! result w be ! exact di/ance 9 sid]eal "t ! /> y h j id5tifi$ is f y\r m]idian1 i4e41 ! "t int]val f local mean noon express$ 9 units ( sid]eal "t4 ,conv]t ?is sid]eal "t int]val into a mean "t int]val by always subtract+ = ! prop] numb] ( h\rs1 m9utes & seconds z p] ,table #h1 ,b[dit*4 ,y w !n h secur$ ! "n ( ! /> desir$ & ! exact local mean "t ( ! />'s m]idian passage4 ,example ,no4 #b3 ,at sea ,dec4 #ad1 #aiai4 ,desir$ to get a /> on my m]idian at #aa ,p4,m4 ,lo4 by ,d4,r4 #gd deg4 ,w4 7474,r4,a4,g4,m4,n4 #ag;h--#bhm--#bfs ,corr4 #gd deg4 ,w4 7#d? - #efm ,w 7 #j --#dh4f 7474,r4,a4 y\r ,m4 #ag;h--#bim--#ad4fs #aa ,r4,a4,m4 #bh;h--#bim--#ad4fs -- #bd #d;h--#bim--#ad4fs ,r4,a4 ( ,/> ,aldeb>an #d;h--#cam--#ah4es ,/> ,r4,a4 #bh;h--#cam--#ah4e 7474,r4,a4 y\r ,m4 #ag -- #bi--ad4f ---------------- ,sid4 ,int4 f ,l4,m4 ,noon #aa;h--#jbm--#jc4is ,r$ = ,sid4 ,int4 7,table #h7 -- #a --#dh ---------------- ,l4,m4,t4 #aa;h--#jjm--#ae4is ,aldeb>an1 !n1 is ! /> & ! exact ,l4,m4,t4 ( its m]idian passage w be #aa;h #jjm #ae4is ,note3 ,if ! ,r4,a4,m4 is m ?an #bd h\rs1 d$uct #bd h\rs4 ,y w "k :e!r ! /> is ,nor? or ,s\? ( y by its decl9ation4 ,if y are 9 ,nor? latitude1 ! /> w be s\? ( y if its decl9ation is ,s\? or if its decl9ation is ,nor? & less ?an y\r latitude4 ,if its decl9ation & y\r latitude are bo? ,nor? & its decl9ation is great]1 ! /> w be nor? ( y4 ,! same pr9ciple applies if y are 9 ,s\? latitude4 ,assign any ( ! foll[+ to be work$ 9 ! class room or at night3 #a4 ,at sea1 ,novemb] #a/1 #aiai4 ,9 ,latitude #dj deg4 ,n41 ,longitude #gd deg4 ,w4 ,,wt #h;h #cjm ,p4,m4 ,obs]v$ unkn[n /> ab\t #hj deg4 ea/ ( my m]idian & #be deg4 s\? ( me4 ,:at 0 ! />8 #b4 ,at sea1 ,decemb] #a/1 #aiai4 ,,ct #aj;h #dem #jas4 ,,cc #bjm #afs sl[4 ,9 ,d4,r4 ,latitude #cj deg4 ,n41 ,longitude #fj deg4 #cj' ,w4 ,obs]v$ unkn[n /> ab\t #fj deg4 we/ ( m]idian & ab\t #bb deg4 ,s4 ,:at 0 ! />8 #c4 ,m>* #ae?1 #aiai4 ,9 ,d4,r4 ,latitude #aj deg4 #db' ,n1 ,longitude #aej deg4 #ad' #bh ,w4 ,,ct #e;h #adm #bhs4 ,,cc--#bm #ajs4 ,obs]v$ unkn[n /> almo/ on my m]idian & ab\t #bh deg4 nor? ( me4 ,:at 0 ! />8 #d4 ,aug4 #c1 #aiai1 ,p4,m4 at %ip4 ,9 ,d4,r4 ,latitude #cg deg4 #cg' ,n4 ,longitude #ch deg4 #cg' ,w4 ,at :at local mean "t w ! ,/> ,ant>es be on ! m]idian8 #e4 ,:at /> w transit at ab\t #d3aj ,a4,m4 on ,aug4 #crd1 #aiai8 ,9 ,d4,r4 position ,latitude #ch deg4 #aj' ,n1 ,longitude #cd deg4 #ch' ,w4 #f4 ,at :at local mean "t w ! ,/> ,arcturus transit on ,july #ag?1 #aiai1 9 ,latitude #de deg4 #ce' ,n41 ,longitude #bh deg4 #jf' ,w48 ,,w$nesday ,,lecture ,,latitude ,,by ,,m]idian ,,altitude ,,( ,a ,,/>--,,latitude ,,by ,,pol>is 7,,pole ,,or ,,nor? ,,/>7 ,to f9d y\r latitude by tak+ an altitude ( a /> :5 x is on y\r m]idian1 is "o ( ! quicke/ & easie/ ( calculations 9 all ,navigation4 ,! =mula is exactly ! same z = latitude by m]idian altitude ( ! sun4 ,9 us+ a />1 h[ev]1 y d n h to consult y\r ,nautical ,almanac to get ! ,g4,m4,t4 & f t ! decl9ation4 ,all y h to d is to turn to page #ie ( ! ,nautical ,almanac1 on :i* is giv5 ! decl9ation = e mon? ( ! ye>1 ( any /> y desire4 ,! re/ ( ! computation is1 z said be=e1 ! same z = latitude by ! sun & foll[s ! =mula ,lat4 ,dec4 - ,z4,d4 7#ij deg4 - true altitude74 ,z :5 work+ latitude by ! sun1 y subtract ! ,z4,d4 & ,dec4 :5 ( opposite "n & add !m :5 ( ! same "n4 ,put 9 y\r ,note-,book3 ,=mula3 ,lat4 ,dec4 - ,z4,d4 7#ij deg4 - true altitude74 ,at sea1 ,dec4 #bd?1 #aiai4 ,m]idian altitude ,/> ,aldeb>an #eb deg4 #cf' ,s4 ,,he #bj ft4 ,requir$ latitude ( %ip4 ,obs4 ,alt4 #eb deg4 #cf' ,s ,corr4 - #e #jh ---------- ,true ,alt4 #eb deg4 #cj' #eb ,s - #ij #jj #jj ---------- ,z4,d4 #cg deg4 #bi' #jh ,n ,dec4 #af #ba #jj ,n ---------- ,lat4 #ec deg4 #ej' #jh ,n ,note to ,in/ructor3 ,h class "w examples su* z ! foll[+ be=e tak+ up ,latitude by ,pole ,/>3 #a4 ,at sea1 ,may #e?1 #aiai4 ,m]idian altitude ,/> ,capella1 #gj deg4 #bi' ,s4 ,,he #cb ft4 ,requir$ latitude ( %ip4 #b4 ,at sea1 ,augu/ #ad?1 #aiai4 ,m]idian altitude ,/> ,vega1 #fj deg4 #ae' #de ,n4 ,,he #bh ft4 ,requir$ latitude ( %ip4 ,etc4 ,latitude by ,pol>is 7,pole or ,nor? ,/>7 ,y rememb] we exam9$ ! =mula 9 ! ,n4,a4 = ,lat4 by ! pole /> :5 we 7 discuss+ sid]eal "t "s weeks ago4 ,we w n[ take up a practical case ( secur+ y\r latitude by ?is me?od4 ,be=e do+ s1 h[ev]1 x may be ( b5efit to und]/& h[ we c get our latitude by ! pole />4 ,9 ! fir/ place1 imag9e t ! ,pole ,/> is directly ov] ! ,n pole ( ! e>? & is fix$4 ,if t 7 s1 & imag9e = a m9ute t x is s1 !n x w\ld be exactly #ij deg4 f ! ,pole ,/> to ! cele/ial equator4 ,n[1 no matt] :]e y /&1 x is #ij deg4 f y\r z5i? to y\r true horizon4 ,h5ce if y /ood at ! equator1 y\r z5i? w\ld be 9 ! cele/ial equator & y\r true horizon w\ld exactly cut ! ,pole ,/>4 ,n[1 suppos+ y w5t #aj deg4 ,n ( ! equator4 ,!n y\r nor!rly horizon w\ld drop by #aj deg4 & ! ,pole ,/> w\ld h an altitude ( #aj deg44 ,9 o!r words1 :5 y 7 9 #aj deg4 ,n latitude1 ! pole /> w\ld measure #aj deg4 high by sextant4 ,& s on up to #ij deg41 :]e ! ,pole ,/> w\ld be directly ov] y & y w\ld be at ! ,nor? ,pole4 ,n[ all ?is is bas$ ^u ! ,pole ,/> be+ 9 ! cele/ial sph]e exactly ov] ! ,nor? ,pole ( ! e>?4 ,x is n1 h[ev]4 ,ow+ to ! revolution ( ! e>?1 ! /> appe>s to move 9 an orbit ( a maximum ( #a deg4 #jh'4 ,j :at "p ( t #a deg4 #jh' is to be appli$ to ! true altitude ( ! /> = any "t ( ! sid]eal day1 has be5 figur$ out 9 ! table on page #ajg ( ! ,nautical ,almanac4 ,:at y h to get fir/ is ! ,l4,s4,t4 ,f9d f ! table ! correction correspond+ to ! ,l4,s4,t4 & apply ?is correction ) ! prop] sign to ! true altitude ( ,pol>is4 ,! result is ! latitude 94 ,put 9 y\r ,note-,book3 ,to get latitude by pole />1 fir/ get ,l4,s4,t4 ,?is c be secur$ by us+ any "o ( ! ?ree =mulas giv5 y 9 ,week ,,iii--,?ursday's ,lecture on ,sid]eal ,"t & ,"r ,asc5sion4 ,!n proce$ z p] =mula 9 ,n4,a4 99 99 99 99 99 ,note to ,in/ructor3 ,sp5d re/ ( "t 9 solv+ examples simil> to ! foll[+3 #a4 ,at sea1 ,feb4 #ad?1 #aiai4 ,,ct #ac;d #ba;h #ebm #ccs4 ,,cc #am #ads fa/4 ,9 ,lo4 #gb deg4 #di' #jj ,w4 ,,ie #a' #aj4 ,,he #ae ft4 ,obs]v$ altitude ,pol>is #db deg4 #ba' #cj ,n4 ,requir$ latitude 94 #b4 ,at sea1 ,m>* #ca/1 #aiai4 ,9 ,lo4 #afj deg4 #ae' ,e4 ,,ct #g;h #aem #ais4 ,obs]v$ altitude ,pol>is #ch deg4 #ah' ,n4 ,,ie #c' #jj4 ,,he #ag ft4 ,requir$ latitude 94 ,etc4 ,,?ursday ,,lecture ,,m>c ,,/4 ,,hilaire ,,me?od ,,by ,a ,,/> ,,sight ,y h already be5 giv5 in/ructions = f9d+ a ,l9e ( ,position by ! ,m>c ,/4 ,hilaire ,me?od1 us+ a sight ( ! sun4 ,today we w "w out ! same me?od by us+ a sight ( a />4 ,put ?is 9 y\r ,note-,book "h & also "u ,i7b7 ( ! =mula giv5 y 9 ,week ,,iv--,friday's ,lecture3 ,get ,g4,m4,t4 f correct$ *ronomet] "t4 ,) y\r ,g4,m4,t4 f9d ! correspond+ ,g4,s4,t4 accord+ to ! =mula already giv5 y4 ,) y\r ,g4,s4,t4 apply ! ,d4,r4 longitude 7- ,w4 ,lo47 ---------- 7 ,l4 ,lo47 to get ! ,l4,s4,t4 ,) ! ,l4,s4,t4 & ! />'s ,r4,a4 subtract ! less f ! great] & ! result is ! />'s ,h4,a4 at ! %ip or t4 ,9 us+ ,sun ,azimu? tables always take t f ! ,p4,m4 column4 ,m>k ,azimu? ,n or ,s accord+ to ! lat4 9 & ,e or ,w1 accord+ z to :e!r ! ,/> is ,ea/ or ,we/ ( y\r m]idian4 ,!n proce$ z 9 ! case ( a sun sight4 ,=mula3 7-,w4 ,lo47 ,g4,m4,t4 7474,r4,a4 77,,cp ,g4,s4,t4 --------- ,l4,s4,t4--,/>'s ,r4,a4 7,e4 ,lo47 7or vice v]sa if ,/>'s ,r4,a4 is great]7 ,/>'s ,h4,a4 at %ip 7t74 ,!n proce$ z 9 case ( sun sight4 ,example3 ,on ,may #ca/1 #aiai1 9 ,d4,r4 ,lat4 #ej deg4 ,n1 ,lo4 #de deg4 ,w1 ,g4,m4,t4 #ca;d #ad;h #ccm #cjs4 ,:at 0 ,/>'s ,h4,a4 at %ip8 ,g4,m4,t4 #ad;h -- #ccm -- #cjs 7474,r4,a4 #d -- #ca -- #dd4b 774,c4,p4 #b -- #bc -------------------- ,g4,s4,t4 #ai;h -- #jgm -- #cg4bs ,w ,lo4-- #c -- #jj -- #jj -------------------- ,l4,s4,t4 #af;h -- #jgm -- #cg4bs ,/>'s ,r4,a47,spica7 #ac -- #bj -- #ei -------------------- ,/>'s ,h4,a4 7t7 #b;h -- #dfm -- #ch4bs ,n[ let u "w out "s examples by ?is me?od3 #a4 ,nov4 #bi?1 #aiai4 ,,ct #cj;d #b;h #adm #cis ,a4,m4 ,,cc #cm #ads fa/4 ,d4,r4 position ,lat4 #da deg4 #ad' ,n1 ,lo4 #fh deg4 #df' ,w4 ,obs]v$ altitude ,/> ,aldeb>an ,ea/ ( m]idian #ej deg4 #bi' #dj4 ,,he #bi ft4 ,requir$ ,l9e ( ,position by ,m>c ,/4 ,hilaire ,me?od & mo/ probable position ( %ip4 #b4 ,jan4 #bcrd1 #aiai4 ,p4,m4 at %ip4 ,,ct #c;h #dem #djs4 ,lat4 by ,d4,r4 #ch deg4 #dd' #ai ,n4 ,lo4 #aba deg4 #af' #ad ,e4 ,obs]v$ altitude ,/> ,rigel #bh deg4 #ei' #bj ,we/ ( m]idian4 ,,ie #d' #cj4 ,,he #db ft4 ,requir$ ,l9e ( ,position by ,m>c ,/4 ,hilaire ,me?od & mo/ probable position ( %ip4 ,assign = ,night ,"w "o or two examples simil> to ! above4 ,,friday ,,lecture ,,examples3 ,,latitude ,,by ,,m]idian ,,altitude ,,( ,a ,,/>1 ,,latitude ,,by ,,pol>is1 ,,m>c ,,/4 ,,hilaire ,,me?od ,,by ,a ,,/> ,,sight #a4 ,at sea1 ,dec4 #e?1 #aiai4 ,obs]v$ m]idian altitude ,/> ,aldeb>an #fi deg4 #bh' #dj ,s4 ,no ,,ie4 ,,he #bf ft4 ,requir$ latitude 94 #b4 ,at sea1 ,jan4 #bj?1 #aiai4 ,,ct #ba;d #b;h #afm #dhs ,a4,m4 ,9 longitude #ef deg4 #bi' #df ,w4 ,obs]v$ altitude ( ,/> ,pol>is #dh deg4 #dd' #cj ,n4 ,,ie #aj' #bj4 ,,he #cg ft4 ,requir$ latitude 94 #c4 ,at sea1 ,june #d?1 #aiai4 ,a4,m4 at %ip4 ,,ct #aj;h #afm #cbs4 ,,cc #em #des fa/4 ,lat4 by ,d4,r4 #db deg4 #dd' ,n1 ,longitude #ec deg4 #ac' #dd ,e4 ,obs]v$ altitude ( ,/> ,altair ,ea/ ( m]idian1 #eb deg4 #ai' #cj4 ,,ie--#ad' #jj4 ,,he #ef ft4 ,requir$ l9e ( position by ,m>c ,/4 ,hilaire ,me?od & mo/ probable position ( %ip4 ,etc4 99 99 99 99 99 ,assign = ,night ,"w ! foll[+ ,articles 9 ,b[dit*3 #ccf ?r\gh #cda1 disreg>d+ ! =mulas4 ,,saturday ,,lecture ,,longitude ,,by ,,*ronomet] ,,sight ,,( ,,! ,,sun 7,,"t ,,sight7 ,y h n[ le>n$1 fir/1 h[ to get y\r latitude by a m]idian altitude ( ! sun or a /> & second1 h[ to get y\r ,l9e ( ,position & mo/ probable fix1 includ+ bo? latitude & longitude1 by ! ,m>c ,/4 ,hilaire ,me?od1 us+ = y\r calculations ei!r ! sun or a />4 ,we are n[ go+ to take up a me?od ( gett+ y\r longitude only4 ,?is me?od requires z mu*1 if n m1 calculation ?an ! ,m>c ,/4 ,hilaire ,me?od4 ,its results1 on ! o!r h&1 are f> less complete1 = :ile ! ,m>c ,/4 ,hilaire ,me?od w give y a fairly accurate idea ( bo? y\r latitude & longitude1 ?is me?od w1 at be/1 only give y y\r longitude4 ,moreov]1 y c use x = accurate results only :5 ! sun be>s almo/ due ,ea/ or ,we/ ( y1 = t is ! be/ "t1 z y h already le>n$1 to get a l9e ( position runn+ due ,nor? & ,s\?1 :i* is no?+ m ?an a m]idian ( longitude4 ,! only reason we expla9 ?is me?od at all is because x is 9 common practice among m]*antm5 & may1 !re=e1 be ( assi/ance to y1 if y g on a m]*ant %ip4 ,rememb]1 h[ev]1 t x belongs to ,old ,navigation z di/+ui%$ f ,new ,navigation1 exemplifi$ by ! ,m>c ,/4 ,hilaire ,me?od4 ,x is und\bt$ly be+ us$ less & less among progressive1 up-to-date navigators1 & w cont9ue to be us$ less z "t goes on4 ,! fact rema9s1 h[ev]1 t at pres5t _m m]*antm5 practice x1 & s x w d y no h>m to become famili> ) ! me?od1 too4 ,?is me?od is bas$ on secur+ y\r longitude by a "t sight or longitude by *ronomet] sight1 mean+ t at ! "t ! sun be>s z ne> due ,ea/ or ,we/ z possible1 y take a sight ( x by sextant & at ! same in/ant note ! "t by *ronomet]4 ,) ?is in=mation y proce$ to "w out y\r problem & secure y\r longitude accord+ to ! foll[+ =mula4 ,put 9 y\r ,note-,book3 ,to f9d y\r longitude by *ronomet] 7or "t7 sight4 #a4 ,take sight by sextant only :5 ! sun be>s z ne> z possible due ,ea/ or ,we/4 ,at exact "t ( tak+ sight1 note *ronomet] "t4 #b4 ,get ,g4,m4,t4 f correct$ *ronomet] "t4 ,apply ,equation ( ,"t to get ! correspond+ ,g4,a4,t4 #c4 ,correct obs]v$ altitude to get ,t4,c4,a4 ,also h at h& ,lat4 by ,d4 ,r4 & ,pol> ,di/ance4 7,note3 ,secure ,p4 ,d4 by subtract+ ,dec4 f #ij deg41 if ,lat4 & ,dec4 are ( same "n4 ,if ,lat4 & ,dec4 are ( opposite "n1 secure ,p4 ,d4 by add+ ,dec4 to #ij deg447 #d4 ,add toge!r ! ,t4,c4,a4 ! ,lat4 by ,d4,r4 & ! ,p4,d4 ,divide ! sum by #b & call ! quoti5t ,half ,sum4 ,f ! ,half ,sum subtract ! ,t4,c4,a4 & call ! answ] ! ,diff]5ce4 #e4 ,add toge!r ! secant ( ! ,latitude1 ! cosecant ( ! ,p4,d41 ! cos9e ( ! ,half ,sum & ! s9e ( ! ,diff]5ce 7,table #dd74 ,! result w be ! log hav]s9e ( ! ,s4,h4,a4 or ,l4,a4,t4 ,x mu/ always be less ?an #aj4 ,if great] ?an #aj1 subtract #aj or #bj to br+ x less ?an #aj4 #f4 ,f ,table #de1 take out ! correspond+ ,s4,h4,a4 7,l4,a4,t471 read+ f ! top ( ! page if ,p4,m4 at %ip1 or f bottom ( page if ,a4,m4 at ! %ip4 #g4 ,f9d ! diff]5ce betwe5 ,l4,a4,t4 & ,g4,a4,t4 ,?is diff]5ce is ,lo4 9 ,"t :i* turns into degrees1 m9utes & seconds by ,table #g4 ,if ,g4,a4,t4 is great] ?an ,l4,a4,t4 longitude is ,we/2 if ,g4,a4,t4 is less ?an ,l4,a4,t4 longitude is ,ea/4 ,example3 ,augu/ #bf?1 #aiai1 ,a4,m4 ,,ct #bf;d #b;h #bim #jcs ,a4,m4 ,,cc #afm #jhs sl[4 77 #dd deg4 #eg' #jj4 ,,ie--#a' #cj4 ,,he #cb ft4 ,d4,r4 ,lat4 #d deg4 #ee' #cb ,n4 ,requir$ longitude 9 at "t ( obs]vation4 #bf;d--#b;h--#bim--#jcs ,a4,m4 - #ab ------------------ ,,ct #be;d--#ad;h--#bim--#jcs --#ij deg4 #jj' #jj ,,cc #af --#jh ,dec4 #aj #di #dh ------------------ -------------- ,g4,m4,t4 #be;d #ad;h #dem--#aas ,p4,d4 #gi deg4 #aj' #ab ,eq4 ,t4 -#b --#je ------------------ ,g4,a4,t4 #be;d #ad;h--#dcm--#jfs - #a' #cj #i #bg 77 #dd deg4 #eg' #jj --------- ,corr4 #g #eg ,corr4 #g' #eg ----------- -7-7- #de deg4 #jd' #eg ,lat4 #d #ee #cb ,n sec4 4#jjafj ,p4,d4 #gi #aj #ab cosec4 4#jjgha ------------ #b7 #abi deg4 #aj' #da ------------ #a_/b ,s #fd deg4 #ce' #bj cos4 #i4fcbff - #i -7-7- #de #jd #eg ------------ ,diff4 #ai deg4 #cj' #bc s94 #i4ebce,o--#ad ------------- #i4afeeg #e #e ------------- log4 hav4 ,s4,h4,a4 7,l4,a4,t47 #i4afefb ,s4,h4,a4 7,l4,a4,t47 #be;d--#ba;h--#jjm--#jas ,g4,a4,t4 #be --#ad --#dc --#jf ----------------- ,lo4 9 ,t4 #f;h--#afm--#ees ,e ,lo4 7,table #g7 #id deg4 #ac' #de ,e ,i wi% to caution y ab\t confus+ ?is me?od ) ! "o ,b[dit* uses1 & /ill ano!r :i* ,h5d]son uses 9 8 book ,elem5ts ( ,navigation4 ,x is n exactly l ei!r "o4 ,x requires "o op]ation less ?an ei!r1 h[ev]1 & x also requires ! use ( few] p>ts ( ! v>i\s tables involv$4 ,= t reason x is giv5 y4 ,assign = "w 9 class room & also = "w at night examples simil> to ! foll[+3 #a4 ,oct4 #a/1 #aiai4 ,a4,m4 77 #ag deg4 #ae' #jj4 ,g4,m4,t4 #a;d #aa;h #cjm #jjs ,a4,m4 ,d4,r4 ,lat4 #dj deg4 #cj' ,n4 ,,ie--#b' #bj4 ,,he #be ft4 ,requir$ longitude 94 #b4 ,oct4 #aj?1 #aiai4 ,p4,m4 77 #be deg4 #ad' #cj4 ,,ct #a;h #aem #bjs4 ,,cc #dm #cis sl[4 ,,ie--#c' #aj4 ,,he #bf ft4 ,d4,r4 ,lat4 #da deg4 #bi' #jj ,s4 ,requir$ longitude 94 #c4 ,may #bg1 #aiai4 ,p4,m4 ,lat4 by ,d4,r4 #dj deg4 #ee' ,n4 77 #cd deg4 #d' #jj4 ,,ie #a' #aj4 ,,he #aj ft4 ,,ct #h;h #eem #dbs4 ,,cc #bm #jbs fa/4 ,requir$ longitude 94 #d4 ,may #ah?1 #aiai4 ,a4,m4 77 #bi deg4 #da' #ae4 ,,wt #g;h #bjm #des4 ,c-,w #b;h #agm #jfs4 ,,cc #dm #eis sl[4 ,latitude by ,d4,r4 #da deg4 #cc' ,n4 ,,ie--#a' #cj4 ,,he #bc ft4 ,requir$ longitude 94 #e4 ,augu/ #bd?1 #aiai4 ,a4,m4 77 #bc deg4 #cb' #aj4 ,,ie--#b'jj4 ,,he #af ft4 ,9 latitude #ci deg4 #jd' ,n4 ,,ct #bd;d #b;h #dgm #bhs ,a4,m4 ,,cc #dm #bhs4 ,requir$ longitude 94 #f4 ,june #bf?1 #aiai4 ,p4,m4 77 #dd deg4 #jh' #bj4 ,,ie--#b' #bj4 ,,he #cg ft4 ,,ct #h;h #ahm #des4 ,,cc #cm #bjs fa/4 ,latitude by ,d4,r4 #f deg4 #dc' ,s4 ,requir$ longitude 94 #g4 ,july #bi?1 #aiai4 ,a4,m4 ,,ct #bi;d #aa;h #adm #cis ,a4,m4 ,,cc #bm #ahs sl[4 77 #bh deg4 #jh' #cj4 ,,ie #j' #cj4 ,,he #ch ft4 ,latitude by ,d4,r4 #ci deg4 #dh' ,n4 ,requir$ longitude 94 #h4 ,may #bbnd1 #aiai4 ,p4,m4 ,,ct #i;h #adm #chs4 ,,cc #em #bhs sl[4 77 #ba deg4 #jg' #dj4 ,9 latitude #da deg4 #bf' ,n4 ,,ie #c' #aj4 ,,he #dj ft4 ,requir$ longitude 94 ,,week ,,vi--,,navigation ,,tuesday ,,lecture ,,longitude ,,by ,,*ronomet] ,,sight ,,( ,a ,,/> ,9 gett+ y\r longitude by a "t sight ( a />1 y proce$ some:at diff]5tly f ! me?od us$ :5 obs]v+ ! sun4 ,:at y wi% to get fir/ is ,g4,s4,t41 i4e41 ! di/ance 9 "t ,gre5wi* is f ! ,fir/ ,po9t ( ,aries4 ,if y c !n get ! di/ance ! %ip is f ! ,fir/ ,po9t ( ,aries1 ! diff]5ce betwe5 ! two w be ! longitude 91 m>k$ ,ea/ or ,we/ accord+ z to :i* is great]4 ,by look+ at ! diagram furni%$ y :5 we 7 talk+ ( ,sid]eal ,"t1 all ?is becomes p]fectly cle>4 ,! full rule = f9d+ longitude by a /> is z foll[s1 :i* put 9 y\r ,note-,book3 ,correct y\r ,,ct to get y\r ,g4,m4,t4 ,f ! ,g4,m4,t4 get ! ,g4,s4,t4 ,f ! obs]v$ altitude ( ! />1 obta9 ! />'s ,h4,a4 at ! %ip 9 ! same way ,l4,a4,t4 is secur$ 9 case ( ! sun4 ,to or f ! ,r4,a4 ( ! /> add1 if ,we/ ( y\r m]idian1 subtract if ,ea/ ( y\r m]idian1 ! />'s ,h4,a4 at ! %ip1 j obta9$4 ,! result is ! ,r4,a4 ( ! %ip's m]idian or ,l4,s4,t4 ,f9d ! diff]5ce betwe5 ,g4,s4,t4 & ,l4,s4,t4 & ! result is ! longitude1 m>k$ ,ea/ or ,we/ accord+ z to :e!r ,g4,s4,t4 is less or great] ?an ,l4,s4,t4 ,note3 ,always take ! />'s ,h4,a4 f ! top ( ! page ( ,table #de4 ,dec4 #b1 #aiai4 ,a4,m4 ,obs]v$ altitude ,/> ,sirius #b,o deg4 #je' #bj1 ,we/ ( m]idian4 ,,ct #aa;h--#dem--#bis ,p4,m4 ,,cc #am--#bhs sl[4 ,,ie--#a' #bj4 ,,he #ba ft4 ,latitude by ,d4 ,r4 #ch deg4 #eg' ,n4 ,requir$ longitude 94 ,,ct #aa;h--#dem--#bis ,,cc #a --#bh ------------------- ,g4,m4,t4 #aa;h--#dfm--#egs 747,,ra #af --#cg --#aj4c 77,,cp #a --#ef4a ------------------- ,g4,s4,t4 #bh;h--#bfm--#jc4ds ,,ie -#a' #bj --#bd ,,he -#g #jh ------------------- ------- ,g4,s4,t4 #d;h--#bfm--#jc4ds ,corr4 -#h' #bh ,obs4 ,alt4 #bj deg4 #je' #bj ,corr4 -#h #bh ---------- ,t4,c4,a4 #ai deg4 #ef' #eb ,lat4 #ch #eg sec4 4#ajiai ,p4,d4 #ajf #cf #bd cosec4 4#jahdi #a #b 7 #afe deg4 #cj' #af ------------- #a_/b ,s #hb deg4 #de' #jh cos4 #i4ajajf - #ac ,t4,c4,a4 #ai #ef #eb ------------- ,diff4 #fb deg4 #dh' #af s94 #i4idiaa #b --------- #i4agghe - #aa --------- log4 hav4 ,/>'s ,h4,a4 at %ip #i4agggd ,/>'s ,h4,a4 #c;h--#jbm--#djs ,/>'s ,r4,a4 #f --#da --#ci -------------- ,l4,s4,t4 #i;h--#ddm--#ais ,g4,s4,t4 #d --#bg --#ja -------------- ,lo4 9 ,t4 #e;h--#agm--#ahs ,e ,longitude 9 #gi deg4 #ai' #cj ,e ,assign = ,night ,"w or "w 9 ! class room examples simil> to ! foll[+3 #a4 ,april #af1 #aiai1 9 ,latitude #aa deg4 #dg' ,s4 ,obs]v$ altitude ( ! ,/> ,aldeb>an1 ,we/ ( ! m]idian #bc deg4 #ac' #bj4 ,,ct #f;h #ehm #bis4 ,,cc #bm #bgs fa/4 ,,ie--#b' #jj4 ,,he #bf ft4 ,requir$ longitude 94 #b4 ,dec4 #aj?1 #aiai4 ,obs]v$ altitude ( ,/> ,sirius #bj deg4 #je' #dj ,we/ ( m]idian4 ,,ct #aa;h #dem #bis4 ,,cc #am #bhs sl[4 ,,ie--#a' #bj4 ,,he #ba ft4 ,d4,r4 latitude #ch deg4 #eg' ,n4 ,requir$ longitude 94 ,note to ,in/ructor3 ,if any "t 9 ! p]iod is left or = ,night ,"w assign examples to be work$ by ,m>c ,/4 ,hilaire ,me?od1 *ang+ slightly ! ,d4,r4 ,lat4 & ,longitude j obta9$ by ! ,"t ,sight ,me?od4 ,,w$nesday ,,lecture ,,examples ,,on ,,longitude ,,by ,,*ronomet] ,,sight ,,( ,a ,,/> #a4 ,dec4 #i?1 #aiai4 ,9 latitude #cf deg4 #dh' ,n4 ,obs]v$ altitude ,/> ,capella1 ,ea/ ( m]idian #df deg4 #ah' #cj4 ,,ie #b' #ej (f arc4 ,,he #cc ft4 ,,ct #aj;d #c;h #jem #jes ,a4,m4 ,,cc #am #ahs sl[4 ,decl9ation ( /> is #de #ee' ,n4 ,requir$ longitude 94 #b4 ,octob] #bf?1 #aiai4 ,9 latitude #ci deg4 #ed' ,s4 ,obs]v$ altitude ,/> ,rigel1 ,we/ ( m]idian #db deg4 #ah' #dj4 ,,ct #bg;d #aj;h #cbm #ees ,a4,m4 ,,cc #bm #ahs fa/4 ,,ie #d' #bj (f arc4 ,,he #db ft4 ,requir$ longitude 94 #c4 ,april #aa?1 #aiai4 ,p4,m4 at %ip4 ,9 latitude #dc deg4 #af' #dh ,s4 ,obs]v$ altitude ,/> ,spica #cc deg4 #ah' #bj1 ,ea/ ( m]idian4 ,,ct #aa;h #jhm #dds ,p4,m4 ,,ie #c' #bj on arc4 ,,cc #dm #ahs sl[4 ,,he #ci ft4 ,requir$ longitude 94 #d4 ,septemb] #ae?1 #aiai4 ,p4,m4 at %ip4 ,9 latitude #di deg4 #ch',n4 ,obs]v$ altitude ,/> ,d5eb1 ,ea/ ( m]idian1 #cf deg4 #af' #ej4 ,,ie #c' #dj (f arc4 ,,he #dj ft4 ,,cc #fm #ahs sl[4 ,,ct #aj;h #jjm #acs ,p4,m4 ,decl9ation ( /> is #dd deg4 #ei' #cf ,n4 ,requir$ longitude 94 ,if any "t is left1 "w same examples by ,m>c ,/4 ,hilaire ,me?od assum+ a position ne> ! "o f\nd by ,"t ,sight4 ,assign = ,night ,"w any ( ! above examples1 to be work$ ei!r z ,"t ,sights or by ! ,m>c ,/4 ,hilaire ,me?od1 & also ! foll[+ ,arts4 9 ,b[dit*3 #cbf-cbg-cbh-cbi4 ,,?ursday ,,lecture ,,latitude ,,by ,,ex-,,m]idian ,,altitude ,,( ,,! ,,sun ,y h le>n$ t :5 y calculate y\r latitude f a m]idian altitude ( ! sun1 "o ( ! necess>y requisites is to h ! sun exactly on y\r m]idian4 ,9 fact1 t is j ano!r way ( express+ m]idian altitude1 i4e41 an altitude tak5 :5 ! sun is on y\r m]idian4 ,n[ suppose t #aj or #ae m9utes be=e noon y fe> t ! sun w be cl\d$ ov] at noon s t a m]idian altitude _c be secur$4 ,!re is a way to calculate y\r latitude1 ev5 ?\gh ! altitude y secure is tak5 by sextant "s m9utes be=e or aft] noon4 ,?is is call$ latitude by an ex-m]idian altitude4 ,x mu/ be kept 9 m9d t ?is me?od c be us$ accurately only )9 #bf m9utes ( noon1 ei!r be=e or aft]1 & only !n :5 y "k y\r longitude accurately4 ,put 9 y\r ,note-,book3 #a4 ,get y\r ,l4,a4,t4 7,s4,h4,a474 #b4 ,subtract x f #bd;h #jjm #jjs1 or vice v]sa1 accord+ z to :e!r ,l4,a4,t4 is j be=e or j aft] local app>5t noon4 ,call ! result ,"t ,int]val f ,m]idian ,passage4 #c4 ,) y\r ,d4,r4 latitude1 decl9ation & ,"t ,int]val f ,m]idian ,passage1 ent] ,table #bf to get ! prop] am\nt ( ,v>iation ( ,altitude 9 "o m9ute f m]idian passage4 #d4 ,) ! ,"t ,int]val f ,m]idian ,passage & ! ,v>iation1 ent] ,table #bg to get ! total am\nt ( ,v>iation ( ,altitude4 #e4 ,add ?is total am\nt ( ,v>iation to ! true obs]v$ altitude tak5 be=e or aft] noon1 & ! result is ! correct$ altitude4 #f4 ,!n proce$ to get y\r latitude accord+ to ! rules already giv5 y = latitude by m]idian altitude4 ,example3 ,at sea1 ,jan4 #bcrd1 #aiai4 ,,ct #d;h #bbm #ads4 ,,cc #am #ajs fa/4 ,longitude #ff deg4 #jd' ,w4 ,latitude by ,d4,r4 #ai deg4 #af' #jj ,n4 77 #ej deg4 #ea' #jj ,s4 ,,he #di ft4 ,,ie--#a' #cj4 ,requir$ latitude 94 ,,ct #d;h - #bbm - #ads ,,cc - #a - #aj --------------------- ,g4,m4,t4 #d;h - #bam - #jds ,eq4 ,t4 - #aa - #ej --------------------- ,g4,a4,t4 #d;h - #jim - #ads ,lo4 9 ,t #d - #bd - #af 7,w-7 --------------------- ,l4,a4,t4 #bb;d - #bc;h - #ddm - #ehs #bd;h - #jjm - #jjs - #bc - #dd - #eh ----------------- #aem - #jbs ,"t ,int]val f ,m]idian ,passage4 ,dec4 #ai deg4 #cd' #dh ,s ,table #bf #b4h ,v>iation ,lat4 #ai deg4 #af' #jj ,n ,= #a m94 #j altitude4 99 99 99 99 99 ,"t ,int]val f ,m]idian ,passage #aem #jbs - #b4h ,v>iation = #a m9ute 7,table #bg7 #b #g' #cj 4#h #c #jj ------------- #aj' #cj ,,ie - #a' #cj 77 #ej deg4 #ea' #jj ,,he #h #db #g #ab --------- ----------- ,corr4 #g' #ab -7-7- #ej deg4 #eh' #ab #aj #cj ----------- #ea deg4 #jh' #db - #ij #jj #jj ----------- ,,zd #ch deg4 #ea' #ah ,n ,dec4 #ai #cd #dh ,s ----------- ,lat4 9 #ai deg4 #af' #cj ,n ,assign = "w 9 class room & ,night ,"w1 examples simil> to ! foll[+3 #a4 ,at sea1 ,july #aa?1 #aiai4 ,latitude by ,d4,r4 #ej deg4 #ja' #jj ,n4 ,longitude #dj deg4 #je' #af ,w4 ,obs]v$ ex-m]idian altitude 77 #fa deg4 #de' #cj ,s4 ,,he #ae ft4 ,,ie--#d' #aj4 ,,ct 7correct$7 #b;h #chm #jjs4 ,requir$ latitude 94 #b4 ,at sea1 ,june #f?1 #aiai4 ,latitude by ,d4 ,r4 #di deg4 #ba' ,n1 ,longitude #ah deg4 #ah' ,w4 ,obs]v$ ex-m]idian altitude 77 #fa deg4 #cj' #bb ,s4 ,,he #db ft4 ,,ct #a;h #jfm #ahs4 ,,cc--#am #ads4 ,,ie #j' #cj (f ! arc4 ,requir$ latitude 9 ( %ip4 ,if any "t is left1 "w simil> examples by ,m>c ,/4 ,hilaire ,me?od4 ,,friday ,,lecture ,,examples3 ,,latitude ,,by ,,ex-,,m]idian ,,altitude ,,( ,,! ,,sun #a4 ,jan4 #a/1 #aiai4 ,,wt #aa;h #ecm #ahs ,a4,m4 ,c-,w #e;h #efm #afs4 ,latitude by ,d4 ,r4 #eh deg4 #je' ,s4 ,longitude #hi deg4 #jj' #dh ,w4 77 ex-m]idian #ee deg4 #af' #cj ,n4 ,,ie #b' #jj (f ! arc4 ,,cc #am #bhs fa/4 ,,he #cf ft4 ,requir$ latitude 94 #b4 ,m>* #aa?1 #aiai4 ,,ct #aa;d #i;h #adm #cis ,a4,m4 ,latitude by ,d4 ,r4 #ci deg4 #bj' ,n1 ,longitude #ci deg4 #dh' #af ,e4 77 ex-m]idian #df deg4 #ag' #cj ,s4 ,,ie #b' #jj on ! arc4 ,,cc #am #afs sl[4 ,,he #bi ft4 ,requir$ latitude 94 #c4 ,april #bf?1 #aiai4 ,,ct #bf;d #d;h #dfm #chs ,a4,m4 ,latitude by ,d4 ,r4 #bd deg4 #be' ,s1 ,longitude #ajg deg4 #af' #ef ,e4 77 ex-m]idian #eb deg4 #ah' #ej ,n4 ,,ie--#b' #dj4 ,,cc #cm #efs sl[4 ,,he #cc ft4 ,requir$ latitude 94 #d4 ,may #aj1 #aiai4 ,,ct #b;h #ahm #dfs ,a4,m4 ,latitude by ,d4 ,r4 #bc deg4 #ed' ,s1 ,longitude #adc deg4 #bj' #ah ,e4 77 ex-m]idian #dh deg4 #bf' #bj ,n4 ,,ie #c' #bj on ! arc4 ,,cc #dm #ahs fa/4 ,,he #da ft4 ,requir$ latitude 94 #e4 ,june #ba/1 #aiai4 ,,ct #d;h4 #efm #ahs4 ,latitude by ,d4 ,r4 #db deg4 #ja' ,n1 ,longitude #ge deg4 #jj' #ah ,w4 77 ex-m]idian #ga deg4 #bi' #dj ,s1 ,,ie--#b' #cj4 ,,cc #cm #jds sl[4 ,,he #bh ft4 ,requir$ latitude 94 #f4 ,dec4 #ah?1 #aiai4 ,,wt #aa;h #ejm #ahs ,a4,m4 ,c-,w #c;h #adm #ahs4 ,latitude by ,d4 ,r4 #aa deg4 #ee' ,s4 ,longitude #dh deg4 #jb' #bi ,w4 77 ex-m]idian #gh deg4 #cb' #cj ,s4 ,,ie #c' #cj on ! arc4 ,,cc #bm #dds sl[4 ,,he #ce ft4 ,requir$ latitude 94 ,if !re is any "t left1 give examples ( latitude by m]idian altitude1 ,m>c ,/4 ,hilaire ,me?od by sun or /> sight1 etc4 ,,saturday ,,lecture ,,f9d+ ,,! ,,wat* ,,"t ,,( ,,local ,,app>5t ,,noon ,noon at ! %ip is ! pivotal po9t ( ! day's "w at sea4 ,x is !n t ! navigator mu/ report to ! comm&+ (fic] ! latitude & longitude by dead reckon+1 ! latitude & longitude by obs]vation1 ! c\rse & di/ance made good1 ! deviation ( ! compass & ! c\rse & di/ance to de/9ation4 ,app>5t noon1 !n1 is a mo/ important "t to calculate accurately1 & to d s :5 ! %ip is "u way1 is n s easy at x fir/ appe>s4 ,if ! %ip is /ation>y1 & y "k ! longitude y are 91 ! problem is simple4 ,!n x is m]ely a "q ( />t+ ) ,l4,a4,t4 ( #jj;h-#jjm-#jjs1 add+ or subtract+ ! longitude1 accord+ z to :e!r x is ,we/ or ,ea/1 to get ,g4,a4,t42 apply+ ! equation ( "t ) sign rev]s$ to get ,g4,m4,t42 apply+ ! ,c4 ,cor4 ) sign rev]s$ to get ! ,c4,t42 & apply+ ! ,c-,w to get ! ,,wt4 ,if1 = in/ance1 ?is ,,wt happ5s to be #aa;h-#dbm-#cas1 :5 ! wat* reads t numb] ( h\rs1 m9utes & seconds1 ! sun w be on ! m]idian & x w be app>5t noon4 ,:5 ! %ip is mov+1 ! problem is m difficult4 ,at fir/ ?\ght y might imag9e t all y w\ld h to d w\ld be to take ! diff]5ce betwe5 ! ,l4,a4,t4 ( ! morn+ sight & #bd h\rs1 calculate ! di/ance ! %ip w\ld run 9 ?is "t & f t det]m9e ! longitude y w\ld be 9 at noon4 ,!n proce$ z 9 ! case ( ! %ip be+ /ation>y4 ,b su* a calculation does n take into consid]ation ! ea/+ or we/+ ( ! %ip itself4 ,suppose t at ! morn+ sight ! ,l4,a4,t4 is f\nd to be #bj;h-#ajm-#cjs4 ,if ! %ip does n move1 x w be #c;h-#dim-#cjs to noon4 ,b suppose ! %ip is mov+ ea/w>d4 ,!n1 9 addition to ! spe$ at :i* ! sun is approa*+ ! %ip1 !re mu/ be add$ ! spe$ at :i* ! %ip is mov+ t[>d ! sun--i4e4 ! *ange 9 longitude p] h\r :i* ! %ip is mak+1 express$ 9 m9utes & seconds ( "t4 ,likewise1 if ! %ip is mov+ we/w>d1 an all[ance mu/ be made = ! we/+ ( ! %ip4 ,& ?is *ange ( longitude 9 m9utes & seconds ( "t mu/ be subtract$ f ! spe$ ( ! sun's approa* s9ce ! %ip1 9 go+ we/1 is travel+ away f ! sun4 ,!re are v>i\s ways to calculate ?is all[ance = ! %ip's spe$1 among ! be/ ( :i* is giv5 9 ,b[dit*1 ,art4 #djc1 p4 #agi4 ,ano!r1 & ev5 easi] way1 is ! foll[+1 :i* 0 expla9$ to ! writ] by ,lieut5ant ,comm&] ,r4,p4 ,/r\gh1 =m]ly head ( ! ,seaman%ip ,dep>tm5t ( ?is ,s*ool3-- #a4 ,take ! morn+ sight = longitude :5 ! sun is on or z ne> z possible to ! prime v]tical4 #b4 ,subtract ! ,l4,a4,t4 ( ! morn+ sight f #bd h\rs4 ,?is w give ! total "t f ! morn+ sight to noon if ! %ip 7 /ation>y4 #c4 ,f ! c\rse to noon & spe$ ( ! %ip1 figure ! *ange 9 longitude p] h\r 9 t]ms ( seconds ( "t4 ,= in/ance1 suppose a %ip 7 /eam+ a c\rse ( #bge deg4 at ! rate ( #aa knots p] h\r 9 approximately #ch deg4 ,nor? latitude4 ,! *ange ( longitude p] h\r = ?is spe$ w\ld be #ad' ( arc or #efs ( "t4 #d4 ,n[ ! sun travels at ! rate ( #fj m9utes or #cfjj seconds p] h\r4 ,to ?is h\rly spe$ ( ! sun mu/ be add$ or subtract$ ! h\rly spe$ ( ! %ip accord+ z to :e!r ! %ip is go+ 9 an ea/]ly or we/]ly direction4 ,if1 z m5tion$ above1 ! %ip is /eam+ a c\rse ( #bge deg4 7,w #a_/b ,n7 & h5ce *ang+ its longitude at ! rate ( #efs p] h\r1 !n ! net rate ( approa* ( ! sun p] h\r w\ld be #cfjjs - #efs1 or #cedds p] h\r4 #e4 ,divide ! total "t to noon f ! ,l4,a4,t4 ( ! morn+ sight 7express$ 9 seconds ( "t7 by ! net rate ( approa* ( ! sun p] h\r4 ,! result w be ! correct$ "t to noon--i4e4 ! "t at :i* ! sun w be on ! %ip's m]idian :5 ! %ip is *ang+ its longitude to ! we/w>d at ! rate ( #efs p] h\r4 #f4 ,"o m /ep is necess>y4 ,to ! wat* "t ( ! morn+ sight1 add ! correct$ "t to noon4 ,! result w be ! wat* "t ( ,local ,app>5t ,noon4 ,?irty m9utes be=e w be ! wat* "t ( #aa3cj ,a4,m4 & at #aa3cj ,a4,m4 all deck clocks %\ld be set to ! local app>5t "t ( ! place ! %ip w be at local app>5t noon4 ,! foll[+ example illu/rates ! explanation j giv5 & %\ld be put 9 y\r ,note ,book3-- ,example3--,at sea1 ,augu/ #g?1 #aiai4 ,ab\t #g3cj ,a4,m4 by %ip's "t1 position by obs]vation j f\nd to be ,latitude #cj deg4 #je' ,n1 ,longitude #eh deg4 #jh' ,w4 ,,wt ( morn+ sight #f;h-#ecm-#acs ,a4,m4 ,c-,w #d;h-#cgm-#bas4 ,,cc #cm-#chs4 ,c\rse #bge deg44 ,spe$ #aa knots4 ,,tz ,n #ij deg4 ,e4 ,:at w be ! ,wat* ,"t ( ,local ,app>5t ,noon8 ,,wt #f;h -- #ecm -- #acs ,a4,m4 #ab ------------------- #ah -- #ec -- #ac ,c-,w #d -- #cg -- #ba ------------------- ,,ct #bc -- #cj -- #cd ,,cc #c -- #ch ------------------- ,g4,m4,t4 #bc -- #cd -- #ab ,eq4 ,t4 -- #e -- #db ------------------- ,g4,a4,t4 #bc -- #bh -- #cj ,lo4 9 ,t4 #c -- #eb -- #cb ------------------- ,l4,a4,t4 #ai -- #ce -- #eh #bd -- #jj -- #jj ------------------- ,total "t to ,noon #d;h #bdm #jbs ,c\rse -- #bge deg4 ,*ange 9 ,lo4 p] hr4-- #ad'1 #efs4 #cfjjs -#ef ----- #cedds1 ,net rate ( approa* ( sun #d;h #fj ---- #bdjm #bd ----- #bfdm x #fj #aehdjs #aehdjs #jb ----- #aehdbs1 ,total "t to noon4 #cedd7 #aehdb 7#d4dg h\rs #adagf ----- #afffj #adagf ----- #bdhdj #bdhjh ----- ,correct$ "t to ,noon #d;h -- #bhm -- #abs ,,wt ( ,a4,m4 sight #f;h -- #ecm -- #acs ----------------- ,,wt ( ,l4,a4,n4 #aa;h -- #bam -- #bes ,,wt ( #aa3cj ,a4,m4 #aj;h -- #eam -- #bes ,:51 !re=e1 ! wat* reads #aj;h--#eam--#bes1 ! deck clocks %\ld be set to #aa4cj ,a4,m4 & ?irty m9utes lat] x w be app>5t noon at ! %ip4 ,9 all ^! calculations x is tak5 = grant$ t ! spe$ ( ! %ip & h5ce ! *ange 9 longitude c be gaug$ accurately4 ,a *eck on ?is c be made by comp>+ ! longitude ( ! ,a4,m4 sight ) ! ,d4,r4 longitude ( ! same "t4 ,any appreciable diff]5ce betwe5 ! two c be ascrib$ to curr5t4 ,n[1 if a proportionate am\nt ( curr5t is all[$ = 9 reckon+ ! spe$ ( ! %ip f ! "t ( ! ,a4,m4 sight to noon1 !n a prop] correction c be made 9 ! net rate ( approa* ( ! sun & ! correct$ "t to noon w be v close to ! exact "t ( noon4 ,( c\rse !re w be an error 9 ?is calculation b x w be small & ! result ga9$ w be accurate en\gh = ord9>y "w4 ,s mu* = f9d+ ! wat* "t ( ,local ,app>5t ,noon4 ,c>eful navigators c>ry ! process fur!r & get ! wat* times ( #ae1 #aj & #e m9utes be=e noon1 s t by ! use ( con/ants = ea* "o ( ^! times1 an accurate *eck on ! noon latitude c be quickly & easily secur$4 ,we h n "t 9 ?is c\rse to expla9 h[ ^! con/ants are work$ out b x is well wor? kn[+4 ,! in=mation reg>d+ x is 9 ,b[dit* ,art4 #cbe1 p4 #abh1 & ,art4 #dje1 p4 #aha4 ,a ^w ab\t ! wat* us$ by ! navigator %\ld be includ$ "h4 ,?is wat* %\ld be a good "o & receive z mu* c>e1 9 its way1 z ! *ronomet]4 ,x %\ld be w\nd at ! same "t e day1 c>efully h&l$ &1 9 o!r respects1 treat$ l ! f9e "t-piece t x is4 ,:ile au?orities diff] on ?is po9t1 ! be/ practice seems to be n to *ange ! navigator's wat* to correspond ) ! app>5t "t ( ea* day's noon position4 ,! reason = ?is is two-fold4 ,fir/1 because con/ant mov+ ( ! h&s w h an injuri\s effect on ! works ( ! wat*1 & second1 because1 by n *ang+ ! wat*1 ! ,c-,w rema9s approximately ! same1 & ?us a good *eck c be kept on bo? ! wat* & ! *ronomet] z well z on ! navigator's figures 9 reckon+ ! times ( 8 v>i\s sights4 ,assign = night read+ ! foll[+ ,arts4 9 ,b[dit*3 #cbc1 #cbd1 #ccc4 ,also problems simil> to ! foll[+3 #a4 ,at sea1 ,july #bh1 #aiai4 ,position by obs]vation j f\nd to be ,latitude #dd deg4 #eh' ,n1 ,longitude #bb deg4 #jf' ,w4 ,,wt ( morn+ sight #f;h-#jbm-#bjs4 ,,cc #cm #cds sl[4 ,c\rse ,s #bd deg4 ,w4 ,,tz ,n #ij deg4 ,e4 ,spe$ #i knots4 ,:at w be ! wat* "t ( ,local ,app>5t ,noon8 #b4 ,at sea1 ,augu/ #i?1 #aiai4 ,position by obs]vation j f\nd to be ,latitude #ch deg4 #dh' ,n1 ,longitude #gj deg4 #df' ,w4 ,,wt ( morn+ sight #h;h-#aem-#jas ,a4,m4 ,c-,w #c;h-#efm-#cbs4 ,,cc #cm-#dcs sl[4 ,c\rse #bgb deg44 ,spe$ #ab knots4 ,,tz ,n #ij deg4 ,e4 ,:at w be ! wat* "t ( ,local ,app>5t ,noon8 ,,week ,,vii--,,navigation ,,tuesday ,,lecture ,,compass ,,error ,,by ,,an ,,azimu? ,! easie/ & mo/ accurate way to f9d ! error ( y\r compass is1 fir/1 to f9d ! be>+ ( ! sun by y\r pelorus4 ,if y set y\r pelorus1 s t x w exactly co9cide ) ! c\rse y are /eam+ z %[n by ! compass 9 y\r *>t h\se & !n get a be>+ ( ! sun by not+ :]e ! %ad[ f ! pelorus vane cuts ! circumf]5ce1 ?is be>+ w be ! be>+ ( ! sun by compass4 ,at ! same "t1 get y\r true be>+ ( ! sun f ! ,azimu? ,tables4 ,! diff]5ce betwe5 ! two w be ! compass error1 m>k$ ,ea/ or ,we/ accord+ to ! foll[+ rule :i* put 9 y\r ,note-,book3 #a4 ,express y\r ,compass ,be>+ & y\r ,true ,be>+ by ,,new compass read+4 #b4 ,if ,,tz is to ! "r ( ,,cz1 ,c4,e4 is ,ea/4 ,=mula3 ,true--,"r--,ea/4 #c4 ,if ,,tz is to ! left ( ,,cz1 ,c4,e4 is ,we/4 ,=mula3 ,true--,left--,we/4 ,y mu/ n[ rememb] t :at y h is a ,compass ,error1 consi/+ ( bo? ,v>iation & ,deviation4 ,to f9d ! ,deviation1 ! ,v>iation & ,c4,e4 be+ giv51 is m]ely to apply ! rules already giv5 y "u ,dead ,reckon+4 ,= in/ance1 if y _h a ,c4,e4 ( #aj deg4 ,w & a ,v>iation ( #d deg4 ,e1 ! ,deviation w\ld be #ad deg4 ,w4 ,put ?is example 9 y\r ,note-,book3 ,,lat #bj;h #eim #egs ,lat4 #d deg4 #ee' ,n ,dec4 #aj deg4 #ci' #cj ,n ,%ip head+ ,n #aa deg4 ,w4 ,,cb ( 747 ,s #hh deg4 ,e4 ,v>iation #aj deg4 ,w4 ,:at 0 ! %ip's true c\rse & ,deviation ( ,compass on direction %ip 0 head+8 ,illu/ration ,illu/ration ,,cz #ib deg4 7,new compass read+7 ,,tz #hj deg4 7,new compass read+7 --- ,,ce #ab deg4 ,,ce #ab deg4 ,w ,v>iation #aj deg4 ,w ----- ,deviation #b deg4 ,w ,true c\rse be+ sail$ ,n #bc deg4 ,w or #ccg deg44 ,let u n[ "w out "s ( ! foll[+ examples3 #a4 ,l4,a4,t4 #bb;h--#adm--#ahs ,lat4 #cj deg4 #bi' ,s ,dec4 #ag deg4 #bh' #dd ,n ,%ip head+ ,s #hd deg4 ,w ,compass ,be>+ #dd deg4 ,v>iation #aj deg4 ,w4 ,requir$ ,t4,c4 & ,deviation on %ip's load+4 #b4 ,augu/ #bi?1 #aiai4 ,,ct #b;h #bim #ahs ,a4,m4 ,longitude #abj deg4 #ai' #df ,e4 ,latitude #dd deg4 #ad' ,n4 ,%ip head+ #ih deg44 ,compass ,be>+ ,s #db deg4 ,e4 ,v>iation #d deg4 ,e4 ,requir$ ,t4,c4 & ,deviation on %ip's head+4 #c4 ,june #ag?1 #aiai4 ,,ct #d;h #ahm #dds ,a4,m4 ,longitude #fj deg4 #ad' #ei ,e4 ,latitude #ch deg4 #dh' #jj ,s4 ,%ip head+ ,,sw x ,s4 ,compass ,be>+ #dj deg4 ,v>iation #ab deg4 ,w4 ,requir$ ,t4,c4 & ,deviation on %ip's head+4 ,etc4 ,,w$nesday ,,lecture ,,correct+ ,,longitude ,,by ,a ,,factor ,we are n[ almo/ ready to beg9 ! discussion ( a day's "w at sea4 ,! only me?od we h n tak5 up is ! "o :i* is ! subject ( today's lecture4 ,x is a me?od to correct y\r longitude to correspond ) ! diff]5ce betwe5 y\r latitude by ,dead ,reckon+ & y\r latitude by obs]vation4 ,suppose y take a sight 9 ! morn+ = longitude4 ,! only latitude y c use is a ,d4 ,r4 latitude1 advanc$ f y\r la/ kn[n position4 ,n[ suppose y run until noon & at t "t take a sight = latitude4 ,9 comp>+ y\r ,d4 ,r4 latitude1 advanc$ ! true c\rse & di/ance /eam$ to noon1 & y\r latitude by obs]vation tak5 at noon1 suppose !re is a diff]5ce ( sev]al m9utes4 ,! "q is--,h[ c we correct our longitude to correspond ) ?is error discov]$ 9 ! latitude8 ,?is is ! me?od :i* put 9 y\r ,note-,book3 ,f9d ! diff]5ce betwe5 ! latitude by ,d4 ,r4 & ! correspond+ latitude by obs]vation 79 mo/ cases secur$ f a sight at noon or f ! ,/> ,pol>is74 ,call ?is ! ,error 9 ,latitude4 ,) ! ,d4 ,r4 ,latitude ( ! prec$+ sight & ! azimu? or be>+ ( ! prec$+ sight 7always express$ z a be>+ ( less ?an #ij deg41 old compass read+7 ent] ,table #dg = ! correct ,longitude ,factor4 ,multiply ?is ,factor by ! ,error 9 ,latitude4 ,! result is ! correction to apply to ! ,longitude4 ,x is appli$ ,ea/ or ,we/ accord+ z to :e!r ! ,latitude by ,obs]vation is to ! ,ea/ or ,we/ ( ! ,d4 ,r4 ,latitude on ! ,l9e ( ,position 7! l9e at "r angles to ! ,azimu?7 ( ! prec$+ sight4 ,example3 ,position ab\t #g3cj ,a4,m4 ,latitude by ,d4 ,r4 #be deg4 #dj' ,s1 ,longitude 7j secur$ by obs]vation7 #ajd deg4 #je' #ch ,e4 ,l4,a4,t4 #g;h #cbm #cjs ,a4,m41 ,decl9ation #d deg4 #ei' ,n4 ,!nce %ip ran to noon #aji deg41 true c\rse1 #df miles1 :5 ! latitude by m]idian altitude ( ! sun 0 f\nd to be #be deg4 #eb' ,s4 ,requir$ correct$ longitude at noon4 #g3cj ,a4,m4 ,d4,r4 ,lat4 #be deg4 #dj' ,s ,lo4 #ajd deg4 #je' #ch ,e #aji deg4--#df k4 #ae ,s #dh #ah ,e ---------- -------------- ,noon--,lat4 by ,d4,r4 #be deg4 #ee' ,s ,lo4 #ajd deg4 #ec' #ef ,e ,noon--,lat4 by obs4 #be deg4 #eb' ,s ---------- ,error 9 ,lat4 #c' ,ent] ,table #dg ) azimu? 7,s #aje deg4 ,e7 ,n #ge deg4 ,e z be>+ & ,latitude #be deg4 #dj' or #bf deg41 ,factor is f\nd to be 4#c4 #c' 7,error 9 ,latitude7 times 4#c 7,factor7 4#i' or #ed1 ,correction 9 ,longitude4 ,is x ,ea/ or ,we/8 ,s9ce azimu? is ,n #gd deg4 ,e1 ,l9e ( ,position is ,n #af deg4 ,w4 ,! ,d4 ,r4 ,latitude & ,latitude by ,obs]vation are plott$ on ?is l9e z foll[s3 99 ,lat4 by obs4 7#be deg4 #eb' ,s7 99 ,lat4 by ,d4,r4 7#be deg4 #ee' ,s7 ,latitude by obs]vation is ,we/ ( ,latitude by ,d4,r4 ,h5ce correction 9 longitude ( #ed is appli$ ,we/4 ,position by obs]vation1 !re=e1 is z foll[s3 ,lo4 #ajd deg4 #ec' #ef ,e ,corr4 9 ,lo4 #ed ,w -------------- ,lo4 by obs4 #ajd deg4 #ec' #jb ,e ,lat4 by obs4 #be deg4 #eb' ,s ,note to ,in/ructor3 ,assign ! foll[+ examples = "w 9 ! class room3 #a4 ,april #bj?1 #aiai ,a4,m4 at ! %ip4 ,g4,m4,t4 #bj;d #aj;h #bhm #bds ,a4,m4 77 #ca deg4 #ee' #dj4 ,,he #cj ft4 ,no ,,ie1 ,,cc4 ,latitude by ,d4 ,r4 #bf deg4 #cj' ,n4 ,longitude #cf deg4 #ee' ,we/4 ,%ip !n sail$ a true c\rse ( ,s #cf deg4 ,e--#dj knots until noon :5 obs]v$ altitude 77 #ge deg4 #dj' #ej ,s4 ,:at 0 ! position at noon correct$ = ,longitude8 7,note3 ,"w ! ,a4,m4 sight by bo? ,"t ,sight & ,m>c ,/4 ,hilaire ,me?od47 #b4 ,june #be?1 #aiai1 ,a4,m4 ,latitude by ,d4 ,r4 #cf deg4 #bj' ,s4 ,longitude #if deg4 #cj' ,e4 ,,ct #a;h #cgm #afs ,a4,m4 ,,cc #am #cjs fa/4 ,,ie #b' #cj (f arc4 ,,he #cf ft4 77 #g deg4 #cd' #bj4 ,log regi/]$ #aad4 ,true c\rse to noon ,s #gf deg4 ,e4 ,log regi/]$ #agd4 ,same ,,ie1 ,,he1 ,,cc4 ,obs]v$ altitude 77 #bi deg4 #dd' #dj ,n4 ,requir$ position at noon by ,longitude factor4 7,note3 ,"w ,a4,m4 ,sight by ,m>c ,/4 ,hilaire ,me?od47 #c4 ,at sea1 ,may #cj?1 #aiai4 ,9 ,d4 ,r4 ,latitude #ch deg4 #ad' #bi ,n4 ,longitude #ae deg4 #ch' #di ,w4 ,obs]v$ altitude 77 #ci deg4 #je' #dj & be>+ by compass #bei deg44 ,,ie #a' #jj on arc4 ,,he #bg ft4 ,,wt #c;h #jdm #dis4 ,c-,w #a;h #cim #ees4 ,,cc #am #ebs fa/4 ,*ang$ c\rse to #id deg4 p4s4c4 & /eam$ #ge knots to ab\t #h o'clock4 ,,wt #h;h #jfm #ahs4 ,c-,w #a;h #cim #ehs4 ,at ?is "t obs]v$ altitude ( ,/> ,arcturus #fh deg4 #cj' #dj1 ,ea/ ( m]idian4 ,same ,,ie1 ,,he1 ,,cc4 ,*ang$ c\rse to #ie deg4 7true74 ,/eam$ #fj knots until midnight :5 ran into heavy fog4 ,sl[$ d[n to #g knots p] h\r until #h ,a4,m4 :5 obs]v$ altitude 77 #dh deg4 #de' #aj4 ,,ct #i;h #dem #ahs ,a4,m4 ,same ,,he1 ,,ie1 ,,cc4 ,requir$ fix at #h ,a4,m4 by ,m>c ,/4 ,hilaire ,me?od1 laid d[n on *>t4 ,note to ,in/ructor3 ,sp5d re/ ( p]iod 9 famili>iz+ pupils ) lay+ d[n runs & int]sect+ l9es ( position on ,m]cator plott+ *>ts4 ,,?ursday ,,lecture ,,! ,,navigator',s ,,r\t9e--,a ,,day',s ,,"w ,,at ,,sea ,y are n[ famili> ) ! pr9cipal k9ds ( sights & ! me?ods us$ 9 work+ !m z expla9$ 9 ! =ego+ pages4 ,?is in=mation1 h[ev]1 relates only to ea* individual k9d ( sight4 ,today ,i w expla9 briefly h[ ^? sights are made use ( 9 y\r daily "w at sea4 ,su* an explanation necess>ily _c include ! navigator's "w "u all conditions & on all classes ( %ips4 ,x m]ely gives a brief outl9e ( & a few sugge/ions relat+ to navigat+ conditions on bo>d a m$ium-siz$ transport1 9 "t ( w>4 ,i say 9 "t ( w> because navigat+ !n is diff]5t1 to "s ext5t1 f ! ord9>y r\t9e 9 "t ( peace4 ,suppose y are ord]$ to a %ip z navigator4 ,:at are y\r duties 7a7 be=e leav+ port1 7b7 :ile at sea1 & 7c7 on ent]+ pilot wat]s8 7a7 ,be=e ,leav+ ,port ,asc]ta9 ! height ( ! eye ( ! bridge & any o!r place on ! %ip :]e y w\ld be likely to take sights4 ,h po/$ 9 ! *>t room & on ! bridge ! deviation ( ! compass on ea* #ae deg4 head+1 s t x c be easily ref]r$ to4 ,keep 9 ea* *ronomet] case or 9 a book ne>by ! error & daily rate ( all *ronomet]s on bo>d4 ,te/ ea* sextant = index error & record ! result :]e y c ref] to x easily4 ,see t all *>ts ( ! h>bor out ( :i* y are to /eam are correct$ to date & are famili> to y1 bo? z to sail+ directions & buoys1 & also z to lights & o!r aids to navigation4 ,exam9e1 9 detail1 ! /e]+ eng9e & /e]+ app>atus4 ,9 case ( its dis>rangem5t y\r intimate k ( x may be mo/ valuable4 ,see t ! pat5t log & s\nd+ ma*9e are 9 good ord]4 ,see t ! lead l9es are well soak$ 9 wat]1 /ret*$1 & prop]ly m>k$4 ,see t ! light+ sy/em 9 ! *>t room & ! navigator's room is su* t :5 any door is n tightly clos$ ! lights 9 ! room are ext+ui%$4 ,likewise1 :5 ! doors are clos$1 see t ! lights w light & )\t repeat$ slamm+ ( ! doors4 ,if possible1 provide y\rself ) a fla%light set back 9 a metal tube s t ! rays ( ! light are n diffus$ b c be focuss$ only on "o spot at a "t4 ,see t y\r *>ts are arrang$ neatly 9 ! draw]s provid$ = !m 9 ! *>t room4 ,if1 z is usual1 ! *>ts mu/ be fold$ to get !m 9 ! draw]s1 m>k !m legibly on ! outside & 9 ! same place on ea* *>t4 ,put 9 ! top draw]s ^? *>ts y "k y w use mo/ frequ5tly4 ,?is w save endless "t & confusion4 ,be sure y h a full complem5t ( necess>y in/rum5ts1 includ+ sextants1 a /adimet]1 b9ocul>s1 wat*es1 /op wat*1 divid]s1 p>allel rul]s1 p5cils1 "w books2 also all necess>y books1 su* z smoo? & deck log books1 sev]al volumes ( ,b[dit*1 ,nautical ,almanacs1 ,azimu? ,tables1 ,pilot books1 ,light & ,buoy li/s1 ,/> ,id5tification ,tables1 etc4 ,y w be repaid a ?\s& times = :atev] ef=t y exp5d to h y\r navigational equipm5t complete to ! smalle/ detail4 ,! %ortage1 = in/ance1 ( a pair ( divid]s w\ld be an un5d+ annoyance to y4 ,?is is also true ( almo/ any o!r item m5tion$ above4 ,prep>e y\rself1 !n1 :ile y are 9 port & h pl5ty ( opportunity to secure ! equipm5t y desire4 7b7 ,:ile at ,sea ,! lea/ am\nt ( "w requir$ ( a navigator 9 "t ( peace w\ld include 7#a7 a morn+ sight = longitude1 7#b7 a noon sight = latitude1 7#c7 an aft]noon sight = longitude1 7#d7 an ,a4,m4 azimu? to *eck ! deviation ( ! compass1 & 7#e7 ! dead reckon+ = ! day's run f noon to noon4 ,navigat+ 9 w> "t requires m "w ?an ?is4 ,if possible1 ! %ip's position mu/ be kn[n accurately at any "t ( day or night =1 9 case ( an em]g5cy1 ! lives ( all on bo>d may be imp]ill$ by inaccurate k ( y\r :]eab\ts4 ,?is means t m sights mu/ be tak5 & m cele/ial bodies obs]v$4 ,:ile e navigator has 8 own idea z to ! prop] am\nt ( "w to d 9 a day1 x w\ld seem z ?\gh ! foll[+ w\ld cov] ! m9imum am\nt ( "w necess>y "u pres5t conditions3 #a4 ,an ,a4,m4 sight ( ! sun = longitude4 #b4 ,an azimu? ( ! sun = *eck+ ! deviation ( ! compass1 tak5 "r aft] ! ,a4,m4 sun sight4 #c4 ,! wat* "t ( ,local ,app>5t ,noon4 #d4 ,ex-m]idian & m]idian altitudes ( ! sun = latitude4 #e4 ,a ,p4,m4 sight ( ! sun = longitude4 #f4 ,an ev5+ twilight sight ( ?ree or f\r />s1 pref]ably "o 9 ea* quadrant4 ,if ^! altitudes are tak5 correctly y\r position c be f\nd to ! dot4 #g4 ,a morn+ twilight sight = a fix or1 at lea/1 = latitude by ,pol>is4 #h4 ,! dead reckon+ f noon to noon4 #i4 ,di/ance run dur+ ! la/ #bd h\rs1 f noon to noon #aj4 ,di/ance to de/9ation4 #aa4 ,set & drift ( ! curr5t4 #a4 ,! ,a4,m4 ,sun ,sight ,9 ord] to make ?is a valuable sight = longitude x %\ld be tak5 :5 ! sun is on or z ne> z possible to ! prime v]tical4 ,z ! sun1 9 ,nor? latitudes1 passes ! prime v]tical be=e sunrise 9 ! w9t]1 ! foll[+ rem>ks d n hold = t season4 ,9 w9t] ! only rule to foll[ is to obs]ve ! sun z soon z x is #aj deg4 or m above ! horizon4 ,9 summ] f9d out f ! ,azimu? ,tables ! local app>5t "t :5 ! sun w be> #ij deg44 ,e/imate1 z closely z possible1 ! longitude y w be 9 ! next morn+ :5 ! local app>5t "t is z j f\nd 9 ! ,azimu? ,tables4 ,?is c be done by calculat+ ! dead reckon+ f ! previ\s sight1 or1 :at is ev5 simpl]1 lay+ ! di/ance (f on ! plott+ *>t4 ,) ?is in=mation f9d ! ,w4,t4 correspond+ to ! ,l4,a4,t4 m5tion$ above by "s su* =mula z ?is3 ,l4,a4,t4 - ,lo4 ,g4,a4,t4 - ,eq4 ,t4 7sign rev]s$7 ,g4,m4,t4 - ,c4,c47sign rev]s$7 ,c4,t4 - 7,c-,w7 ,w4,t4 ,?is w n be absolutely accurate1 = ! longitude y are 9 is only approximate1 b x w be close en\gh = good results4 ,?is result+ ,w4,t4 w be ! "t to take ! ,a4,m4 sight4 ,ab\t fifte5 m9utes be=e t "t comp>e y\r wat* ) y\r *ronomet] to get ! ,c-,w4 ,also br+ up ! ,c4,c4 to date & make a note ( x s t z mu* z possible ( ?is detail "w is accompli%$ be=e ! sight is tak54 ,next1 take y\r sextant & te/ x = index error4 ,?is %\ld be done regul>ly be=e ea* s]ies ( sights z x is impossible to tell :at may h happ5$ :5 ! sextant is ly+ idle1 except by ! above te/4 ,n[1 ) y\r sextant1 wat* & notebook1 g to ! place f :i* y h decid$ to take y\r obs]vations &1 at ! prop] wat* "t1 />t tak+ y\r altitudes4 ,x is always advisable to take a numb] ( sights1 closely foll[+ ea* o!r1 s t an error 9 "o may be correct$ some:at by ! o!rs4 ,take at lea/ ?ree sights 9 close succession4 ,at ! same "t h ! log read & ent] x 9 y\r notebook4 ,an equally good me?od 9 fair wea!r is to secure ! di/ance run f ! revolutions ( ! propell]4 ,hav+ tak5 y\r sights1 g to ! /&>d compass & get a be>+ ( ! sun1 at ! same "t not+ 9 y\r book ! ,w4,t4 ( ! be>+ & ! compass head+ ( ! %ip4 ,y are n[ ready to g bel[ into ! *>t room & "w out y\r position4 ,:at me?od %all y use8 ,t dep5ds ^u y\r pref]5ce4 ,y h miss$ ! po9t ( ! previ\s lectures1 h[ev]1 if y =get t ! ,new ,navigation is bas$ ^u ! ,m>c ,/4 ,hilaire ,me?od1 & ?is is und\bt$ly ! me?od y\r capta9 w pref] y to use if he is an ,annapolis graduate4 ,9 ?is connection let me rem9d y aga9 ( ! "o fact1 ! ov]sight ( :i* disc\rages s _m beg9n]s ) ! ,m>c ,/4 ,hilaire ,me?od4 ,! mo/ probable fix1 :i* y get by "o sight only1 is n actually a fix at all4 ,nor does any o!r me?od give y an accurate fix "u l conditions4 ,:at ! mo/ probable fix is1 & all x claims to be1 is a po9t ?r\gh :i* ! requir$ ,sumn] l9e is to be drawn4 ,if y\r ,d4,r4 position happ5s to be only "o mile away f ! mo/ probable fix1 t is no assurance t ! mo/ probable fix is ne> ! actual position ( ! %ip4 ,y may be #be miles away f x4 ,b ! important in=mation ga9$ is t1 ?\gh y may be #be miles away1 y "k on :at l9e y are1 & :5 ?is l9e is lat] cross$ ) ano!r l9e ( position t fix w be accurate4 ,two sights make a fix is ! :ole matt] 9 a nut%ell4 #b4 ,! ,compass ,error ,hav+ secur$ y\r morn+ sight1 ! next duty is to get ! compass error4 ,f y\r morn+ sight computation y "k ! wat* "t correspond+ to ! ,l4,a4,t4 ( ! same sight4 ,f9d ! diff]5ce betwe5 ! two & apply ?is diff]5ce to ! wat* "t ( ! compass azimu?4 ,t w give y ! ,l4,a4,t4 ) :i* to ent] ! ,azimu? ,tables to get ! true be>+ correspond+ to ! compass be>+ rec5tly obs]v$4 ,apply ! v>iation f ! *>t to get ! magnetic be>+4 ,! diff]5ce betwe5 ?is magnetic be>+ & ! compass be>+ w be ! requir$ deviation1 :i* y %\ld comp>e ) y\r ,deviation ,table4 ,if !re is a m>k$ diff]5ce1 & y are sure ( y\r figures1 use ! new deviation 9 comput+ c\rses on ?is head+ ( ! %ip4 #c4 ,! ,wat* ,"t ( ,local ,app>5t ,noon ,y are n[ ready to figure ! wat* "t ( local app>5t noon4 ,unless y h a decid$ pref]5ce to ! contr>y1 d ?is by ! me?od expla9$ 9 ! ,saturday ,lecture1 ,week ,,vi4 ,d n =get t 9 subtract+ ! ,l4,a4,t4 ( ! morn+ sight f #bd h\rs to get ! total "t to noon1 9 case ! %ip 7 /ation>y1 y d n use ! ,l4,a4,t4 ( ! ,d4,r4 position1 b ! ,l4,a4,t4 f\nd by subtract+ f ,g4,a4,t4 ! longitude ( ! mo/ probable fix4 ,?is w give y ! ,l4,a4,t41 bas$ on ! longitude ( ! mo/ probable fix1 :i* w be slightly diff]5t f ! ,l4,a4,t4 bas$ on ! ,d4,r4 longitude4 ,:5 y h secur$ ! wat* "t ( local app>5t noon1 subtract #cj m9utes f x & notify ! qu>t]ma/] t at t "t by y\r wat* ! deck clocks are to be set to #aa4cj ,a4,m4 ,if ?is *ange ( "t is v great 7provid+ y are on an almo/ ea/]ly or we/]ly c\rse71 x is wise to h ! clocks set back 9 ! night wat*es to all[ = mo/ ( ! "t y figure y w lose4 ,?is w n "w su* a h>d%ip or su* an advantage to ! (fic]s & m5 :o h ! =5oon wat* & w also be easi] = ! cooks4 ,! clocks c !n be slightly b accurately *ang$ at #aa4cj ,a4,m41 z m5tion$ above4 #d4 ,ex-,m]idian & ,m]idian ,altitudes ,y "k ! pr9ciples & me?ods gov]n+ sights ( ?is "*4 ,to "k y\r latitude exactly at noon is usually requir$ :5 y are /eam+ 9 convoy1 = at t "t y\r position signals are hoi/$1 & x is a matt] ( pride ) ! navigator n only to h 8 position exact b promptly4 ,if y\r ,a4,m4 sight 0 tak5 :5 ! sun 0 on or ne> ! prime v]tical1 a *ange 9 latitude at noon w make no *ange 9 longitude4 ,h5ce y c figure y\r longitude at noon j z soon z y h secur$ ! correct$ "t f ! ,a4,m4 sight to noon 7:i* y h done "r aft] work+ ! ,a4,m4 sight74 ,y w h y\r longitude1 !n1 be=e y g on ! bridge to obs]ve = ex-m]idian & m]idian altitudes4 ,%>ply at noon y take y\r m]idian altitude & tell a mess5g] to notify ! capta9 t x is noon at ! %ip4 ,! capta9 !n ord]s eight bells /ruck1 & y are ready to h& 9 y\r noon report1 consi/+ ( latitude & longitude by obs]vation1 latitude & longitude by dead reckon+1 deviation ( ! compass on ! %ip's head at #h ,a4,m41 di/ance made good s9ce ! prec$+ noon1 di/ance to de/9ation1 set & drift ( curr5t 7,note3--,:5 /eam+ 9 convoy ?is is unnecess>y & usually omitt$71 & any o!r p]t95t rem>ks4 ,if ! sun 0 n tak5 on or ne> ! prime v]tical at ! "t ( ! ,a4,m4 sight1 take out y\r longitude factor = ! com+ noon position & calculate y\r ,d4,r4 latitude at noon4 ,by correct+ ! longitude ( ! ,a4,m4 sight1 run to noon1 ) ! diff]5ce ( longitude1 readily f\nd at noon ) ! longitude factor & ! error 9 latitude1 y w h ! correct noon longitude to h& 91 ) only a mom5t's delay4 ,x w be v h>d1 h[ev]1 to get all ?is in=mation 9 on "t )\t ! use ( latitude con/ants4 ,!re is no room = a discussion ( ^! con/ants "h1 b !y are easy to "w & y %\ld le>n h[ to use !m4 ,! in=mation is 9 ,b[dit* ,art4 #cbe1 p4 #abh1 & ,art4 #dje1 p4 #aha4 #e4 ,! ,p4,m4 ,sun ,sight ,?is is ano!r longitude sight & s any previ\s rem>ks ab\t sights ( ?is "* are applicable "h4 ,if ! day is f9e y ne$ n "w out ?is sight until aft] ev5+ twilight1 = a fix !n by />s w give bo? latitude & longitude1 :]eas y\r aft]noon sun sight w only give y a longitude4 ,?is ,p4,m4 sun sight is a good *eck sight1 to be us$ or n1 accord+ z to :e!r o!r e>li] or lat] sights h be5 obta9$4 #f4 ,! ,ev5+ ,twilight ,sight ,! beauty ( us+ />s is t by almo/ simultane\s altitudes ( diff]5t ones y c asc]ta9 y\r position1 bo? z to latitude & longitude4 ,9 ! ,nor? ,atlantic dur+ ! summ] mon?s ,vega1 ,d5eb or ,altair 9 ! ,ea/1 ,ant>es or ,d5eb ,kaitos 9 ! ,s\?1 ,arcturus 9 ! ,we/1 & ,pol>is1 ,miz>1 or ,ko*ab 9 ! ,nor? =m an ideal comb9ation :i* includes e quadrant ( ! compass4 ,9 ! w9t] mon?s1 ,capella1 ,ca/or or ,pollux 9 ! ,ea/1 ,sirius or any /> 9 ,orion's belt 9 ! ,s\?1 ,d5eb 9 ! ,we/1 & ,pol>is 9 ! ,nor? are equally z good4 #g4 ,! ,morn+ ,twilight ,sight ,9 cle> wea!r ?is %\ld be prim>ily a sight = latitude1 s9ce ! ,a4,m4 sun sight = longitude w foll[ x4 ,a latitude by ,pol>is1 & at ! same "t "s /> 9 "o ( ! s\!rn quadrants1 z a *eck1 w give admirable results4 #h4 ,! ,dead ,reckon+ f ,noon to ,noon ,if !re is no *ange ( c\rse 9 ! late =5oon1 z is usually ! case1 ! dead reckon+ = ! day's run c be figur$ any "t be=e noon s t x w be all ready to h& 9 to ! capta9 ) ! o!r noon data4 ,x is mu* easi] to lay ?is (f on ! *>t ?an to g to ! tr\ble ( calculat+ x by ,table #b1 ,b[dit*4 ,on ! o!r h&1 su* a calculation *ecks ! *>t "w & %\ld be work$ out if y wi% to make assurance d\bly sure4 #i4 ,di/ance ,run ,dur+ ! ,la/ #bd ,h\rs ,"h1 aga91 an answ] by *>t & an answ] by figures is a good ?+ to secure4 ,z y become accu/om$ to y\r "w y w f9d ! answ] by *>t inf9itely easi] & quick] to get4 ,x is j z accurate1 too1 if y lay ! di/ances (f c>efully ) ! divid]s & p>allel rul]s4 #aj4 ,di/ance to ,de/9ation ,! same rem>ks z are made "u 7#i7 hold true "h4 #aa4 ,set & ,drift ( ,curr5t ,f9d ! diff]5ce betwe5 y\r ,d4,r4 position & y\r position by obs]vation at noon1 i4e41 ! c\rse & di/ance f y\r ,d4,r4 position to y\r position by obs]vation4 ,! c\rse is ! set ( ! curr5t1 ! di/ance ! am\nt ( drift1 all ( :i* is easily calculat$ by ,table #b1 ,b[dit*4 ,?is diff]5ce betwe5 ! two positions is seldom due to curr5t4 ,x is due to all errors ( /e]+ & ! l4 ,b ^! are all ascrib$ to curr5t1 = ! sake ( conv5i5ce4 ,?is calculation ( ! curr5t is seldom us$ n[1 p>ticul>ly :5 /eam+ 9 convoy4 ,x is obvi\s t a s*$ule1 su* z outl9$ above1 _c be adh]$ to 9 all k9ds ( wea!r or "u all conditions4 ,x is m]ely an outl9e ( :at might prop]ly be includ$ 9 a #bd h\r day1 ! wea!r conditions ( :i* w l5d !mselves at any "t to tak+ ! obs]vations m5tion$4 ,! wea!r ( ea* succe$+ day may =ce y to adopt a diff]5t r\t9e4 ,nev]!less1 ! clos] y c keep to ! above s*$ule ! m exact w y\r v>i\s positions be4 7c7 ,on ,ent]+ ,pilot ,wat]s ,see t all *>ts ( ! locality y int5d to ent] are correct$ to date4 ,/udy ^! *>ts c>efully1 mak+ notes1 9 detail1 ( ! aids to navigation t y int5d to pick up4 ,9 not+ lights give _! di/9ctive appe>ance1 range ( visibility1 approximate "t ( sight+ !m1 & any o!r in=mation t y ?9k y may ne$4 ,if y h ?is in=mation ) y :5 on ! bridge x w save mu* "t & tr\ble t y w\ld o!rwise h to sp5d1 at possibly a critical "t1 9 ! *>t room4 ,see t log l9es1 s\nd+ ma*9e1 etc41 are 9 ord] = in/ant use4 ,rememb] t 9 ent]+ pilot wat]s ! safe/ l&m>ks are p]man5t ones4 ,buoys1 cans1 etc41 may drag f _! positions or be lo/ altoge!r4 ,?is c also happ5 to light%ips4 ,become famili> ) s\nd+s1 rise & fall ( ! tides1 & ! l1 9 ! neighborhood 9 :i* y int5d to an*or4 ,if possible *oose an an*orage t w enable y to get be>+s f two or ?ree fix$ po9ts on %ore4 ,z soon z possible aft] an*or+ secure y\r be>+s by pelorus & h !m *eck$ up by ! qu>t]ma/] at regul> int]vals4 ,?is w det]m9e h[ mu*1 if any1 dragg+ has tak5 place4 ,la/ly1 always rememb] t no am\nt ( advice c make up = y\r own c>elessness4 ,hold y\rself ready = any em]g5cy1 keep cool1 keep pati5t & keep pleasant4 ,common s5se is ! be/ antidote 9 ! _w = /range situations4 ,if y h t1 & ! k y %\ld h secur$ f ^! lectures1 y _c g f> wrong4 ,:ile ! day's "w :i* foll[s does n include e sight 9 regul> sequ5ce z giv5 9 ! above discussion1 x w give a fair idea ( ! navigator's "w dur+ a day's run4 ,put x 9 y\r notebook4 7,note to ,in/ructor3--,sp5d ! re/ ( ! p]iod 9 expla9+ c>efully ea* /ep ( ?is example47 ,a ,,day',s ,,"w ,,at ,,sea ,dep>ture tak5 f noon position ,jan4 #be?1 #aiai1 9 ,latitude #cj deg4 #ja' ,n1 ,longitude #gc deg4 #dg' #bj ,w4 ,c\rse p4s4c4 ,,ne #c_/d ,n4 ,deviation #b deg4 ,e4 ,v>iation #d deg4 ,w4 ,log regi/]$ #bj4 ,%ip cont9u$ on ?is c\rse until ab\t #f3cj ,p4,m4 :5 log regi/]$ #ih & obs]v$ altitude ( ,/> ,rigel1 ,ea/ ( m]idian1 #ci deg4 #cf' #bj4 ,,wt #f;h #ccm #ais ,p4,m4 ,c-,w #d;h #eem #jds4 ,,cc #bm #afs sl[4 ,,he #cg ft4 ,,ie #j' #bj (f arc4 ,*ang$ c\rse to #dj deg4 7true7 & /eam$ until #c ,a4,m4 :5 log regi/]$ #aih4 ,at ?is "t %ip ran into heavy ,,ne gale4 ,sl[$ d[n to #g knots p] h\r until ab\t #h3cj ,a4,m4 :5 obs]v$ 77 #ah deg4 #be' #aj & be>+ by compass ,s #df deg4 ,e4 ,v>iation #g deg4 ,w4 ,,wt #h;h #cam #afs ,a4,m4 ,c-,w #d;h #eem #jds4 ,,ie #j' #aj4 ,same ,,he1 ,,cc4 ,%ip !n /eam$ on true c\rse ( #ci deg4 at #g knots p] h\r until noon :5 log regi/]$ #bfa & obs]v$ m]idian altitude 77 #cg deg4 #ei' ,s4 ,same ,,ie 7 #j' #aj71 ,,he1 ,,cc4 ,requir$3-- #a4 ,position by ,d4 ,r4 at noon4 #b4 ,position by obs]vation at noon 7correct$ = ,longitude by a factor74 #c4 ,deviation ( compass at #h3cj ,a4,m4 #d4 ,wat* ,"t ( ,local ,app>5t ,noon4 7,see ,next ,page7 ,at ,sea1 ,jan4 #be1 #aiai4 ,lat4 9 #cj deg4 #ja' ,n ,lo4 9 #gc deg4 #dg' #bj ,w ,/eam$ until #f3cj ,p4,m4 ,c\rse ,di/4 ,d4 ,lat4 ,dep4 ,d4 ,lo4 ---------------------------------------- -- ,n #ce deg4 ,e #gh #fc4i #dd4g #ea4e ,lat4 ,left #cj deg4 #ja' ,n ,lo4 ,left #gc deg4 #dg' #bj ,w ,d4 ,lat4 #a #jc #ed ,n ,d4 ,lo4 #ea #cj ,e ------------ ------------ ,lat4 9 #ca deg4 #jd' #ed ,n ,lo4 9 #gb deg4 #ee' #ej ,w ,mid ,lat4 #cj deg4 #cj' ,n ---------------------------------------- ------------------------ ,at #f3cj ,p4,m4 ,obs4 99 ,rigel4 ,obs4 ,alt4 99 #ci deg4 #cf' #bj ,w4,t4 #f;h #ccm #ais ,log hav t #h4ibejb ,e #jj #bj ,c4,w4 #d #ee #jd ,log cos ,lat4 #i4icbfi ------------- ,c4,c4 #b #af ,log cos4 ,dec4 #i4iiedd #ci deg4 #cf' #dj ----------- -------- ,,he - #g #ji ,g4,m4,t4 #aa;h #cjm #cis ,log hav ,s #h4hecae ,nat hav ,s 4#jgacj ------------- 7474,r4,a4 #bj #ad #eh ,nat hav ,l--,d 4#aacdi ,t4,c4,a4 99 #ci deg4 #bi' #ca 774,c4,p4 #a #ec4c ------ ------------- ----------- ,nat hav ,,zd 4#ahdgi ,dec4 ( 99 #h deg4 #ag' #db,s ,g4,s4,t4 #ca;h #dgm #cj4cs #ej deg4 #ee' #jj ,,zd ,lat4 #ca #jd #ed ,n --,w4,lo4 #d #ea #dc -#ij #jj #jj ------------- ----------- ------------ ,l4,d4 #ci deg4 #bb' #cf ,l4,s4,t4 #b;h #eem #dg4cs #ci deg4 #je' #jj ,c4,alt4 ------------- 99,r4,a4 #e #aj #da #ci #bi #ca ,t4,alt ----------- ------------ t #b;h #adm #eds #bd' #ca ,alt4 ,diff4 ,t[>d4 ,illu/ration3 ,,tz ,n #ace deg4 ,e1 ,s #de deg4 ,e ,c\rse ,di/ ,d4 ,lat4 ,dep4 ,d4 ,lo4 ---------------------------------------- -------- ,s#de deg4 ,e #bd4e #ag4c #ag4c #bj ,lat4 ,left #ca deg4 #jd' #ed ,n ,lo4 ,left #gb deg4 #ee' #ej ,w #ag #ah ,s #bj ,e ------------- ------------- ,lat4 9 #cj deg4 #dg' #cf ,n ,lo4 9 #gb deg4 #ce' #ej ,w ,*ang$ c\rse to #dj deg4 7true7 ,c\rse ,di/ ,d4 ,lat4 ,dep4 ,d4 ,lo4 ---------------------------------------- ------- ,n#dj deg4 ,e #ach4e #ajf4a #hi #aje ,lat4 ,left #cj deg4 #dg' #cf ,n ,lo4 ,left #gb deg4 #ce' #ej ,w #a #df #jf ,n #a #de ,e ------------- ------------- ,lat4 9 #cb deg4 #cc' #db ,n ,lo4 9 #gj deg4 #ej' #ej ,w #h4cj ,a4,m4 77 #ah deg4 #be' #aj ,w4,t #bj;h #cam #afs ,log hav t #i4bhbhd ,,ie #aj ,c-,w #d #ee #jd ,log cos ,lat4 #i4ibegc ---------- ,c4,c4 #b #af ,log cos ,dec4 #i4igeie #ah deg4 #be' #bj ----------- ------- ,,he #g #cd ,g4,m4,t4 #a;h #bhm #cfs ,log hav ,s #i4ahdeb ,nat hav ,s 4#aebid ---------- ,eq4,t - #ab #cb ,nat hav ,l,d 4#ahhda -77- #ah deg4 #cb' #ed ----------- ------ ,g4,a4,t4 #a;h #afm #jds #ga deg4 #cj' #jj ,,zd ,nat hav ,,zd 4#cdace ,dec4 #ah deg4 #ec' #bd ,s -,w4,lo4 #d #dc #ea -#ij #jj #jj ,lat4 #cb deg4 #cc #db ,n ----------- ----------- ------------ ,l4,a4,t47t7 #bj;h #cbm #acs #ah deg4 #cj' #jj ,c4,alt4 ,l,d #ea deg4 #bg #jf #ah #cb #ed ,t4,alt4 ----------- #b' #ed ,t[>d ,illu/ration3 ,,tz ,n #abh deg4 ,e ,s #eb deg4,e ,c\rse ,di/4 ,d4,lat4 ,dep4 ,d4,lo4 --------------------------------------- ,s #eb deg4 ,e #c #a4h #b4d #c ,lat4 ,left #cb deg4 #cc' #db ,n ,lo4 #gj deg4 #ej' #ej ,w #a #dh ,s #c ,e ----------- ----------- ,lat4 9 #cb deg4 #ca' #ed ,n ,lo4 9 #gj deg4 #dg' #ej ,w ,be>+ ( ,sun by ,compass ,s #df deg4 ,e ,true ,be>+ ( ,sun ,s #eb deg4 ,e ------- ,total ,error #f deg4 ,w ,v>iation #g deg4 ,w ----- ,deviation #a deg4 ,e ,c\rse ,di/4 ,d4 ,lat ,dep4 ,d4 ,lo4 -------------------------------------- ,n #ci deg4 ,e #bd4e #ai #ae4d #ah4d ,lat4 ,left #cb deg4 #ca' #ed ,n ,lo4 ,left #gj deg4 #dg' #ej ,w #ai ,n #ah #bd ,e ------------ ------------ ,lat4 9 #cb deg4 #ej' #ed ,n ,lo4 9 #gj deg4 #bi' #bf ,w ,at ,noon4 ,l4,a4,t4 #jj;h #jjm #jjs 77 #cg deg4 #ei' ,s ,w4 ,lo4 #d #da #eh ----------- ,,ie #aj ,g4,a4,t4 #d;h #dam #ehs ------------ ,e4,t4 7sign rev]s$7 #ab #cd #cg deg4 #ei' #aj ----------- ,,he #h #ee ,g4,m4,t4 #d;h #edm #cbs #ag ---------- -7-7- #ch deg4 #jh' #bb ,s #ea deg4 #ea' #ch ,n 7,,zd7 #ah #ea #ab ,s 7,dec47 ---------- #cc deg4 #jj' #bf ,n4 ,lat4 9 at ,noon4 ,lo4 ,factor 4#ic ,lat4 by ,obs4 #cc deg4 #jj' #bf ,n ,lat4 ,diff4 #i4e ,lat4 by ,d4,r4 #cb deg4 #ej' #ed ,n ------ ------------ ,diff4 ,lo4 #h4hc ,lat4 ,diff4 #i' #cb ,s9ce ,obs4 ,lat4 is ,ea/ ( ,d4,r4 ,lat4 on ,l9e ( ,pos4 ,lo4 ,diff4 is appli$ ,ea/4 _/ ,lo4 by ,d4,r4 #gj deg4 #bi' #bf ,w _/ ,lo4 ,diff4 #h #ej ,e ,obs4 ,lat4 99 ------------ _/ ,lo4 9 at ,noon #gj deg4 #bj' #cf ,w ,d4,r4 ,lat4 99 _/ _/ ,by ,dead ,reckon+ f ,noon to ,noon ,c\rse ,di/4 ,d4 ,lat4 ,dep4 ,d4 ,lo4 ---------------------------------------- --------------- ,n #ce deg4 ,e #gh #fc4i #dd4g #agf' or #b deg4 #ef' ,n #dj deg4 ,e #ach4e #ajf4a #hi4 ,n #ci deg4 ,e #bd4e #ai4 #ae4d ----- ---- #ahi4 #adi4a ,lat4 left4 #cj deg4 #ja' ,n ,lo4 left #gc deg4 #dg' #bj ,w #c #ji ,n #b #ef ,e --------- ------------- ,lat4 9 #cc deg4 #aj' ,n ,lo4 9 #gj deg4 #ea' #bj ,w ,m94 ,lat4 #ca deg4 #ce' ,! ,wat* ,"t ( ,local ,app>5t ,noon ,date--,jan4 #bf1 #aiai ,g4,a4,t4 ( ,a4,m4 ,sight #a;h #afm #jds ,lo4 9 ,t4 ( ,a4,m4 sight #d #dc #ab ----------- ,l4,a4,t4 #bj;h #cbm #ebs ,total ,"t to ,noon #c;h #bgm #jhs ,c\rse to ,noon -- #ci deg4 ,*ange 9 ,lo4 p] hr4 -- #e4b'1 #bas #cfjjs #bas #cfbas #c ,x #fj #ahj #bg ----- #bjg #fj ------ #ab1dbj #jh -------- #cfba 7 #ab1dbh 7#c4dc hrs #aj1hfc ------ #ae1fej #ad1dhd ------ #aa1ffj #aj1hfc ------ #c4dc hrs #c;h #bem #dhs ,w4,t4 ( ,a4,m4 sight #h #ca #af ,a4,m4 ---------- ,w4,t4 ( ,l4,a4,n4 #aa;h #egm #jds ,a4,m4 ,,answ]4 ,by ,d4,r4 ,lat4 #cc deg4 #aj' ,n ,lo4 #gj deg4 #ea' #bj ,w ,by ,obs]vation ,lat4 #cc deg4 #jj' #bf ,n ,lo4 #gj deg4 #bj' #cf ,w ,dev4 at #h3cj ,a4,m4 #a deg4 ,e ,w4,t4 ( ,l4,a4,n4 #aa;h #egm #jds ,a4,m4 ,,friday ,,lecture ,,day',s ,,"w ,at sea1 ,novemb] #bh?1 #aiah4 ,dep>ture tak5 at noon 9 ,latitude #bj deg4 #ej' ,n1 ,longitude #gc deg4 #ae' #bj ,w4 ,log at noon regi/]$ #cd4 ,sail$ on c\rse p4s4c4 #gc deg41 ,deviation #c deg4 ,e1 ,v>iation #a deg4 ,w until twilight :5 log regi/]$ #aeb4 ,*ang$ c\rse to ,e #c_/d ,n p4s4c4 & obs]v$ altitude ( ,/> ,aldeb>an1 ,ea/ ( m]idian #cg deg4 #aj' #aj & be>+ by compass ,n #hi deg4 ,e1 ,v>iation #b deg4 ,w4 ,,wt #h;h #ajm #afs4 ,c-,w #d;h4 #eam #cjs4 ,,cc #dm #jhs sl[4 ,,ie #a' #aj (f ! arc4 ,,he #ch ft4 ,%ip /eam$ on ?is c\rse1 9 heavy fog & ra91 until #b3cj ,a4,m4 :5 log regi/]$ #bjj4 ,%ip *ang$ c\rse to ,e #a_/b ,n 7true7 & /eam$ at #h knots p] h\r until #f3cj ,a4,m4 :5 wea!r cle>$ & obs]v$ altitude ,/> ,pol>is #ba deg4 #jd' #bj ,n4 ,,wt #f;h #cem #dgs ,a4,m4 ,c-,w #d;h #eam #cjs4 ,same ,,ie1 ,,he & ,,cc4 ,%ip cont9u$ on same c\rse & spe$ until ab\t #i3cj ,a4,m4 :5 obs]v$ altitude ( 77 #ch deg4 #de' #bj4 ,,wt #i;h #cim #ajs ,a4,m4 ,c-,w #d;h #eam #cjs4 ,same ,,ie1 ,,he & ,,cc4 ,%ip !n /eam$ a true c\rse ( #ic deg4 at a rate ( #aj knots p] h\r until noon :5 log regi/]$ #bid & obs]v$ m]idian altitude 77 #df deg4 #di' #cj4 ,same ,,ie1 ,,he & ,,cc4 ,requir$ #a4 ,d4 ,r4 position at noon4 #b4 ,position by obs]vation at noon 7correct$ = ,longitude by a factor74 #c4 ,deviation at #h3aj ,p4,m4 #d4 ,wat* ,"t ( ,local ,app>5t ,noon4 ,,saturday ,,lecture ,,day',s ,,"w ,at sea1 ,april #ba/1 #aiah4 ,dep>ture tak5 f noon position 9 ,latitude #ca deg4 #ej' ,n1 ,longitude #gf deg4 #cj' #ca ,w4 ,log regi/]$ #abh at noon4 ,c\rse p4s4c4 until ab\t #d3cj ,p4,m4 0 ,n #aj deg4 ,e4 ,deviation #a deg4 ,w4 ,v>iation #c deg4 ,w4 ,at ab\t #d3cj ,p4,m4 obs]v$ altitude ( sun's l[] limb #be deg4 #ac' #aj & be>+ by compass ,n #hg deg4 ,w4 ,,wt #d;h #bfm #dfs4 ,c-,w #e;h #jdm #ebs4 ,,cc #am #jcs sl[4 ,,ie #j' #aj (f arc4 ,,he #bi ft4 ,log regi/]$ at ?is "t #ahh4 ,c\rse 0 !n *ang$ to ,,ne x ,n 7true74 ,wea!r cl\dy4 ,at ab\t twilight cl\ds broke away & obs]v$ altitude ( ,/> ,procyon ,we/ ( m]idian #dj deg4 #ja' #jj4 ,,ct #a;h #cgm #bhs ,a4,m4 ,,cc #am #jcs sl[4 ,,ie #j' #aj (f arc4 ,,he #bi ft4 ,log regi/]$ #bcf4 ,cont9u$ on same c\rse until midnight1 at :i* "t log regi/]$ #bij4 ,at midnight %ip ran into d5se fog & sl[$ d[n to #h knots until ab\t #f3cj ,a4,m41 :5 fog blew away & obs]v$ altitude ( ,/> ,pol>is #ce deg4 #bi' #aj ,n4 ,,wt #f;h #cbm #ads ,a4,m4 ,c-,w #d;h #eim #jbs4 ,,ie #j' #aj (f arc4 ,,cc #am #jcs sl[4 ,,he #bi ft4 ,f #f3cj ,a4,m4 %ip /eam$ a true c\rse ( ,n #cb deg4 ,e until noon at a rate ( #ae knots p] h\r1 at :i* "t a m]idian altitude ( ! 77 0 obs]v$ #fe deg4 #cg' #aj ,s4 ,log regi/]$ #dbd4 ,,he #bi ft4 ,,ie #j' #aj (f arc4 ,,cc #am #jcs sl[4 ,requir$ #a4 ,d4 ,r4 position at noon4 #b4 ,position by obs]vation at noon 7correct$ = ,longitude by a factor74 #c4 ,deviation ( ,compass at #d3cj ,p4 ,m4 sight4 #d4 ,wat* ,"t ( ,local ,app>5t ,noon4 ,,week ,,viii--,,navigation ,,monday ,,lecture ,,day',s ,,"w ,at sea1 ,nov4 #ab?1 #aiah4 ,dep>ture tak5 f noon position 9 ,latitude #ci deg4 #dj' ,n1 ,longitude #cc deg4 #bj' #jd ,w4 ,log regi/]$ at noon #a4 ,c\rse p4s4c4 0 #bid deg4 until ab\t #c3cj ,p4,m41 ,deviation #a deg4 ,w1 ,v>iation #bd deg4 ,w1 at :i* "t obs]v$ altitude 77 #ac deg4 #ee' #aj & be>+ by pelorus ,s #gi deg4 ,w4 ,,wt #c;h #bbm #ahs4 ,c-,w #b;h #acm #bj,s4 ,,cc #am #ajs4 ,,ie #a' #aj (f arc4 ,,he #cb ft4 ,log regi/]$ #df4 ,c\rse 0 !n *ang$ to #bij deg4 p4s4c4 until ab\t #f3cj ,p4,m4 :5 obs]v$ altitude ,/> ,pol>is #dj deg4 #ae' #dj ,n4 ,,wt #f;h #cbm #ahs4 ,c-,w #b;h #acm #bjs4 ,same ,,he1 ,,ie1 ,,cc4 ,log regi/]$ #ij4 ,%ip /eam$ on same c\rse until #a3cj ,a4,m4 :5 log regi/]$ #aif4 ,at #a3cj ,a4,m4 sight$ sub4 on port b[4 ,ord]$ full spe$ ahead & made #ag knots p] h\r until #h ,a4,m4 :5 obs]v$ altitude 77 #h deg4 #dj' #jj4 ,,wt #h;h #jam #cjs ,a4,m4 ,c-,w #b;h #acm #bjs4 ,same ,,he1 ,,ie1 ,,cc4 ,%ip !n /eam$ a true c\rse ( #bgb deg4 at a rate ( #ae knots p] h\r until noon1 at :i* "t obs]v$ m]idian altitude 77 #cb deg4 #ce' #dj ,s4 ,same ,,he1 ,,ie1 ,,cc4 ,log regi/]$ #cfb4 ,requir$ #a4 ,d4 ,r4 position at noon4 #b4 ,position by obs]vation at noon 7correct$ = ,longitude by a factor74 #c4 ,deviation ( ,compass at #c3cj ,p4,m4 #d4 ,wat* ,"t ( ,local ,app>5t ,noon4 ,,tuesday ,,lecture ,,day',s ,,"w ,at sea1 ,dec4 #aj?1 #aiah4 ,dep>ture tak5 f ,latitude #ai deg4 #ej' ,n1 ,longitude #bj deg4 #ja' #bj ,w4 ,noon position4 ,log regi/]$ #bj4 ,c\rse p4s4c4 ,n #af deg4 ,e4 ,deviation #b deg4 ,e1 ,v>iation #ah deg4 ,w4 ,%ip /eam$ on ?is c\rse until #h ,p4,m4 :5 *ang$ c\rse to ,n #ah deg4 ,e p4s4c4 & obs]v$ altitude ,/> ,pol>is #bb deg4 #cc' #ad ,n4 ,,wt #h;h #jim #ajs4 ,c-,w #a;h #bjm #jes4 ,,cc #bm #jjs fa/4 ,,ie none4 ,,he #ci ft4 ,log regi/]$ #ajd4 ,%ip !n /eam$ at #ad knots p] h\r until midnight4 ,at midnight *ang$ c\rse to ,n #ad deg4 ,e p4s4c4 & /eam$ at #ab knots p] h\r until #d ,a4,m4 ,at #d ,a4,m4 sl[$ d[n to #i knots p] h\r & /eam$ at t rate until #h3cj ,a4,m4 :5 c\rse p4s4c4 0 *ang$ to ,n #ag deg4 ,e & obs]v$ altitude 77 #bb deg4 #dj' #cj4 ,,wt #h;h #cdm #afs ,a4,m4 ,c-,w #a;h #bjm #jes4 ,same ,,ie1 ,,he1 ,,cc4 ,sun bore by compass ,s #fe deg4 ,e1 ,v>iation #ah deg4 ,w4 ,cont9u$ on ?is c\rse p4s4c4 = two h\rs1 spe$ #ab knots4 ,!nce /eam$ a true c\rse ( #d deg4 at same spe$ to noon :5 obs]v$ m]idian altitude 77 #db deg4 #cf' #ej ,s4 ,same ,,ie1 ,,he1 ,,cc4 ,requir$ #a4 ,d4 ,r4 position at noon4 #b4 ,position by obs]vation at noon 7correct$ = ,longitude by a factor74 #c4 ,deviation ( ,compass at #h3cj ,a4,m4 #d4 ,log read+ at noon4 ,,w$nesday ,,lecture ,,day',s ,,"w ,at sea1 ,july #ai?1 #aiah4 ,dep>ture tak5 f ,latitude #dj deg4 #cj' ,n1 ,longitude #de deg4 #jj' #aj ,w4 ,noon position4 ,log regi/]$ at noon #fh4 ,/eam$ until #b3cj ,p4,m4 on a c\rse p4s4c4 #aae deg44 ,deviation #a deg4 ,w4 ,v>iation #be deg4 ,w4 ,log regi/]$ #abe4 ,*ang$ c\rse to #aah deg4 p4s4c4 7,same ,v>iation & ,deviation7 & /eam$ until ab\t #e ,p4,m4 ,at ab\t #e ,p4,m4 obs]v$ altitude 747 #bb deg4 #dj' #bj & be>+ by pelorus ,n #ee deg4 ,w4 ,,wt #e;h #jam #afs4 ,c-,w #c;h #jjm #jbs4 ,,ie #b' #bj on arc4 ,,cc #cm #cbs sl[4 ,,he #cb ft4 ,log regi/]$ #afh4 ,c\rse p4s4c4 0 !n *ang$ to #aac deg4 until ab\t #h ,p4,m4 :5 obs]v$ m]idian altitude ( ,/> ,vega #hh deg4 #ae' #aj ,s4 ,,wt #h;h #jbm #bfs4 ,c-,w #c;h #jjm #jbs4 ,same ,,he1 ,,ie1 ,,cc4 ,log regi/]$ #baj4 ,cont9u$ on same c\rse p4s4c4 until ab\t #b ,a4,m4 :5 obs]v$ altitude ( ,/> ,vega #dg deg4 #ai' #bj ,we/ ( m]idian4 ,,wt #b;h #jdm #bds ,a4,m4 ,c-,w #c;h #jjm #jbs4 ,same ,,ie1 ,,he1 ,,cc4 ,log regi/]$ #bii4 ,,tz ( ,/> ,n #hf deg4 ,w4 ,cont9u$ on same c\rse until #d ,a4,m4 :5 log regi/]$ #cbi4 ,at #d ,a4,m4 heavy fog & ra9 =c$ %ip to sl[ d[n to #e knots p] h\r until ab\t #i ,a4,m4 :5 wea!r cle>$ & obs]v$ altitude 77 #ea deg4 #eb' #dj4 ,,wt #i;h #jcm #ahs ,a4,m4 ,c-,w #c;h #jjm #jbs4 ,same ,,he1 ,,ie1 ,,cc4 ,!nce %ip /eam$ a true c\rse ( #hh deg4 at a rate ( #ac knots p] h\r to noon1 :5 log regi/]$ #cid & obs]v$ m]idian altitude 77 #fi deg4 #eb' #bj ,s4 ,same ,,ie1 ,,he1 ,,cc4 ,requir$ #a4 ,d4 ,r4 position at noon4 #b4 ,position by obs]vation at noon 7correct$ = ,longitude by a factor74 #c4 ,deviation ( ,compass at #e ,p4,m4 #d4 ,wat* ,"t ( ,local ,app>5t ,noon4 ,,?ursday ,,lecture ,,day',s ,,"w ,at sea1 ,nov4 #be?1 #aiah4 ,dep>ture tak5 at noon f ,latitude #be deg4 #je' ,n1 ,longitude #cg deg4 #aj' #dj ,w4 ,log regi/]$ at noon #cb4 ,c\rse p4s4c4 0 #aai deg41 ,deviation #b deg4 ,e1 ,v>iation #ai deg4 ,w until twilight :5 log regi/]$ #aaj & obs]v$ altitude ,/> ,pol>is #be deg4 #cj' #dj ,n4 ,,ie #a' #aj (f arc4 ,,he #bh ft4 ,,wt #e;h #djm #ahs4 ,c-,w #b;h #bhm #aas4 ,,cc #dm #aes sl[4 ,*ang$ c\rse to ,,se x ,e #c_/d ,e1 same ,v>iation & ,deviation1 & /eam$ on ?is c\rse until ab\t #h3cj ,p4,m4 :5 obs]v$ altitude ( ,/> ,m>kab1 ,we/ ( m]idian1 #ei deg4 #dh' #aj4 ,log regi/]$ #aeg4 ,,wt #h;h #cdm #dhs4 ,c-,w #b;h #bhm #aas4 ,same ,,he1 ,,ie1 ,,cc4 ,/eam$ on same c\rse until midnight :5 log regi/]$ #baj4 ,*ang$ c\rse to #aaj deg4 p4s4c4 7same ,v>iation & ,deviation71 & /eam$ at #ab knots spe$ until ab\t #h ,a4,m4 :5 obs]v$ altitude 77 #bc deg4 #je' #aj & be>+ by compass ,s #cc deg4 ,e4 ,v>iation #ai deg4 ,w4 ,,wt #h;h #jdm #ajs1 ,a4,m4 ,c-,w #b;h #bhm #aas4 ,same ,,he1 ,,ie1 ,,cc4 ,cont9u$ on same c\rse p4s4c4 at a spe$ ( #ae knots p] h\r until noon :5 obs]v$ m]idian altitude 77 #dd #cj' #ej ,s4 ,same ,,ie1 ,,he1 ,,cc4 ,log regi/]$ #cff4 ,requir$ #a4 ,d4 ,r4 position at noon4 #b4 ,position by obs]vation at noon 7correct$ = ,longitude by a factor74 #c4 ,deviation ( compass at #h3jd ,a4,m4 #d4 ,wat* ,"t ( ,local ,app>5t ,noon4 ,,additional ,,lecture ,,compass ,,adju/m5t ,! aim ( ?is lecture is to give y a v few facts ab\t magnetism 9 g5]al & compass adju/m5t 9 p>ticul>4 ,! reason = includ+ ! lecture 9 ?is book is because ( repeat$ reque/s on ! "p ( graduates :o h be5 consult$ ab\t ! adju/m5t ( ! compass on _! %ips & :o h realiz$ t _! advice might h be5 m helpful if !y _h le>n$ m ab\t ! matt] :ile at ?is s*ool4 ,! e>? is a huge magnet4 ,x is ! effect ( ! magnetism 9 ! e>? ^u ! compass ne$le :i* causes ! compass error & makes x necess>y to correct x4 ,h[ c x be correct$8 ,to "k t we mu/ fir/ "k ! fundam5tal law ( magnetism1 namely1 t opposite poles ( two magnets attract ea* o!r & simil> poles repel ea* o!r4 ,f :i* x foll[s t if we decide to color r$1 = in/ance1 t end ( a magnetic ne$le :i* po9ts to ,nor?1 ! magnetism ( t "p ( ! e>? mu/ be consid]$ blue1 i4e41 ( opposite magnetism to ! nor?-seek+ end ( ! r$ magnetic ne$le4 ,n[1 !re are v>i\s k9ds ( magnetism :i* affect a %ip's compass4 ,"o is f ! e>?1 ano!r f ! iron 9 ! %ip1 etc4 ,to discuss !m &1 ! !oretical cause ( !m 9 detail is beyond ! scope ( ?is lecture4 ,to correct !m1 f\r sets ( magnets are necess>y1 two ( :i* are usually f\nd 9 ! b9nacle ( ! compass itself4 ,"o is a =e & aft magnet or set ( magnets1 ! o!r an a?w>t%ip magnet or set ( magnets4 ,! ?ird set consi/s ( ! two globes ( ca/ iron plac$ on ei!r side ( ! compass b[l 7call$ ,quadrantal ,correctors74 ,! f\r? magnet1 or set ( magnets1 is to correct ! compass 9 case ( sev]e heel+ by ! %ip4 ,if y are ord]$ to adju/ ! compass ! fir/ ?+ to d is to *oose a f9e day ) smoo? wat]4 ,take y\r %ip to a c]ta9 spot1 ! exact location ( :i* y h f\nd f ! *>t1 & :]e y are c]ta9 y w h pl5ty ( sea-way 9 :i* to sw+4 ,set y\r wat* to local app>5t "t 7:i* y h calculat$ be=e com+ out74 ,take f ! ,azimu? ,tables ! sun's true be>+ = e f\r m9utes ( ! "t dur+ :i* y w be occupi$ adju/+1 & conv]t x into ! magnetic be>+ by apply+ ! v>iation at ! place select$ 7secur$ f ! *>t74 ,write d[n 9 a small book ^! times & correspond+ magnetic be>+s4 ,n[ g to y\r compass & see t its lubb] l9e is exactly =e & aft & 9 ! keel l9e ( ! %ip4 ,h ano!r (fic] :o is ?or\ghly famili> ) ! pelorus /& by x z ! %ip is swung4 ,all be+ ready1 secure ! lubb]'s po9t ( ! pelorus at ,nor? & clamp ! sight vane to ! sun's magnetic be>+ at ! "t y h figur$ to take ! fir/ head+4 ,/>bo>d or port y\r helm until at ! "t calculat$ ! reflection ( ! sight vane on ! pelorus dial cuts on ! prop] magnetic be>+4 ,! vessel's head w !n be po9t+ to magnetic ,nor?4 ,if1 n[1 ! compass 7 correct x w\ld agree ) ! pelorus 9 %[+ ! %ip's head to be ,nor?4 ,if x does n d s1 !re is ,deviation 9 ! compass & its am\nt is ! am\nt ( ,deviation on t p>ticul> c\rse4 ,suppose ! ,deviation 7 to />bo>d1 i4e41 ,ea/]ly1 & 7 due to magnetism 9 ! %ip's />bo>d side4 ,!n1 if ! magnetism 9 ! ,nor? end ( ! ne$le be consid]$ r$1 ! magnetism 9 ! />bo>d side ( ! vessel1 9 ord] to attract ! r$ end ( ! ne$le1 w\ld be consid]$ blue & ! %ip's magnetism1 ) ! compass ne$le includ$1 w\ld look l ?is3 ,illu/ration ,to c\nt]act ?is blue attractive =ce on ! />bo>d side1 screw up ! a?w>t%ip magnet 9 ! b9nacle t[>d ! compass dial4 ,its magnetism1 if x 7 laid on ! deck1 w\ld look l ?is3 ,illu/ration ,9 o!r words1 z ?is magnet is mov$ ne>] ! compass ne$le1 by ! law ( magnetism j giv51 ! r$ end ( ! magnet repels ! r$ end ( ! compass ne$le f ! />bo>d side & ! blue end ( ! magnet attracts ! r$ end ( ! compass ne$le t[>d ! port side4 ,:5 ! compass ne$le po9ts to ,nor?1 z %[n by ! correct pelorus be>+1 ! ,deviation on ?is head+ 7i4e41 ,nor?7 is correct$4 ,n[ turn ! lubb] l9e ( ! pelorus to ,ea/4 ,/eady ! %ip on ?is head+ until ! %ad[ f ! pelorus vane at ! prop] ,l4,a4,t4 cuts ! circumf]5ce ( ! pelorus dial at ! prop] magnetic be>+4 ,! %ip's compass %\ld !n %[ ! %ip's head po9t+ to ,ea/4 ,suppose t x does n 7z w usually be ! case7 b po9ts to ! "r ( ,ea/4 ,!n ! %ip's magnetism & compass w\ld look l ?is3 ,illu/ration ,to br+ ! compass ne$le back to ,nor? x w\ld be necess>y to move up ne>] ! compass dial ! =e-&-aft magnet 7%[n bel[71 ^: magnetism w\ld act on ! compass ne$le on ?is head+ ( ! %ip exactly z ! a?w>t%ip magnet act$ on ! compass ne$le :5 ! %ip 0 head$ ,nor?3 ,illu/ration ,n[ ! %ip's compass has be5 correct$ = ! ,nor? & ,ea/ head+s respectively4 ,! next correction is = ! head+ half way betwe51 i4e41 ,nor?-ea/4 ,if !re is any ,deviation on ?is head+1 adju/ ! ca/ iron cyl9d]s 7call$ ,quadrantal ,correctors71 :i* are on ea* side ( ! compass b[l1 by mov+ !m t[>d or away f ! compass until ! %ip's head by compass is ,nor?-ea/ at ! prop] "t & be>+ by pelorus4 ,! %ip's compass has n[ be5 correct$ = "o :ole quadrant1 namely1 f ,nor? to ,ea/1 & ?is w suffice = all f\r quadrants s9ce ! relation%ips ( ! magnets !mselves & ! magnetism ( ! compass ne$le is ! same = any ( ! o!r ?ree quadrants z = ! fir/4 ,compass adju/m5t1 h[ev]1 c nev] be absolutely accurate4 ,= t reason1 x is wise to /eam ! %ip completely ar\nd1 /eady+ on e fifte5 degrees by pelorus to det]m9e & keep a record ( rema9+ errors4 ,!re is "o m correction to make1 i4e41 = ! heel+ error4 ,?is correction is necess>y 9 case ! %ip is yaw+ 9 a sea-way s mu* t ! relation%ip ( ! %ip's magnetism to ! compass ne$le is decid$ly diff]5t f :at x is :5 ! %ip is on a comp>atively ev5 keel4 ,x is comp5sat$ by a v]tical magnet directly und]nea? 7or ov]7 ! b9nacle1 details 9 reg>d to :i* c be secur$ f ,b[dit* ,art4 #abe1 p4 #ec4 ,x mu/ be borne 9 m9d t compass adju/m5t is n an exact sci5ce1 t an adju/m5t = "o latitude is n correct = ano!r1 t anyone ( a hundr$ diff]5t causes c affect ! magnetism ( ! %ip or ( ! compass ne$le1 :i* 9 turn directly affects ! ,deviation4 ,9 ?is connection1 x w\ld be well to read ,b[dit* ,art4 #abi1 p4 #ee4 ,y %\ld also read ,arts4 #aai-acj 9 :i* are giv51 m fully & 9 m sci5tific language1 ! cont5ts ( ?is lecture4