,transcriber's ,note3- ,words and phrases surrounded by underscores are italicised4 ,there are four symbols which are denoted by 3- 747 ,circle surrounding a centred dot - ,right ,ascension of the ,meridian2 77 ,circle surrounding a cross - ,earth's ,central ,progress2 77 ,circle with centre dot and line under - ,observed altitude of sun's lower limb2 -7-7- ,circle with line through - ,true ,altitude4 ,,lectures ,,in ,,navigation ,prepared for ,use as a ,text ,book at the ,,officers' ,,material ,,school ,,naval ,,auxiliary ,,reserve by ,lieutenant ,,ernest ,g4 ,,draper1 ,u4,s4,n4,r4,f4 ,head of the ,department of ,navigation ,officers' ,material ,school1 ,naval ,auxiliary ,reserve ,,copyright ,,by ,,ernest ,g4 ,,draper ,,foreword ,these ,lectures have been compiled as speedily as possible to meet the demand for some quick but fairly comprehensive method whereby large bodies of men1 divided into small classes1 might learn the elements of ,navigation and thus assume1 without delay1 their responsibilities as ,junior ,officers of the deck1 ,navigators and ,assistant ,navigators in the ,united ,states ,naval ,auxiliary ,reserve4 ,i realize that the haste with which the book has been written is apparent in many places1 and it is hoped that many evidences of this haste will disappear in case further editions are printed4 ,besides acknowledging the help and information which was secured from the list of navigational works1 mentioned on another page1 ,i wish to mention particularly ,prof4 ,charles ,lane ,poor's book1 entitled ,nautical ,science1 from which was secured practically all of the information in the ,lecture on ,planets and ,stars 7,tuesday--,week ,v72 ,commander ,w4 ,c4 ,p4 ,muir's book1 ,navigation and ,compass ,deviations1 and ,lieutenant ,w4 ,j4 ,henderson's book1 ,elements of ,navigation1 the text of which was followed closely in discussing ,variation and ,deviation and ,traverse ,sailing4 ,i desire to express my gratitude to ,lieutenant ,commander ,r4 ,t4 ,merrill1 #bnd1 ,u4 ,s4 ,n41 for suggesting a detailed outline of the whole course2 to ,lieutenant ,commander ,b4 ,o4 ,wills1 ,u4 ,s4 ,n41 for his valuable criticisms and almost daily help during the preparation of these ,lectures2 to ,lieutenant 7j4 g47 ,c4 ,d4 ,draper1 ,u4 ,s4 ,n4 ,r4 ,f42 ,lieutenant 7j4 g47 ,r4 ,brush1 ,u4 ,s4 ,n4 ,r4 ,f41 and ,lieutenant 7j4 g47 ,p4 ,c4 ,mc,pherson1 ,u4 ,s4 ,n4 ,r4 ,f41 for many criticisms and suggestions2 and to ,captain ,huntington1 ,seamen's ,church ,institute1 for suggesting helpful diagrams1 particularly the one on page #dd4 ,this opportunity is also taken for thanking the many ,instructors in the ,school for their opinions on various questions that have come up in connection with the course and for assistance in eliminating errors from the text4 ,e4 ,g4 ,d4 ,,list ,,of ,,books ,,consulted ,,american ,,practical ,,navigator1 ,,bowditch ,,navigation ,,and ,,compass ,,deviations1 ,,muir ,,nautical ,,science1 ,,poor ,,elements ,,of ,,navigation1 ,,henderson ,,wrinkles ,,in ,,practical ,,navigation1 ,,lecky ,,whys ,,and ,,wherefores ,,of ,,navigation1 ,,bradford ,,epitome ,,of ,,navigation1 ,,norie ,,navigation1 ,,hosmer ,,finding ,a ,,ship',s ,,position ,,at ,,sea1 ,,sumner ,,general ,,astronomy1 ,,young ,,preface ,,to ,,those ,,taking ,,this ,,course ,,in ,,navigation3 ,these lectures have been written with the idea of explaining1 in as simple language as possible1 the fundamental elements of ,navigation as set forth in ,bowditch's ,american ,practical ,navigator4 ,they will be given you during the time at the ,training ,school devoted to this subject4 ,at present this time includes two morning periods of one and a half hours each1 separated by a recess of fifteen minutes4 ,in general the plan is to devote the first period to the lecture and the second period to practical work4 ,not many examples for practical work have been included in this book1 but one example1 illustrating each new method1 has been worked out4 ,if you understand these examples you should be able to understand others similar to them4 ,toward the end of the course a portion of each second period will be devoted to handling the sextant1 work with charts1 taking sights1 etc4 ,in short1 every effort will be made to duplicate1 as nearly as possible1 navigating conditions on board a modern merchant ship4 ,,department ,,of ,,navigation1 ,officers' ,material ,school1 ,naval ,auxiliary ,reserve ,,contents ,,week ,i--,,piloting ,tuesday--,the ,compass #a ,wednesday--,pelorus2 ,parallel ,rulers2 ,the ,lead1 ,sounding ,machine1 ,dividers and ,log #f ,thursday--,the ,chart #aj ,friday--,the ,protractor and ,sextant #ac ,saturday--,fixes1 ,angles by ,bearings and ,sextant #af ,,week ,,ii--,,dead ,,reckoning ,tuesday--,latitude and ,longitude #bj ,wednesday--,useful ,tables--,plane and ,traverse ,sailing #bc ,thursday--,examples on ,plane and ,traverse ,sailing 7,continued7 #bg ,friday--,mercator ,sailing #bh ,saturday--,great ,circle ,sailing--,the ,chronometer #cj ,,week ,,iii--,,celestial ,,navigation ,tuesday--,celestial ,co-ordinates1 ,equinoctial ,system1 etc4 #cd ,wednesday--,time by the ,sun--,mean ,time1 ,solar ,time1 ,conversion1 etc4 #cf ,thursday--,sidereal ,time--,right ,ascension #dc ,friday--,the ,nautical ,almanac #dg ,saturday--,correction of ,observed ,altitudes #eb ,,week ,,iv--,,navigation ,tuesday--,the ,line of ,position #ee ,wednesday--,latitude by ,meridian ,altitude #eh ,thursday--,azimuths of the ,sun #fa ,friday---,marc ,st4 ,hilaire ,method by a ,sun ,sight #fc ,saturday--,examples on ,marc ,st4 ,hilaire ,method by a ,sun ,sight #ff ,,week ,v--,,navigation ,tuesday--,a ,short ,talk on the ,planets and ,stars--,identification of ,stars--,time of ,meridian ,passage of a ,star #ff ,wednesday--,latitude by ,meridian ,altitude of a ,star--,latitude by ,polaris #gc ,thursday--,marc ,st4 ,hilaire ,method by a ,star ,sight #gd ,friday--,examples3 ,latitude by ,meridian ,altitude of a ,star2 ,latitude by ,polaris2 ,marc ,st4 ,hilaire ,method by a ,star ,sight #ge ,saturday--,longitude by ,chronometer ,sight of the ,sun #gf ,,week ,,vi--,,navigation ,tuesday--,longitude by ,chronometer ,sight of a ,star #gi ,wednesday--,examples on ,longitude by ,chronometer ,sight of a ,star #hj ,thursday--,latitude by ,ex-,meridian ,altitude of the ,sun #ha ,friday--,examples3 ,latitude by ,ex-,meridian ,altitude of the ,sun #hc ,saturday--,finding the ,watch ,time of ,local ,apparent ,noon #hc ,,week ,,vii--,,navigation ,tuesday--,compass ,error by an ,azimuth #hh ,wednesday--,correcting ,longitude by a ,factor #hi ,thursday--,the ,navigator's ,routine--,a ,day's ,work at ,sea #ia ,friday--,day's ,work #aje ,saturday--,day's ,work #aje ,,week ,,viii--,,navigation ,monday to ,thursday--,day's ,work #ajg-ajh ,additional ,lecture--,compass ,adjustment #aji ,,week ,i--,,piloting ,,tuesday ,,lecture ,,the ,,compass ,everyone is supposed to know what a compass looks like4 ,it is marked in two ways--the old way and the new way4 ,put in your ,note-,book this diagram3 ,illustration ,the new way marked on the outside of the diagram1 starts at ,north with #j deg41 increases toward the right through ,east at #ij deg41 ,south at #ahj deg41 ,west at #bgj deg4 and back to ,north again at #cfj deg4 or #j deg44 ,the old way1 marked on the inside of the diagram1 starts at ,north with #j deg41 goes to the right to #ij deg4 at ,east and to the left to #ij deg4 at ,west4 ,it also starts at ,south with #j deg41 goes to the right to ,east at #ij deg4 and to the left to ,west at #ij deg44 ,a ,compass ,course can be named in degrees1 according to either the new or old way4 ,for instance1 the new way is just #de deg44 ,the old way for the same course is ,n #de deg4 ,e4 ,new way--#ajj deg44 ,old way for same course--,s #hj deg4 ,e4 ,there is another way to name a compass course4 ,it is by using the name of the point toward which the ship is heading4 ,on every ship the compass is placed with the lubber line 7a vertical black line on the compass bowl7 vertical and in the keel line of the ship4 ,the lubber line1 therefore1 will always represent the bow of the ship1 and the point on the compass card nearest the lubber line will be the point toward which the ship is heading4 ,the compass card of #cfj deg4 is divided into #cb points4 ,each point1 therefore1 represents #aa-a_/d deg44 ,the four principal points are called cardinal points4 ,they are--,north1 ,east1 ,south1 ,west4 ,each cardinal point is #ij deg4 from the one immediately adjacent to it4 ,it is also #h points from the one adjacent to it1 as #ij deg4 is #h points1 i4e41 #aa-a_/d deg4 7one point7 times #h4 ,midway between the cardinal points are the inter-cardinal points4 ,they are--,n ,e1 ,s ,e1 ,s ,w1 ,n ,w1 and are #de deg4 or #d points from the nearest cardinal point4 ,midway between each cardinal and inter-cardinal point--at an angular distance of #bb-a_/b deg4 or #b points1 is a point named by combining a cardinal point with an inter-cardinal point4 ,for instance1 ,,nne1 ,,ene1 ,,ese1 ,,sse1 ,,ssw1 ,,wsw1 ,,wnw1 ,,nnw4 ,midway between the last points named and a cardinal or inter-cardinal point1 at an angular distance of #aa-a_/d deg41 is a point which bears the name of that cardinal or inter-cardinal point joined by the word by to that of the cardinal point nearest to it4 ,as1 for instance1 ,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 ,the angular distance between each and every whole point is divided into #d parts called half and quarter points and each representing an angular measure of approximately #b deg4 #di'4 ,in mentioning fractional points1 the ,u4 ,s4 ,navy regulations are to name each point from ,north and ,south toward ,east and ,west except that divisions adjacent to a cardinal or inter-cardinal point are always referred to that point3 ,for instance1 ,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 ,boxing the compass is naming each point and quarter-point in rotation1 i4e41 starting at ,north and going around to the right back to ,north again4 ,every man should be able to identify and name any point or quarter-point on the compass card4 ,in changing a point course into a degree course1 for either new or old compass1 a guide is herewith furnished you4 ,this should be pasted into the front of your ,bowditch ,epitome4 ,it shows1 from left to right1 the name of the point course1 its angular measure in the new compass and its angular measure in the old compass4 ,it also shows at the bottom1 the angular measure of each division of one point4 ,in understanding this guide1 remember that each course is expressed in degrees or degrees and minutes4 ,put in your ,note-,book3 ,in ,navigation1 each degree is written thus deg44 ,each fraction of a degree is expressed in minutes and written thus '4 ,there are #fj' in each degree4 ,each fraction of a minute is expressed in seconds and is written 4 ,there are #fj in each minute4 ,four degrees1 ten minutes and thirty seconds would be written thus3 #d deg4 #aj' #cj4 ,although this guide just given you is given as an aid to quickly transfer a point course into a new or old compass course--or vice versa--you should learn to do this yourself1 after awhile1 without the guide4 ,put in your ,note-,book3 ---------------------------------------- ----------- ,ship's ,head ,new ,old ,by ,point ---------------------------------------- ----------- ,,ne #de deg4 ,n #de deg4 ,e ,,ne #ij deg4 #ij deg4 ,n #ij deg4 ,e ,,east ,,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 will show you just how each one of these courses is secured from the guide just given you4 ,note to ,instructor3 ,after explaining these courses in detail1 assign for reading in the class room the following articles in ,bowditch3 ,arts4 #be-bf-bg-bh-bi-cj-ca-cb1 #gd-ge-gf-gg-gh-gi-hj-ha-hb4 ,every compass1 if correct1 would have its needle point directly to the real or true ,north4 ,but practically no compass with which you will become familiar will be correct4 ,it will have an error in it due to the magnetism of the earth4 ,this is called ,variation4 ,it will also have an error in it due to the magnetism of the iron in the ship4 ,this is called ,deviation4 ,you are undoubtedly familiar with the fact that the earth is a huge magnet and that the magnets in a compass are affected thereby4 ,in other words1 the ,north and ,south magnetic poles1 running through the center of the earth1 do not point true ,north and ,south4 ,they point at an angle either ,east or ,west of the ,north and ,south4 ,the amount of this angle in any one spot on the earth is the amount of ,variation at that spot4 ,in navigating a ship you must take into account the amount of this ,variation4 ,the amount of allowance to be made and the direction 7i4e4 either ,east or ,west7 in which it is to be applied are usually indicated on the chart4 ,on large charts1 such as those of the ,north ,atlantic1 will be found irregular lines running over the chart1 and having beside them such notations as #aj deg4 ,w1 #ae deg4 ,w1 etc4 ,some lines are marked ,no ,variation4 ,in such cases no allowance need be made4 ,on harbor charts or other small charts1 the ,variation is shown by the compass-card printed on the chart4 ,the ,north point of this card will be found slewed around from the point marking ,true ,north and in the compass card will be some such inscription as this3 ,variation #i deg4 ,west in #aiad4 ,increasing #f' per year4 ,now let us see how we apply this ,variation so that although our compass needle does not point to true ,north1 we can make a correction which will give us our true course in spite of the compass reading4 ,note these diagrams3 ,illustration ,the outer circle represents the sea horizon with the long arrow pointing to true ,north4 ,the inner circle represents the compass card4 ,in the diagram to the left1 the compass needle is pointing three whole points to the left or ,west of ,true ,north4 ,in other words1 if your compass said you were heading ,,ne x ,n1 you would not actually be heading ,,ne x ,n4 ,you would be heading true ,north4 ,illustration ,in other words1 standing in the center of the compass and looking toward the circumference1 you would find that every true course you sailed would be three points to the left of the compass course4 ,that is called ,westerly ,variation4 ,now look at the diagram to the right4 ,the compass needle is pointing three whole points to the right or ,east of ,true ,north4 ,in other words1 standing in the center of the compass and looking toward the circumference1 you would find that every true course you sailed would be three points to the right of the compass course4 ,that is called ,easterly ,variation4 ,hence we have these rules1 which put in your ,note-,book3 ,to convert a compass course into a true course ,when the ,variation is westerly1 the true course will be as many points to the left of the compass course as there are points or degrees of ,variation4 ,when the ,variation is easterly1 the true course will be as many points or degrees to the right of the compass course4 ,to convert a true course into a compass course ,the converse of the above rule is true4 ,in other words1 ,variation westerly1 compass to the right of true course2 variation easterly1 compass course to the left4 ,,deviation ,as stated before1 ,deviation causes an error in the ,compass due to the magnetism of the iron in the ship4 ,when a ship turns1 the compass card does not turn1 but the relation of the iron's magnetism to the magnets in the compass is altered4 ,hence1 every change in course causes a new amount of ,deviation which must be allowed for in correcting the compass reading4 ,it is customary in merchant vessels to have the compasses adjusted while the ship is in port4 ,the adjuster tries to counteract the ,deviation all he can by magnets1 and then gives the master of the ship a table of the ,deviation errors remaining4 ,these tables are not to be depended upon1 as they are only accurate for a short time4 ,ways will be taught you to find the ,deviation yourself1 and those ways are the only ones you can depend upon4 ,put in your ,note-,book3 ,westerly ,deviation is applied exactly as westerly ,variation4 ,easterly ,deviation is applied exactly as easterly ,variation4 ,the amount of ,variation plus the amount of ,deviation is called the ,compass ,error4 ,for instance1 a ,variation of #aj deg4 ,w plus a ,deviation of #e deg4 ,w equals a compass error of #ae deg4 ,w1 or a ,variation of #aj deg4 ,w plus a ,deviation of #e deg4 ,e leaves a net compass error of #e deg4 ,w4 ,,leeway ,leeway is not an error of the compass1 but it has to be compensated for in steaming any distance4 ,hence it is mentioned here4 ,a ship steaming with a strong wind or current abeam1 will slide off to the leeward more or less4 ,hence1 her course will have to be corrected for ,leeway as well as for ,variation and ,deviation4 ,put in your ,note-,book3 ,leeway on the starboard tack is the same as westerly ,variation4 ,leeway on the port tack is the same as easterly ,variation4 ,this is apparent from the following diagram3 ,illustration ,as the wind1 blowing from the ,north1 hits the left hand ship1 for instance1 on her starboard side1 it shoves the ship to the left of her true course by the number of points or degrees of leeway4 ,leave a space and put the following heading in your ,note-,book3 ,i4 ,complete rule for converting a compass course into a true course3 #a4 ,change the compass course into a new compass reading4 #b4 ,apply ,easterly ,variation and ,deviation 4 #c4 ,apply ,westerly ,variation and ,deviation -4 #d4 ,apply port tack ,leeway 4 #e4 ,apply starboard tack ,leeway -4 ,,ii4 ,complete rule for converting a true course into a compass course3 #a4 ,reverse the above signs in applying each correction4 ,i will now correct a few courses1 and these are to be put into your ,note-,book3 ---------------------------------------- -------------------- ,c ,cos ,wind ,leeway ,dev4 ,var4 ,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 for ,night ,work the following arts4 in ,bowditch3 #cf-h-aj-ac-ad-ae-af-ag-ah-ai-bj-ba-bb-b c-bd4 ,,wednesday ,,lecture ,,pelorus1 ,,parallel ,,rulers1 ,,the ,,lead1 ,,sounding ,,machine1 ,,dividers ,,and ,,log ,i4 ,the ,pelorus ,this is an instrument for taking bearings of distant objects1 and for taking bearings of celestial bodies such as the sun1 stars1 etc4 ,it consists of a circular1 flat metallic ring1 mounted on gimbals1 upon a vertical standard4 ,the best point to mount it is in the bow or on the bridge of the ship1 where a clear view for taking bearings can be had4 ,the center line of the pelorus should also be directly over the keel line of the ship4 ,the inner edge of the metallic ring is engraved in degrees--the #j deg4 or #cfj deg4 and the #ahj deg4 marks indicating a fore-and-aft line parallel to the keel of the ship4 ,within this ring a ground glass dial is pivoted4 ,this ground glass dial has painted upon it a compass card divided into points and sub-divisions and into #cfj deg44 ,this dial is capable of being moved around1 but can also be clamped to the outside ring4 ,pivoted with the glass dial and flat ring is a horizontal bar carrying at both of its extremes a sight vane4 ,this sight vane can be clamped in any position independently of the ground glass dial1 which can be moved freely beneath it4 ,an indicator showing the direction the sight vane points can be read upon the compass card on the glass dial4 ,if the glass dial be revolved until the degree of demarcation1 which is coincident with the right ahead marking on the flat ring1 is the same as that which points to the lubber's line of the ship's compass1 then all directions indicated by the glass dial will be parallel to the corresponding directions of the ship's compass1 and all bearings taken will be compass bearings1 i4e41 as though taken from the compass itself4 ,in other words1 it is just as though you took the compass out of its place in the pilot house1 or wherever it is regularly situated1 put it down where the pelorus is1 and took a bearing from it of any object desired4 ,in taking a bearing by pelorus1 two facts must be kept in mind4 ,first1 that when the bearing is taken1 the exact heading1 as shown by the ship's compass1 is the heading shown by the pelorus4 ,in other words1 if the ship is heading ,,nw1 the pelorus must be set with the ,,nw point on the lubber line when the bearing is taken of any object4 ,second1 it must be remembered that the bearing of any object obtained from the pelorus is the bearing by compass4 ,to get the true bearing of the same object you must make the proper corrections for ,variation and ,deviation4 ,this can be compensated for by setting the glass dial at a point to the right or left of the compass heading to correspond with the compass error2 then the bearing of any object will be the true bearing4 ,but naturally1 you will not be able to make compensation for these errors unless you have immediately before found the correct amount of the compass error4 ,parallel ,rulers ,the parallel rulers need no explanation except for the way in which they are used on a chart4 ,supposing1 for instance1 you wish to steam from ,pelham ,bay to the red buoy off the westerly end of ,great ,captain's ,island4 ,take your chart1 mark by a pencil point the place left and the place to go to and draw a straight line intersecting these two points4 ,now place the parallel rulers along that line and slide them over until the nearest edge intersects the center of the compass rose at the bottom or side of the chart4 ,look along the ruler's edge to find where it cuts the circumference of the compass rose4 ,that point on the compass rose will be the true compass course1 and can be expressed in either the new or old compass1 as1 for instance1 #fj deg4 or ,n #fj deg4 ,e4 ,remember1 however1 that this is the true course4 ,in order to change it into the compass course of your ship1 you must make the proper corrections for the compass error1 i4e41 ,variation and ,deviation and for ,leeway1 if any4 ,the ,lead and ,sounding ,machine ,the lead1 as you know1 is used to ascertain the depth of the water and1 when necessary1 the character of the bottom4 ,there are two kinds of leads3 the hand lead and deep-sea lead4 ,the first weighs from #g to #ad pounds and has markings to #be fathoms4 ,the second weighs from #cj to #ajj pounds and is used in depths up to and over #ajj fathoms4 ,put in your ,note-,book3 ,fathoms which correspond with the depths marked are called marks4 ,all other depths are called deeps4 ,the hand lead is marked as follows3 #b fathoms--#b strips of leather4 #c fathoms--#c strips of leather or blue rag4 #e fathoms--,a white rag4 #g fathoms--,a red rag4 #aj fathoms--,a piece of leather with one hole in it4 #ac fathoms--,same as at #c4 #ae fathoms--,same as at #e4 #ag fathoms--,same as at #g4 #bj fathoms--#b knots or piece of leather with #b holes4 #be fathoms--#a knot4 #cj fathoms--#c knots4 #ce fathoms--#a knot4 #dj fathoms--#d knots4 ,and so on up to #ajj fathoms4 ,the large hand leads are hollowed out on the lower end so that an arming of tallow can be put in4 ,this will bring up a specimen of the bottom1 which should be compared with the description found on the chart4 ,all up-to-date sea-going ships should be fitted with ,sir ,william ,thompson's ,sounding ,machine 7see picture in ,b4 ,j4 ,manual74 ,this machine consists of a cylinder around which are wound about #cjj fathoms of piano wire4 ,to the end of this is attached a heavy lead4 ,an index on the side of the instrument records the number of fathoms of wire paid out4 ,above the lead is a copper cylindrical case in which is placed a glass tube open only at the bottom and chemically colored inside4 ,the pressure of the sea forces water up into this tube1 as it goes down1 a distance proportionate to the depth1 and the color is removed4 ,when hoisted1 the tube is laid upon a prepared scale1 and the height to which the water has been forced inside shows the depth in fathoms on the scale4 ,,dividers ,the dividers are nothing but an instrument for measuring distances1 etc41 on the chart4 ,,the ,,log ,there are two kinds of logs--the chip log1 used for measuring the speed of the ship1 and the patent log1 used for measuring distance run4 ,the chip log consists of a reel1 line1 toggle and chip4 ,usually a second glass is used for measuring time4 ,the chip is the triangular piece of wood ballasted with lead to ride point up4 ,the toggle is a little wooden case into which a peg1 joining the ends of the two lower lines of the bridle1 is set in such a way that a jerk on the line will free it1 causing the log to lie flat so that it can be hauled in4 ,the first #aj or #ae fathoms of line from the log-chip are called stray line1 and the end of this is distinguished by a mark of red bunting4 ,its purpose is to let the chip get clear of the vessel's wake4 ,the marks on the line 7called knots7 are pieces of fish line running through the strands of the reel line to the number of two1 three1 four1 etc4 ,a piece of white bunting marks every two-tenths of a knot4 ,this is because the run of the ship is recorded in knots and tenths4 ,the knots of fish line are #dg feet #d inches from each other4 ,the log glass measures #bh seconds in time4 ,for high rates of speed1 a #ad second glass is used4 ,then the number of knots shown by the log line must be doubled4 ,the principle of the chip log is that each division of the log line bears the same ratio to a nautical mile that the log glass does to the hour4 ,in other words1 if #aj knots or divisions of the log line run out while the #bh second glass empties itself1 the ship's speed is #aj knots per hour4 ,if ten knots or divisions run out while the #ad second glass empties itself1 the ship's speed is #bj knots per hour4 ,the patent or towing log consists of a dial1 line and rotator4 ,the large circle of the dial records the knots and the small circle tenths of knots4 ,when changing course1 read the log and enter it in the log book4 ,when changing course again1 read the log again4 ,the difference between the two readings will be the distance run4 ,both logs are liable to error4 ,a following sea makes them under-rate1 a head sea over-rate4 ,with both logs you must allow for currents4 ,if a current is against you--and you know its rate--you must deduct its rate from that recorded in the log and vice versa4 ,the reason for this is that your log measures your speed through the water4 ,what you must find is your actual distance made good over the earth's surface4 ,put in your ,note-,book3 ,between ,sandy ,hook and ,fort ,hamilton1 bound due ,north1 speed by chip-log was #aj knots1 tidal current setting ,north #b knots per hour2 what did the ship make per hour8 ,answer3 #ab knots4 ,at sea in ,north ,sea ship heading ,s x ,w1 patent log bet4 #h ,a4,m4 and #ab ,m4 registered #cb miles1 current running ,n x ,e #b knots per hour2 what was the actual distance made good8 ,answer3 #bd miles4 ,directions for allowing for a current setting diagonally across a ship's course will be given in the proper place4 ,assign for ,night ,work the following articles in ,bowditch3 ,arts4 #afa-afb-afc-afd-afe4 ,,thursday ,,lecture ,,the ,,chart ,aids to ,navigation ,a chart is a map of an ocean1 bay1 sound or other navigable water4 ,it shows the character of the coast1 heights of mountains1 depths at low water1 direction and velocity of tidal currents1 location1 character1 height and radius of visibility of all beacon lights1 location of rocks1 shoals1 buoys1 and nature of the bottom wherever soundings can be obtained4 ,the top of the chart is ,north unless otherwise noted4 ,when in doubt as to where ,north is1 consult the compass card printed somewhere on the chart4 ,on sea charts1 such as those of the ,north ,atlantic1 only the true compass is printed1 with the amount and direction of ,variation indicated by lines on the chart4 ,parallels of latitude are shown by straight lines running parallel to each other across the chart4 ,the degrees and minutes of these parallels are given on the perpendicular border of the chart4 ,meridians of longitude are shown by straight lines running up and down1 perpendicular to the parallels of latitude1 and the degrees and minutes of these meridians are given on the horizontal border of the chart4 ,put in your ,note-,book3 ,a minute of latitude is always a mile1 because parallels of latitude are equidistant at all places4 ,a minute of longitude is a mile only on the equator1 for the meridians are coming closer to each other as they converge toward either pole4 ,they come together at the ,north and ,south poles1 and here there is no longitude4 99 99 99 99 99 ,i can explain this very easily by reference to the following illustration3 ,illustration ,as every parallel of latitude is a circle of #cfj deg4 the distance from ,a to ,b will be the same number of degrees1 minutes and seconds whether measured upon parallel ,,aa' or ,,ee'1 but it will not be the same number of miles as the meridians of longitude are gradually converging toward the poles4 ,on the other hand1 the distances from ,a to ,c1 ,c to ,d1 ,d to ,e1 etc41 must be the same because the lines ,,aa'1 ,,cc'1 ,,dd'1 ,,ee' are all parallel4 ,that is why the distance is always measured on the latitude scale 7i4e4 on the vertical border of the chart71 and a minute of latitude is always a mile on the chart1 no matter in what locality your ship happens to be4 ,you should be able to understand any kind of information given you on a chart4 ,for instance1 what are the various kinds of buoys and how are they marked8 ,put in your ,note-,book3 #a4 ,in coming from seaward1 red buoys mark the starboard side of the channel1 and black buoys the port side4 #b4 ,dangers and obstructions which may be passed on either hand are marked by buoys with red and black horizontal stripes4 #c4 ,buoys indicating the fairway are marked with black and white vertical stripes and should be passed close to4 #d4 ,sunken wrecks are marked by red and black striped buoys described in ,no4 #b4 ,in foreign countries green buoys are frequently used to mark sunken wrecks4 #e4 ,quarantine buoys are yellow4 #f4 ,as white buoys have no especial significance1 they are frequently used for special purposes not connected with ,navigation4 #g4 ,starboard and port buoys are numbered from the seaward end of the channel1 the black bearing the odd and red bearing the even numbers4 #h4 ,perches with balls1 cages1 etc41 will1 when placed on buoys1 be at turning points1 the color and number indicating on which side they shall be passed4 #i4 ,soundings in plain white are in fathoms2 those on shaded parts are in feet4 ,on large ocean charts fathom curves1 showing the range of soundings of #aj1 #bj1 #cj1 #dj1 etc41 fathoms are shown4 #aj4 ,a light is indicated by a red and yellow spot4 ,f4 means fixed1 ,fl41 flashing2 ,int41 intermittent2 ,rev41 revolving1 etc4 #aa4 ,an arrow indicates a current and its direction4 ,the speed is always given4 #ab4 ,rocks just under water are shown by a cross surrounded by a dotted circle2 rocks above water1 by a dotted circle with dots inside it4 ,practically all charts you will use will be called ,mercator charts4 ,just how they are constructed is a difficult mathematical affair but1 roughly1 the idea of their construction is based upon the earth being a cylinder1 instead of a sphere4 ,hence1 the meridians of longitude1 instead of converging at the poles1 are parallel lines4 ,this compels the parallels of latitude to be adjusted correspondingly4 ,although such a chart in any one locality is out of proportion compared with some distant part of the earth's surface1 it is nevertheless in proportion for the distance you can travel in a day or possibly a week--and that is all you desire4 ,the ,hydrographic ,office publishes blank ,mercator charts for all latitudes in which they can be used for plotting your position4 ,it makes no difference what longitude you are in for1 on a ,mercator chart1 meridians of longitude are all marked parallel4 ,it makes a great difference1 however1 what latitude you are in1 as in each a mile is of different length on the chart4 ,hence1 it will be impossible for you to correctly plot your course and distance sailed unless you have a chart which shows on it the degrees of latitude in which you are4 ,for instance1 if your ,mercator chart shows parallels of latitude from #cj deg4 to #dj deg4 that chart must be used when you are in one of those latitudes4 ,when you move into #da deg4 or #bi deg41 you must be sure to change your plotting chart accordingly4 ,in very high latitudes and near the ,north pole1 the ,mercator chart is worthless4 ,how can you steer for the ,north pole when the meridians of your chart never come together at any pole8 ,for the same reason1 bearings of distant objects may be slightly off when laid down on this chart in a straight line4 ,on the whole1 however1 the ,mercator chart answers the mariner's needs so far as all practical purposes are concerned4 ,the instruments used in consulting a chart1 i4e41 parallel rulers1 dividers1 etc4 have already been described4 ,the only way to lay down a course and read it is by practice4 ,the one important thing to remember in laying down a course1 is that what you lay down is a true course4 ,to steam this course yourself1 you must make the proper correction for your compass error4 ,assign for ,night ,work in ,bowditch1 ,arts4 #i-bci-bdj-bda-bdc-bdd-bde-bdf-bdg-bdh-b di-bea-beb-bec-bed-bee-bef-beg-beh4 ,if any time in class room is left1 spend it in laying down courses on the chart and reading them2 also in answering such questions as these3 #a4 ,i desire to sail a true course of ,,ne4 ,my compass error is #b points ,westerly ,variation and #a point ,easterly ,deviation4 ,what compass course shall ,i sail8 #b4 ,i desire to sail a true course of ,,sw x ,w4 ,my ,variation is #aa deg4 ,w1 ,deviation #b pts4 ,w and ,leeway #a pt4 starboard4 ,what compass course shall ,i sail8 #c4 ,i desire to sail a true course of #bce deg44 ,my compass error is #d pts4 ,e ,variation1 #bg deg4 ,w ,deviation1 ,leeway #a pt4 port4 ,what compass course shall ,i sail8 #d4 ,i desire to sail a true course of ,s #fe deg4 ,w4 ,my compass error is #aj deg4 ,e ,variation1 #c deg4 ,e ,deviation1 ,leeway #a_/d point starboard4 ,what compass course shall ,i sail8 ,,friday ,,lecture ,,the ,,protractor ,,and ,,sextant ,the protractor is an instrument used to shape long courses4 ,there are many kinds4 ,the simplest and the one most in use is merely a piece of transparent celluloid with a compass card printed on it and a string attached to the center of the compass card4 ,to find your course by protractor1 put the protractor down on the chart so that the ,north and ,south line on the compass card of the protractor will be immediately over a meridian of longitude on the chart1 or be exactly parallel to one1 and will intersect the point from which you intend to depart4 ,then stretch your string along the course you desire to steam4 ,where this string cuts the compass card1 will be the direction of your course4 ,remember1 however1 that this will be the true course to sail4 ,in order to convert this true course into your compass course1 allow for ,variation and ,deviation according to the rules already given you4 ,in case you know the exact amount of ,variation and ,deviation at the time you lay down the course--and your course is not far--you can get your compass course in one operation by setting the ,north point of your protractor as far ,east or ,west of the meridian as the amount of your compass error is4 ,by then proceeding as before1 the course indicated on the compass card will be the compass course to sail4 ,this method should not be used where your course in one direction is long or where your course is short but in two or more directions4 ,the reason for this is that in both cases1 either your ,variation or ,deviation may change and throw you off4 ,practically all navigation in strange waters in sight of land and in all waters out of sight of land depends upon the determination of angles4 ,the angle at which a lighthouse is seen from your ship will give you much information that may be absolutely necessary for your safety4 ,the angular altitude of the sun1 star or planet does the same4 ,the very heart of ,navigation is based upon dealing with angles of all kinds4 ,the instrument1 therefore1 that measures these angles is the most important of any used in ,navigation and you must become thoroughly familiar with it4 ,it is the sextant or some member of the sextant family--such as the quadrant1 octant1 etc4 ,the sextant is the one most in use and so will be described first4 ,put in your ,note-,book3 ,the sextant has the following parts3 7,instructor points to each47 #a4 ,mirror #b4 ,telescope #c4 ,horizon ,glass #d4 ,shade ,glasses #e4 ,back ,shade ,glasses #f4 ,handle #g4 ,sliding ,limb #h4 ,reading ,glass #i4 ,tangent ,screw #aj4 ,arc ,in getting angles of land-marks or buoys1 the sextant is held by the handle ,no4 #f in a horizontal position4 ,the vernier arrow in the sliding limb is set on zero4 ,now1 suppose you wish to get the angular distance between two lighthouses as seen from the bridge of your ship4 7,draw diagram47 ,illustration ,look at one lighthouse through the line of sight and true horizon part of the horizon glass4 ,now1 move the sliding limb along the arc gradually until you see the other lighthouse in the reflected horizon of the horizon glass4 ,when one lighthouse in the true horizon is directly on top of the other lighthouse in the reflected horizon1 clamp the sliding limb4 ,if any additional adjustment must be made1 make it with the tangent screw ,no4 #i4 ,now look through the reading glass ,no4 #h4 ,you should see that the arc is divided into degrees and sixths of degrees in the following manner3 #aa deg4 #aj deg4 ------------------------------ ---------------------- ---------------------- ,now1 as every degree is divided into sixty minutes1 one-sixth of a degree is #aj minutes4 ,in other words1 each of the divisions of a degree on this arc represents #aj minutes4 ,now on the vernier in the sliding limb1 directly under the arc1 is the same kind of a division4 ,but these divisions on the vernier represent minutes and sixths of a minute1 or #aj seconds4 ,to read the angle1 the zero point on the vernier is used as a starting point4 ,if it exactly coincides with one of the lines on the scale of the arc1 that line gives the measurement of the angle4 ,in the following illustration the angle is #aj-a_/b degrees or #aj deg4 #cj'3 #aj deg4 #i deg4 --------------------------------------- ------------------------------------ ---------------------------------- ---------- #j ,if however1 you find the zero on the vernier has passed a line of the arc1 your angle is more than #aj deg4 #cj' as in this3 #aa deg4 #aj deg4 ----------------------------------- ------------------------------ ------------------------------ --------------------- #j ,you must then look along the vernier to the left until you find the point where the lines do coincide4 ,then add the number of minutes and sixths of a minute shown on the vernier between zero and the point where the lines coincide to the number of degrees and minutes shown on the arc at the line which the vernier zero has passed1 and the sum will be the angle measured by the instrument4 ,now in measuring the altitude of the sun or other celestial body1 exactly the same process is gone through except that the sextant is held vertically instead of horizontally4 ,you look through the telescope toward that part of the sea directly beneath the celestial body to be observed4 ,you then move the sliding limb until the image of the celestial body appears in the horizon glass1 and is made to kiss the horizon1 i4e41 its lowest point just touching the horizon4 ,the sliding limb is then screwed down and the angle read4 ,more about this will be mentioned when we come to ,celestial ,navigation4 ,every sextant is liable to be in error4 ,to detect this error there are four adjustments to be made4 ,these adjustments do not need to be learned by heart1 but ,i will mention them3 #a4 ,the mirror must be perpendicular to the plane of the arc4 ,to prove whether it is or not1 set the vernier on about #fj deg41 and look slantingly through the mirror4 ,if the true and reflected images of the arc coincide1 no adjustment is necessary4 ,if not1 the glass must be straightened by turning the screws at the back4 #b4 ,the horizon glass must be perpendicular to the plane of the arc4 ,set the vernier on zero and look slantingly through the horizon glass4 ,if the true and reflected horizons show one unbroken line1 no adjustment is necessary4 ,if not1 turn the screw at the back until they do4 #c4 ,horizon glass and mirror must be parallel4 ,set the vernier on zero4 ,hold the instrument vertically and look through the line of sight and horizon glass4 ,if the true and reflected horizons coincide1 no adjustment is necessary4 ,if they do not1 adjust the horizon glass4 #d4 ,the line of sight 7telescope7 must be parallel to the plane of the arc4 ,this adjustment is verified by observing two stars in a certain way and then performing other operations that are described in ,bowditch1 ,art4 #bdg4 ,do not try to adjust your sextant yourself4 ,have it adjusted by an expert on shore4 ,then1 if there is any error1 allow for it4 ,an error after adjustment is called the ,index ,error4 ,put in your ,note-,book3 ,how to find and apply the ,,ie 7,index ,error73 ,set the sliding limb at zero on the arc1 hold the instrument perpendicularly and look at the horizon4 ,move the sliding limb forward or backward slowly until the true horizon and reflected horizon form one unbroken line4 ,clamp the limb and read the angle4 ,this is the ,,ie4 ,if the vernier zero is to the left of the zero on the arc1 the ,,ie is minus and it is to be subtracted from any angle you read1 to get the correct angle4 ,if the vernier zero is to the right of the zero on the arc1 the ,,ie is plus and is to be added to any angle you read to get the correct angle4 ,index error is expressed thus3 ,,ie #b' #cj or ,,ie - #b' #cj4 ,quadrants1 octants and quintants work on exactly the same principles as the sextant1 except that the divisions on the arc and the vernier differ in number from the sixth divisions on the arc and vernier of the sextant4 ,if any time is left1 spend it in marking courses with the protractor and handling the sextant4 ,assign for ,night ,work the following ,arts4 in ,bowditch3 #acd-ace-acf-ach-adb-add-ade-aea-aeb-aeg -aeh-aei-afj-afa-afb-afc4 ,,saturday ,,lecture ,,fixes1 ,,angles ,,by ,,bearings ,,and ,,sextant ,there are five good ways of fixing your position 7obtaining a fix1 as it is called7 providing you are within sight of landmarks which you can identify or in comparatively shoal water4 ,put in your ,note-,book3 #a4 ,cross bearings of two known objects4 #b4 ,bearing and distance of a known object1 the height of which is known4 #c4 ,two bearings of a known object separated by an interval of time1 with a run during that interval4 #d4 ,sextant angles between three known objects4 #e4 ,using the compass1 log and lead in a fog or in unfamiliar waters4 #a4 ,cross bearings of two known objects4 ,select two objects marked on the chart1 so far apart that each will bear about #de deg4 off your bow but in opposite directions4 ,these bearings will be secured in the best way by the use of your pelorus4 ,correct each bearing for ,variation and ,deviation so that it will be a true bearing4 ,then with the parallel rulers carry the bearing of one object from the chart compass card until you can intersect the object itself and draw a line through it4 ,do exactly the same with the other object4 ,where the two lines intersect1 will be the position of the ship at the time the bearings were taken4 ,illustration ,now supposing you wish to find the latitude and longitude of that position of the ship4 ,for the latitude1 measure the distance of the place from the nearest parallel with the dividers4 ,take the dividers to the latitude scale at the side of the chart and put one point of them on the same parallel4 ,where the other point touches on the latitude scale1 will be the latitude desired4 ,for the longitude1 do exactly the same thing1 but use a meridian of longitude instead of a parallel of latitude and read from the longitude scale at the top or bottom of the chart instead of from the side4 #b4 ,bearing and distance of a known object1 the height of which is known4 ,take a bearing of1 say1 a lighthouse the height of which is known4 ,the height of all lighthouses on the ,atlantic ,coast can be found in a book published by the ,u4,s4 ,dept4 of ,commerce4 ,correct the bearing1 as mentioned in case ,no4 #a4 ,now read the angle of the height of that light by using your sextant4 ,do this by putting the vernier #j on the arc #j1 sliding the limb slowly forward until the top of the lighthouse in the reflected horizon just touches the bottom of the lighthouse in the true horizon4 ,with this angle and the known height of the light1 enter ,table #cc in ,bowditch4 ,at the left of the ,table will be found the distance off in knots4 ,this method can be used with any fairly perpendicular object1 the height of which is known and which is not more than #e knots away1 as ,table #cc is not made out for greater distances4 #c4 ,two bearings of the same object1 separated by an interval of time and with a run during that interval4 ,take a compass bearing of some prominent object when it is either #b1 #c or #d points off the bow4 ,take another bearing of the same object when it is either #d1 #f or #h points off the bow4 ,the distance run by the ship between the two bearings will be her distance from the observed object at the second bearing4 ,the distance run is the distance off4 ,a diagram will show clearly just why this is so3 ,illustration ,the ship at ,a finds the light bearing ,,nnw #b points off her bow4 ,at ,b1 when the light bears ,,nw and #d points off1 the log registers the distance from ,a to ,b #i miles4 #i miles1 then1 will be the distance from the light itself when the ship is at ,b4 ,the mathematical reason for this is that the distance run is one side of an isosceles triangle4 ,such triangles have their two sides of equal length4 ,for that reason1 the distance run is the distance off4 ,now the same fact holds true in running from ,b1 which is #d points off the bow1 to ,c1 which is #h points off the bow1 or directly abeam4 ,the log shows the distance run between ,b and ,c is #f4c miles4 ,hence1 the ship is #f4c miles from the light when directly abeam of it4 ,this last #d and #h point bearing is what is known as the bow and beam bearing1 and is the standard method used in coastwise navigation4 ,any one of these methods is of great value in fixing your position with relation to the land1 when you are about to go to sea4 #d4 ,sextant angles between three known objects4 ,this method is the most accurate of all4 ,because of its precision it is the one used by the ,government in placing buoys1 etc4 ,take three known objects such as ,a1 ,b and ,c which are from #cj deg4 to #fj deg4 from each other4 ,illustration ,with a sextant1 read the angle from ,a to ,b and from ,b to ,c4 ,place a piece of transparent paper over the compass card and draw three lines from the center of the compass card to the circumference in such a way that the angles secured by the sextant will be formed by the three lines drawn4 ,now take this paper with the angles on it and fit it on the chart so that the three objects of which angles were taken will be intersected by the three lines on the paper4 ,where the point ,s is 7in my diagram7 will be the point of the ship's position at the time of sight4 ,to secure greater accuracy the two angles should be taken at the same time by two observers4 #e4 ,using a compass1 log and lead when you are in a fog or unfamiliar waters4 ,supposing that you are near land and want to fix your position but have no landmarks which you can recognize4 ,here is a method to help you out3 ,take a piece of tracing paper and rule a vertical line on it4 ,this will represent a meridian of longitude4 ,take casts of the lead at regular intervals1 noting the time at which each is taken1 and the distance logged between each two4 ,the compass corrected for ,variation and ,deviation will show your course4 ,rule a line on the tracing paper in the direction of your course1 using the vertical line as a ,n and ,s meridian4 ,measure off on the course line by the scale of miles in your chart1 the distance run between casts and opposite each one note the time1 depth ascertained and1 if possible1 nature of the bottom4 ,now lay this paper down on the chart which can be seen under it1 in about the position you believe yourself in when you made the first cast4 ,if your chain of soundings agrees with those on the chart1 you are all right4 ,if not1 move the paper about1 keeping the vertical line due ,n and ,s1 till you find the place on the chart that does agree with you4 ,that is your line of position4 ,you will never find in that locality any other place where the chain of soundings are the same on the same course you are steaming4 ,this is the only method by soundings that you can use in thick weather and it is an invaluable one4 ,put in your ,note-,book this 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 for ,night ,work1 ,review for ,weekly ,examination to be held on ,monday4 ,add an explanation of the ,deviation ,card in ,bowditch1 page #da4 ,put in your ,note-,book3 ,entering ,new ,york ,harbor1 ship heading ,w #c_/d ,n1 ,variation #i deg4 ,w4 ,observed by pelorus the following objects3 ,buoy ,no4 #a--;,,ene #a_/d ,e #b--;,e #a_/b ,n #c--,,ne #a_/d ,e #d--,,nw #a_/d ,n ,required true bearings of objects observed4 ,answer3 ,from ,deviation ,card in ,bowditch1 p4 #da1 ,deviation on ,w #c_/d ,n course is #e deg4 ,e4 ,hence1 ,compass ,error is #e deg4 ,e 7,dev47 #i deg4 ,w 7,var47 #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 ,,reckoning ,,tuesday ,,lecture ,,latitude ,,and ,,longitude ,illustration ,we have been using the words ,latitude and ,longitude a good deal since this course began4 ,let us see just what the words mean4 ,before doing that1 there are a few facts to keep in mind about the earth itself4 ,the earth is a spheroid slightly flattened at the poles4 ,the axis of the earth is a line running through the center of the earth and intersecting the surface of the earth at the poles4 ,the equator is the great circle1 formed by the intersection of the earth's surface with a plane perpendicular to the earth's axis and equidistant from the poles4 ,every point on the equator is1 therefore1 #ij deg4 from each pole4 ,meridians are great circles formed by the intersection with the earth's surface of planes perpendicular to the equator4 ,parallels of latitude are small circles parallel to the equator4 ,the ,latitude of a place on the surface of the earth is the arc of the meridian intercepted between the equator and that place4 ,it is measured by the angle running from the equator to the center of the earth and back through the place in question4 ,latitude is reckoned from the equator 7#j deg47 to the ,north ,pole 7#ij deg47 and from the equator 7#j deg47 to the ,south ,pole 7#ij deg474 ,the difference of ,latitude between any two places is the arc of the meridian intercepted between the parallels of ,latitude of the places and is marked ,n or ,s according to the direction in which you steam 7,t n'74 ,the ,longitude of a place on the surface of the earth is the arc of the equator intercepted between the meridian of the place and the meridian at ,greenwich1 ,england1 called the ,prime ,meridian4 ,longitude is reckoned ,east or ,west through #ahj deg4 from the ,meridian at ,greenwich4 ,difference of ,longitude between any two places is the arc of the equator intercepted between their meridians1 and is called ,east or ,west according to direction4 ,example3 ,diff4 ,lo4 ,t and ,t' ,e' ,m1 and ,e or ,w according as to which way you go4 ,departure is the actual linear distance measured on a parallel of ,latitude between two meridians4 ,difference of ,latitude is reckoned in minutes because miles and minutes of ,latitude are always the same4 ,departure1 however1 is only reckoned in miles1 because while a mile is equal to #a' of longitude on the equator1 it is equal to more than #a' as the latitude increases2 the reason being1 of course1 that the meridians of ,lo4 converge toward the pole1 and the distance between the same two meridians grows less and less as you leave the equator and go toward either pole4 ,example3 ,,tn1 ,n'n'4 #aj mi4 departure on the equator #aj' difference in ,lo4 #aj mi4 departure in ,lat4 #ee deg4 equals something like #ah' difference in ,lo4 ,the curved line which joins any two places on the earth's surface1 cutting all the meridians at the same angle1 is called the ,rhumb ,line4 ,the angle which this line makes with the meridian of ,lo4 intersecting any point in question is the ,course1 and the length of the line between any two places is called the distance between them4 ,example3 ,t or ,t'4 ,chart ,projections ,the earth is projected1 so to speak1 upon a chart in three different ways--the ,mercator ,projection1 the ,polyconic ,projection and the ,gnomonic ,projection4 ,the ,mercator ,projection ,you already know something about the ,mercator ,projection and a ,mercator chart4 ,as explained before1 it is constructed on the theory that the earth is a cylinder instead of a sphere4 ,the meridians of longitude1 therefore1 run parallel instead of converging1 and the parallels of latitude are lengthened out to correspond to the widening out of the ,lo4 meridians4 ,just how this ,mercator chart is constructed is explained in detail in the ,arts4 in ,bowditch you were given to read last night4 ,you do not have to actually construct such a chart1 as the ,government has for sale blank ,mercator charts for every parallel of latitude in which they can be used4 ,it is well to remember1 however1 that since a mile or minute of latitude has a different value in every latitude1 there is an appearance of distortion in every ,mercator chart which covers any large extent of surface4 ,for instance1 an island near the pole1 will be represented as being much larger than one of the same size near the equator1 due to the different scale used to preserve the accurate character of the projection4 ,the ,polyconic ,projection ,the theory of the ,polyconic ,projection is based upon conceiving the earth's surface as a series of cones1 each one having the parallel as its base and its vertex in the point where a tangent to the earth at that latitude intersects the earth's axis4 ,the degrees of latitude and longitude on this chart are projected in their true length and the general distortion of the earth's surface is less than in any other method of projection4 ,illustration ,a straight line on the polyconic chart represents a near approach to a great circle1 making a slightly different angle with each meridian of longitude as they converge toward the poles4 ,the parallels of latitude are also shown as curved lines1 this being apparent on all but large scale charts4 ,the ,polyconic ,projection is especially adapted to surveying1 but is also employed to some extent in charts of the ,u4 ,s4 ,coast ,geodetic ,survey4 ,gnomonic ,projection ,the theory of this projection is to make a curved line appear and be a straight line on the chart1 i4e41 as though you were at the center of the earth and looking out toward the circumference4 ,the ,gnomonic ,projection is of particular value in sailing long distance courses where following a curved line over the earth's surface is the shortest distance between two points that are widely separated4 ,this is called ,great ,circle ,sailing and will be talked about in more detail later on4 ,the point to remember here is that the ,hydrographic ,office prints ,great ,circle ,sailing ,charts covering all the navigable waters of the globe4 ,since all these charts are constructed on the ,gnomonic ,projection1 it is only necessary to join any two points by a straight line to get the curved line or great circle track which your ship is to follow4 ,the courses to sail and the distance between each course are easily ascertained from the information on the chart4 ,this is the way it is done3 7,note to ,instructor3 ,provide yourself with a chart and explain from the chart explanation just how these courses are laid down47 ,spend the rest of the time in having pupils lay down courses on the different kinds of charts4 ,if these charts are not available assign for night work the following articles in ,bowditch1 part of which reading can be done immediately in the class room--so that as much time as possible can be given to the reading on ,dead ,reckoning3 #afg-afh-afi-agb-agc-agd-age-agf--;first two sentences #agh-bjb-bjc-bjd-bje-bjf-bjg-bjh4 ,note to pupils3 ,in reading articles #afg-agh1 disregard the formulae and the examples worked out by logarithms4 ,just try to get a clear idea of the different sailings mentioned and the theory of ,dead ,reckoning in ,arts4 #bjb-bji4 ,,wednesday ,,lecture ,,useful ,,tables--,,plane ,,and ,,traverse ,,sailing ,the whole subject of ,navigation is divided into two parts1 i4e41 finding your position by what is called ,dead ,reckoning and finding your position by observation of celestial bodies such as the sun1 stars1 planets1 etc4 ,to find your position by dead reckoning1 you go on the theory that small sections of the earth are flat4 ,the whole affair then simply resolves itself into solving the length of right-angled triangles except1 of course1 when you are going due ,east and ,west or due ,north and ,south4 ,for instance1 any courses you sail like these will be the hypotenuses of a series of right-angled triangles4 ,the problem you have to solve is1 having left a point on land1 the latitude and longitude of which you know1 and sailed so many miles in a certain direction1 in what latitude and longitude have you arrived8 ,illustration ,if you sail due ,north or ,south1 the problem is merely one of arithmetic4 ,suppose your position at noon today is ,latitude #ci deg4 #ae' ,n1 ,longitude #dj deg4 ,w1 and up to noon tomorrow you steam due ,north #cjj miles4 ,now you have already learned that a minute of latitude is always equal to a nautical mile4 ,hence1 you have sailed #cjj minutes of latitude or #e deg44 ,this #e deg4 is called difference of latitude1 and as you are in ,north latitude and going ,north1 the difference of latitude1 #e deg41 should be added to the latitude left1 making your new position #dd deg4 #ae' ,n and your ,longitude the same #dj deg4 ,w1 since you have not changed your longitude at all4 ,in sailing ,east or ,west1 however1 your problem is more difficult4 ,only on the equator is a minute of longitude and a nautical mile of the same length4 ,as the meridians of longitude converge toward the poles1 the lengths between each lessen4 ,we now have to rely on tables to tell us the number of miles in a degree of longitude at every distance ,north or ,south of the equator1 i4e41 in every latitude4 ,longitude1 then1 is reckoned in miles4 ,the number of miles a ship makes ,east or ,west is called ,departure1 and it must be converted into degrees1 minutes and seconds to find the difference of longitude4 ,a ship1 however1 seldom goes due ,north or ,south or due ,east or ,west4 ,she usually steams a diagonal course4 ,suppose1 for instance1 a vessel in ,latitude #dj deg4 #cj' ,n1 ,longitude #gj deg4 #be' ,w1 sails ,,ssw #ej miles4 ,what is the new latitude and longitude she arrives in8 ,she sails a course like this3 ,illustration ,now suppose we draw a perpendicular line to represent a meridian of longitude and a horizontal one to represent a parallel of latitude4 ,then we have a right-angled triangle in which the line ,,ac represents the course and distance sailed1 and the angle at ,a is the angle of the course with a meridian of longitude4 ,if we can ascertain the length of ,,ab1 or the distance ,south the ship has sailed1 we shall have the difference of latitude1 and if we can get the length of the line ,,bc1 we shall have the ,departure and from it the difference of longitude4 ,this is a simple problem in trigonometry1 i4e41 knowing the angle and the length of one side of a right triangle1 what is the length of the other two sides8 ,but you do not have to use trigonometry4 ,the whole problem is worked out for you in ,table #b of ,bowditch4 ,find the angle of the course ,,ssw1 i4e41 ,s #bb deg4 ,w in the old or #bjb deg4 in the new compass reading4 ,look down the distance column to the left for the distance sailed1 i4e41 #ej miles4 ,opposite this you find the difference of latitude #df-d_/aj 7#df4d7 and the departure #ah-g_/aj 7#ah4g74 ,now the position we were in at the start was ,lat4 #dj deg4 #cj' ,n1 ,longitude #gj deg4 #be' ,w4 ,in sailing ,,ssw #ej miles1 we made a difference of latitude of #df' #bd 7#df4d71 and as we went ,south--toward the equator--we should subtract this #df' #bd from our latitude left to give us our latitude in4 ,now we must find our difference of longitude and from it the new or ,longitude in4 ,the first thing to do is to find the average or middle latitude in which you have been sailing4 ,do this by adding the latitude left and the latitude in and dividing by #b4 #dj deg4 #cj' #jj #ci #dc #cf ----------- #b7hj #ac #cf ----------- #dj deg4 #jf' #dh ,mid4 ,lat4 ,take the nearest degree1 i4e41 #dj deg41 as your answer4 ,with this #dj deg4 enter the same ,table #b and look for your departure1 i4e41 #ah4g in the difference of latitude column4 #ah4d is the nearest to it4 ,now look to the left in the distance column opposite #ah4d and you will find #bd1 which means that in ,lat4 #dj deg4 a departure of #ah4g miles is equivalent to #bd' of difference of ,longitude4 ,we were in #gj deg4 #be' ,west ,longitude and we sailed ,south and ,west1 so this difference of ,longitude should be added to the ,longitude left to get the ,longitude in3 ,lo4 left #gj deg4 #be' ,w ,diff4 ,lo4 #bd ----------- ,lo4 in #gj deg4 #di' ,w ,the whole problem therefore would look like this3 ,lat4 left #dj deg4 #cj' ,n ,lo4 left #gj deg4 #be' ,w ,diff4 ,lat4 #df #bd ,diff4 ,lo4 #bd ------------- ---------- ,lat4 in #ci deg4 #dc' #cf ,n ,lo4 in #gj deg4 #di' ,w ,there is one more fact to explain4 ,when the course is #de deg4 or less 7old compass reading7 you read from the top of the page of ,table #b down4 ,when the course is more than #de deg4 7old compass reading7 you read from the bottom of the page up4 ,the distance is taken out in exactly the same way in both cases1 but the difference of ,latitude and the ,departure1 you will notice1 are reversed4 7,instructor3 ,read a few courses to thoroughly explain this47 ,from all this explanation we get the following rules1 which put in your ,note-,book3 ,to find the new or ,lat4 in3 ,enter ,table #b with the true course at the top or bottom of the page according as to whether it is less or greater than #de deg4 7old compass reading74 ,take out the difference of ,latitude and ,departure and mark the difference of ,latitude minutes 7'74 ,when the ,latitude left and the difference of ,latitude are both ,north or both ,south1 add them4 ,when one is ,north and the other ,south1 subtract the less from the greater and the remainder1 named ,north or ,south after the greater1 will be the new ,latitude1 known as the ,latitude in4 ,to find the new or ,lo4 in3 ,find the middle latitude by adding the latitude left to the latitude in and dividing by #b4 ,with this middle latitude1 enter ,table #b4 ,seek for the departure in the difference of latitude column4 ,opposite to it in the distance column will be the figures indicating the number of minutes in the difference of longitude4 ,with this difference of ,longitude1 apply it in the same way to the ,longitude left as you applied the difference of ,latitude to the ,latitude left4 ,the result will be the new or ,longitude in4 ,now if a ship steamed a whole day on the same course1 you would be able to get her ,dead ,reckoning position without any further work1 but a ship does not usually sail the same course #bd hours straight4 ,she usually changes her course several times1 and as a ship's position by ,d4,r4 is only computed once a day--at noon--it becomes necessary to have a method of obtaining the result after several courses have been sailed4 ,this is called working a traverse and sailing on various courses in this fashion is called ,traverse ,sailing4 ,put in your ,note-,book the following example and the way in which it is worked3 ,departure taken from ,barnegat ,light in ,lat4 #ci deg4 #df' ,n1 ,lo4 #gd deg4 #jf' ,w1 bearing by compass ,,nnw1 #ae knots away4 ,ship heading ,south with a ,deviation of #d deg4 ,w4 ,she sailed on the following courses3 ---------------------------------------- -------------------------- ,course ,wind ,leeway,deviation,distance ,remarks ---------------------------------------- -------------------------- ,,se #c_/d ,e ,,ne #a pt4 #c deg4 ,e #cj ,variation throughout day #h deg4 ,w4 ,s #aa deg4 ,w ,,ne #j #f deg4 ,e #ee ,a current set ,,ne magnetic ,,nnw ,,ne #j #b deg4 ,w #ad #a_/b mi4 per hr4 for the day4 ,s #hg deg4,e ,,ne #j #c deg4 ,e #ej ,required ,lat4 and ,lo4 in and course and distance made good4 ---------------------------------------- -------------------------- ---------------------------------------- ------------------------------------- ,c4 ,cos4 ,wind,leeway ,dev4 ,var4 ,,new ,,old ,dist4,diff4 ,lat4 ,departure ,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 in4 #ch -#da -#ed ,n ,table #b--,under #ci deg4 ,dep4 in #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 in4 #gb deg4-#cd'-jj ,w ,table #b--;,diff4 ,lat4 #fd4a1 ,dep4 #ga4e4 ,course ,s #dh deg4 ,e--,distance #if miles4 ,the rule covering all these operations is as follows3 #a4 ,write out the various courses with their corrections for ,leeway1 ,deviation1 ,variation and the distance run on each4 #b4 ,in four adjoining columns headed ,n1 ,s1 ,e1 ,w respectively1 put down the ,difference of ,latitude and ,departure for each course4 #c4 ,add together all the northings1 all the southings1 all the eastings and all the westings4 ,subtract to find the difference between northings and southings and you will get the whole difference of ,latitude4 ,the difference between the eastings and westings will be the whole departure4 #d4 ,find the latitude in1 as already explained4 #e4 ,find the ,lo4 in1 as already explained4 #f4 ,with the whole difference of ,latitude and whole ,departure1 seek in ,table #b for the page where the nearest agreement of ,difference of ,latitude and ,departure can be found4 ,the number of degrees at the top or bottom of the page 7according as to whether the ,diff4 of ,lat4 or ,dep4 is greater7 will give you the true course made good1 and the number in the distance column opposite the proper ,difference of ,latitude and ,departure will give you the distance made4 ,it is often convenient to use the reverse of the above method1 i4e41 being given the latitude and longitude of the position left and the latitude and longitude of the position arrived in1 to find the course and distance between them by ,middle ,latitude ,sailing4 ,the full rule is as follows3 #a4 ,find the algebraic difference between the latitudes and longitudes respectively4 #b4 ,using the middle 7or average7 latitude as a course1 find in ,table #b of ,bowditch the ,diff4 of ,lo4 in the distance column4 ,opposite1 in the ,diff4 of ,lat4 column1 will be the correct ,departure4 #c4 ,with the ,diff4 of ,lat4 between the position left and the position arrived in1 and the ,departure1 just secured1 seek in ,table #b for the page where the nearest agreement to these values can be found4 ,on this page will be secured the true course and distance made1 as explained in the preceding method4 #d4 ,use this method only when steaming approximately an ,east and ,west course4 ,for an example of this method1 see ,bowditch1 p4 #gg1 example #c4 ,,thursday ,,lecture ,,examples ,,on ,,plane ,,and ,,traverse ,,sailing 7,continued7 #a4 ,departure taken from ,cape ,horn4 ,lat4 #ee deg4 #eh' #da ,s1 ,lo4 #fg deg4 #af' #ae ,w1 bearing by compass ,,ssw #bj knots4 ,ship heading ,,sw x ,s1 ,deviation #d deg4 ,e1 steamed the following courses3 ---------------------------------------- ------------ ,c4 ,cos4 ,wind ,leeway ,deviation ,distance ---------------------------------------- ------------ ,,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 ---------------------------------------- ------------ ,remarks ,variation #ah deg4 ,e throughout4 ,current set ,,nw magnetic #cj mi4 for the day4 ,required ,latitude and ,longitude in and course and distance made good4 #b4 ,departure taken from ,st4 ,agnes ,lighthouse1 ,scilly ,islands1 ,lat4 #di deg4 #ec' ,s1 ,lo4 #f deg4 #bj' ,w1 bearing by compass ,e x ,s1 distance #ah knots1 ,deviation #aj deg4 ,w1 ,variation #bc deg4 ,w4 ,ship headed ,n steamed on the following courses3 ---------------------------------------- ----------------------- ,c4 ,cos4 ,wind ,leeway ,devia- ,dis- ,remarks tion tance ---------------------------------------- ----------------------- ,n 44 #aj deg4 ,w #fj ,variation #bc deg4 ,w4 ,current set ,s #a_/b ,e ,w #c pts4 #aj deg4 ,e #dj ,,se mg #a-a_/b miles for #bd hrs4 ,,nne ,,nnw #b pts4 #h deg4 ,w #de ,req4 ,lat4 and ,lo4 in and course and distance made good1 ---------------------------------------- ----------------------- ,assign for ,night ,work the following articles in ,bowditch3 #agi-ahj-aha-ahb4 ,also additional problems in ,dead ,reckoning4 ,,friday ,,lecture ,,mercator ,,sailing ,this is a method to find the true course and distance between two points4 ,the method can be used in two ways1 i4e41 by the use of ,tables #b and #c 7called the inspection method7 and by the use of logarithms4 ,the first method is the quicker and will do for short distances4 ,the second method1 however1 is more accurate in all cases1 and particularly where the distances are great4 ,the inspection method is as follows 7,put in your ,note-,book73 ,find the algebraic difference between the meridional parts corresponding to the ,lat4 in and ,lat4 sought by ,table #c4 ,call this ,meridional difference of ,latitude4 ,find the algebraic difference between ,longitude in and ,longitude sought and call this difference of ,longitude4 ,with the ,meridional difference of ,latitude and the difference of ,longitude1 find the course by searching in ,table #b for the page where they stand opposite each other in the latitude and departure columns4 ,now find the real difference of latitude4 ,under the course just found and opposite the real difference of ,latitude1 will be found the distance sailed in the distance column4 ,example3 ,what is the course and distance from ,lat4 #dj deg4 #bh' ,n1 ,lo4 #gc deg4 #ej' ,w1 to ,lat4 #ci deg4 #ea' ,n1 ,lo4 #gb deg4 #de' ,w8 ,lat4 in #dj deg4 #bh' ,n ,meridional pts4 #bfdd4b ,lat4 sought #ci #ea ,n ,meridional pts4 #beif4j --------- ------ #j deg4 #cg' ,mer4 diff4 ,lat4 #dh4b ,lo4 in #gc deg4 #ej' ,w ,lo4 sought #gb #de ,w --------- #a deg4 #je' #fe' ,on page #fjd ,bowditch you will find #dh4g and #fd4g opposite each other1 and as #dh4g is in the ,lat4 column only when you read from the bottom1 the course is ,s #ec deg4 ,e4 ,the real difference of ,lat4 under this course is opposite #fb in the distance column4 ,hence the distance to be sailed is #fb miles4 ,if distances are too great1 divide meridional difference of ,lat41 real difference of ,latitude and difference of ,longitude by #aj or any other number to bring them within the scope of the distances in ,table #b4 ,when distance to be sailed is found1 it must be multiplied by the same number4 ,for instance1 if the difference of ,lat41 difference of ,lo41 etc41 are divided by #aj to bring them in the scope of ,table #b1 and with these figures #bai is the distance found1 the real distance would be #aj times #bai or #baij4 ,now let us work out the same problem by logarithms4 ,this will acquaint us with two new ,tables1 i4e41 ,tables #db and #dd4 ,put this in your ,note-,book3 ,lat4 in #dj deg4 #bh' ,n ,mer4 pts4 #bfdd4b ,lo4 in #gc deg4 #ej' ,lat4 sought #ci #ea ,mer4 pts4 #beif4j ,lo4 sought #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 ,distance 7,table #db7 #fb4aa miles ,find algebraically the real difference of latitude1 meridional difference of latitude and the difference of longitude4 ,reduce real difference of latitude and difference of longitude to minutes4 ,take log of the difference of longitude 7,table #db7 and add #aj4 ,from this log subtract the log of difference of meridional parts4 ,the result will be the log tan of the ,true ,course1 which find in ,table #dd4 ,on the same page find the log sec of true course4 ,add to this the log of the real difference of latitude1 and if the result is more than #aj1 subtract #aj4 ,this result will be the log of the distance sailed4 ,this method should be used only when steaming approximately a ,north and ,south course4 ,note4--,for detailed explanation of ,tables #db and #dd see ,bowditch1 pp4 #bga-bgf4 ,assign for ,night ,reading ,arts1 in ,bowditch3 #ahc-ahd-ahe-ahf-ahg-ahh-ahi-aid-bei-bfj -bfa-bfb-bfc-bfd-bfe-bff-bfg-bfh4 ,also1 one of the examples of ,mercator sailing to be done by both the ,inspection and ,logarithmic method4 ,,saturday ,,lecture ,,great ,,circle ,,sailing--,,the ,,chronometer ,in ,tuesday's ,lecture of this week1 ,i explained how a ,great ,circle track was laid down on one of the ,great ,circle ,sailing ,charts which are prepared by the ,hydrographic ,office4 ,supposing1 however1 you do not have these charts on hand4 ,there is an easy way to construct a great circle track yourself4 ,turn to ,art4 #aid1 page #hb1 in ,bowditch4 ,here is a table with an explanation as to how to use it4 ,take1 for instance1 the same two points between which you just drew a line on the great circle track4 ,find the center of this line and the latitude of that point4 ,at this point draw a line perpendicular to the course to be sailed1 the other end of which must intersect the corresponding parallel of latitude given in the table4 ,with this point as the center of a circle1 sweep an arc which will intersect the point left and the point sought4 ,this arc will be the great circle track to follow4 ,to find the courses to be sailed1 get the difference between the course at starting and that at the middle of the circle1 and find how many quarter points are contained in it4 ,now divide the distance from the starting point to the middle of the circle by the number of quarter points4 ,that will give the number of miles to sail on each quarter point course4 ,see this illustration3 ,illustration ,difference between ,,ene and ,e #b pts4 #h quarter points4 ,say distance is #afjj miles measured by dividers or secured by ,mercator ,sailing ,method4 ,divide #afjj by #h #bjj4 ,every #bjj miles you should change your course #a_/d point ,east4 ,the ,chronometer ,the chronometer is nothing more than a very finely regulated clock4 ,with it we ascertain ,greenwich ,mean ,time1 i4e41 the mean time at ,greenwich ,observatory1 ,england4 ,just what the words ,greenwich ,mean ,time signify1 will be explained in more detail later on4 ,what you should remember here is that practically every method of finding your exact position at sea is dependent upon knowing ,greenwich ,mean ,time1 and the only way to find it is by means of the chronometer4 ,it is essential to keep the chronometer as quiet as possible4 ,for that reason1 when you take an observation you will probably note the time by your watch4 ,just before taking the observation1 you will compare your watch with the chronometer to notice the exact difference between the two4 ,when you take your observation1 note the watch time1 apply the difference between the chronometer and watch1 and the result will be the ,,ct4 ,for instance1 suppose the chronometer read #c;h #bem #ajs1 and your watch1 at the same instant1 read #a;h #ajm #es4 ,c--,w would be3 #c;h -- #bem -- #ajs -- #a -- #aj -- #je ---------------- #b;h -- #aem -- #jes ,now suppose you took an observation which1 according to your watch1 was at #b;h #ajm #jes4 ,what would be the corresponding ,c ,t8 ,it would be ,,wt #b;h -- #ajm -- #jes ,c -- ,w #b -- #ae -- #je -------------------- ,,ct #d;h -- #bem -- #ajs ,if the chronometer time is less than the ,w ,t add #ab hours to the ,c ,t1 so that it will always be the larger and so that the amount to be added to ,w ,t will always be 4 ,for instance1 ,,ct #a;h--#bem--#des1 ,,wt #d;h--#acm--#bes1 what is the ,c-,w8 ,,ct #ac;h--#bem--#des ,,wt #d --#ac --#be ---------------- ,c--,w #i;h--#abm--#bjs ,now1 suppose an observation was taken at #f;h #acm #bes according to watch time4 ,what would be the corresponding ,,ct8 ,,wt #f;h--#acm--#bes ,c--,w #i --#ab --#bj ---------------- #ae;h--#bem--#des --#ab ---------------- ,,ct #c;h--#bem--#des ,put in your ,note-,book3 ,,ct ,,wt ,c - ,w4 ,if1 in finding ,c-,w1 ,c is less than ,w1 add #ab hours to ,c1 subtracting same after ,,ct is secured4 ,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 ,there is one more very important fact to know about the chronometer4 ,it is physically impossible to keep it absolutely accurate over a long period of time4 ,instead of continually fussing with its adjustment and hands1 the daily rate of error is ascertained1 and from this the exact time for any given day4 ,it is an invariable practice among good mariners to leave the chronometer alone4 ,when you are in port1 you can find out from a time ball or from some chronometer maker what your error is4 ,with this in mind1 you can apply the new correction from day to day4 ,here is an example 7,put in your ,note-,book73 ,on ,june #ast1 ,,ct #g;h--#bjm--#aes1 ,,cc #bm--#djs fast4 ,on ,june #afth1 7same ,,ct7 ,,cc #am--#cjs fast4 ,what was the corresponding ,g4,m4,t4 on ,june #ajth8 ,june #ast #bm--#djs fast #afth #am--#cjs fast ---------------- #am--#ajs #fj -- #fj #aj -- #ae7 #gjs 7#d4f sec4 ,daily ,rate of error losing ,june #ast-#ajth1 #i days times #d4f sec4 #da sec4 losing ,june #ast #bm--#djs fast ,june #ajth #das losing --------- ,june #ajth #am--#eis fast ,,ct #g;h--#bjm--#aes ,,cc -- #a --#ei ------------ ,g4,m4,t4 #g;h--#ahm--#afs on ,june #ajth ,if ,,cc is fast1 subtract from ,,ct ,if ,,cc is slow1 add to ,,ct ,,week ,,iii--,,celestial ,,navigation ,,tuesday ,,lecture ,,celestial ,,co-,,ordinates1 ,,equinoctial ,,system1 ,,etc4 ,we have already discussed the way in which the earth is divided so as to aid us in finding our position at sea1 i4e41 with an equator1 parallels of latitude1 meridians of longitude starting at the ,greenwich meridian1 etc4 ,we now take up the way in which the celestial sphere is correspondingly divided and also simple explanations of some of the more important terms used in ,celestial ,navigation4 ,as you stand on any point of the earth and look up1 the heavenly bodies appear as though they were situated upon the surface of a vast hollow sphere1 of which your eye is the center4 ,of course this apparent concave vault has no existence and we cannot accurately measure the distance of the heavenly bodies from us or from each other4 ,we can1 however1 measure the direction of some of these bodies and that information is of tremendous value to us in helping us to fix our position4 ,now we could use our eye as the center of the celestial sphere but more accurate than that is to use the center of the earth4 ,suppose we do use the center of the earth as the place from which to observe these celestial bodies and1 in imagination1 transfer our eye there4 ,then we will find projected on the celestial sphere not only the heavenly bodies but the imaginary points and circles of the earth's surface4 ,parallels of latitude1 meridians of longitude1 the equator1 etc41 will have the same imaginary position on the celestial sphere that they have on the earth4 ,your actual position on the earth will be projected in a point called your zenith1 i4e41 the point directly overhead4 ,illustration ,from this we get the definition that the ,zenith of an observer on the earth's surface is the point in the celestial sphere directly overhead4 ,it would be a simple matter to fix your position if your position never changed4 ,but it is always changing with relation to these celestial bodies4 ,first1 the earth is revolving on its own axis4 ,second1 the earth is moving in an elliptic track around the sun1 and third1 certain celestial bodies themselves are moving in a track of their own4 ,the changes produced by the daily rotation of the earth on its axis are different for observers at different points on the earth and1 therefore1 depend upon the latitude and longitude of the observer4 ,but the changes arising from the earth's motion in its orbit and the motion of various celestial bodies in their orbits1 are true no matter on what point of the earth you happen to be4 ,these changes1 therefore1 in their relation to the center of the earth1 may be accurately gauged at any instant4 ,to this end the facts necessary for any calculation have been collected and are available in the ,nautical ,almanac1 which we will take up in more detail later4 ,now with these facts in mind1 let us explain in simple words the meaning of some of the terms you will have to become acquainted with in ,celestial ,navigation4 ,in the illustration 7,bowditch p4 #hh7 the earth is supposed to be projected upon the celestial sphere ,n ,e ,s ,w4 ,the ,zenith of the observer is projected at ,z and the pole of the earth which is above the horizon is projected at ,p4 ,the other pole is not given4 ,the ,celestial ,equator is marked here ,e ,q ,w and like all other points and lines previously mentioned1 it is the projection of the ,equator until it intersects the celestial sphere4 ,another name for the ,celestial ,equator is the ,equinoctial4 ,all celestial meridians of longitude corresponding to longitude meridians on the earth are perpendicular to the equinoctial and likewise ,p ,s1 the meridian of the observer1 since it passes through the observer's zenith at ,z1 is formed by the extension of the earth's meridian of the observer and hence intersects the horizon at its ,n and ,s points4 ,this makes clear again just what is the meridian of the observer4 ,it is the meridian of longitude which passes through the ,n and ,s poles and the observer's zenith4 ,in other words1 when the sun or any other heavenly body is on your meridian1 a line stretched due ,n and ,s1 intersecting the ,n and ,s poles1 will pass through your zenith and the center of the sun or other celestial body4 ,to understand this is important1 for no sight with the sextant is of value except with relation to your meridian4 ,the ,declination of any point in the celestial sphere is its distance in arc1 ,north or ,south of the celestial equator1 i4e41 ,n or ,s of the ,equinoctial4 ,north declinations1 i4e41 declinations north of the equinoctial are always marked1 2 those south of the equinoctial1 -4 ,for instance1 in the ,nautical ,almanac1 you will never see a declination of the sun or other celestial body marked1 ,n #ah deg4 #bh' #cj4 ,it will always be marked #ah deg4 #bh' #cj and a south declination will be marked -#ah deg4 #bh' #cj4 ,another fact to remember is that ,declination on the celestial sphere corresponds to latitude on the earth4 ,if1 for instance1 the ,sun's declination is #ah deg4 #bh' #cj at noon1 ,greenwich1 then at that instant1 i4e41 noon at ,greenwich1 the sun will be directly overhead a point on earth which is in latitude ,n #ah deg4 #bh' #cj4 ,the ,polar ,distance of any point is its distance in arc from either pole4 ,it must1 therefore1 equal #ij deg4 minus the declination1 if measured from the pole of the same name as the declination or #ij deg4 plus the declination if measured from the pole of the opposite name4 ,p ,m is the polar distance of ,m from ,p1 or ,p ,b the polar distance of ,b from ,p4 ,the true altitude of a celestial body is its angular height from the true horizon4 ,the zenith distance of any point or celestial body is its angular distance from the zenith of the observer4 ,the ,ecliptic is the great circle representing the path in which the sun appears to move in the celestial sphere4 ,as a matter of fact1 you know that the earth moves around the sun1 but as you observe the sun from some spot on the earth1 it appears to move around the earth4 ,this apparent track is called the ,ecliptic as stated before1 and in the illustration the ,ecliptic is represented by the curved line1 ,c ,v ,t4 ,the plane of the ,ecliptic is inclined to that of the ,equinoctial at an angle of #bc deg4 #bg-a_/b'1 and this inclination is called the obliquity of the ,ecliptic4 ,the ,equinoxes are those points at which the ,ecliptic and ,equinoctial intersect1 and when the sun occupies either of these two positions1 the days and nights are of equal length4 ,the ,vernal ,equinox is that one which the sun passes through or intersects in going from ,s to ,n declination1 and the ,autumnal ,equinox that which it passes through or intersects in going from ,n to ,s declination4 ,the ,vernal ,equinox 7,v in the illustration7 is also designated as the ,first ,point of ,aries which is of use in reckoning star time and will be mentioned in more detail later4 ,the ,solstitial ,points1 or ,solstices1 are points of the ,ecliptic at a distance of #ij deg4 from the ,equinoxes1 at which the sun attains its highest declination in each hemisphere4 ,they are called the ,summer and ,winter ,solstice according to the season in which the sun appears to pass these points in its path4 ,to sum up3 ,the way to find any point on the earth is to find the distance of this point ,n or ,s of the equator 7i4e41 its ,latitude7 and its distance ,e or ,w of the meridian at ,greenwich 7i4e41 its longitude74 ,in the celestial sphere1 the way to find the location of a point or celestial body such as the sun is to find its declination 7i4e41 distance in arc ,n or ,s of the equator7 and its hour angle4 ,by hour angle1 ,i mean the distance in time from your meridian to the meridian of the point or celestial body in question4 ,assign for ,night reading1 ,arts1 in ,bowditch3 #bgj-bga-bgb-bgc-bgd-bge-bgg-bgh-bgi-bhj -bhb-bhc-bhd4 ,,wednesday ,,lecture ,,time ,,by ,,the ,,sun--,,mean ,,time1 ,,solar ,,time1 ,,conversion1 ,,etc4 ,there is nothing more important in all ,navigation than the subject of ,time4 ,every calculation for determining the position of your ship at sea must take into consideration some kind of time4 ,put in your ,note-,book3 ,there are three kinds of time3 #a4 ,apparent or solar time1 i4e41 time by the sun4 #b4 ,mean ,time1 i4e41 clock time4 #c4 ,sidereal ,time1 or time by the stars4 ,so far as this lecture is concerned1 we will omit any mention of sidereal time1 i4e41 time by the stars4 ,we will devote this morning to sun time1 i4e41 apparent time1 and mean time4 ,apparent or ,solar ,time is1 as stated before1 nothing more than sun time or time by the sun4 ,the hour angle of the center of the sun is the measure of apparent or solar time4 ,an apparent or solar day is the interval of time it takes for the earth to revolve completely around on its axis every #bd hours4 ,it is apparent noon at the place where you are when the center of the sun is directly on your meridian1 i4e41 on the meridian of longitude which runs through the ,north and ,south poles and also intersects your zenith4 ,this is the most natural and the most accurate measure of time for the navigator at sea and the unit of time adopted by the mariner is the apparent solar day4 ,apparent noon is the time when the latitude of your position can be most easily and most exactly determined and on the latitude by observation just secured we can get data which will be of great value to us for longitude sights taken later in the day4 ,now it would be very easy for the mariner if he could measure apparent time directly so that his clock or other instrument would always tell him just what the sun time was4 ,it is impossible1 however1 to do this because the earth does not revolve at a uniform rate of speed4 ,consequently the sun is sometimes a little ahead and sometimes a little behind any average time4 ,you cannot manufacture a clock which will run that way because the hours of a clock must be all of exactly the same length and it must make noon at precisely #ab o'clock every day4 ,hence we distinguish clock time from sun time by calling clock time1 mean 7or average7 time and sun time1 apparent or solar time4 ,from this explanation you are ready to understand such expressions as ,local ,mean ,time1 which1 in untechnical language1 signifies clock time at the place where you are2 ,greenwich ,mean ,time which signifies clock time at ,greenwich2 ,local ,apparent ,time1 which signifies sun time at the place where you are2 ,greenwich ,apparent ,time1 which signifies sun time at ,greenwich4 ,now the difference between apparent time and mean time can be found for any minute of the day by reference to the ,nautical ,almanac which we will take up later in more detail4 ,this difference is called the ,equation of ,time4 ,there is one more fact to remember in regard to apparent and mean time4 ,it is the relation of the sun's hour angle to apparent time4 ,in the first place1 what is a definition of the sun's ,,ha8 ,it is the angle at the celestial pole between the meridian intersecting any given point and the meridian intersecting the center of the sun4 ,it is measured by the arc of the celestial equator intersected between the meridian of any point and the meridian intersecting the center of the sun4 ,illustration ,for instance1 in the above diagram1 suppose ,,pg is the meridian at ,greenwich1 and ,,ps the meridian intersecting the sun4 ,then the angle at the pole ,,gps1 measured by the arc ,,gs would be the ,hour ,angle of ,greenwich1 or the ,greenwich ,hour ,angle4 ,and now you notice that this angular measure is exactly the same as apparent time at ,greenwich or ,greenwich ,apparent ,time1 for ,greenwich ,apparent ,time is nothing more than the distance in time ,greenwich1 ,england1 or the meridian at ,greenwich is from the sun1 i4e41 the time it takes the earth to revolve from ,greenwich to the sun2 and that distance is exactly measured by the ,greenwich ,hour ,angle or the arc on the celestial equator1 ,,gs4 ,the same is correspondingly true of ,local ,apparent ,time and the ship's ,hour ,angle4 ,suppose1 for instance1 ,,pl is the meridian intersecting the place where your ship is4 ,then your ship's hour angle would be the angle at the pole intersecting the meridian of your ship and the meridian of the sun or ,,lps and measured by the arc ,,ls4 ,and you will note that this distance is exactly the same as apparent time at the ship1 for ,apparent ,time at ship is nothing more than the distance in time which the ship is from the sun4 ,we can sum up all this information in a few simple rules1 which put in your ,note-,book3 ,mean ,time ,clock ,time4 ,g4,m4,t4 ,greenwich ,mean ,time4 ,l4,m4,t4 ,local ,mean ,time4 ,apparent ,time ,actual or ,sun ,time4 ,g4,a4,t4 7,g4,h4,a47 ,greenwich ,apparent ,time or ,greenwich ,hour ,angle4 ,l4,a4,t4 7,s4,h4,a47 ,local ,apparent ,time or ,ship's ,hour ,angle4 ,difference between apparent and mean time or mean and apparent time--,equation of ,time4 ,right under this in your ,note-,book put the following diagram1 which ,i will explain3 ,illustration ,you will see from this diagram that civil time commences at midnight and runs through #ab hours to noon4 ,it then commences again and runs through #ab hours to midnight4 ,the ,civil ,day1 then1 is from midnight to midnight1 divided into two periods of #ab hours each4 ,the astronomical day commences at noon of the civil day of the same date4 ,it comprises #bd hours1 reckoned from ,o to #bd1 from noon of one day to noon of the next4 ,astronomical time1 either apparent or mean1 is the hour angle of the true or mean sun respectively1 measured to the westward throughout its entire daily circuit4 ,since the civil day begins #ab hours before the astronomical day and ends #ab hours before it1 ,a4,m4 of a new civil day is ,p4,m4 of the astronomical day preceding4 ,for instance1 #f hours ,a4,m41 ,april #aeth civil time is equivalent to #ah hours ,april #adth1 astronomical time4 ,now1 all astronomical calculations in which time is a necessary fact to be known1 must be expressed in astronomical time4 ,as chronometers have their face marked only from #j to #ab as in the case of an ordinary watch1 it is necessary to transpose this watch or chronometer time into astronomical time4 ,no transposing is necessary if the time is ,p4,m41 as you can see from the diagram that both civil and astronomical times up to #ab ,p4,m4 are the same4 ,but in ,a4,m4 time1 such transposing is necessary4 ,put in your ,note-,book3 ,whenever local or chronometer time is ,a4,m41 deduct #ab hours from such time to get the correct astronomical time3 ,,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 ,now we come to a very important application of time4 ,you will remember that in one of the former lectures we stated that to find our latitude1 we had to find how far ,north or ,south of the equator we were1 and to find our longitude1 we had to find how far ,east or ,west of the meridian at ,greenwich we were4 ,never mind about latitude for the present4 ,we can find our longitude exactly if we know our ,greenwich time and our time at ship4 ,for instance1 in the accompanying diagram3 ,illustration ,suppose ,,pg is the meridian at ,greenwich1 then anything to the west of ,,pg is ,west longitude and anything to the ,east of ,,pg is ,east longitude4 ,now suppose ,,gps is the ,h4,a4 of ,g4 or ,g4,a4,t4--i4e41 the distance in time ,g4 is from the sun4 ,and ,l ,p ,s is the ,h4,a4 of the ship or ,l4,a4,t4--i4e41 the distance in time the ship is from the sun4 ,then the difference between ,g ,p ,s and ,l ,p ,s is ,g ,p ,l1 measured by the arc ,l ,g1 and that is the difference that the ship1 represented by its meridian ,,pl1 is from the ,greenwich meridian ,,pg4 ,in other words1 that is the ship's longitude for1 as mentioned before1 longitude is the distance ,east or ,west of ,greenwich that any point is1 measured on the arc of the celestial equator4 ,the longitude is ,west1 for you can see ,,lpg or the arc ,,lg is west of the meridian ,,pg4 ,likewise if ,p ,e is the meridian of your ship1 the ,longitude in time is the ,s4,h4,a4 or ,l4,a4,t41 ,e ,p ,s 7the distance your ship is from the sun7 less the ,g4,h4,a4 or ,g4,a4,t41 ,g ,p ,s 7the distance ,greenwich is from the sun7 which is the angle ,g ,p ,e measured by the arc ,g ,e4 ,and this ,longitude is ,east for you can see ,g ,p ,e1 measured by ,g ,e1 is east of the ,greenwich meridian1 ,p ,g4 ,in both these cases1 however1 the longitude is expressed in time1 i4e41 so many hours1 minutes and seconds from the ,greenwich meridian and we wish to express this distance in degrees1 minutes and seconds of arc4 ,the earth describes a circle of #cfj deg4 every #bd hours4 ,then if you are #a hour from ,greenwich1 you are #a_/bd of #cfj deg4 or #ae deg4 from ,greenwich and if you are #ab hours from ,greenwich1 you are #a_/b of #cfj deg4 or #ahj deg4 from ,greenwich4 ,by keeping this in mind1 you should be able to transpose time into degrees1 minutes and seconds of arc for any fraction of time4 ,it is1 however1 all worked out in ,table #g of ,bowditch which turn to4 7,note to ,instructor3 ,explain this table carefully74 ,put in your ,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 in your ,note-,book this diagram and these formulas3 7,for diagram use illustration on p4 #dj47 ,l4,m4,t4 ,west ,lo4 ,g4,m4,t4 ,l4,a4,t4 ,west ,lo4 ,g4,a4,t4 ,l4,m4,t4 - ,east ,lo4 ,g4,m4,t4 ,l4,a4,t4 - ,east ,lo4 ,g4,a4,t4 ,g4,m4,t4 - ,west ,lo4 ,l4,m4,t4 ,g4,a4,t4 - ,west ,lo4 ,l4,a4,t4 ,g4,m4,t4 ,east ,lo4 ,l4,m4,t4 ,g4,a4,t4 ,east ,lo4 ,l4,a4,t4 ,if ,g4,m4,t4 or ,g4,a4,t4 is greater than ,l4,m4,t4 or ,l4,a4,t4 respectively1 ,lo4 is ,west4 ,if ,g4,m4,t4 or ,g4,a4,t4 is less than ,l4,m4,t4 or ,l4,a4,t4 respectively1 ,lo4 is ,east4 ,example3 ,in longitude #ha deg4 #ae' ,w1 ,l4,m4,t4 is ,april #ae;d--#aj;h--#agm--#cjs ,a4,m4 ,what 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 ,in what ,lo4 is ship8 ,g4,m4,t4 #ae;d #c;h--#dbm--#cjs ,l4,m4,t4 #ad;d #bb;h--#agm--#cjs ------------------ ,lo4 in ,t #e;h--#bem--#jjs ,w ,lo4 #ha deg4 #ae',w ,assign also for ,night ,work reading the following articles in ,bowditch3 #bgf-bgh-bgi-bbf-bbh-bhf-bhg-bhh-bij-bia -bid 7omitting everything on page #aad47 ,,thursday ,,lecture ,,sidereal ,,time--,,right ,,ascension ,our last lecture was devoted to a discussion of sun time4 ,today we are going to talk about star time1 or1 using the more common words1 sidereal time4 ,now1 just one word of review4 ,you remember that we have learned that astronomical time is reckoned from noon of one day to noon of the next and hence the astronomical day corresponds to the #bd hours of a ship's run4 ,the hours are counted from #j to #bd1 so that #aj o'clock in the morning of ,october #beth is astronomically ,october #bdth1 #bb hours or #bb o'clock of ,october #bdth4 ,now ,right ,ascension is different from both astronomical and civil time4 ,right ,ascension is practically celestial longitude4 ,for instance1 the position of a place on the earth is fixed by its latitude and longitude2 the position of a heavenly body is fixed by its declination and right ascension4 ,but ,right ,ascension is not measured in degrees and minutes nor is it measured ,east and ,west4 ,it is reckoned in hours and minutes all the way around the sky1 eastward from a certain point1 through the approximate #bd hours4 ,the point from which this celestial longitude begins is not at ,greenwich1 but the point where the celestial equator intersects the ecliptic in the spring of the year1 i4e41 the point where the sun1 coming ,north in the ,spring1 crosses the celestial equator4 ,this point is called the ,first ,point of ,aries4 ,you will frequently hear me speak of a star having1 for instance1 a ,right ,ascension of #e;h #afm #cbs4 ,i mean by that1 that starting at the celestial meridian1 i4e41 the meridian passing through the ,first ,point of ,aries1 it will take a spot on the earth #e;h #afm #cbs to travel until it reaches the meridian of the star in question4 ,roughly speaking then1 just as ,greenwich ,apparent ,time means the distance ,east or ,west the ,greenwich meridian is from the sun and ,local ,apparent ,time means the distance ,east or ,west your ship is from the sun1 so ,r4,a4,m4,g4 means the distance in time the ,meridian of ,greenwich is from the ,first ,point of ,aries1 measured eastward in a circle4 ,and this distance is the same as ,greenwich ,sidereal ,time1 i4e41 ,sidereal ,time at ,greenwich or the distance in time the meridian of ,greenwich is from the ,first ,point of ,aries4 ,now1 what is the star time that corresponds to local time8 ,it is called the ,right ,ascension of the ,meridian1 which means the ,r4 ,a4 of the meridian which intersects your zenith4 ,just as ,l4,a4,t4 is the distance in time your meridian is from the sun1 so ,local ,sidereal ,time is the ,r4 ,a4 of your meridian1 i4e41 the distance in time your meridian is from the ,first ,point of ,aries4 ,put in your ,note-,book3 ,g4,s4,t4 and ,r4,a4,m4,g4 are one and the same thing4 ,l4,s4,t4 and ,r4,a4,m4 are one and the same thing4 ,g4,m4,t4 7474,r4,a4 774,c4,p4 ,g4,s4,t4 7,r4,a4,m4,g47 ,if the result is more than #bd hours1 subtract #bd hours4 ,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 can explain all these formulas very easily by the following illustration which put in your ,note-,book3 7,note to ,instructor3 ,if possible have copies of this illustration mimeographed and distributed to each student47 ,illustration3 ,,first ,,point ,,of ,,aries4 ,there is one term ,i have used which does not appear in the illustration4 ,it is the ,earth's ,central ,progress 7774,c4,p474 ,the astronomical day based on the sun1 is #bd hours long1 as said before4 ,the sidereal day1 however1 is only #bc;h #efm #jds long4 ,this is due to the fact that whereas the earth is moving in its ecliptic track around the sun while revolving on its own axis1 the ,first ,point of ,aries is a fixed point and hence never moves4 ,the correction1 then1 for the difference in the length of time between a sidereal day and a mean solar day is called the ,earth's ,central ,progress and1 of course1 has to be figured for all amounts of time after mean noon at ,greenwich1 since the ,sun's ,right ,ascension tables in the ,nautical ,almanac are based on time at mean noon at ,greenwich4 ,now you have a formula for practically all kinds of conversion except for converting ,l4,m4,t4 into ,l4,s4,t4 ,you could do it by the formula ,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 ,but that involves too many operations4 ,a shorter way1 though not so simple perhaps1 is as follows3 ,l4,m4,t4 ,reduction page #b ,n4,a4 for time after local mean noon 7474,r4,a4 of ,greenwich mean noon - ,reduction page #b ,n4,a4 for ,lo4 in ,t4 7,w1 ,e-7 ,l4,s4,t4 ,note to ,instructor3 ,explain this formula by turning to page #ajg ,n4,a4 and work it out by the formula ,l4,m4,t4 ,lo4 in ,t 7,w7 ,g4,m4,t4 7474,r4,a4 774,c4,p4 ,g4,s4,t4 - ,lo4 in ,t 7,w7 ,l4,s4,t4 ,example3 ,l4,m4,t4 #aj;h--#djm--#cjs ,lo4 in ,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 ,now ,bowditch gets this ,l4,s4,t4 in still another way4 ,turn to page #aaj1 ,article #bij4 ,there the formula used is ,l4,m4,t4 7474,r4,a4 774,c4,p4 ,l4,s4,t1 and in order to get the correct 7474,r4,a4 and 774,c4,p4 the ,g4,m4,t4 has to be secured by the formula ,l4,m4,t4 ,w4,lo4 ,g4,m4,t4 - ,e4,lo4 ,let us work this same example in ,bowditch by the other two methods4 ,first by the formula ,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 ,the small difference between this answer and that of ,bowditch's is that the 7474,r4,a4 for #aiaf is slightly different from that of #aiai4 ,bowditch used the #aiaf ,almanac1 whereas we are working from the #aiai ,almanac4 ,now turn to page #ajg of the ,n4,a4 and let us work the same example in ,bowditch by the method used here3 ,l4,m4,t4 #b;h - #jjm - #jjs ,red4 for #b;h #j - #bj 7474,r4,a4 #j;h #a - #eg - #ei ,red4 ,lo4 #e;h - #bem #j - #ec --------------- ,l4,s4,t4 #c;h - #eim - #abs ,the reason ,i am going so much into detail in explaining methods of finding ,l4,s4,t4 is because1 by a very simple calculation which will be explained later1 we can get our latitude at night if we know the altitude of ,polaris 7,the ,north ,star7 and if we know the ,l4,s4,t4 at the time of observation4 ,some of you may think that the ,n4,a4 way is the simplest4 ,it is given in the ,n4,a41 and in an examination it would be permissible for you to use the ,n4,a4 as a guide because1 in an examination1 ,i propose to let you have at hand the same books you would have in the chart house of a ship4 ,on the other hand1 the method given in the ,n4,a4 is not as clear to my mind as the method which starts with ,l4,m4,t41 then finds with the ,longitude the ,g4,m4,t4 ,that gives you1 roughly speaking1 the distance in time ,greenwich is from the sun4 ,add to that the sun's ,r4,a4 or the distance in time the sun is from the ,first ,point of ,aries at ,greenwich ,mean ,noon4 ,add to that the correction for the time past noon4 ,the result is ,g4,s4,t4 ,now all you have to do is to apply the longitude correctly to find the ,l4,s4,t41 just as when you have ,g4,m4,t4 and apply the longitude correctly you get ,l4,m4,t4 ,that is a method which does not seem easy to forget1 for it depends more upon simple reasoning where the others1 for a beginner1 depend more upon memory4 ,however1 any of the three methods is correct and can be used by you4 ,perhaps the best way is to work a problem by two of the three that seem easiest4 ,in this way you can check your figures4 ,when ,i give you a problem that involves finding the ,l4,s4,t4 ,i do not care how you get the ,l4,s4,t4 providing it is correct when you get it4 ,assign for ,night ,reading in ,bowditch the following ,arts43 #bhb-bhc-bhd-bhe4 ,also the following questions3 #a4 ,given the ,g4,m4,t4 and the longitude in ,t which is ,w1 what is the formula for ,l4,s4,t48 #b4 ,given the ,l4,a4,t4 and longitude in ,t which is ,e1 what is the formula for ,g4,s4,t48 #c4 ,given the ,l4,s4,t4 and longitude in ,t which is ,w4 ,required ,g4,m4,t4 ,etc4 ,,friday ,,lecture ,,the ,,nautical ,,almanac ,for the last two days we have been discussing ,time--sun time or solar time and star time or sidereal time4 ,now let us examine the ,nautical ,almanac to see how that time is registered and how we read the various kinds of time for any instant of the day or night4 ,before starting in1 put a large cross on pages #d and #e4 ,for any calculations you are going to make1 these pages are unnecessary and they are liable to lead to confusion4 ,sun time of the mean sun at ,greenwich is given for every minute of the day in the year #aiai in the pages from #f to #cj4 ,this is indicated by the column to the left headed ,g4,m4,t4 ,turn to page #f under ,wednesday1 ,jan4 #ast4 ,you can see that the even hours are given from #j to #bd4 ,remember that these are expressed in astronomical time1 so that if you had ,jan4 #bnd--#aj hours ,a4,m41 you would not look in the column under ,jan4 #bnd but under the column for ,jan4 #ast1 #bb hours1 since #aj ,a4,m4 ,jan4 #bnd is #bb o'clock ,jan4 #ast1 and no reading is used in this ,almanac except a reading expressed in astronomical time4 ,now at the bottom of the column under ,jan4 #ast you see the letters ,h4,d4 ,that stands for hourly difference and represents the amount to be added or subtracted for an odd hour from the nearest even hour4 ,in this instance it is 4#b4 ,you note that even hours #b1 #d1 #f1 etc41 are given4 ,to find an odd hour during this astronomical day1 subtract 4#b from the preceding even hour4 ,for any fraction of an hour you simply take the corresponding fraction of the ,h4,d4 and subtract it from the preceding even hour4 ,for instance1 the declination for ,jan4 #ast--#ab hours would be #bc deg4 #a4h' or #bc deg4--#a'--dh1 #ac hours would be #bc deg4 #a4f' or #bc deg4--#a'--cf1 #ab-a_/b hours would be #bc deg4 #a4g' or #bc deg4--#a'--db1 and #ac-a_/b hours would be #bc deg4 #a4e' or #bc deg4--#a'--cj4 ,now to the right of the hours you note there is given the corresponding amount of ,declination and the ,equation of ,time4 ,before going further1 let us review a few facts about ,declination4 ,the declination of a celestial body is its angular distance ,n or ,s of the celestial equator or equinoctial4 ,now get clearly in your mind how we measure the angular distance from the celestial equator of any heavenly body4 ,it is measured by the angle one of whose sides is an imaginary line drawn to the center of the earth and the other of whose sides is an imaginary line passing from the center of the earth into the celestial sphere through the center of the heavenly body whose declination you desire4 ,now as you stand on any part of the earth1 you are standing at right angles to the earth itself4 ,hence if this imaginary line passed through you it would intersect the celestial sphere at your zenith1 i4e41 the point in the celestial sphere which is directly above you4 ,now suppose you happen to be standing at a certain point on the earth and suppose that point was in #ae deg4 ,n latitude4 ,and suppose at noon the center of the sun was directly over you1 i4e41 the center of the sun and your zenith were one and the same point4 ,then the declination of the sun at that moment would be #ae deg4 ,n4 ,in other words1 your angular distance from the earth's equator 7which is another way of expressing your latitude7 would be precisely the same as the angular distance of the center of the sun from the celestial equator4 ,suppose you were standing directly on the equator and the center of the sun was directly over you1 then the declination of the sun would be #j deg44 ,now if the axis of the earth were always perpendicular to the plane of the sun's orbit1 then the sun would always be immediately over the equator and the sun's declination would always be #j deg44 ,but you know that the axis of the earth is inclined to the plane of the sun's orbit4 ,as the earth1 then1 revolves around the sun1 the amount of the declination increases and then decreases according to the location of the earth at any one time with relation to the sun4 ,on ,march #bast and ,sept4 #bcrd1 #aiai1 the sun is directly over the equator and the declination is #j deg44 ,from ,march #bast to ,june #bast the sun is coming ,north and the declination is increasing until on ,june #bast--#ab hours--it reaches its highest declination4 ,from then on the sun starts to travel ,south1 crosses the equator on ,sept4 #bc;d and reaches its highest declination in ,south latitude on ,dec4 #bbnd1 when it starts to come ,north again4 ,this explains easily the length of days4 ,when the sun is in ,north latitude1 it is nearer our zenith1 i4e41 higher in the heavens4 ,it can1 therefore1 be seen for a longer time during the #bd hours that it takes the earth to revolve on its axis4 ,hence1 when the sun reaches its highest declination in ,north latitude--,june #bast--i4e41 when it is farthest ,north from the equator and nearest our zenith 7which is in #dj deg4 ,n latitude7 it can be seen for the longest length of time4 ,in other words1 that day is the longest of the year4 ,for the same reason1 ,dec4 #bbnd1 when the sun reaches its highest declination in ,south latitude1 i4e41 when it is farthest away to the ,south1 is the shortest day in the year for us2 for on that day1 the sun being farthest away from our zenith and hence lowest down toward the horizon1 can be seen for the shortest length of time4 ,put in your ,note-,book3 ,north ,declination is expressed 4 ,south ,declination is expressed ---4 ,now turn to page #f of the ,nautical ,almanac4 ,you will see opposite ,jan4 #ast #j;h1 a declination of --#bc deg4 #d4b'4 ,every calculation in this ,almanac is based on time at ,greenwich1 i4e41 ,g4,m4,t4 ,so at #j;h ,jan4 #ast at ,greenwich--that is at noon--the ,sun's declination is ,s #bc deg4 #d4b'4 ,you learned in the lecture the other day on solar time1 that the difference between mean time and apparent time was called the equation of time4 ,this equation of time1 with the sign showing in which way it is to be applied1 is given for any minute of any day in the column marked ,equation of ,time4 ,you will also notice that there is an ,h4,d4 for equations of time just as there is for each declination1 and this ,h4,d4 should be used when finding the equation of time for an odd hour4 ,put in your ,note-,book3 #a4 ,the equation of time is to be applied as given in the ,nautical ,almanac when changing ,mean ,time into ,apparent ,time4 #b4 ,when changing ,apparent ,time into ,mean ,time1 reverse the sign as given in the ,nautical ,almanac4 ,that is all there is to finding sun time1 either mean or apparent1 for any instant of any day in the year #aiai4 ,do not forget1 however1 that all this data is based upon ,greenwich ,mean ,time4 ,to find ,local ,mean ,time you must apply the ,longitude you are in4 ,to find ,local ,apparent ,time you must first secure ,g4,a4,t4 from ,g4,m4,t4 and then apply the ,longitude4 7,note to ,instructor3 ,make the class work out conversions here if you have time to do so and can finish the rest of the lecture by the end of the period47 ,so much for time by the sun4 ,now let us examine time by the stars--sidereal time4 ,turn to pages #b-c4 ,there you find the ,right ,ascension of the ,mean ,sun at ,greenwich ,mean ,noon for every day in the year4 ,you remember that1 roughly speaking1 the ,sun's ,right ,ascension was the distance in time the sun was from the ,first ,point of ,aries4 ,so these tables give that distance 7expressed in time7 for noon at ,greenwich of every day4 ,for the correction to be applied for all time after noon at ,greenwich 7i4e41 774,c4,p471 use the table at the bottom of the page4 ,for instance1 the 7474,r4,a4 at ,greenwich #i;h #bdm on ,jan4 #ast would be 7474,r4,a4 #ah;h--#djm--#bas 774,c4,p4 #a #cc -------------- #ah;h--#dam--#eds ,now we must go back to some of the formulas we learned when discussing star time and apply them with the information we now have from the ,nautical ,almanac4 ,if the ,g4,m4,t4 on ,april #bjth is #d;h--#afm--#cjs1 what is the ,g4,s4,t4 for the same moment8 ,that is1 when ,greenwich is #d;h--#afm--#cjs from the sun1 how far is ,greenwich from the ,first ,point of ,aries8 ,you remember the formula was ,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 you were in ,lo4 #gd deg4 ,w4 ,what would be the ,r4,a4,m4 7,l4,s4,t478 ,you remember the formula for ,l4,s4,t4 from ,g4,s4,t4 was the same relatively as ,l4,m4,t4 from ,g4,m4,t41 i4e41 ,l4,s4,t4 ,g4,s4,t4 - ,w4 ,lo4 ,e4 ,lo1 ,here it would be ,g4,s4,t4 #f;h--#jgm--#ahs 7#gd deg4 ,w7 - #d --#ef --#jj --------------- ,l4,s4,t4 #a;h--#aam--#ahs ,now these are not a collection of abstruse formulas that you are learning just for the sake of practice4 ,they are used every clear night on board ship1 or should be1 and are just as vital to know as time by the sun4 ,suppose you are at sea in ,lo4 #gj deg4 ,w and your ,,ct is ,october #bjth #f;h--#dm--#cjs ,a4,m41 ,,cc #bm--#cjs fast4 ,you wish to get the ,r4,a4 of your ,m1 i4e41 the ,l4,s4,t4 ,how would you go about it8 ,the first thing to do would be to get your ,g4,m4,t4 ,it 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 ,then get your ,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 ,then get your ,l4,s4,t4 ,g4,s4,t4 #g;h--#ebm--#cf4bs ,w4,lo 7--7 #d --#dj -------------- ,l4,s4,t4 #c;h--#abm--#cf4bs ,the last fact to know at this time about the ,almanac is found on pages #id-ie4 ,here is given a list of the brighter stars with their positions respectively in the heavens1 i4e41 their celestial longitude or ,r4,a4 on page #id and their celestial latitude or declination on page #ie4 ,these stars have very little apparent motion4 ,they are practically fixed4 ,hence1 their position in the heavens is almost the same from ,january to ,december though1 of course1 their position with relation to you is constantly changing1 since you on the earth are constantly moving4 ,the relationship between these various kinds of time is clearly expressed by the following diagram1 which put in your ,note ,book3 ,illustration3 ,going with arrow1 add4 ,going against arrow1 subtract4 ,assign for reading in ,bowditch1 ,articles #bid-bie-bif-big-bii-cjj-cja-cjb-cjc-cjd -cje-cjf-cjg4 ,if any time is left1 have the class work out such examples as these3 #a4 ,g4,m4,t4 ,june #bjth1 #aiai1 #e;h--#adm--#cis4 ,in ,lo4 #fh deg4 #di' ,w4 ,required ,l4,s4,t41 ,g4,s4,t41 ,l4,m4,t41 ,l4,a4,t4 #b4 ,l4,m4,t4 ,oct4 #aeth1 #aiai1 #f;h--#cjm--#bjs ,a4,m4 ,in ,lo4 #di deg4 #ce' #af ,e4 ,required ,l4,s4,t4 #c4 ,l4,m4,t4 ,may #adth1 #aiai1 #aj;h--#aem4--#bjs ,a4,m4 ,lo4 #ef deg4 #ba' #ci ,w4 ,required ,l4,a4,t4 #d4 ,w4,t4 ,april #bjth1 #aiai1 #aa;h--#cjm--#ads ,c-,w #b;h--#adm--#eis ,,cc #dm--#cjs slow4 ,in ,lo4 #hi deg4 #dh' #cj ,w4 ,required ,g4,m4,t41 ,g4,a4,t41 ,l4,m4,t41 ,l4,a4,t41 ,g4,s4,t41 ,l4,s4,t4 #e4 ,what is ,declination and ,r4,a4 on ,may #aeth1 #aiai1 of ,polaris1 ,arcturus1 ,capella1 ,regulus1 ,altair1 ,deneb1 ,vega1 ,aldebaran8 #f4 ,what is the sun's declination and ,r4,a41 ,time at ,greenwich1 ,july #cjth3 #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 ,,of ,,observed ,,altitudes ,the true altitude of a heavenly body is the angular distance of its center as measured from the center of the earth4 ,the observed altitude of a heavenly body as seen at sea by the sextant may be converted to the true altitude by the application of the following four corrections3 ,dip1 ,refraction1 ,parallax and ,semi-diameter4 ,dip of the horizon means an increase in the altitude caused by the elevation of the eye above the level of the sea4 ,the following diagram illustrates this clearly3 ,illustration ,if the eye is on the level of the sea at ,a1 it is in the plane of the horizon ,,cd1 and the angles ,,eac and ,,ead are right angles or #ij deg4 each4 ,if the eye is elevated above ,a1 say to ,b1 it is plain that the angles ,,ebc and ,,ebd are greater than right angles1 or in other words1 that the observer sees more than a semi-circle of sky4 ,hence all measurements made by the sextant are too large4 ,in other words1 the elevation of the eye makes the angle too great and therefore the correction for dip is always subtracted4 ,refraction is a curving of the rays of light caused by their entering the earth's atmosphere1 which is a denser medium than the very light ether of the outer sky4 ,the effect of refraction is seen when an oar is thrust into the water and looks as if it were bent4 ,refraction always causes a celestial object to appear higher than it really is4 ,this refraction is greatest at the horizon and diminishes toward the zenith1 where it disappears4 ,table #bj;,a in ,bowditch gives the correction for mean refraction4 ,it is always subtracted from the altitude4 ,in the higher altitudes1 select the correction for the nearest degree4 ,you should avoid taking low altitudes 7#ae deg4 or less7 when the atmosphere is not perfectly clear4 ,haziness increases refraction4 ,parallax is simply the difference in angular altitude of a heavenly body as measured from the center of the earth and as measured from the corresponding point on the surface of the earth4 ,parallax is greatest when the body is in the horizon1 and disappears when it is at the zenith4 ,illustration ,when the angular altitude of the sun in this diagram is #j1 the parallax ,,abc is greatest4 ,when the altitude is highest there is no parallax4 ,the sun is so far away that its parallax never exceeds #i4 ,the stars have practically none at all from the earth's surface4 ,parallax is always to be added in the case of the sun4 ,the semi-diameter of a heavenly body is half the angle subtended by the diameter of the visible disk at the eye of the observer4 ,for the same body1 the ,,sd varies with the distance4 ,thus1 the difference of the sun's ,,sd at different times of the year is due to the change of the earth's distance from the sun4 ,illustration ,the ,,sd is to be added to the observed altitude in case the lower limb is brought in contact with the horizon1 and subtracted if the upper limb is used4 ,probably most of the sights you take will be of the sun's lower limb1 i4e41 when the lower limb is brought in contact with the horizon1 so all you need to remember is that in that event the ,,sd is additive4 ,now at first we will correct altitudes by applying each correction separately1 but as soon as you get the idea1 there is a short way to apply all four corrections at once4 ,this is done in ,table #df4 ,however1 disregard that for the moment4 ,put this in your ,note-,book3 ,dip is -4 ,table #ad ,bowditch ,refraction is -4 #bj ,a ,bowditch ,parallax is 4 #af ,bowditch ,s4,d4 is 4 ,nautical ,almanac ,observed altitude of ,sun's lower limb is expressed 774 ,true altitude is expressed -7-7-4 ,remember that before an observation is at all accurate1 it must be corrected to make it a true altitude4 ,remember also that the ,,ie must be applied1 in addition to these other corrections1 in order to make the observed altitude a -7-7- altitude4 ,so there are really five corrections to make instead of four1 providing1 of course1 your sextant has an ,,ie4 ,examples3 #a4 ,june #bjth1 #aiai1 observed altitude of 77 #fi deg4 #be' #cj4 ,,ie #b' #cj4 ,,he #af ft4 ,required -7-7-4 #b4 ,april #aeth1 #aiai1 observed altitude of 77 #eh deg4 #bi' #dj4 ,,ie - #b' #cj4 ,,he #ah ft4 ,required -7-7-4 #c4 ,march #dth1 #aiai1 observed altitude of 77 #dd deg4 #dd' #aj4 ,,ie - #d' #bj4 ,,he #bj ft4 ,required -7-7-4 ,etc4 ,,week ,,iv--,,navigation ,,tuesday ,,lecture ,,the ,,line ,,of ,,position ,it is practically impossible to fix your position exactly by one observation of any celestial body4 ,the most you can expect from one sight is to fix your line of position1 i4e41 the line somewhere along which you are4 ,if1 for instance1 you can get a sight by sextant of the sun1 you may be able to work out from this sight a very accurate calculation of what your latitude is4 ,say it is #ej deg4 ,n4 ,you are practically certain1 then1 that you are somewhere in latitude #ej deg4 ,n1 but just where you are you cannot tell until you get another sight for your longitude4 ,similarly1 you may be able to fix your longitude1 but not be able to fix your latitude until another sight is made4 ,celestial ,navigation1 then1 reduces itself to securing lines of position and by manipulating these lines of position in a way to be described later1 so that they intersect4 ,if1 for instance1 you know you are on one line running ,north and ,south and on another line running ,east and ,west1 the only spot where you can be on both lines is where they intersect4 ,this diagram will make that clear3 ,illustration ,illustration ,just what a line of position is will now be explained4 ,wherever the sun is1 it must be perpendicularly above the same spot on the surface of the earth marked in the accompanying diagram by ,s and suppose a circle be drawn around this spot as ,,abcde4 ,then if a man at ,a takes an altitude1 he will get precisely the same one as men at ,b1 ,c1 ,d1 and ,e1 because they are all at equal distances from the sun1 and hence on the circumference of a circle whose center is ,s4 ,conversely1 if several observers situated at different parts of the earth's surface take simultaneous altitudes1 and these altitudes are all the same1 then the observers must all be on the circumference of a circle and only one circle4 ,if they are not on that circle1 the altitude they take will be greater or less than the one in question4 ,illustration ,now such a circle on the surface of the earth would be very large--so large that a small arc of its circumference1 say #be or #cj miles1 would be practically a straight line4 ,suppose ,s to be the point over which the sun is vertical and ,,gf part of the circumference of a circle drawn around the point4 ,suppose you were at ,b and from an altitude of the sun1 taken by sextant1 you worked out your position4 ,you would find yourself on a little arc ,,abc which1 for all purposes in ,navigation1 is a straight line at right angles to the true bearing of the sun from the point ,s4 ,you can readily see this from the above diagram4 ,suppose your observer is at ,h4 ,his line is ,,ghi1 which is again a straight line at right angles to the true bearing of the sun4 ,he is not certain he is at ,h4 ,he may be at ,g or ,i4 ,he knows1 however1 he is somewhere on the line ,,ghi1 though where he is on that line he cannot tell exactly4 ,that line ,,ghi or ,,abc or ,,def is the line of position and such a line is called a ,sumner ,line1 after ,capt4 ,thomas ,sumner1 who explained the theory some #de years ago4 ,put in your ,note-,book3 ,any person taking an altitude of a celestial body must be1 for all practical purposes1 on a straight line which is at right angles to the true bearing of the body observed4 ,it should be perfectly clear now that if the sun bears due ,north or ,south of the observer1 i4e41 if the sun is on the observer's meridian1 the resulting line of position must run due ,east and ,west4 ,in other words it is a parallel of latitude4 ,and that explains why a noon observation is the best of the day for getting your latitude accurately4 ,again1 if the sun bears due ,east or ,west the line of position must bear due ,north and ,south4 ,and that explains why a morning or afternoon sight--about #h-i ,a4,m4 or #c-d ,p4,m41 if the sun bears either ,east or ,west respectively1 is the best time for determining your ,north and ,south line1 or longitude4 ,now suppose you take an observation at #h ,a4,m4 and you are not sure of your ,d4,r4 latitude4 ,your #h ,a4,m4 position when the sun was nearly due ,east1 will give1 you an almost accurate ,north and ,south line and longitude4 ,suppose that from #h ,a4,m4 to noon you sailed ,,ne #fj miles4 ,suppose at noon you get another observation4 ,that will give you an ,east and ,west line1 for then the sun bears true ,north and ,south4 ,an ,east and ,west line is your correct latitude4 ,now you have an #h ,a4,m4 observation which is nearly correct for longitude and a noon position which is correct for latitude4 ,how can you combine the two so as to get accurately both your latitude and longitude8 ,put in your ,note-,book3 ,through the #h ,a4,m4 position1 draw a line on the chart at right angles to the sun's true bearing4 ,suppose the sun bore true ,e #a_/b ,s4 ,then your line of position would run ,n #a_/b ,e4 ,mark it #ast ,position ,line4 ,illustration ,now draw a line running due ,east and ,west at right angles to the ,n-,s noon bearing of the sun and mark this line ,second ,position ,line4 ,advance your ,first ,position ,line the true course and distance sailed from #h ,a4,m4 to noon1 and through the extremity draw a third line exactly parallel to the first line of position4 ,where a third line 7the ,first ,position ,line advanced7 intersects the ,second ,position ,line1 will be your position at noon4 ,it cannot be any other if your calculations are correct4 ,you knew you were somewhere on your #h ,a4,m4 line1 you know you are somewhere on your noon line1 and the only spot where you can be on both at once is the point where they intersect4 ,you don't necessarily have to wait until noon to work two lines4 ,you can do it at any time if a sufficient interval of time between sights is allowed4 ,the whole matter simply resolves itself into getting your two lines of position1 having them intersect and taking the point of intersection as the position of your ship4 ,there is one other way to get two lines to intersect and it is one of the best of all for fixing your position accurately4 ,it is by getting lines of position by observation of two stars4 ,if1 for instance1 you can get two stars1 one ,east and the other ,west of you1 you can take observations of both so closely together as to be practically simultaneous4 ,then your ,easterly star would give you a line like ,,aa' and the westerly star the line ,,bb' and you would be at the intersection ,s4 ,illustration ,assign for reading3 ,articles in ,bowditch #cba-cbb-cbc-cbd4 ,spend the rest of the period in getting times from the ,n4 ,a41 getting true altitudes from observed altitudes1 working examples in ,mercator sailing1 etc4 ,,wednesday ,,lecture ,,latitude ,,by ,,meridian ,,altitude ,a meridian altitude is an altitude taken when the sun or other celestial body observed bears true ,south or ,north of the observer or directly overhead4 ,in other words1 when the celestial body is on your meridian and you take an altitude of the body by sextant at that instant1 the altitude you get is called a meridian altitude4 ,in the case of the sun1 such a meridian altitude is at apparent noon4 ,now latitude is always secured most accurately at noon by means of your meridian altitude4 ,the reason for this was explained in yesterday's lecture4 ,the general formula for latitude by meridian altitude is 7,put in your ,note-,book73 ,latitude by meridian altitude ,zenith ,distance 7,,zd7 - ,declination 7,dec74 ,zenith distance is the distance in degrees1 minutes and seconds from your zenith to the center of the observed body4 ,for simplicity's sake1 we will consider the sun only as the observed body4 ,then the zenith distance is the distance from your zenith to the center of the sun4 ,now suppose that you and the sun are both ,north of the equator and you are ,north of the sun4 ,if you can determine exactly how far ,north you are of the sun and how far ,north the sun is of the equator1 you will1 by adding these two measurements together1 know how far ,north of the equator you are1 i4e41 your latitude4 ,as already explained1 the declination of the sun is its distance in degrees1 minutes and seconds from the equator and the exact amount of declination is1 of course1 corrected to the proper ,g4,m4,t4 ,your zenith distance is the distance in the celestial sphere you are from the sun4 ,you know that it is #ij deg4 from your zenith to the horizon4 ,your zenith distance1 therefore1 is the difference between the true meridian altitude of the sun1 obtained by your sextant1 and #ij deg44 ,hence1 having secured the true meridian altitude of the sun1 you have only to subtract it from #ij deg4 to find your zenith distance1 i4e41 how far you are from the sun4 ,this diagram will make the whole matter clear3 ,illustration3 ,a ,b 7,sun7 _/ _/ _/ _/ -_/- _/ #ij deg4 _/ ------v---------------------- ,c ,a ,zenith1 ,b ,sun1 ,c ,horizon4 ,the arc ,,abc measures #ij deg44 ,that is the distance from your zenith to the horizon4 ,now if ,,bc is the true meridian altitude of the sun at noon1 #ij deg4-,,bc or ,,ab is your zenith distance4 ,if ,,bc measures by sextant #fj deg41 ,,ab measures #ij deg4-#fj deg4 or #cj deg44 ,this #cj deg4 is your ,zenith ,distance4 ,now suppose that from the ,nautical ,almanac we find that the ,g4,m4,t4 corresponding to the time at which we measured the meridian altitude of the sun shows the sun's declination to be #aj deg4 ,n4 ,well1 if you are #cj deg4 ,north of the sun1 and the sun is #aj deg4 ,north of the equator1 you must be #dj deg4 ,north of the equator or in latitude #dj deg4 ,n4 ,for that is all latitude is1 namely1 the distance in degrees1 minutes and seconds you are due ,north or ,south of the equator4 ,that is the first and simplest case4 ,another case is when you are somewhere in ,north latitude and the sun's declination is ,south4 ,then the situation would1 roughly1 look like this3 ,illustration3 ,,bc ,altitude of the sun1 ,,ab ,zenith ,distance and ,,db ,sun's ,declination4 ,in this case1 your distance ,north of the equator ,,ad would be your zenith distance ,,ab minus the sun's declination ,,db4 ,this diagram is not strictly correct1 for the observer's position on the earth #j appears to be ,south of the equator instead of ,north of the equator4 ,that is because the diagram is on a flat piece of paper instead of on a globe4 ,so far as illustrating the ,zenith ,distance minus the ,declination1 however1 the diagram is correct4 ,the last case is where you are1 say1 #aj deg4 ,n of the sun 7your zenith ,distance is #aj deg47 and the sun is in #bj deg4 ,s declination4 ,in that case you would have to subtract your zenith distance from the sun's declination to get your latitude1 for the sun's latitude 7its declination7 is greater than yours4 ,now from these three cases we deduce the following directions1 which put in your ,note-,book3 ,begin to measure the altitude of the sun shortly before noon4 ,by bringing its image down to the horizon1 you can detect when its altitude stops increasing and starts to decrease4 ,at that instant the sun is on your meridian1 it is noon at the ship1 and the angle you read from your sextant is the meridian altitude of the sun4 ,to work out your latitude1 name the meridian altitude ,s if the sun is south of you and ,n if north of you4 ,correct the observed altitude to a true altitude by ,table #df4 ,if the altitude is ,s1 the ,zenith ,distance is ,n or vice versa4 7,note to ,instructor3 ,if the sun is ,south of you1 you are ,north of the sun and vice versa47 ,correct the declination for the proper ,g4,m4,t4 as shown by chronometer 7corrected74 ,if zenith distance and declination are both ,north or both ,south1 add them and the sum will be the latitude1 ,n or ,s as indicated4 ,if one is ,n1 and the other ,s1 subtract the less from the greater and the result will be the latitude in1 named ,n or ,s after the greater4 ,example3 ,at sea ,june #aeth1 observed altitude of 77 #ga deg4 #ae' ,s1 ,,ie--#dg'1 ,,he #be ft4 ,,ct #c;h--#cdm--#aes ,p4,m4 ,required latitude of ship4 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 for ,night ,work or to be worked in class room such examples as the following3 #a4 ,june #ast1 #aiai4 77 #cc deg4 #ej' #jj ,s4 ,g4,m4,t4 #h;h #eem #dds4 ,,he #bj ft4 ,,ie #d' #c4 ,required latitude in at noon4 #b4 ,april #bnd1 #aiai4 77 #ab deg4 #dd' #cj ,n4 ,,ct was #b;d #e;h #adm #cis ,a4,m41 which was #am #djs slow on ,march #ast 7same ,,ct7 and #dm #bis fast on ,march #aeth 7same ,,ct74 ,,ie -- #b' #bj4 ,,he #bb ft4 ,required latitude in at noon4 ,assign for ,night ,work reading also1 the following ,articles in ,bowditch3 #cdd and #bbc4 ,,thursday ,,lecture ,,azimuths ,,of ,,the ,,sun ,this is a peculiar word to spell and pronounce but its definition is really very simple4 ,put in your ,note-,book3 ,the azimuth of a heavenly body is the angle at the zenith of the observer formed by the observer's meridian and a line drawn to the center of the body observed4 ,azimuths are named from the latitude in and toward the ,e in the ,a4,m4 and from the latitude in and toward the ,w in the ,p4,m4 ,all this definition means is that1 no matter where you are in ,n latitude1 for instance1 if you face ,n1 the azimuth of the sun will be the true bearing of the sun from you4 ,the same holds true for moon1 star or planet1 but in this lecture we will say nothing of the star azimuths for1 in some other respects1 they are found somewhat differently from the sun azimuths4 ,put this in your ,note-,book3 ,to find an azimuth of the sun3 ,note the time of taking the azimuth by chronometer4 ,apply chronometer correction1 if any1 to get the ,g4,m4,t4 ,convert ,g4,m4,t4 into ,g4,a4,t4 by applying the equation of time4 ,convert ,g4,a4,t4 into ,l4,a4,t4 by applying the longitude in time4 ,the result is ,l4,a4,t4 or ,s4,h4,a4 ,with the correct ,l4,a4,t41 latitude and declination1 enter the azimuth tables to get the sun's true bearing1 i4e41 its azimuth4 ,example3 ,march #aeth1 #aiai4 ,,ct #aj;h -- #dm -- #cbs4 ,d4,r4 latitude #dj deg4 #aj' ,n1 longitude #gd deg4 ,w4 ,find the ,,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 in ,t4 #d --#ef --#jj 7,w--7 ,l4,a4,t4 #d;h--#eim--#bbs ,latitude and ,declination opp4 name4 ,,tz ,n #aja deg4 #cj',w ,we will take up later a further use of azimuths to find the error of your compass4 ,right now all you have to keep in mind is what an azimuth is and how you apply the formulas already given you to get the information necessary to enter the ,azimuth ,tables for the sun's true bearing at any time of the astronomical day when the sun can be seen4 ,in consulting these tables it must be remembered that if your ,l4,a4,t4 or ,s4,h4,a4 is1 astronomically1 #bj;h 7,a4,m471 you must subtract #ab hours in order to bring the time within the scope of these tables which are arranged from apparent six o'clock ,a4,m4 to noon and from apparent noon to #f ,p4,m4 respectively4 ,we are taking up sun azimuths today in order to get a thorough understanding of them before beginning a discussion of the ,marc ,st4 ,hilaire ,method which we will have tomorrow4 ,you must get clearly in your minds just what a line of position is and how it is found4 ,yesterday ,i tried to explain what a line of position was1 i4e41 a line at right angles to the sun's or other celestial body's true bearing--in other words1 a line at right angles to the sun's or other celestial body's azimuth4 ,today ,i tried to show you how to find your azimuth from the azimuth tables for any hour of the day4 ,tomorrow we will start to use azimuths in working out sights for lines of position by the ,marc ,st4 ,hilaire ,method4 ,note to ,instructor3 ,spend the rest of the time in finding sun azimuths in the tables by working out such examples as these3 #a4 ,april #bith1 #aiai4 ,d4,r4 latitude #dj deg4 #dj' ,n1 ,longitude #gd deg4 #ee' #ad ,w4 ,,ct #aj;h--#adm--#bds4 ,,cc #dm--#cjs slow4 ,find ,,tz4 #b4 ,may #aeth1 #aiai4 ,d4,r4 latitude #ai deg4 #bj' ,s1 ,longitude #dj deg4 #ae' #dd ,e4 ,,ct #aj;h--#ddm--#ees ,a4,m4 ,,cc #cm--#ajs fast4 ,find ,,tz4 ,note to ,instructor3 ,if possible1 give more examples to find ,,tz and also some examples on latitude by meridian altitude4 ,assign for ,night ,work reading the following ,articles in ,bowditch3 #cga-cgb-cgc-cgd-cge4 ,also1 examples to find ,,tz4 ,,friday ,,lecture ,,marc ,,st4 ,,hilaire ,,method ,,by ,a ,,sun ,,sight ,you have learned how to get your latitude by an observation at noon4 ,by the ,marc ,st4 ,hilaire ,method1 which we are to take up today1 you will learn how to get a line of position1 at any hour of the day4 ,by having this line of position intersect your parallel of latitude1 you will be able to establish the position of your ship1 both as to its latitude and longitude4 ,now you have already learned that in order to get your latitude accurately1 you must wait until the sun is on your meridian1 i4e41 bears due ,north or ,south of you1 and then you apply a certain formula to get your latitude4 ,when the sun is on or near the prime vertical 7i4e41 due ,east or ,west7 you might apply another set of rules1 which you have not yet learned1 to get your longitude4 ,by the ,marc ,st4 ,hilaire method1 the same set of rules apply for getting a line of position at any time of the day1 no matter what the position of the observed body in the heavens may be4 ,just one condition is necessary1 and this condition is necessary in all calculations of this character1 i4e41 an accurate measurement of the observed body's altitude is essential4 ,what we do in working out the ,marc ,st4 ,hilaire method1 is to assume our ,dead ,reckoning position to be correct4 ,with this ,d4 ,r4 position as a basis1 we compute an altitude of the body observed4 ,now this altitude would be correct if our ,d4 ,r4 position were correct and vice versa4 ,at the same time we measure by sextant the altitude of the celestial body observed1 say1 the sun4 ,if the computed altitude and the actual observed altitude coincide1 the ,d4 ,r4 position is correct4 ,if they do not1 the computed altitude must be corrected and the ,d4 ,r4 position corrected to coincide with the observed altitude4 ,just how this is done will be explained in a moment4 ,put in your ,note-,book3 ,formula for obtaining ,line of ,position by ,m4 ,st4 ,h4 ,method4 ,i4 ,three quantities must be known either from observation or from ,dead ,reckoning4 #a4 ,the ,s4 ,h4 ,a41 marked t4 ,note3 ,the method for finding ,s4 ,h4 ,a4 7t7 differs when the sun or star is used as follows3 7a7 ,for the ,sun3 ,get ,g4,m4,t4 from the corrected chronometer time4 ,apply the equation of time to find the ,g4,a4,t4 ,apply the ,d4,r4 ,lo4 7-,w7 7,e7 and the result is ,l4,a4,t4 or ,s4,h4,a4 as required4 7b7 ,for a ,star3 7,note to pupils3 ,leave this blank to be filled in when we take up stars in more detail47 #b4 ,the ,latitude1 marked ,l4 #c4 ,the ,declination of the observed body1 marked ,d4 ,,ii4 ,add together the log haversine of the ,s4,h4,a4 7,table #de71 the log cosine of the ,lat4 7,table #dd71 and the log cosine of the ,dec4 7,table #dd7 and call the sum ,s4 ,s is a log haversine and must always be less than #aj4 ,if greater than #aj1 subtract #aj or #bj to bring it less than #aj4 ,,iii4 ,with the log haversine ,s enter table #de in the adjacent parallel column1 take out the corresponding ,natural ,haversine1 which mark ,n,s4 ,,iv4 ,find the algebraic difference of the ,latitude and ,declination1 and from ,table #de take out the ,natural ,haversine of this algebraic difference angle4 ,mark it ,n,d-,l ,v4 ,add the ,n,s to the ,n,d-,l1 and the result will be the ,natural ,haversine of the calculated zenith distance4 ,formula ,n,,zd ,n,s ,n,d-,l ,,vi4 ,subtract this calculated zenith distance from #ij deg4 to get the calculated altitude4 ,,vii4 ,find the difference between the calculated altitude and the true altitude and call it the altitude difference4 ,,viii4 ,in your ,azimuth ,table1 find the azimuth for the proper t1 ,l and ,d4 ,,ix4 ,lay off the altitude difference along the azimuth either away from or toward the body observed1 according as to whether the true altitude1 observed by sextant1 is less or greater than the calculated altitude4 ,illustration ,x4 ,through the point thus reached1 draw a line at right angles to the azimuth4 ,this line will be your ,line of ,position1 and the point thus reached1 which may be read from the chart or obtained by use of ,table #b from the ,d4 ,r4 ,position1 is the nearest to the actual position of the observer which you can obtain by the use of any method from one sight only4 ,example3 ,at sea1 ,may #ahth1 #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 ,required ,line of ,position and most probable position of ship4 ,,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 in ,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 found from table to be ,cal4 ,alt4 #bi deg4 #dc' #cj ,n #ij deg4 ,e4 -7-7- #bi deg4 #ej' #jd ------------- ,alt4 ,diff #f' #cd ,toward4 ,course4 ,dist4 ,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 ---------- ------------- ,most probable fix ,lat4 #da deg4 #cj' ,n ,lo4 #cc deg4 #cj' #ji ,w ,as azimuth is ,n #ij deg4 ,e1 ,line of ,position runs due ,n ,s 7#cfj deg47 through ,lat4 #da deg4 #cj' ,n4 ,lo4 #cc deg4 #cj' #ji ,w4 ,assign for work in class and for ,night ,work examples such as the following3 #a4 ,july #aath1 #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 7corrected7 #e;h4 #chm #jjs ,p4,m4 ,required ,line of ,position by ,marc ,st4 ,hilaire ,method and most probable fix of ship4 #b4 ,may #afth1 #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 ,required ,line of ,position by ,marc ,st4 ,hilaire ,method and most probable fix of ship4 ,etc4 ,,saturday ,,lecture ,,examples ,,on ,,marc ,,st4 ,,hilaire ,,method ,,by ,a ,,sun ,,sight #a4 ,nov4 #ast1 #aiai4 ,a4,m4 at ship4 ,,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 ,required ,line of ,position by ,marc ,st4 ,hilaire ,method and most probable position of ship4 #b4 ,may #cjth1 #aiai4 ,p4,m4 at ship4 ,d4 ,r4 ,lat4 #ch #ad' #cc ,n1 ,lo4 #ae deg4 #ch' #di' ,w4 ,the mean of a series of observations of 77 was #ci deg4 #je' #dj deg44 ,,ie--#ja' #jj4 ,,he #bg ft4 ,,wt #c;h #dm #dis4 ,c--,w #a;h #cim #ees4 ,c4,c4 fast1 #jam #ebs4 ,required ,line of ,position by ,marc ,st4 ,hilaire ,method1 and most probable position of ship4 #c4 ,oct4 #bast1 #aiai1 ,a4,m4 ,d4 ,r4 ,lat4 #dj deg4 #ab' #ch ,n1 ,lo4 #fi deg4 #dh' #ed ,w4 ,the mean of a series of observations of 77 was #ai deg4 #ba' #bj4 ,,ie #jb' #aj4 ,,he #bf ft4 ,,wt #g;h #ehm #dis4 ,c--,w #d;h #eam #des4 ,c4 slow1 #jcm #jcs4 ,required ,line of ,position by ,marc ,st4 ,hilaire ,method and most probable position of ship4 #d4 ,june #ast1 #aiai1 ,p4,m4 at ship4 ,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 slow4 77 #af deg4 #ae' #dj4 ,,ie #b' #aj4 ,,he #bf ft4 ,required ,line of ,position and most probable fix of ship4 #e4 ,jan4 #eth1 #aiai4 ,a4,m4 ,d4 ,r4 ,lat4 #cf deg4 #bi' #ch ,n1 ,lo4 #ea deg4 #jg' #dd ,w4 ,the mean of a series of observations of 77 was #bc deg4 #ag' #bj4 ,,ie #ja' #ej4 ,,he #ai ft4 ,,wt #g;h #aam #cgs4 ,c--,w #e;h #eim #dis4 ,c4 slow #ehs4 ,required ,line of ,position and most probable fix of ship4 ,,week ,v--,,navigation ,,tuesday ,,lecture ,a ,,short ,,talk ,,on ,,the ,,planets ,,and ,,stars ,,identification ,,of ,,stars #a4 ,the ,planets ,you should acquaint yourself with the names of the planets and their symbols4 ,these can be found opposite ,page #a in the ,nautical ,almanac4 ,all the planets differ greatly in size and in physical condition4 ,three of them--,mercury1 ,venus and ,mars--are somewhat like the earth in size and in general characteristics4 ,so far as we know1 they are solid1 cool bodies similar to the earth and like the earth1 surrounded by atmospheres of cool vapors4 ,the outer planets on the other hand1 i4e41 ,jupiter1 ,saturn1 ,uranus1 and ,neptune1 are tremendously large--many times the size of the earth1 and resemble the sun more than the earth in their physical appearance and condition4 ,they are globes of gases and vapors so hot as to be practically self luminous4 ,they probably contain a small solid nucleus1 but the greater part of them is nothing but an immense gaseous atmosphere filled with minute liquid particles and heated to an almost unbelievably high temperature4 ,of the actual surface conditions on ,venus and ,mercury1 little is definitely known4 ,mercury is a very difficult object to observe on account of its proximity to the sun4 ,it is never visible at night2 it must be examined in the twilight just before sunrise or just after sunset1 or in the full daylight4 ,in either case the glare of the sun renders the planet indistinct1 and the heat of the sun disturbs our atmosphere so as to make accurate visibility almost impossible4 ,the surface of ,mercury is probably rough and irregular and much like the moon4 ,like the moon1 too1 it has practically no atmosphere4 ,mercury rotates on its axis once in #hh days4 ,its day and year are of the same length4 ,thus the planet always presents the same face toward the sun and on that side there is perpetual day while on the other side is night--unbroken and cold beyond all imagination4 ,venus resembles the earth more nearly than any other heavenly body4 ,its diameter is within #abj miles of the earth's diameter4 ,the exasperating fact about ,venus1 however1 is that it is shrouded in deep banks of clouds and vapors which make it impossible for us to secure any definite facts about it4 ,the atmosphere about ,venus is so dense that sunlight is reflected from the upper surface of the clouds around the planet and so reaches our telescopes without having penetrated to the surface at all4 ,from time to time markings have been discovered that at first seemed real but whether they are just clouds or tops of mountains has never really been established4 ,of all the planets1 we know more about ,mars than any other4 ,and yet practically nothing is actually known in regard to conditions on the surface of this planet4 ,we do know1 however1 that ,mars more nearly resembles a miniature of our earth than any other celestial body4 ,the diameter of ,mars is #d1baj miles--almost exactly half the earth's diameter4 ,the surface area of ,mars is just about equal to the total area of dry land on the earth4 ,like the earth1 ,mars rotates about an axis inclined to the plane of its orbit1 and the length of a ,martian day is very nearly equal to our own4 ,the latest determinations give the length of a ,martian solar day as #bd;h #cim #ces4 ,fortunately for us1 ,mars is surrounded by a very light and transparent atmosphere through which we are able to discover with our telescopes1 many permanent facts4 ,the most noticeable of these are the dazzling white polar caps first identified by ,sir ,william ,herschel in #aghd4 ,during the long winter in the northern hemisphere1 the cap at the ,north pole steadily increases in size1 only to diminish during the next summer under the hot rays of the sun4 ,these discoveries establish without doubt the presence of vapors in the ,martian atmosphere which precipitate with cold and evaporate with heat4 ,the polar caps1 then1 are some form of snow and ice or possible hoar frost4 ,outside the polar caps the surface of ,mars is rough1 uneven and of different colors4 ,some of the darker markings appear to be long1 straight hollows4 ,they are the so-called canals discovered by ,schiaparelli in #ahgg4 ,the term canal is an unfortunate one4 ,the word implies the existence of water and the presence of beings of sufficient intelligence and mechanical ability to construct elaborate works4 ,flammarion in ,france and ,lowell in the ,united ,states claim the word is correctly used1 i4e41 that these markings are really canals and that ,mars is actually inhabited4 ,the consensus of opinion among the most celebrated astronomers is contrary to this view4 ,most astronomers agree that these canals may not exist as drawn--that they are to great extent due to defective vision4 ,there is no conclusive proof of man-made work on ,mars1 nor of the existence of conscious life of any kind4 ,it may be there but conclusive proof of it is still lacking4 #b4 ,the ,stars ,the planets are often called wanderers in the sky because of their ever changing position4 ,sharply distinguished from them1 therefore1 are the fixed stars4 ,these appear as mere points of light and always maintain the same relative positions in the heavens4 ,thousands of years ago the ,great ,dipper hung in the northern sky just as it will hang tonight and as it will hang for thousands of years to come4 ,yet these bodies are not actually fixed in space4 ,in reality they are all in rapid motion1 some moving one way and some another4 ,it is their tremendous distance from us that makes this motion inappreciable4 ,the sun seems far away from us1 but the nearest star is #bjj1jjj times as far away from us as is the sun4 ,expressed in miles1 the figure is so huge as to be incomprehensible4 ,a special unit has1 therefore1 been invented--a unit represented by the distance traversed by light in one year4 ,in one second1 light travels over #ahf1jjj miles4 ,in #h-a_/c minutes1 light reaches us from the sun and1 in doing so1 covers the distance that would take the ,vaterland over four centuries to travel4 ,yet the nearest star is over four light years distant--it is so far away that it requires over four years for its light to reach us4 ,when you look at the stars tonight you see them1 not as they are1 but as they were1 even centuries ago4 ,polaris1 for instance1 is distant some sixty light years4 ,had it disappeared from the heavens at the time ,lee surrendered to ,grant1 we should still be seeing it and entirely unaware of its disappearance4 ,now each star in the heavens is in reality a sun1 i4e41 a vast globe of gas and vapor1 intensely hot and in a continuous state of violent agitation1 radiating forth heat and light1 every pulsation of which is felt throughout the universe4 ,so closely indeed do many of the stars resemble the sun1 that the light which they emit cannot be distinguished from sunlight4 ,some of them are larger and hotter than the sun--some smaller and cooler4 ,yet the sun we see can be regarded as a typical star and from our knowledge of it we can form a fairly correct idea of the nature and characteristics of these other stars4 ,anyone knows that the stars vary in brightness4 ,some of this variation is due partly to actual differences among the stars themselves and partly to varying distances4 ,if all the stars were alike1 then those which were farthest away would be faintest and we could judge a star's distance by its brilliancy4 ,this is not the case1 however4 ,some of the more brilliant stars are far more distant than some of the fainter ones4 ,there are stars near and remote and an apparently faint star may in reality be larger and more brilliant than a star of the first magnitude4 ,vega1 for instance1 is infinitely farther away from us than the sun1 yet its brightness is more than #ej times that of the sun4 ,polaris1 still farther away1 has #ajj times the light and heat of the sun4 ,in fact the sun1 considered as a star1 is relatively small and feeble4 #c4 ,identification of ,stars ,only the brighter stars can be used in navigation4 ,so much light is lost in the double reflection in the mirrors of the sextant1 that stars fainter than the third magnitude can seldom be observed4 ,this reduces the number of stars available for navigation to within very narrow limits1 for there are only #adb stars all told which are of the third magnitude or brighter4 ,the ,nautical ,almanac gives a list of some #aej stars which may be used1 but as a matter of fact1 the list might be reduced to some #ej or #fj without serious detriment to the practical navigator4 ,about #cj of these are of the second magnitude or greater and hence easily found4 ,it is not difficult to learn to know #cj or #dj of the brighter stars1 so that they can be recognized at any time4 ,to aid in locating the stars1 many different star charts and atlases have been published1 but most of them are so elaborate that they confuse as much as they help4 ,the simpler the chart1 the fewer stars it pretends to locate1 the better for practical purposes4 ,also1 all charts are of necessity printed on a flat surface and such a surface can never represent in their true values1 all parts of a sphere4 ,a chart1 therefore1 which covers a large part of the heavens1 is bound to give a distorted idea of distances or directions in some part of the sky and must be used with caution4 ,there are a few stars which form striking figures of one kind or another4 ,these can always be easily located and form a starting point1 so to speak1 from which to begin a search for other stars4 ,of these groups the ,great ,dipper is the most prominent in the northern sky and beginning with this the other constellations can be located one by one4 ,when the groups or constellations are not known1 then any individual star can be readily found by means of its ,right ,ascension1 and ,declination4 ,as you have already learned1 ,declination is equivalent to latitude on the earth and ,right ,ascension practically equivalent to longitude on the earth1 except that whereas longitude on the earth is measured ,e4 and ,w4 from ,greenwich1 ,right ,ascension is measured to the east all the way around the sky1 from the ,first ,point of ,aries4 ,with this in mind1 you can easily see that if a star's ,r4,a4 is less than yours1 i4e41 less than ,l4,s4,t4 or the ,r4,a4 of your ,meridian1 the star is not as far eastward in the heavens1 as is your zenith4 ,in other words it is to the west of you4 ,and vice versa1 if the ,star's ,r4,a4 is greater than yours1 the ,star is more to the eastward than you and hence to the east of you4 ,moreover1 as ,r4,a4 is reckoned all around a circle and in hours1 each hour's difference between the ,star's ,r4,a4 and yours is #a_/bd of #cfj deg4 or #ae deg44 ,hence if a star's ,r4,a4 is1 for instance1 #b hours greater than yours1 the star will be found to the east of your meridian and approximately #cj deg4 from your meridian1 providing the star is in approximately the same vertical east and west plane as is your zenith4 ,when the general east or west direction of any star has been determined1 its north or south position can at once be found from its declination4 ,if you are in ,latitude #dj deg4 ,n4 your celestial horizon to the ,south will be #ij deg4 from #dj deg4 ,n4 or #ej deg4 ,s4 and to the ,north it will be #ij deg4 #dj deg4 ,n4 #acj deg4 or #dj deg4 ,n4 7below the ,n4 pole74 ,the general position of the equator in the sky is always readily found according to the latitude you are in4 ,if you are in #dj deg4 ,n4 latitude1 the celestial equator would intersect the celestial sphere at a point #dj deg4 ,south of you4 ,knowing this1 the angular distance of a star ,north or ,south of the equator 7which is its declination7 should be easily found4 ,remember1 however1 that the equator in the sky is a curved line and hence a star in the ,east or ,west which looks to be slightly ,north of you may actually be ,south of you4 ,put in your ,note-,book3 ,if the star is west of you its ,r4,a4 is less than yours4 ,if east of you1 its ,r4,a4 is greater than yours4 ,star will be found approximately #ae deg4 to east or west of you for each hourly difference between the star's ,r4,a4 and your ,r4,a4 7,l4,s4,t474 ,having established the star's general east and west direction1 its north and south position can be found from its declination4 #d4 ,time of ,meridian ,passage of a ,star ,it is often invaluable to know first1 when a certain star will be on your meridian or second1 what star will be on your meridian at a certain specified time4 ,here is the formula for each case1 which put in your ,note ,book3 #a4 ,to find when a certain star will cross your meridian1 take from the ,nautical ,almanac1 the ,r4,a4 of the ,mean ,sun for ,greenwich ,mean ,noon of the proper astronomical day4 ,apply to it the correction for longitude in time 7,west 1 ,east -7 as per ,table at bottom of page #b1 ,nautical ,almanac1 and the result will be the ,r4,a4 of the ,mean ,sun at local mean noon1 i4e41 the distance in sidereal time the mean sun is from the ,first ,point of ,aries when it is on your meridian4 ,subtract this from the star's ,r4,a41 i4e41 the distance in sidereal time the star is from the ,first ,point of ,aries 7adding #bd hours to the star's ,r4,a41 if necessary to make the subtraction possible74 ,the result will be the distance in sidereal time the star is from your meridian i4e41 the time interval from local mean noon expressed in units of sidereal time4 ,convert this sidereal time interval into a mean time interval by always subtracting the reduction for the proper number of hours1 minutes and seconds as given in ,table #h1 ,bowditch4 ,the result will be the local mean time of the star's meridian passage4 ,example3 ,april #bbnd1 #aiai1 ,a4,m4 at ship4 ,in ,lo4 #ge deg4 ,e4 ,what is the local mean time of the ,star ,etamin's meridian passage8 ,r4,a4,m4,s4 ,gr4 #ba;d--#j;h #a;h--#edm--#jbs ,red4 for #ge deg4 ,e 7--#e;h7 --#di4c ,r4,a4,m4,s4 local mean noon #a;h--#ecm--#ab4gs ,star's ,r4,a4 #ag;h--#edm--#dds -- #a --#ec --#ab4g ,sidereal interval from ,l4,m4 ,noon #af;h--#jam--#ca4cs ,red4 for ,sid4 ,int4 7,table #h7 -- #b --#cg4c ,l4,m4,t4 #ba d #ae;h--#ehm--#eds ,hence1 star will cross meridian at #c;h--#ehm--#eds ,a4,m4 ,april #bbnd4 #b4 ,to find at any hour desired what star will cross your meridian1 take the ,r4,a4 of the ,mean ,sun for ,greenwich ,mean ,noon of the proper astronomical day4 ,apply to it the correction for longitude in time 7,west 1 ,east -7 as per table at bottom of page #b1 ,nautical ,almanac1 and the result will be the ,r4,a4 of the ,mean ,sun at local mean noon2 i4e41 the distance in sidereal time the mean sun is from the ,first ,point of ,aries when it is on your meridian4 ,suppose you wish to find the star at #aj ,p4,m4 ,add #aj sidereal hours to the sun's ,r4,a4 just found4 ,the result will be the ,r4,a4 of your meridian at approximately #aj ,p4,m4 ,select in the table on p4 #id the ,r4,a4 of the star nearest in time to your ,r4,a4 just secured4 ,subtract the ,r4,a4 of the ,mean ,sun at local mean noon from the star's ,r4,a4 just found on p4 #id of the ,n4,a4 and the result will be the exact distance in sidereal time the star you have just identified is from your meridian1 i4e41 the time interval from local mean noon expressed in units of sidereal time4 ,convert this sidereal time interval into a mean time interval by always subtracting for the proper number of hours1 minutes and seconds as per ,table #h1 ,bowditch4 ,you will then have secured the name of the star desired and the exact local mean time of the star's meridian passage4 ,example ,no4 #b3 ,at sea ,dec4 #ad1 #aiai4 ,desired to get a star on my meridian 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#dth - #efm ,w 7 #j --#dh4f 7474,r4,a4 your ,m4 #ag;h--#bim--#ad4fs #aa ,r4,a4,m4 #bh;h--#bim--#ad4fs -- #bd #d;h--#bim--#ad4fs ,r4,a4 of ,star ,aldebaran #d;h--#cam--#ah4es ,star ,r4,a4 #bh;h--#cam--#ah4e 7474,r4,a4 your ,m4 #ag -- #bi--ad4f ---------------- ,sid4 ,int4 from ,l4,m4 ,noon #aa;h--#jbm--#jc4is ,red for ,sid4 ,int4 7,table #h7 -- #a --#dh ---------------- ,l4,m4,t4 #aa;h--#jjm--#ae4is ,aldebaran1 then1 is the star and the exact ,l4,m4,t4 of its meridian passage will be #aa;h #jjm #ae4is ,note3 ,if the ,r4,a4,m4 is more than #bd hours1 deduct #bd hours4 ,you will know whether the star is ,north or ,south of you by its declination4 ,if you are in ,north latitude1 the star will be south of you if its declination is ,south or if its declination is ,north and less than your latitude4 ,if its declination and your latitude are both ,north and its declination is greater1 the star will be north of you4 ,the same principle applies if you are in ,south latitude4 ,assign any of the following to be worked in the class room or at night3 #a4 ,at sea1 ,november #ast1 #aiai4 ,in ,latitude #dj deg4 ,n41 ,longitude #gd deg4 ,w4 ,,wt #h;h #cjm ,p4,m4 ,observed unknown star about #hj deg4 east of my meridian and #be deg4 south of me4 ,what was the star8 #b4 ,at sea1 ,december #ast1 #aiai4 ,,ct #aj;h #dem #jas4 ,,cc #bjm #afs slow4 ,in ,d4,r4 ,latitude #cj deg4 ,n41 ,longitude #fj deg4 #cj' ,w4 ,observed unknown star about #fj deg4 west of meridian and about #bb deg4 ,s4 ,what was the star8 #c4 ,march #aeth1 #aiai4 ,in ,d4,r4 ,latitude #aj deg4 #db' ,n1 ,longitude #aej deg4 #ad' #bh ,w4 ,,ct #e;h #adm #bhs4 ,,cc--#bm #ajs4 ,observed unknown star almost on my meridian and about #bh deg4 north of me4 ,what was the star8 #d4 ,aug4 #c1 #aiai1 ,p4,m4 at ship4 ,in ,d4,r4 ,latitude #cg deg4 #cg' ,n4 ,longitude #ch deg4 #cg' ,w4 ,at what local mean time will the ,star ,antares be on the meridian8 #e4 ,what star will transit at about #d3aj ,a4,m4 on ,aug4 #crd1 #aiai8 ,in ,d4,r4 position ,latitude #ch deg4 #aj' ,n1 ,longitude #cd deg4 #ch' ,w4 #f4 ,at what local mean time will the ,star ,arcturus transit on ,july #agth1 #aiai1 in ,latitude #de deg4 #ce' ,n41 ,longitude #bh deg4 #jf' ,w48 ,,wednesday ,,lecture ,,latitude ,,by ,,meridian ,,altitude ,,of ,a ,,star--,,latitude ,,by ,,polaris 7,,pole ,,or ,,north ,,star7 ,to find your latitude by taking an altitude of a star when it is on your meridian1 is one of the quickest and easiest of calculations in all ,navigation4 ,the formula is exactly the same as for latitude by meridian altitude of the sun4 ,in using a star1 however1 you do not have to consult your ,nautical ,almanac to get the ,g4,m4,t4 and from that the declination4 ,all you have to do is to turn to page #ie of the ,nautical ,almanac1 on which is given the declination for every month of the year1 of any star you desire4 ,the rest of the computation is1 as said before1 the same as for latitude by the sun and follows the formula ,lat4 ,dec4 - ,z4,d4 7#ij deg4 - true altitude74 ,as when working latitude by the sun1 you subtract the ,z4,d4 and ,dec4 when of opposite name and add them when of the same name4 ,put in your ,note-,book3 ,formula3 ,lat4 ,dec4 - ,z4,d4 7#ij deg4 - true altitude74 ,at sea1 ,dec4 #bdth1 #aiai4 ,meridian altitude ,star ,aldebaran #eb deg4 #cf' ,s4 ,,he #bj ft4 ,required latitude of ship4 ,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 ,instructor3 ,have class work examples such as the following before taking up ,latitude by ,pole ,star3 #a4 ,at sea1 ,may #eth1 #aiai4 ,meridian altitude ,star ,capella1 #gj deg4 #bi' ,s4 ,,he #cb ft4 ,required latitude of ship4 #b4 ,at sea1 ,august #adth1 #aiai4 ,meridian altitude ,star ,vega1 #fj deg4 #ae' #de ,n4 ,,he #bh ft4 ,required latitude of ship4 ,etc4 ,latitude by ,polaris 7,pole or ,north ,star7 ,you remember we examined the formula in the ,n4,a4 for ,lat4 by the pole star when we were discussing sidereal time some weeks ago4 ,we will now take up a practical case of securing your latitude by this method4 ,before doing so1 however1 it may be of benefit to understand how we can get our latitude by the pole star4 ,in the first place1 imagine that the ,pole ,star is directly over the ,n pole of the earth and is fixed4 ,if that were so1 and imagine for a minute that it is so1 then it would be exactly #ij deg4 from the ,pole ,star to the celestial equator4 ,now1 no matter where you stand1 it is #ij deg4 from your zenith to your true horizon4 ,hence if you stood at the equator1 your zenith would be in the celestial equator and your true horizon would exactly cut the ,pole ,star4 ,now1 supposing you went #aj deg4 ,n of the equator4 ,then your northerly horizon would drop by #aj deg4 and the ,pole ,star would have an altitude of #aj deg44 ,in other words1 when you were in #aj deg4 ,n latitude1 the pole star would measure #aj deg4 high by sextant4 ,and so on up to #ij deg41 where the ,pole ,star would be directly over you and you would be at the ,north ,pole4 ,now all this is based upon the ,pole ,star being in the celestial sphere exactly over the ,north ,pole of the earth4 ,it is not1 however4 ,owing to the revolution of the earth1 the star appears to move in an orbit of a maximum of #a deg4 #jh'4 ,just what part of that #a deg4 #jh' is to be applied to the true altitude of the star for any time of the sidereal day1 has been figured out in the table on page #ajg of the ,nautical ,almanac4 ,what you have to get first is the ,l4,s4,t4 ,find from the table the correction corresponding to the ,l4,s4,t4 and apply this correction with the proper sign to the true altitude of ,polaris4 ,the result is the latitude in4 ,put in your ,note-,book3 ,to get latitude by pole star1 first get ,l4,s4,t4 ,this can be secured by using any one of the three formulas given you in ,week ,,iii--,thursday's ,lecture on ,sidereal ,time and ,right ,ascension4 ,then proceed as per formula in ,n4,a4 99 99 99 99 99 ,note to ,instructor3 ,spend rest of time in solving examples similar to the following3 #a4 ,at sea1 ,feb4 #adth1 #aiai4 ,,ct #ac;d #ba;h #ebm #ccs4 ,,cc #am #ads fast4 ,in ,lo4 #gb deg4 #di' #jj ,w4 ,,ie #a' #aj4 ,,he #ae ft4 ,observed altitude ,polaris #db deg4 #ba' #cj ,n4 ,required latitude in4 #b4 ,at sea1 ,march #cast1 #aiai4 ,in ,lo4 #afj deg4 #ae' ,e4 ,,ct #g;h #aem #ais4 ,observed altitude ,polaris #ch deg4 #ah' ,n4 ,,ie #c' #jj4 ,,he #ag ft4 ,required latitude in4 ,etc4 ,,thursday ,,lecture ,,marc ,,st4 ,,hilaire ,,method ,,by ,a ,,star ,,sight ,you have already been given instructions for finding a ,line of ,position by the ,marc ,st4 ,hilaire ,method1 using a sight of the sun4 ,today we will work out the same method by using a sight of a star4 ,put this in your ,note-,book here and also under ,i7b7 of the formula given you in ,week ,,iv--,friday's ,lecture3 ,get ,g4,m4,t4 from corrected chronometer time4 ,with your ,g4,m4,t4 find the corresponding ,g4,s4,t4 according to the formula already given you4 ,with your ,g4,s4,t4 apply the ,d4,r4 longitude 7- ,w4 ,lo47 ---------- 7 ,l4 ,lo47 to get the ,l4,s4,t4 ,with the ,l4,s4,t4 and the star's ,r4,a4 subtract the less from the greater and the result is the star's ,h4,a4 at the ship or t4 ,in using ,sun ,azimuth tables always take t from the ,p4,m4 column4 ,mark ,azimuth ,n or ,s according to the lat4 in and ,e or ,w1 according as to whether the ,star is ,east or ,west of your meridian4 ,then proceed as in the case of a sun sight4 ,formula3 7-,w4 ,lo47 ,g4,m4,t4 7474,r4,a4 77,,cp ,g4,s4,t4 --------- ,l4,s4,t4--,star's ,r4,a4 7,e4 ,lo47 7or vice versa if ,star's ,r4,a4 is greater7 ,star's ,h4,a4 at ship 7t74 ,then proceed as in case of sun sight4 ,example3 ,on ,may #cast1 #aiai1 in ,d4,r4 ,lat4 #ej deg4 ,n1 ,lo4 #de deg4 ,w1 ,g4,m4,t4 #ca;d #ad;h #ccm #cjs4 ,what was ,star's ,h4,a4 at ship8 ,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 ,star's ,r4,a47,spica7 #ac -- #bj -- #ei -------------------- ,star's ,h4,a4 7t7 #b;h -- #dfm -- #ch4bs ,now let us work out some examples by this method3 #a4 ,nov4 #bith1 #aiai4 ,,ct #cj;d #b;h #adm #cis ,a4,m4 ,,cc #cm #ads fast4 ,d4,r4 position ,lat4 #da deg4 #ad' ,n1 ,lo4 #fh deg4 #df' ,w4 ,observed altitude ,star ,aldebaran ,east of meridian #ej deg4 #bi' #dj4 ,,he #bi ft4 ,required ,line of ,position by ,marc ,st4 ,hilaire ,method and most probable position of ship4 #b4 ,jan4 #bcrd1 #aiai4 ,p4,m4 at ship4 ,,ct #c;h #dem #djs4 ,lat4 by ,d4,r4 #ch deg4 #dd' #ai ,n4 ,lo4 #aba deg4 #af' #ad ,e4 ,observed altitude ,star ,rigel #bh deg4 #ei' #bj ,west of meridian4 ,,ie #d' #cj4 ,,he #db ft4 ,required ,line of ,position by ,marc ,st4 ,hilaire ,method and most probable position of ship4 ,assign for ,night ,work one or two examples similar to the above4 ,,friday ,,lecture ,,examples3 ,,latitude ,,by ,,meridian ,,altitude ,,of ,a ,,star1 ,,latitude ,,by ,,polaris1 ,,marc ,,st4 ,,hilaire ,,method ,,by ,a ,,star ,,sight #a4 ,at sea1 ,dec4 #eth1 #aiai4 ,observed meridian altitude ,star ,aldebaran #fi deg4 #bh' #dj ,s4 ,no ,,ie4 ,,he #bf ft4 ,required latitude in4 #b4 ,at sea1 ,jan4 #bjth1 #aiai4 ,,ct #ba;d #b;h #afm #dhs ,a4,m4 ,in longitude #ef deg4 #bi' #df ,w4 ,observed altitude of ,star ,polaris #dh deg4 #dd' #cj ,n4 ,,ie #aj' #bj4 ,,he #cg ft4 ,required latitude in4 #c4 ,at sea1 ,june #dth1 #aiai4 ,a4,m4 at ship4 ,,ct #aj;h #afm #cbs4 ,,cc #em #des fast4 ,lat4 by ,d4,r4 #db deg4 #dd' ,n1 ,longitude #ec deg4 #ac' #dd ,e4 ,observed altitude of ,star ,altair ,east of meridian1 #eb deg4 #ai' #cj4 ,,ie--#ad' #jj4 ,,he #ef ft4 ,required line of position by ,marc ,st4 ,hilaire ,method and most probable position of ship4 ,etc4 99 99 99 99 99 ,assign for ,night ,work the following ,articles in ,bowditch3 #ccf through #cda1 disregarding the formulas4 ,,saturday ,,lecture ,,longitude ,,by ,,chronometer ,,sight ,,of ,,the ,,sun 7,,time ,,sight7 ,you have now learned1 first1 how to get your latitude by a meridian altitude of the sun or a star and second1 how to get your ,line of ,position and most probable fix1 including both latitude and longitude1 by the ,marc ,st4 ,hilaire ,method1 using for your calculations either the sun or a star4 ,we are now going to take up a method of getting your longitude only4 ,this method requires as much1 if not more1 calculation than the ,marc ,st4 ,hilaire ,method4 ,its results1 on the other hand1 are far less complete1 for while the ,marc ,st4 ,hilaire ,method will give you a fairly accurate idea of both your latitude and longitude1 this method will1 at best1 only give you your longitude4 ,moreover1 you can use it for accurate results only when the sun bears almost due ,east or ,west of you1 for that is the best time1 as you have already learned1 to get a line of position running due ,north and ,south1 which is nothing more than a meridian of longitude4 ,the only reason we explain this method at all is because it is in common practice among merchantmen and may1 therefore1 be of assistance to you1 if you go on a merchant ship4 ,remember1 however1 that it belongs to ,old ,navigation as distinguished from ,new ,navigation1 exemplified by the ,marc ,st4 ,hilaire ,method4 ,it is undoubtedly being used less and less among progressive1 up-to-date navigators1 and will continue to be used less as time goes on4 ,the fact remains1 however1 that at present many merchantmen practice it1 and so it will do you no harm to become familiar with the method1 too4 ,this method is based on securing your longitude by a time sight or longitude by chronometer sight1 meaning that at the time the sun bears as near due ,east or ,west as possible1 you take a sight of it by sextant and at the same instant note the time by chronometer4 ,with this information you proceed to work out your problem and secure your longitude according to the following formula4 ,put in your ,note-,book3 ,to find your longitude by chronometer 7or time7 sight4 #a4 ,take sight by sextant only when the sun bears as near as possible due ,east or ,west4 ,at exact time of taking sight1 note chronometer time4 #b4 ,get ,g4,m4,t4 from corrected chronometer time4 ,apply ,equation of ,time to get the corresponding ,g4,a4,t4 #c4 ,correct observed altitude to get ,t4,c4,a4 ,also have at hand ,lat4 by ,d4 ,r4 and ,polar ,distance4 7,note3 ,secure ,p4 ,d4 by subtracting ,dec4 from #ij deg41 if ,lat4 and ,dec4 are of same name4 ,if ,lat4 and ,dec4 are of opposite name1 secure ,p4 ,d4 by adding ,dec4 to #ij deg447 #d4 ,add together the ,t4,c4,a4 the ,lat4 by ,d4,r4 and the ,p4,d4 ,divide the sum by #b and call the quotient ,half ,sum4 ,from the ,half ,sum subtract the ,t4,c4,a4 and call the answer the ,difference4 #e4 ,add together the secant of the ,latitude1 the cosecant of the ,p4,d41 the cosine of the ,half ,sum and the sine of the ,difference 7,table #dd74 ,the result will be the log haversine of the ,s4,h4,a4 or ,l4,a4,t4 ,it must always be less than #aj4 ,if greater than #aj1 subtract #aj or #bj to bring it less than #aj4 #f4 ,from ,table #de1 take out the corresponding ,s4,h4,a4 7,l4,a4,t471 reading from the top of the page if ,p4,m4 at ship1 or from bottom of page if ,a4,m4 at the ship4 #g4 ,find the difference between ,l4,a4,t4 and ,g4,a4,t4 ,this difference is ,lo4 in ,time which turns into degrees1 minutes and seconds by ,table #g4 ,if ,g4,a4,t4 is greater than ,l4,a4,t4 longitude is ,west2 if ,g4,a4,t4 is less than ,l4,a4,t4 longitude is ,east4 ,example3 ,august #bfth1 #aiai1 ,a4,m4 ,,ct #bf;d #b;h #bim #jcs ,a4,m4 ,,cc #afm #jhs slow4 77 #dd deg4 #eg' #jj4 ,,ie--#a' #cj4 ,,he #cb ft4 ,d4,r4 ,lat4 #d deg4 #ee' #cb ,n4 ,required longitude in at time of observation4 #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 sin4 #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 in ,t4 #f;h--#afm--#ees ,e ,lo4 7,table #g7 #id deg4 #ac' #de ,e ,i wish to caution you about confusing this method with the one ,bowditch uses1 and still another which ,henderson uses in his book ,elements of ,navigation4 ,it is not exactly like either one4 ,it requires one operation less than either1 however1 and it also requires the use of fewer parts of the various tables involved4 ,for that reason it is given you4 ,assign for work in class room and also for work at night examples similar to the following3 #a4 ,oct4 #ast1 #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 ,required longitude in4 #b4 ,oct4 #ajth1 #aiai4 ,p4,m4 77 #be deg4 #ad' #cj4 ,,ct #a;h #aem #bjs4 ,,cc #dm #cis slow4 ,,ie--#c' #aj4 ,,he #bf ft4 ,d4,r4 ,lat4 #da deg4 #bi' #jj ,s4 ,required longitude in4 #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 fast4 ,required longitude in4 #d4 ,may #ahth1 #aiai4 ,a4,m4 77 #bi deg4 #da' #ae4 ,,wt #g;h #bjm #des4 ,c-,w #b;h #agm #jfs4 ,,cc #dm #eis slow4 ,latitude by ,d4,r4 #da deg4 #cc' ,n4 ,,ie--#a' #cj4 ,,he #bc ft4 ,required longitude in4 #e4 ,august #bdth1 #aiai4 ,a4,m4 77 #bc deg4 #cb' #aj4 ,,ie--#b'jj4 ,,he #af ft4 ,in latitude #ci deg4 #jd' ,n4 ,,ct #bd;d #b;h #dgm #bhs ,a4,m4 ,,cc #dm #bhs4 ,required longitude in4 #f4 ,june #bfth1 #aiai4 ,p4,m4 77 #dd deg4 #jh' #bj4 ,,ie--#b' #bj4 ,,he #cg ft4 ,,ct #h;h #ahm #des4 ,,cc #cm #bjs fast4 ,latitude by ,d4,r4 #f deg4 #dc' ,s4 ,required longitude in4 #g4 ,july #bith1 #aiai4 ,a4,m4 ,,ct #bi;d #aa;h #adm #cis ,a4,m4 ,,cc #bm #ahs slow4 77 #bh deg4 #jh' #cj4 ,,ie #j' #cj4 ,,he #ch ft4 ,latitude by ,d4,r4 #ci deg4 #dh' ,n4 ,required longitude in4 #h4 ,may #bbnd1 #aiai4 ,p4,m4 ,,ct #i;h #adm #chs4 ,,cc #em #bhs slow4 77 #ba deg4 #jg' #dj4 ,in latitude #da deg4 #bf' ,n4 ,,ie #c' #aj4 ,,he #dj ft4 ,required longitude in4 ,,week ,,vi--,,navigation ,,tuesday ,,lecture ,,longitude ,,by ,,chronometer ,,sight ,,of ,a ,,star ,in getting your longitude by a time sight of a star1 you proceed somewhat differently from the method used when observing the sun4 ,what you wish to get first is ,g4,s4,t41 i4e41 the distance in time ,greenwich is from the ,first ,point of ,aries4 ,if you can then get the distance the ship is from the ,first ,point of ,aries1 the difference between the two will be the longitude in1 marked ,east or ,west according as to which is greater4 ,by looking at the diagram furnished you when we were talking of ,sidereal ,time1 all this becomes perfectly clear4 ,the full rule for finding longitude by a star is as follows1 which put in your ,note-,book3 ,correct your ,,ct to get your ,g4,m4,t4 ,from the ,g4,m4,t4 get the ,g4,s4,t4 ,from the observed altitude of the star1 obtain the star's ,h4,a4 at the ship in the same way ,l4,a4,t4 is secured in case of the sun4 ,to or from the ,r4,a4 of the star add1 if ,west of your meridian1 subtract if ,east of your meridian1 the star's ,h4,a4 at the ship1 just obtained4 ,the result is the ,r4,a4 of the ship's meridian or ,l4,s4,t4 ,find the difference between ,g4,s4,t4 and ,l4,s4,t4 and the result is the longitude1 marked ,east or ,west according as to whether ,g4,s4,t4 is less or greater than ,l4,s4,t4 ,note3 ,always take the star's ,h4,a4 from the top of the page of ,table #de4 ,dec4 #b1 #aiai4 ,a4,m4 ,observed altitude ,star ,sirius #b,o deg4 #je' #bj1 ,west of meridian4 ,,ct #aa;h--#dem--#bis ,p4,m4 ,,cc #am--#bhs slow4 ,,ie--#a' #bj4 ,,he #ba ft4 ,latitude by ,d4 ,r4 #ch deg4 #eg' ,n4 ,required longitude in4 ,,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 sin4 #i4idiaa #b --------- #i4agghe - #aa --------- log4 hav4 ,star's ,h4,a4 at ship #i4agggd ,star's ,h4,a4 #c;h--#jbm--#djs ,star's ,r4,a4 #f --#da --#ci -------------- ,l4,s4,t4 #i;h--#ddm--#ais ,g4,s4,t4 #d --#bg --#ja -------------- ,lo4 in ,t4 #e;h--#agm--#ahs ,e ,longitude in #gi deg4 #ai' #cj ,e ,assign for ,night ,work or work in the class room examples similar to the following3 #a4 ,april #af1 #aiai1 in ,latitude #aa deg4 #dg' ,s4 ,observed altitude of the ,star ,aldebaran1 ,west of the meridian #bc deg4 #ac' #bj4 ,,ct #f;h #ehm #bis4 ,,cc #bm #bgs fast4 ,,ie--#b' #jj4 ,,he #bf ft4 ,required longitude in4 #b4 ,dec4 #ajth1 #aiai4 ,observed altitude of ,star ,sirius #bj deg4 #je' #dj ,west of meridian4 ,,ct #aa;h #dem #bis4 ,,cc #am #bhs slow4 ,,ie--#a' #bj4 ,,he #ba ft4 ,d4,r4 latitude #ch deg4 #eg' ,n4 ,required longitude in4 ,note to ,instructor3 ,if any time in the period is left or for ,night ,work assign examples to be worked by ,marc ,st4 ,hilaire ,method1 changing slightly the ,d4,r4 ,lat4 and ,longitude just obtained by the ,time ,sight ,method4 ,,wednesday ,,lecture ,,examples ,,on ,,longitude ,,by ,,chronometer ,,sight ,,of ,a ,,star #a4 ,dec4 #ith1 #aiai4 ,in latitude #cf deg4 #dh' ,n4 ,observed altitude ,star ,capella1 ,east of meridian #df deg4 #ah' #cj4 ,,ie #b' #ej off arc4 ,,he #cc ft4 ,,ct #aj;d #c;h #jem #jes ,a4,m4 ,,cc #am #ahs slow4 ,declination of star is #de #ee' ,n4 ,required longitude in4 #b4 ,october #bfth1 #aiai4 ,in latitude #ci deg4 #ed' ,s4 ,observed altitude ,star ,rigel1 ,west of meridian #db deg4 #ah' #dj4 ,,ct #bg;d #aj;h #cbm #ees ,a4,m4 ,,cc #bm #ahs fast4 ,,ie #d' #bj off arc4 ,,he #db ft4 ,required longitude in4 #c4 ,april #aath1 #aiai4 ,p4,m4 at ship4 ,in latitude #dc deg4 #af' #dh ,s4 ,observed altitude ,star ,spica #cc deg4 #ah' #bj1 ,east of meridian4 ,,ct #aa;h #jhm #dds ,p4,m4 ,,ie #c' #bj on arc4 ,,cc #dm #ahs slow4 ,,he #ci ft4 ,required longitude in4 #d4 ,september #aeth1 #aiai4 ,p4,m4 at ship4 ,in latitude #di deg4 #ch',n4 ,observed altitude ,star ,deneb1 ,east of meridian1 #cf deg4 #af' #ej4 ,,ie #c' #dj off arc4 ,,he #dj ft4 ,,cc #fm #ahs slow4 ,,ct #aj;h #jjm #acs ,p4,m4 ,declination of star is #dd deg4 #ei' #cf ,n4 ,required longitude in4 ,if any time is left1 work same examples by ,marc ,st4 ,hilaire ,method assuming a position near the one found by ,time ,sight4 ,assign for ,night ,work any of the above examples1 to be worked either as ,time ,sights or by the ,marc ,st4 ,hilaire ,method1 and also the following ,arts4 in ,bowditch3 #cbf-cbg-cbh-cbi4 ,,thursday ,,lecture ,,latitude ,,by ,,ex-,,meridian ,,altitude ,,of ,,the ,,sun ,you have learned that when you calculate your latitude from a meridian altitude of the sun1 one of the necessary requisites is to have the sun exactly on your meridian4 ,in fact1 that is just another way of expressing meridian altitude1 i4e41 an altitude taken when the sun is on your meridian4 ,now suppose that #aj or #ae minutes before noon you fear that the sun will be clouded over at noon so that a meridian altitude cannot be secured4 ,there is a way to calculate your latitude1 even though the altitude you secure is taken by sextant some minutes before or after noon4 ,this is called latitude by an ex-meridian altitude4 ,it must be kept in mind that this method can be used accurately only within #bf minutes of noon1 either before or after1 and only then when you know your longitude accurately4 ,put in your ,note-,book3 #a4 ,get your ,l4,a4,t4 7,s4,h4,a474 #b4 ,subtract it from #bd;h #jjm #jjs1 or vice versa1 according as to whether ,l4,a4,t4 is just before or just after local apparent noon4 ,call the result ,time ,interval from ,meridian ,passage4 #c4 ,with your ,d4,r4 latitude1 declination and ,time ,interval from ,meridian ,passage1 enter ,table #bf to get the proper amount of ,variation of ,altitude in one minute from meridian passage4 #d4 ,with the ,time ,interval from ,meridian ,passage and the ,variation1 enter ,table #bg to get the total amount of ,variation of ,altitude4 #e4 ,add this total amount of ,variation to the true observed altitude taken before or after noon1 and the result is the corrected altitude4 #f4 ,then proceed to get your latitude according to the rules already given you for latitude by meridian altitude4 ,example3 ,at sea1 ,jan4 #bcrd1 #aiai4 ,,ct #d;h #bbm #ads4 ,,cc #am #ajs fast4 ,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 ,required latitude in4 ,,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 in ,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 ,time ,interval from ,meridian ,passage4 ,dec4 #ai deg4 #cd' #dh ,s ,table #bf #b4h ,variation ,lat4 #ai deg4 #af' #jj ,n ,for #a min4 #j altitude4 99 99 99 99 99 ,time ,interval from ,meridian ,passage #aem #jbs - #b4h ,variation for #a minute 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 in #ai deg4 #af' #cj ,n ,assign for work in class room and ,night ,work1 examples similar to the following3 #a4 ,at sea1 ,july #aath1 #aiai4 ,latitude by ,d4,r4 #ej deg4 #ja' #jj ,n4 ,longitude #dj deg4 #je' #af ,w4 ,observed ex-meridian altitude 77 #fa deg4 #de' #cj ,s4 ,,he #ae ft4 ,,ie--#d' #aj4 ,,ct 7corrected7 #b;h #chm #jjs4 ,required latitude in4 #b4 ,at sea1 ,june #fth1 #aiai4 ,latitude by ,d4 ,r4 #di deg4 #ba' ,n1 ,longitude #ah deg4 #ah' ,w4 ,observed ex-meridian altitude 77 #fa deg4 #cj' #bb ,s4 ,,he #db ft4 ,,ct #a;h #jfm #ahs4 ,,cc--#am #ads4 ,,ie #j' #cj off the arc4 ,required latitude in of ship4 ,if any time is left1 work similar examples by ,marc ,st4 ,hilaire ,method4 ,,friday ,,lecture ,,examples3 ,,latitude ,,by ,,ex-,,meridian ,,altitude ,,of ,,the ,,sun #a4 ,jan4 #ast1 #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-meridian #ee deg4 #af' #cj ,n4 ,,ie #b' #jj off the arc4 ,,cc #am #bhs fast4 ,,he #cf ft4 ,required latitude in4 #b4 ,march #aath1 #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-meridian #df deg4 #ag' #cj ,s4 ,,ie #b' #jj on the arc4 ,,cc #am #afs slow4 ,,he #bi ft4 ,required latitude in4 #c4 ,april #bfth1 #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-meridian #eb deg4 #ah' #ej ,n4 ,,ie--#b' #dj4 ,,cc #cm #efs slow4 ,,he #cc ft4 ,required latitude in4 #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-meridian #dh deg4 #bf' #bj ,n4 ,,ie #c' #bj on the arc4 ,,cc #dm #ahs fast4 ,,he #da ft4 ,required latitude in4 #e4 ,june #bast1 #aiai4 ,,ct #d;h4 #efm #ahs4 ,latitude by ,d4 ,r4 #db deg4 #ja' ,n1 ,longitude #ge deg4 #jj' #ah ,w4 77 ex-meridian #ga deg4 #bi' #dj ,s1 ,,ie--#b' #cj4 ,,cc #cm #jds slow4 ,,he #bh ft4 ,required latitude in4 #f4 ,dec4 #ahth1 #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-meridian #gh deg4 #cb' #cj ,s4 ,,ie #c' #cj on the arc4 ,,cc #bm #dds slow4 ,,he #ce ft4 ,required latitude in4 ,if there is any time left1 give examples of latitude by meridian altitude1 ,marc ,st4 ,hilaire ,method by sun or star sight1 etc4 ,,saturday ,,lecture ,,finding ,,the ,,watch ,,time ,,of ,,local ,,apparent ,,noon ,noon at the ship is the pivotal point of the day's work at sea4 ,it is then that the navigator must report to the commanding officer the latitude and longitude by dead reckoning1 the latitude and longitude by observation1 the course and distance made good1 the deviation of the compass and the course and distance to destination4 ,apparent noon1 then1 is a most important time to calculate accurately1 and to do so when the ship is under way1 is not so easy at it first appears4 ,if the ship is stationary1 and you know the longitude you are in1 the problem is simple4 ,then it is merely a question of starting with ,l4,a4,t4 of #jj;h-#jjm-#jjs1 adding or subtracting the longitude1 according as to whether it is ,west or ,east1 to get ,g4,a4,t42 applying the equation of time with sign reversed to get ,g4,m4,t42 applying the ,c4 ,cor4 with sign reversed to get the ,c4,t42 and applying the ,c-,w to get the ,,wt4 ,if1 for instance1 this ,,wt happens to be #aa;h-#dbm-#cas1 when the watch reads that number of hours1 minutes and seconds1 the sun will be on the meridian and it will be apparent noon4 ,when the ship is moving1 the problem is more difficult4 ,at first thought you might imagine that all you would have to do would be to take the difference between the ,l4,a4,t4 of the morning sight and #bd hours1 calculate the distance the ship would run in this time and from that determine the longitude you would be in at noon4 ,then proceed as in the case of the ship being stationary4 ,but such a calculation does not take into consideration the easting or westing of the ship itself4 ,suppose that at the morning sight the ,l4,a4,t4 is found to be #bj;h-#ajm-#cjs4 ,if the ship does not move1 it will be #c;h-#dim-#cjs to noon4 ,but suppose the ship is moving eastward4 ,then1 in addition to the speed at which the sun is approaching the ship1 there must be added the speed at which the ship is moving toward the sun--i4e4 the change in longitude per hour which the ship is making1 expressed in minutes and seconds of time4 ,likewise1 if the ship is moving westward1 an allowance must be made for the westing of the ship4 ,and this change of longitude in minutes and seconds of time must be subtracted from the speed of the sun's approach since the ship1 in going west1 is traveling away from the sun4 ,there are various ways to calculate this allowance for the ship's speed1 among the best of which is given in ,bowditch1 ,art4 #djc1 p4 #agi4 ,another1 and even easier way1 is the following1 which was explained to the writer by ,lieutenant ,commander ,r4,p4 ,strough1 formerly head of the ,seamanship ,department of this ,school3-- #a4 ,take the morning sight for longitude when the sun is on or as near as possible to the prime vertical4 #b4 ,subtract the ,l4,a4,t4 of the morning sight from #bd hours4 ,this will give the total time from the morning sight to noon if the ship were stationary4 #c4 ,from the course to noon and speed of the ship1 figure the change in longitude per hour in terms of seconds of time4 ,for instance1 suppose a ship were steaming a course of #bge deg4 at the rate of #aa knots per hour in approximately #ch deg4 ,north latitude4 ,the change of longitude per hour for this speed would be #ad' of arc or #efs of time4 #d4 ,now the sun travels at the rate of #fj minutes or #cfjj seconds per hour4 ,to this hourly speed of the sun must be added or subtracted the hourly speed of the ship according as to whether the ship is going in an easterly or westerly direction4 ,if1 as mentioned above1 the ship is steaming a course of #bge deg4 7,w #a_/b ,n7 and hence changing its longitude at the rate of #efs per hour1 then the net rate of approach of the sun per hour would be #cfjjs - #efs1 or #cedds per hour4 #e4 ,divide the total time to noon from the ,l4,a4,t4 of the morning sight 7expressed in seconds of time7 by the net rate of approach of the sun per hour4 ,the result will be the corrected time to noon--i4e4 the time at which the sun will be on the ship's meridian when the ship is changing its longitude to the westward at the rate of #efs per hour4 #f4 ,one more step is necessary4 ,to the watch time of the morning sight1 add the corrected time to noon4 ,the result will be the watch time of ,local ,apparent ,noon4 ,thirty minutes before will be the watch time of #aa3cj ,a4,m4 and at #aa3cj ,a4,m4 all deck clocks should be set to the local apparent time of the place the ship will be at local apparent noon4 ,the following example illustrates the explanation just given and should be put in your ,note ,book3-- ,example3--,at sea1 ,august #gth1 #aiai4 ,about #g3cj ,a4,m4 by ship's time1 position by observation just found to be ,latitude #cj deg4 #je' ,n1 ,longitude #eh deg4 #jh' ,w4 ,,wt of morning sight #f;h-#ecm-#acs ,a4,m4 ,c-,w #d;h-#cgm-#bas4 ,,cc #cm-#chs4 ,course #bge deg44 ,speed #aa knots4 ,,tz ,n #ij deg4 ,e4 ,what will be the ,watch ,time of ,local ,apparent ,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 in ,t4 #c -- #eb -- #cb ------------------- ,l4,a4,t4 #ai -- #ce -- #eh #bd -- #jj -- #jj ------------------- ,total time to ,noon #d;h #bdm #jbs ,course -- #bge deg4 ,change in ,lo4 per hr4-- #ad'1 #efs4 #cfjjs -#ef ----- #cedds1 ,net rate of approach of sun #d;h #fj ---- #bdjm #bd ----- #bfdm x #fj #aehdjs #aehdjs #jb ----- #aehdbs1 ,total time to noon4 #cedd7 #aehdb 7#d4dg hours #adagf ----- #afffj #adagf ----- #bdhdj #bdhjh ----- ,corrected time to ,noon #d;h -- #bhm -- #abs ,,wt of ,a4,m4 sight #f;h -- #ecm -- #acs ----------------- ,,wt of ,l4,a4,n4 #aa;h -- #bam -- #bes ,,wt of #aa3cj ,a4,m4 #aj;h -- #eam -- #bes ,when1 therefore1 the watch reads #aj;h--#eam--#bes1 the deck clocks should be set to #aa4cj ,a4,m4 and thirty minutes later it will be apparent noon at the ship4 ,in all these calculations it is taken for granted that the speed of the ship and hence the change in longitude can be gauged accurately4 ,a check on this can be made by comparing the longitude of the ,a4,m4 sight with the ,d4,r4 longitude of the same time4 ,any appreciable difference between the two can be ascribed to current4 ,now1 if a proportionate amount of current is allowed for in reckoning the speed of the ship from the time of the ,a4,m4 sight to noon1 then a proper correction can be made in the net rate of approach of the sun and the corrected time to noon will be very close to the exact time of noon4 ,of course there will be an error in this calculation but it will be small and the result gained will be accurate enough for ordinary work4 ,so much for finding the watch time of ,local ,apparent ,noon4 ,careful navigators carry the process further and get the watch times of #ae1 #aj and #e minutes before noon1 so that by the use of constants for each one of these times1 an accurate check on the noon latitude can be quickly and easily secured4 ,we have not time in this course to explain how these constants are worked out but it is well worth knowing4 ,the information regarding it is in ,bowditch ,art4 #cbe1 p4 #abh1 and ,art4 #dje1 p4 #aha4 ,a word about the watch used by the navigator should be included here4 ,this watch should be a good one and receive as much care1 in its way1 as the chronometer4 ,it should be wound at the same time every day1 carefully handled and1 in other respects1 treated like the fine time-piece that it is4 ,while authorities differ on this point1 the best practice seems to be not to change the navigator's watch to correspond with the apparent time of each day's noon position4 ,the reason for this is two-fold4 ,first1 because constant moving of the hands will have an injurious effect on the works of the watch1 and second1 because1 by not changing the watch1 the ,c-,w remains approximately the same1 and thus a good check can be kept on both the watch and the chronometer as well as on the navigator's figures in reckoning the times of his various sights4 ,assign for night reading the following ,arts4 in ,bowditch3 #cbc1 #cbd1 #ccc4 ,also problems similar to the following3 #a4 ,at sea1 ,july #bh1 #aiai4 ,position by observation just found to be ,latitude #dd deg4 #eh' ,n1 ,longitude #bb deg4 #jf' ,w4 ,,wt of morning sight #f;h-#jbm-#bjs4 ,,cc #cm #cds slow4 ,course ,s #bd deg4 ,w4 ,,tz ,n #ij deg4 ,e4 ,speed #i knots4 ,what will be the watch time of ,local ,apparent ,noon8 #b4 ,at sea1 ,august #ith1 #aiai4 ,position by observation just found to be ,latitude #ch deg4 #dh' ,n1 ,longitude #gj deg4 #df' ,w4 ,,wt of morning sight #h;h-#aem-#jas ,a4,m4 ,c-,w #c;h-#efm-#cbs4 ,,cc #cm-#dcs slow4 ,course #bgb deg44 ,speed #ab knots4 ,,tz ,n #ij deg4 ,e4 ,what will be the watch time of ,local ,apparent ,noon8 ,,week ,,vii--,,navigation ,,tuesday ,,lecture ,,compass ,,error ,,by ,,an ,,azimuth ,the easiest and most accurate way to find the error of your compass is1 first1 to find the bearing of the sun by your pelorus4 ,if you set your pelorus1 so that it will exactly coincide with the course you are steaming as shown by the compass in your chart house and then get a bearing of the sun by noting where the shadow from the pelorus vane cuts the circumference1 this bearing will be the bearing of the sun by compass4 ,at the same time1 get your true bearing of the sun from the ,azimuth ,tables4 ,the difference between the two will be the compass error1 marked ,east or ,west according to the following rule which put in your ,note-,book3 #a4 ,express your ,compass ,bearing and your ,true ,bearing by ,,new compass reading4 #b4 ,if ,,tz is to the right of ,,cz1 ,c4,e4 is ,east4 ,formula3 ,true--,right--,east4 #c4 ,if ,,tz is to the left of ,,cz1 ,c4,e4 is ,west4 ,formula3 ,true--,left--,west4 ,you must now remember that what you have is a ,compass ,error1 consisting of both ,variation and ,deviation4 ,to find the ,deviation1 the ,variation and ,c4,e4 being given1 is merely to apply the rules already given you under ,dead ,reckoning4 ,for instance1 if you had a ,c4,e4 of #aj deg4 ,w and a ,variation of #d deg4 ,e1 the ,deviation would be #ad deg4 ,w4 ,put this example in your ,note-,book3 ,,lat #bj;h #eim #egs ,lat4 #d deg4 #ee' ,n ,dec4 #aj deg4 #ci' #cj ,n ,ship heading ,n #aa deg4 ,w4 ,,cb of 747 ,s #hh deg4 ,e4 ,variation #aj deg4 ,w4 ,what was the ship's true course and ,deviation of ,compass on direction ship was heading8 ,illustration ,illustration ,,cz #ib deg4 7,new compass reading7 ,,tz #hj deg4 7,new compass reading7 --- ,,ce #ab deg4 ,,ce #ab deg4 ,w ,variation #aj deg4 ,w ----- ,deviation #b deg4 ,w ,true course being sailed ,n #bc deg4 ,w or #ccg deg44 ,let us now work out some of the following examples3 #a4 ,l4,a4,t4 #bb;h--#adm--#ahs ,lat4 #cj deg4 #bi' ,s ,dec4 #ag deg4 #bh' #dd ,n ,ship heading ,s #hd deg4 ,w ,compass ,bearing #dd deg4 ,variation #aj deg4 ,w4 ,required ,t4,c4 and ,deviation on ship's loading4 #b4 ,august #bith1 #aiai4 ,,ct #b;h #bim #ahs ,a4,m4 ,longitude #abj deg4 #ai' #df ,e4 ,latitude #dd deg4 #ad' ,n4 ,ship heading #ih deg44 ,compass ,bearing ,s #db deg4 ,e4 ,variation #d deg4 ,e4 ,required ,t4,c4 and ,deviation on ship's heading4 #c4 ,june #agth1 #aiai4 ,,ct #d;h #ahm #dds ,a4,m4 ,longitude #fj deg4 #ad' #ei ,e4 ,latitude #ch deg4 #dh' #jj ,s4 ,ship heading ,,sw x ,s4 ,compass ,bearing #dj deg4 ,variation #ab deg4 ,w4 ,required ,t4,c4 and ,deviation on ship's heading4 ,etc4 ,,wednesday ,,lecture ,,correcting ,,longitude ,,by ,a ,,factor ,we are now almost ready to begin the discussion of a day's work at sea4 ,the only method we have not taken up is the one which is the subject of today's lecture4 ,it is a method to correct your longitude to correspond with the difference between your latitude by ,dead ,reckoning and your latitude by observation4 ,suppose you take a sight in the morning for longitude4 ,the only latitude you can use is a ,d4 ,r4 latitude1 advanced from your last known position4 ,now suppose you run until noon and at that time take a sight for latitude4 ,in comparing your ,d4 ,r4 latitude1 advanced the true course and distance steamed to noon1 and your latitude by observation taken at noon1 suppose there is a difference of several minutes4 ,the question is--,how can we correct our longitude to correspond with this error discovered in the latitude8 ,this is the method which put in your ,note-,book3 ,find the difference between the latitude by ,d4 ,r4 and the corresponding latitude by observation 7in most cases secured from a sight at noon or from the ,star ,polaris74 ,call this the ,error in ,latitude4 ,with the ,d4 ,r4 ,latitude of the preceding sight and the azimuth or bearing of the preceding sight 7always expressed as a bearing of less than #ij deg41 old compass reading7 enter ,table #dg for the correct ,longitude ,factor4 ,multiply this ,factor by the ,error in ,latitude4 ,the result is the correction to apply to the ,longitude4 ,it is applied ,east or ,west according as to whether the ,latitude by ,observation is to the ,east or ,west of the ,d4 ,r4 ,latitude on the ,line of ,position 7the line at right angles to the ,azimuth7 of the preceding sight4 ,example3 ,position about #g3cj ,a4,m4 ,latitude by ,d4 ,r4 #be deg4 #dj' ,s1 ,longitude 7just secured by observation7 #ajd deg4 #je' #ch ,e4 ,l4,a4,t4 #g;h #cbm #cjs ,a4,m41 ,declination #d deg4 #ei' ,n4 ,thence ship ran to noon #aji deg41 true course1 #df miles1 when the latitude by meridian altitude of the sun was found to be #be deg4 #eb' ,s4 ,required corrected 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 in ,lat4 #c' ,enter ,table #dg with azimuth 7,s #aje deg4 ,e7 ,n #ge deg4 ,e as bearing and ,latitude #be deg4 #dj' or #bf deg41 ,factor is found to be 4#c4 #c' 7,error in ,latitude7 times 4#c 7,factor7 4#i' or #ed1 ,correction in ,longitude4 ,is it ,east or ,west8 ,since azimuth is ,n #gd deg4 ,e1 ,line of ,position is ,n #af deg4 ,w4 ,the ,d4 ,r4 ,latitude and ,latitude by ,observation are plotted on this line as follows3 99 ,lat4 by obs4 7#be deg4 #eb' ,s7 99 ,lat4 by ,d4,r4 7#be deg4 #ee' ,s7 ,latitude by observation is ,west of ,latitude by ,d4,r4 ,hence correction in longitude of #ed is applied ,west4 ,position by observation1 therefore1 is as follows3 ,lo4 #ajd deg4 #ec' #ef ,e ,corr4 in ,lo4 #ed ,w -------------- ,lo4 by obs4 #ajd deg4 #ec' #jb ,e ,lat4 by obs4 #be deg4 #eb' ,s ,note to ,instructor3 ,assign the following examples for work in the class room3 #a4 ,april #bjth1 #aiai ,a4,m4 at the ship4 ,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' ,west4 ,ship then sailed a true course of ,s #cf deg4 ,e--#dj knots until noon when observed altitude 77 #ge deg4 #dj' #ej ,s4 ,what was the position at noon corrected for ,longitude8 7,note3 ,work the ,a4,m4 sight by both ,time ,sight and ,marc ,st4 ,hilaire ,method47 #b4 ,june #beth1 #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 fast4 ,,ie #b' #cj off arc4 ,,he #cf ft4 77 #g deg4 #cd' #bj4 ,log registered #aad4 ,true course to noon ,s #gf deg4 ,e4 ,log registered #agd4 ,same ,,ie1 ,,he1 ,,cc4 ,observed altitude 77 #bi deg4 #dd' #dj ,n4 ,required position at noon by ,longitude factor4 7,note3 ,work ,a4,m4 ,sight by ,marc ,st4 ,hilaire ,method47 #c4 ,at sea1 ,may #cjth1 #aiai4 ,in ,d4 ,r4 ,latitude #ch deg4 #ad' #bi ,n4 ,longitude #ae deg4 #ch' #di ,w4 ,observed altitude 77 #ci deg4 #je' #dj and bearing 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 fast4 ,changed course to #id deg4 p4s4c4 and steamed #ge knots to about #h o'clock4 ,,wt #h;h #jfm #ahs4 ,c-,w #a;h #cim #ehs4 ,at this time observed altitude of ,star ,arcturus #fh deg4 #cj' #dj1 ,east of meridian4 ,same ,,ie1 ,,he1 ,,cc4 ,changed course to #ie deg4 7true74 ,steamed #fj knots until midnight when ran into heavy fog4 ,slowed down to #g knots per hour until #h ,a4,m4 when observed altitude 77 #dh deg4 #de' #aj4 ,,ct #i;h #dem #ahs ,a4,m4 ,same ,,he1 ,,ie1 ,,cc4 ,required fix at #h ,a4,m4 by ,marc ,st4 ,hilaire ,method1 laid down on chart4 ,note to ,instructor3 ,spend rest of period in familiarizing pupils with laying down runs and intersecting lines of position on ,mercator plotting charts4 ,,thursday ,,lecture ,,the ,,navigator',s ,,routine--,a ,,day',s ,,work ,,at ,,sea ,you are now familiar with the principal kinds of sights and the methods used in working them as explained in the foregoing pages4 ,this information1 however1 relates only to each individual kind of sight4 ,today ,i will explain briefly how those sights are made use of in your daily work at sea4 ,such an explanation necessarily cannot include the navigator's work under all conditions and on all classes of ships4 ,it merely gives a brief outline of and a few suggestions relating to navigating conditions on board a medium-sized transport1 in time of war4 ,i say in time of war because navigating then is different1 to some extent1 from the ordinary routine in time of peace4 ,suppose you are ordered to a ship as navigator4 ,what are your duties 7a7 before leaving port1 7b7 while at sea1 and 7c7 on entering pilot waters8 7a7 ,before ,leaving ,port ,ascertain the height of the eye of the bridge and any other place on the ship where you would be likely to take sights4 ,have posted in the chart room and on the bridge the deviation of the compass on each #ae deg4 heading1 so that it can be easily referred to4 ,keep in each chronometer case or in a book nearby the error and daily rate of all chronometers on board4 ,test each sextant for index error and record the result where you can refer to it easily4 ,see that all charts of the harbor out of which you are to steam are corrected to date and are familiar to you1 both as to sailing directions and buoys1 and also as to lights and other aids to navigation4 ,examine1 in detail1 the steering engine and steering apparatus4 ,in case of its disarrangement your intimate knowledge of it may be most valuable4 ,see that the patent log and sounding machine are in good order4 ,see that the lead lines are well soaked in water1 stretched1 and properly marked4 ,see that the lighting system in the chart room and the navigator's room is such that when any door is not tightly closed the lights in the room are extinguished4 ,likewise1 when the doors are closed1 see that the lights will light and without repeated slamming of the doors4 ,if possible1 provide yourself with a flashlight set back in a metal tube so that the rays of the light are not diffused but can be focussed only on one spot at a time4 ,see that your charts are arranged neatly in the drawers provided for them in the chart room4 ,if1 as is usual1 the charts must be folded to get them in the drawers1 mark them legibly on the outside and in the same place on each chart4 ,put in the top drawers those charts you know you will use most frequently4 ,this will save endless time and confusion4 ,be sure you have a full complement of necessary instruments1 including sextants1 a stadimeter1 binoculars1 watches1 stop watch1 dividers1 parallel rulers1 pencils1 work books2 also all necessary books1 such as smooth and deck log books1 several volumes of ,bowditch1 ,nautical ,almanacs1 ,azimuth ,tables1 ,pilot books1 ,light and ,buoy lists1 ,star ,identification ,tables1 etc4 ,you will be repaid a thousand times for whatever effort you expend to have your navigational equipment complete to the smallest detail4 ,the shortage1 for instance1 of a pair of dividers would be an unending annoyance to you4 ,this is also true of almost any other item mentioned above4 ,prepare yourself1 then1 while you are in port and have plenty of opportunity to secure the equipment you desire4 7b7 ,while at ,sea ,the least amount of work required of a navigator in time of peace would include 7#a7 a morning sight for longitude1 7#b7 a noon sight for latitude1 7#c7 an afternoon sight for longitude1 7#d7 an ,a4,m4 azimuth to check the deviation of the compass1 and 7#e7 the dead reckoning for the day's run from noon to noon4 ,navigating in war time requires more work than this4 ,if possible1 the ship's position must be known accurately at any time of day or night for1 in case of an emergency1 the lives of all on board may be imperilled by inaccurate knowledge of your whereabouts4 ,this means that more sights must be taken and more celestial bodies observed4 ,while every navigator has his own idea as to the proper amount of work to do in a day1 it would seem as though the following would cover the minimum amount of work necessary under present conditions3 #a4 ,an ,a4,m4 sight of the sun for longitude4 #b4 ,an azimuth of the sun for checking the deviation of the compass1 taken right after the ,a4,m4 sun sight4 #c4 ,the watch time of ,local ,apparent ,noon4 #d4 ,ex-meridian and meridian altitudes of the sun for latitude4 #e4 ,a ,p4,m4 sight of the sun for longitude4 #f4 ,an evening twilight sight of three or four stars1 preferably one in each quadrant4 ,if these altitudes are taken correctly your position can be found to the dot4 #g4 ,a morning twilight sight for a fix or1 at least1 for latitude by ,polaris4 #h4 ,the dead reckoning from noon to noon4 #i4 ,distance run during the last #bd hours1 from noon to noon #aj4 ,distance to destination4 #aa4 ,set and drift of the current4 #a4 ,the ,a4,m4 ,sun ,sight ,in order to make this a valuable sight for longitude it should be taken when the sun is on or as near as possible to the prime vertical4 ,as the sun1 in ,north latitudes1 passes the prime vertical before sunrise in the winter1 the following remarks do not hold for that season4 ,in winter the only rule to follow is to observe the sun as soon as it is #aj deg4 or more above the horizon4 ,in summer find out from the ,azimuth ,tables the local apparent time when the sun will bear #ij deg44 ,estimate1 as closely as possible1 the longitude you will be in the next morning when the local apparent time is as just found in the ,azimuth ,tables4 ,this can be done by calculating the dead reckoning from the previous sight1 or1 what is even simpler1 laying the distance off on the plotting chart4 ,with this information find the ,w4,t4 corresponding to the ,l4,a4,t4 mentioned above by some such formula as this3 ,l4,a4,t4 - ,lo4 ,g4,a4,t4 - ,eq4 ,t4 7sign reversed7 ,g4,m4,t4 - ,c4,c47sign reversed7 ,c4,t4 - 7,c-,w7 ,w4,t4 ,this will not be absolutely accurate1 for the longitude you are in is only approximate1 but it will be close enough for good results4 ,this resulting ,w4,t4 will be the time to take the ,a4,m4 sight4 ,about fifteen minutes before that time compare your watch with your chronometer to get the ,c-,w4 ,also bring up the ,c4,c4 to date and make a note of it so that as much as possible of this detail work is accomplished before the sight is taken4 ,next1 take your sextant and test it for index error4 ,this should be done regularly before each series of sights as it is impossible to tell what may have happened when the sextant is lying idle1 except by the above test4 ,now1 with your sextant1 watch and notebook1 go to the place from which you have decided to take your observations and1 at the proper watch time1 start taking your altitudes4 ,it is always advisable to take a number of sights1 closely following each other1 so that an error in one may be corrected somewhat by the others4 ,take at least three sights in close succession4 ,at the same time have the log read and enter it in your notebook4 ,an equally good method in fair weather is to secure the distance run from the revolutions of the propeller4 ,having taken your sights1 go to the standard compass and get a bearing of the sun1 at the same time noting in your book the ,w4,t4 of the bearing and the compass heading of the ship4 ,you are now ready to go below into the chart room and work out your position4 ,what method shall you use8 ,that depends upon your preference4 ,you have missed the point of the previous lectures1 however1 if you forget that the ,new ,navigation is based upon the ,marc ,st4 ,hilaire ,method1 and this is undoubtedly the method your captain will prefer you to use if he is an ,annapolis graduate4 ,in this connection let me remind you again of the one fact1 the oversight of which discourages so many beginners with the ,marc ,st4 ,hilaire ,method4 ,the most probable fix1 which you get by one sight only1 is not actually a fix at all4 ,nor does any other method give you an accurate fix under like conditions4 ,what the most probable fix is1 and all it claims to be1 is a point through which the required ,sumner line is to be drawn4 ,if your ,d4,r4 position happens to be only one mile away from the most probable fix1 that is no assurance that the most probable fix is near the actual position of the ship4 ,you may be #be miles away from it4 ,but the important information gained is that1 though you may be #be miles away1 you know on what line you are1 and when this line is later crossed with another line of position that fix will be accurate4 ,two sights make a fix is the whole matter in a nutshell4 #b4 ,the ,compass ,error ,having secured your morning sight1 the next duty is to get the compass error4 ,from your morning sight computation you know the watch time corresponding to the ,l4,a4,t4 of the same sight4 ,find the difference between the two and apply this difference to the watch time of the compass azimuth4 ,that will give you the ,l4,a4,t4 with which to enter the ,azimuth ,tables to get the true bearing corresponding to the compass bearing recently observed4 ,apply the variation from the chart to get the magnetic bearing4 ,the difference between this magnetic bearing and the compass bearing will be the required deviation1 which you should compare with your ,deviation ,table4 ,if there is a marked difference1 and you are sure of your figures1 use the new deviation in computing courses on this heading of the ship4 #c4 ,the ,watch ,time of ,local ,apparent ,noon ,you are now ready to figure the watch time of local apparent noon4 ,unless you have a decided preference to the contrary1 do this by the method explained in the ,saturday ,lecture1 ,week ,,vi4 ,do not forget that in subtracting the ,l4,a4,t4 of the morning sight from #bd hours to get the total time to noon1 in case the ship were stationary1 you do not use the ,l4,a4,t4 of the ,d4,r4 position1 but the ,l4,a4,t4 found by subtracting from ,g4,a4,t4 the longitude of the most probable fix4 ,this will give you the ,l4,a4,t41 based on the longitude of the most probable fix1 which will be slightly different from the ,l4,a4,t4 based on the ,d4,r4 longitude4 ,when you have secured the watch time of local apparent noon1 subtract #cj minutes from it and notify the quartermaster that at that time by your watch the deck clocks are to be set to #aa4cj ,a4,m4 ,if this change of time is very great 7providing you are on an almost easterly or westerly course71 it is wise to have the clocks set back in the night watches to allow for most of the time you figure you will lose4 ,this will not work such a hardship or such an advantage to the officers and men who have the forenoon watch and will also be easier for the cooks4 ,the clocks can then be slightly but accurately changed at #aa4cj ,a4,m41 as mentioned above4 #d4 ,ex-,meridian and ,meridian ,altitudes ,you know the principles and methods governing sights of this character4 ,to know your latitude exactly at noon is usually required when you are steaming in convoy1 for at that time your position signals are hoisted1 and it is a matter of pride with the navigator not only to have his position exact but promptly4 ,if your ,a4,m4 sight was taken when the sun was on or near the prime vertical1 a change in latitude at noon will make no change in longitude4 ,hence you can figure your longitude at noon just as soon as you have secured the corrected time from the ,a4,m4 sight to noon 7which you have done right after working the ,a4,m4 sight74 ,you will have your longitude1 then1 before you go on the bridge to observe for ex-meridian and meridian altitudes4 ,sharply at noon you take your meridian altitude and tell a messenger to notify the captain that it is noon at the ship4 ,the captain then orders eight bells struck1 and you are ready to hand in your noon report1 consisting of latitude and longitude by observation1 latitude and longitude by dead reckoning1 deviation of the compass on the ship's head at #h ,a4,m41 distance made good since the preceding noon1 distance to destination1 set and drift of current 7,note3--,when steaming in convoy this is unnecessary and usually omitted71 and any other pertinent remarks4 ,if the sun was not taken on or near the prime vertical at the time of the ,a4,m4 sight1 take out your longitude factor for the coming noon position and calculate your ,d4,r4 latitude at noon4 ,by correcting the longitude of the ,a4,m4 sight1 run to noon1 with the difference of longitude1 readily found at noon with the longitude factor and the error in latitude1 you will have the correct noon longitude to hand in1 with only a moment's delay4 ,it will be very hard1 however1 to get all this information in on time without the use of latitude constants4 ,there is no room for a discussion of these constants here1 but they are easy to work and you should learn how to use them4 ,the information is in ,bowditch ,art4 #cbe1 p4 #abh1 and ,art4 #dje1 p4 #aha4 #e4 ,the ,p4,m4 ,sun ,sight ,this is another longitude sight and so any previous remarks about sights of this character are applicable here4 ,if the day is fine you need not work out this sight until after evening twilight1 for a fix then by stars will give both latitude and longitude1 whereas your afternoon sun sight will only give you a longitude4 ,this ,p4,m4 sun sight is a good check sight1 to be used or not1 according as to whether other earlier or later sights have been obtained4 #f4 ,the ,evening ,twilight ,sight ,the beauty of using stars is that by almost simultaneous altitudes of different ones you can ascertain your position1 both as to latitude and longitude4 ,in the ,north ,atlantic during the summer months ,vega1 ,deneb or ,altair in the ,east1 ,antares or ,deneb ,kaitos in the ,south1 ,arcturus in the ,west1 and ,polaris1 ,mizar1 or ,kochab in the ,north form an ideal combination which includes every quadrant of the compass4 ,in the winter months1 ,capella1 ,castor or ,pollux in the ,east1 ,sirius or any star in ,orion's belt in the ,south1 ,deneb in the ,west1 and ,polaris in the ,north are equally as good4 #g4 ,the ,morning ,twilight ,sight ,in clear weather this should be primarily a sight for latitude1 since the ,a4,m4 sun sight for longitude will follow it4 ,a latitude by ,polaris1 and at the same time some star in one of the southern quadrants1 as a check1 will give admirable results4 #h4 ,the ,dead ,reckoning from ,noon to ,noon ,if there is no change of course in the late forenoon1 as is usually the case1 the dead reckoning for the day's run can be figured any time before noon so that it will be all ready to hand in to the captain with the other noon data4 ,it is much easier to lay this off on the chart than to go to the trouble of calculating it by ,table #b1 ,bowditch4 ,on the other hand1 such a calculation checks the chart work and should be worked out if you wish to make assurance doubly sure4 #i4 ,distance ,run ,during the ,last #bd ,hours ,here1 again1 an answer by chart and an answer by figures is a good thing to secure4 ,as you become accustomed to your work you will find the answer by chart infinitely easier and quicker to get4 ,it is just as accurate1 too1 if you lay the distances off carefully with the dividers and parallel rulers4 #aj4 ,distance to ,destination ,the same remarks as are made under 7#i7 hold true here4 #aa4 ,set and ,drift of ,current ,find the difference between your ,d4,r4 position and your position by observation at noon1 i4e41 the course and distance from your ,d4,r4 position to your position by observation4 ,the course is the set of the current1 the distance the amount of drift1 all of which is easily calculated by ,table #b1 ,bowditch4 ,this difference between the two positions is seldom due to current4 ,it is due to all errors of steering and the like4 ,but these are all ascribed to current1 for the sake of convenience4 ,this calculation of the current is seldom used now1 particularly when steaming in convoy4 ,it is obvious that a schedule1 such as outlined above1 cannot be adhered to in all kinds of weather or under all conditions4 ,it is merely an outline of what might properly be included in a #bd hour day1 the weather conditions of which will lend themselves at any time to taking the observations mentioned4 ,the weather of each succeeding day may force you to adopt a different routine4 ,nevertheless1 the closer you can keep to the above schedule the more exact will your various positions be4 7c7 ,on ,entering ,pilot ,waters ,see that all charts of the locality you intend to enter are corrected to date4 ,study these charts carefully1 making notes1 in detail1 of the aids to navigation that you intend to pick up4 ,in noting lights give their distinctive appearance1 range of visibility1 approximate time of sighting them1 and any other information that you think you may need4 ,if you have this information with you when on the bridge it will save much time and trouble that you would otherwise have to spend1 at possibly a critical time1 in the chart room4 ,see that log lines1 sounding machine1 etc41 are in order for instant use4 ,remember that in entering pilot waters the safest landmarks are permanent ones4 ,buoys1 cans1 etc41 may drag from their positions or be lost altogether4 ,this can also happen to lightships4 ,become familiar with soundings1 rise and fall of the tides1 and the like1 in the neighborhood in which you intend to anchor4 ,if possible choose an anchorage that will enable you to get bearings from two or three fixed points on shore4 ,as soon as possible after anchoring secure your bearings by pelorus and have them checked up by the quartermaster at regular intervals4 ,this will determine how much1 if any1 dragging has taken place4 ,lastly1 always remember that no amount of advice can make up for your own carelessness4 ,hold yourself ready for any emergency1 keep cool1 keep patient and keep pleasant4 ,common sense is the best antidote in the world for strange situations4 ,if you have that1 and the knowledge you should have secured from these lectures1 you cannot go far wrong4 ,while the day's work which follows does not include every sight in regular sequence as given in the above discussion1 it will give a fair idea of the navigator's work during a day's run4 ,put it in your notebook4 7,note to ,instructor3--,spend the rest of the period in explaining carefully each step of this example47 ,a ,,day',s ,,work ,,at ,,sea ,departure taken from noon position ,jan4 #beth1 #aiai1 in ,latitude #cj deg4 #ja' ,n1 ,longitude #gc deg4 #dg' #bj ,w4 ,course p4s4c4 ,,ne #c_/d ,n4 ,deviation #b deg4 ,e4 ,variation #d deg4 ,w4 ,log registered #bj4 ,ship continued on this course until about #f3cj ,p4,m4 when log registered #ih and observed altitude of ,star ,rigel1 ,east of meridian1 #ci deg4 #cf' #bj4 ,,wt #f;h #ccm #ais ,p4,m4 ,c-,w #d;h #eem #jds4 ,,cc #bm #afs slow4 ,,he #cg ft4 ,,ie #j' #bj off arc4 ,changed course to #dj deg4 7true7 and steamed until #c ,a4,m4 when log registered #aih4 ,at this time ship ran into heavy ,,ne gale4 ,slowed down to #g knots per hour until about #h3cj ,a4,m4 when observed 77 #ah deg4 #be' #aj and bearing by compass ,s #df deg4 ,e4 ,variation #g deg4 ,w4 ,,wt #h;h #cam #afs ,a4,m4 ,c-,w #d;h #eem #jds4 ,,ie #j' #aj4 ,same ,,he1 ,,cc4 ,ship then steamed on true course of #ci deg4 at #g knots per hour until noon when log registered #bfa and observed meridian altitude 77 #cg deg4 #ei' ,s4 ,same ,,ie 7 #j' #aj71 ,,he1 ,,cc4 ,required3-- #a4 ,position by ,d4 ,r4 at noon4 #b4 ,position by observation at noon 7corrected for ,longitude by a factor74 #c4 ,deviation of compass at #h3cj ,a4,m4 #d4 ,watch ,time of ,local ,apparent ,noon4 7,see ,next ,page7 ,at ,sea1 ,jan4 #be1 #aiai4 ,lat4 in #cj deg4 #ja' ,n ,lo4 in #gc deg4 #dg' #bj ,w ,steamed until #f3cj ,p4,m4 ,course ,dist4 ,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 in #ca deg4 #jd' #ed ,n ,lo4 in #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 of 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 ,toward4 ,illustration3 ,,tz ,n #ace deg4 ,e1 ,s #de deg4 ,e ,course ,dist ,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 in #cj deg4 #dg' #cf ,n ,lo4 in #gb deg4 #ce' #ej ,w ,changed course to #dj deg4 7true7 ,course ,dist ,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 in #cb deg4 #cc' #db ,n ,lo4 in #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 ,toward ,illustration3 ,,tz ,n #abh deg4 ,e ,s #eb deg4,e ,course ,dist4 ,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 in #cb deg4 #ca' #ed ,n ,lo4 in #gj deg4 #dg' #ej ,w ,bearing of ,sun by ,compass ,s #df deg4 ,e ,true ,bearing of ,sun ,s #eb deg4 ,e ------- ,total ,error #f deg4 ,w ,variation #g deg4 ,w ----- ,deviation #a deg4 ,e ,course ,dist4 ,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 in #cb deg4 #ej' #ed ,n ,lo4 in #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 reversed7 #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 in 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 ,since ,obs4 ,lat4 is ,east of ,d4,r4 ,lat4 on ,line of ,pos4 ,lo4 ,diff4 is applied ,east4 _/ ,lo4 by ,d4,r4 #gj deg4 #bi' #bf ,w _/ ,lo4 ,diff4 #h #ej ,e ,obs4 ,lat4 99 ------------ _/ ,lo4 in at ,noon #gj deg4 #bj' #cf ,w ,d4,r4 ,lat4 99 _/ _/ ,by ,dead ,reckoning from ,noon to ,noon ,course ,dist4 ,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 in #cc deg4 #aj' ,n ,lo4 in #gj deg4 #ea' #bj ,w ,min4 ,lat4 #ca deg4 #ce' ,the ,watch ,time of ,local ,apparent ,noon ,date--,jan4 #bf1 #aiai ,g4,a4,t4 of ,a4,m4 ,sight #a;h #afm #jds ,lo4 in ,t4 of ,a4,m4 sight #d #dc #ab ----------- ,l4,a4,t4 #bj;h #cbm #ebs ,total ,time to ,noon #c;h #bgm #jhs ,course to ,noon -- #ci deg4 ,change in ,lo4 per 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 of ,a4,m4 sight #h #ca #af ,a4,m4 ---------- ,w4,t4 of ,l4,a4,n4 #aa;h #egm #jds ,a4,m4 ,,answer4 ,by ,d4,r4 ,lat4 #cc deg4 #aj' ,n ,lo4 #gj deg4 #ea' #bj ,w ,by ,observation ,lat4 #cc deg4 #jj' #bf ,n ,lo4 #gj deg4 #bj' #cf ,w ,dev4 at #h3cj ,a4,m4 #a deg4 ,e ,w4,t4 of ,l4,a4,n4 #aa;h #egm #jds ,a4,m4 ,,friday ,,lecture ,,day',s ,,work ,at sea1 ,november #bhth1 #aiah4 ,departure taken at noon in ,latitude #bj deg4 #ej' ,n1 ,longitude #gc deg4 #ae' #bj ,w4 ,log at noon registered #cd4 ,sailed on course p4s4c4 #gc deg41 ,deviation #c deg4 ,e1 ,variation #a deg4 ,w until twilight when log registered #aeb4 ,changed course to ,e #c_/d ,n p4s4c4 and observed altitude of ,star ,aldebaran1 ,east of meridian #cg deg4 #aj' #aj and bearing by compass ,n #hi deg4 ,e1 ,variation #b deg4 ,w4 ,,wt #h;h #ajm #afs4 ,c-,w #d;h4 #eam #cjs4 ,,cc #dm #jhs slow4 ,,ie #a' #aj off the arc4 ,,he #ch ft4 ,ship steamed on this course1 in heavy fog and rain1 until #b3cj ,a4,m4 when log registered #bjj4 ,ship changed course to ,e #a_/b ,n 7true7 and steamed at #h knots per hour until #f3cj ,a4,m4 when weather cleared and observed altitude ,star ,polaris #ba deg4 #jd' #bj ,n4 ,,wt #f;h #cem #dgs ,a4,m4 ,c-,w #d;h #eam #cjs4 ,same ,,ie1 ,,he and ,,cc4 ,ship continued on same course and speed until about #i3cj ,a4,m4 when observed altitude of 77 #ch deg4 #de' #bj4 ,,wt #i;h #cim #ajs ,a4,m4 ,c-,w #d;h #eam #cjs4 ,same ,,ie1 ,,he and ,,cc4 ,ship then steamed a true course of #ic deg4 at a rate of #aj knots per hour until noon when log registered #bid and observed meridian altitude 77 #df deg4 #di' #cj4 ,same ,,ie1 ,,he and ,,cc4 ,required #a4 ,d4 ,r4 position at noon4 #b4 ,position by observation at noon 7corrected for ,longitude by a factor74 #c4 ,deviation at #h3aj ,p4,m4 #d4 ,watch ,time of ,local ,apparent ,noon4 ,,saturday ,,lecture ,,day',s ,,work ,at sea1 ,april #bast1 #aiah4 ,departure taken from noon position in ,latitude #ca deg4 #ej' ,n1 ,longitude #gf deg4 #cj' #ca ,w4 ,log registered #abh at noon4 ,course p4s4c4 until about #d3cj ,p4,m4 was ,n #aj deg4 ,e4 ,deviation #a deg4 ,w4 ,variation #c deg4 ,w4 ,at about #d3cj ,p4,m4 observed altitude of sun's lower limb #be deg4 #ac' #aj and bearing by compass ,n #hg deg4 ,w4 ,,wt #d;h #bfm #dfs4 ,c-,w #e;h #jdm #ebs4 ,,cc #am #jcs slow4 ,,ie #j' #aj off arc4 ,,he #bi ft4 ,log registered at this time #ahh4 ,course was then changed to ,,ne x ,n 7true74 ,weather cloudy4 ,at about twilight clouds broke away and observed altitude of ,star ,procyon ,west of meridian #dj deg4 #ja' #jj4 ,,ct #a;h #cgm #bhs ,a4,m4 ,,cc #am #jcs slow4 ,,ie #j' #aj off arc4 ,,he #bi ft4 ,log registered #bcf4 ,continued on same course until midnight1 at which time log registered #bij4 ,at midnight ship ran into dense fog and slowed down to #h knots until about #f3cj ,a4,m41 when fog blew away and observed altitude of ,star ,polaris #ce deg4 #bi' #aj ,n4 ,,wt #f;h #cbm #ads ,a4,m4 ,c-,w #d;h #eim #jbs4 ,,ie #j' #aj off arc4 ,,cc #am #jcs slow4 ,,he #bi ft4 ,from #f3cj ,a4,m4 ship steamed a true course of ,n #cb deg4 ,e until noon at a rate of #ae knots per hour1 at which time a meridian altitude of the 77 was observed #fe deg4 #cg' #aj ,s4 ,log registered #dbd4 ,,he #bi ft4 ,,ie #j' #aj off arc4 ,,cc #am #jcs slow4 ,required #a4 ,d4 ,r4 position at noon4 #b4 ,position by observation at noon 7corrected for ,longitude by a factor74 #c4 ,deviation of ,compass at #d3cj ,p4 ,m4 sight4 #d4 ,watch ,time of ,local ,apparent ,noon4 ,,week ,,viii--,,navigation ,,monday ,,lecture ,,day',s ,,work ,at sea1 ,nov4 #abth1 #aiah4 ,departure taken from noon position in ,latitude #ci deg4 #dj' ,n1 ,longitude #cc deg4 #bj' #jd ,w4 ,log registered at noon #a4 ,course p4s4c4 was #bid deg4 until about #c3cj ,p4,m41 ,deviation #a deg4 ,w1 ,variation #bd deg4 ,w1 at which time observed altitude 77 #ac deg4 #ee' #aj and bearing by pelorus ,s #gi deg4 ,w4 ,,wt #c;h #bbm #ahs4 ,c-,w #b;h #acm #bj,s4 ,,cc #am #ajs4 ,,ie #a' #aj off arc4 ,,he #cb ft4 ,log registered #df4 ,course was then changed to #bij deg4 p4s4c4 until about #f3cj ,p4,m4 when observed altitude ,star ,polaris #dj deg4 #ae' #dj ,n4 ,,wt #f;h #cbm #ahs4 ,c-,w #b;h #acm #bjs4 ,same ,,he1 ,,ie1 ,,cc4 ,log registered #ij4 ,ship steamed on same course until #a3cj ,a4,m4 when log registered #aif4 ,at #a3cj ,a4,m4 sighted sub4 on port bow4 ,ordered full speed ahead and made #ag knots per hour until #h ,a4,m4 when observed altitude 77 #h deg4 #dj' #jj4 ,,wt #h;h #jam #cjs ,a4,m4 ,c-,w #b;h #acm #bjs4 ,same ,,he1 ,,ie1 ,,cc4 ,ship then steamed a true course of #bgb deg4 at a rate of #ae knots per hour until noon1 at which time observed meridian altitude 77 #cb deg4 #ce' #dj ,s4 ,same ,,he1 ,,ie1 ,,cc4 ,log registered #cfb4 ,required #a4 ,d4 ,r4 position at noon4 #b4 ,position by observation at noon 7corrected for ,longitude by a factor74 #c4 ,deviation of ,compass at #c3cj ,p4,m4 #d4 ,watch ,time of ,local ,apparent ,noon4 ,,tuesday ,,lecture ,,day',s ,,work ,at sea1 ,dec4 #ajth1 #aiah4 ,departure taken from ,latitude #ai deg4 #ej' ,n1 ,longitude #bj deg4 #ja' #bj ,w4 ,noon position4 ,log registered #bj4 ,course p4s4c4 ,n #af deg4 ,e4 ,deviation #b deg4 ,e1 ,variation #ah deg4 ,w4 ,ship steamed on this course until #h ,p4,m4 when changed course to ,n #ah deg4 ,e p4s4c4 and observed altitude ,star ,polaris #bb deg4 #cc' #ad ,n4 ,,wt #h;h #jim #ajs4 ,c-,w #a;h #bjm #jes4 ,,cc #bm #jjs fast4 ,,ie none4 ,,he #ci ft4 ,log registered #ajd4 ,ship then steamed at #ad knots per hour until midnight4 ,at midnight changed course to ,n #ad deg4 ,e p4s4c4 and steamed at #ab knots per hour until #d ,a4,m4 ,at #d ,a4,m4 slowed down to #i knots per hour and steamed at that rate until #h3cj ,a4,m4 when course p4s4c4 was changed to ,n #ag deg4 ,e and observed 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 ,variation #ah deg4 ,w4 ,continued on this course p4s4c4 for two hours1 speed #ab knots4 ,thence steamed a true course of #d deg4 at same speed to noon when observed meridian altitude 77 #db deg4 #cf' #ej ,s4 ,same ,,ie1 ,,he1 ,,cc4 ,required #a4 ,d4 ,r4 position at noon4 #b4 ,position by observation at noon 7corrected for ,longitude by a factor74 #c4 ,deviation of ,compass at #h3cj ,a4,m4 #d4 ,log reading at noon4 ,,wednesday ,,lecture ,,day',s ,,work ,at sea1 ,july #aith1 #aiah4 ,departure taken from ,latitude #dj deg4 #cj' ,n1 ,longitude #de deg4 #jj' #aj ,w4 ,noon position4 ,log registered at noon #fh4 ,steamed until #b3cj ,p4,m4 on a course p4s4c4 #aae deg44 ,deviation #a deg4 ,w4 ,variation #be deg4 ,w4 ,log registered #abe4 ,changed course to #aah deg4 p4s4c4 7,same ,variation and ,deviation7 and steamed until about #e ,p4,m4 ,at about #e ,p4,m4 observed altitude 747 #bb deg4 #dj' #bj and bearing 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 slow4 ,,he #cb ft4 ,log registered #afh4 ,course p4s4c4 was then changed to #aac deg4 until about #h ,p4,m4 when observed meridian altitude of ,star ,vega #hh deg4 #ae' #aj ,s4 ,,wt #h;h #jbm #bfs4 ,c-,w #c;h #jjm #jbs4 ,same ,,he1 ,,ie1 ,,cc4 ,log registered #baj4 ,continued on same course p4s4c4 until about #b ,a4,m4 when observed altitude of ,star ,vega #dg deg4 #ai' #bj ,west of meridian4 ,,wt #b;h #jdm #bds ,a4,m4 ,c-,w #c;h #jjm #jbs4 ,same ,,ie1 ,,he1 ,,cc4 ,log registered #bii4 ,,tz of ,star ,n #hf deg4 ,w4 ,continued on same course until #d ,a4,m4 when log registered #cbi4 ,at #d ,a4,m4 heavy fog and rain forced ship to slow down to #e knots per hour until about #i ,a4,m4 when weather cleared and observed altitude 77 #ea deg4 #eb' #dj4 ,,wt #i;h #jcm #ahs ,a4,m4 ,c-,w #c;h #jjm #jbs4 ,same ,,he1 ,,ie1 ,,cc4 ,thence ship steamed a true course of #hh deg4 at a rate of #ac knots per hour to noon1 when log registered #cid and observed meridian altitude 77 #fi deg4 #eb' #bj ,s4 ,same ,,ie1 ,,he1 ,,cc4 ,required #a4 ,d4 ,r4 position at noon4 #b4 ,position by observation at noon 7corrected for ,longitude by a factor74 #c4 ,deviation of ,compass at #e ,p4,m4 #d4 ,watch ,time of ,local ,apparent ,noon4 ,,thursday ,,lecture ,,day',s ,,work ,at sea1 ,nov4 #beth1 #aiah4 ,departure taken at noon from ,latitude #be deg4 #je' ,n1 ,longitude #cg deg4 #aj' #dj ,w4 ,log registered at noon #cb4 ,course p4s4c4 was #aai deg41 ,deviation #b deg4 ,e1 ,variation #ai deg4 ,w until twilight when log registered #aaj and observed altitude ,star ,polaris #be deg4 #cj' #dj ,n4 ,,ie #a' #aj off arc4 ,,he #bh ft4 ,,wt #e;h #djm #ahs4 ,c-,w #b;h #bhm #aas4 ,,cc #dm #aes slow4 ,changed course to ,,se x ,e #c_/d ,e1 same ,variation and ,deviation1 and steamed on this course until about #h3cj ,p4,m4 when observed altitude of ,star ,markab1 ,west of meridian1 #ei deg4 #dh' #aj4 ,log registered #aeg4 ,,wt #h;h #cdm #dhs4 ,c-,w #b;h #bhm #aas4 ,same ,,he1 ,,ie1 ,,cc4 ,steamed on same course until midnight when log registered #baj4 ,changed course to #aaj deg4 p4s4c4 7same ,variation and ,deviation71 and steamed at #ab knots speed until about #h ,a4,m4 when observed altitude 77 #bc deg4 #je' #aj and bearing by compass ,s #cc deg4 ,e4 ,variation #ai deg4 ,w4 ,,wt #h;h #jdm #ajs1 ,a4,m4 ,c-,w #b;h #bhm #aas4 ,same ,,he1 ,,ie1 ,,cc4 ,continued on same course p4s4c4 at a speed of #ae knots per hour until noon when observed meridian altitude 77 #dd #cj' #ej ,s4 ,same ,,ie1 ,,he1 ,,cc4 ,log registered #cff4 ,required #a4 ,d4 ,r4 position at noon4 #b4 ,position by observation at noon 7corrected for ,longitude by a factor74 #c4 ,deviation of compass at #h3jd ,a4,m4 #d4 ,watch ,time of ,local ,apparent ,noon4 ,,additional ,,lecture ,,compass ,,adjustment ,the aim of this lecture is to give you a very few facts about magnetism in general and compass adjustment in particular4 ,the reason for including the lecture in this book is because of repeated requests on the part of graduates who have been consulted about the adjustment of the compass on their ships and who have realized that their advice might have been more helpful if they had learned more about the matter while at this school4 ,the earth is a huge magnet4 ,it is the effect of the magnetism in the earth upon the compass needle which causes the compass error and makes it necessary to correct it4 ,how can it be corrected8 ,to know that we must first know the fundamental law of magnetism1 namely1 that opposite poles of two magnets attract each other and similar poles repel each other4 ,from which it follows that if we decide to color red1 for instance1 that end of a magnetic needle which points to ,north1 the magnetism of that part of the earth must be considered blue1 i4e41 of opposite magnetism to the north-seeking end of the red magnetic needle4 ,now1 there are various kinds of magnetism which affect a ship's compass4 ,one is from the earth1 another from the iron in the ship1 etc4 ,to discuss them and1 the theoretical cause of them in detail is beyond the scope of this lecture4 ,to correct them1 four sets of magnets are necessary1 two of which are usually found in the binnacle of the compass itself4 ,one is a fore and aft magnet or set of magnets1 the other an athwartship magnet or set of magnets4 ,the third set consists of the two globes of cast iron placed on either side of the compass bowl 7called ,quadrantal ,correctors74 ,the fourth magnet1 or set of magnets1 is to correct the compass in case of severe heeling by the ship4 ,if you are ordered to adjust the compass the first thing to do is to choose a fine day with smooth water4 ,take your ship to a certain spot1 the exact location of which you have found from the chart1 and where you are certain you will have plenty of sea-way in which to swing4 ,set your watch to local apparent time 7which you have calculated before coming out74 ,take from the ,azimuth ,tables the sun's true bearing for every four minutes of the time during which you will be occupied adjusting1 and convert it into the magnetic bearing by applying the variation at the place selected 7secured from the chart74 ,write down in a small book these times and corresponding magnetic bearings4 ,now go to your compass and see that its lubber line is exactly fore and aft and in the keel line of the ship4 ,have another officer who is thoroughly familiar with the pelorus stand by it as the ship is swung4 ,all being ready1 secure the lubber's point of the pelorus at ,north and clamp the sight vane to the sun's magnetic bearing at the time you have figured to take the first heading4 ,starboard or port your helm until at the time calculated the reflection of the sight vane on the pelorus dial cuts on the proper magnetic bearing4 ,the vessel's head will then be pointing to magnetic ,north4 ,if1 now1 the compass were correct it would agree with the pelorus in showing the ship's head to be ,north4 ,if it does not do so1 there is ,deviation in the compass and its amount is the amount of ,deviation on that particular course4 ,suppose the ,deviation were to starboard1 i4e41 ,easterly1 and were due to magnetism in the ship's starboard side4 ,then1 if the magnetism in the ,north end of the needle be considered red1 the magnetism in the starboard side of the vessel1 in order to attract the red end of the needle1 would be considered blue and the ship's magnetism1 with the compass needle included1 would look like this3 ,illustration ,to counteract this blue attractive force on the starboard side1 screw up the athwartship magnet in the binnacle toward the compass dial4 ,its magnetism1 if it were laid on the deck1 would look like this3 ,illustration ,in other words1 as this magnet is moved nearer the compass needle1 by the law of magnetism just given1 the red end of the magnet repels the red end of the compass needle from the starboard side and the blue end of the magnet attracts the red end of the compass needle toward the port side4 ,when the compass needle points to ,north1 as shown by the correct pelorus bearing1 the ,deviation on this heading 7i4e41 ,north7 is corrected4 ,now turn the lubber line of the pelorus to ,east4 ,steady the ship on this heading until the shadow from the pelorus vane at the proper ,l4,a4,t4 cuts the circumference of the pelorus dial at the proper magnetic bearing4 ,the ship's compass should then show the ship's head pointing to ,east4 ,suppose that it does not 7as will usually be the case7 but points to the right of ,east4 ,then the ship's magnetism and compass would look like this3 ,illustration ,to bring the compass needle back to ,north it would be necessary to move up nearer the compass dial the fore-and-aft magnet 7shown below71 whose magnetism would act on the compass needle on this heading of the ship exactly as the athwartship magnet acted on the compass needle when the ship was headed ,north3 ,illustration ,now the ship's compass has been corrected for the ,north and ,east headings respectively4 ,the next correction is for the heading half way between1 i4e41 ,north-east4 ,if there is any ,deviation on this heading1 adjust the cast iron cylinders 7called ,quadrantal ,correctors71 which are on each side of the compass bowl1 by moving them toward or away from the compass until the ship's head by compass is ,north-east at the proper time and bearing by pelorus4 ,the ship's compass has now been corrected for one whole quadrant1 namely1 from ,north to ,east1 and this will suffice for all four quadrants since the relationships of the magnets themselves and the magnetism of the compass needle is the same for any of the other three quadrants as for the first4 ,compass adjustment1 however1 can never be absolutely accurate4 ,for that reason1 it is wise to steam the ship completely around1 steadying on every fifteen degrees by pelorus to determine and keep a record of remaining errors4 ,there is one more correction to make1 i4e41 for the heeling error4 ,this correction is necessary in case the ship is yawing in a sea-way so much that the relationship of the ship's magnetism to the compass needle is decidedly different from what it is when the ship is on a comparatively even keel4 ,it is compensated by a vertical magnet directly underneath 7or over7 the binnacle1 details in regard to which can be secured from ,bowditch ,art4 #abe1 p4 #ec4 ,it must be borne in mind that compass adjustment is not an exact science1 that an adjustment for one latitude is not correct for another1 that anyone of a hundred different causes can affect the magnetism of the ship or of the compass needle1 which in turn directly affects the ,deviation4 ,in this connection1 it would be well to read ,bowditch ,art4 #abi1 p4 #ee4 ,you should also read ,arts4 #aai-acj in which are given1 more fully and in more scientific language1 the contents of this lecture4