Class _Jifit£i Book Copyright}!?. CQEHUGHT DEPOSffi Uttmark's Guide to the United States Local Inspectors Examination for Masters and Mates of Ocean Going Steam and Sailing Ships :: :: :: By CAPTAIN F. E. UTTMARK President of Uttmark's Nautical Academy 8 State Street, New York Professor in Navigation and Nautical Astronomy Author of a New System of Navigation and Nautical Astronomy Text Book on Marc St. Hilaire Method Inventor of Uttmark's Plotting Chart, Etc. Editor Uttmark's Nautical News u Fourth Edition, 1919 Parts I, II and III Published by the Author Price $3.50 ^i^ 5^ COPYRIGHTED 1915 BY FRITZ E. UTTMARK CopyriKhted 1919 by Fritz E. Uttmark hm ^'^ 19^9 ©CI.A515904 '\a.4D ( NATIONAL COLORS WORN BY ALL UNITED STATES VESSELS. ENSIGN . . .■ ¥ ¥ . ■¥¥--¥■¥-*- if V ^ V¥ *'*■ V UNION JACK SMALL CRAFT, STORM, AND HURRICANE WARNINGS storm pi m Northeasterly Southeasterly Southwesterly Northwesterly winds winds winds winds Flags, 8 feet square. Pennants, 8-foot hoist, IS-foot fly NIGHT SIGNALS NE. SE. SW. NW. Hurricane storm storm storm orwholegale I I Small craft I I I k Hurricane For explanation see pageW 158 Flags and Pennants used in the International Code. m '^ m M3 B 'pi 'U 'W Code Signal The backbone of a nation is its oversea commerce, and its strength is her merchant marine, backed and supported by an ade- quate and efficient Navy. To those who follow the maritime pro- fession this work is dedicated. The Author. Captain F. E. UTTMARK k Preface to the First Edition In the venture of placing this volume on an already crowded field the Author wishes to state that he does not pretend to be accomplishing anything new, but if he has managed to furnish a guide to U. S. Local Examinations for Masters and Mates and in a clear, concise and comprehensive, yet scientifi- cally accurate way, handle the subject so that it will be a real help to the student and lighten his work in studying for license as Master or Mate and enable him to pass his examination in a satisfactory manner, this little volume has fulfilled its purpose. Preface to the Fourth Edition The third edition being exhausted, the author takes this opportunity to thank the many students and navigators for their kind remarks and favorable comments on the work. The present edition is re- vised and enlarged and Part II added. This part contains a complete set of problems fully worked out and explained. I hope this edition will be as favor- ably received as the others and be of help and use to the navigator. The Author. Preface The questions contained in this work are to be answered by all applicants for license as Master and Mate of Ocean-going steamships in their examination before the U. S. Local Inspectors of Steam-vessels. The Examiner will select a number of questions from those found in this list, therefore the applicant should be familiar with all the answers belonging to his examination. The applicant for a master's license should be able to answer all the questions, and the applicant for a mate's license should be able to answer those questions marked with an asterisk (*). The exam- ination questions for First, Second and Third Mates are the same. The answers to the various questions in this work are clear, and as short as possible for a com- prehensive explanation. The applicant may use his own words if desired in explaining the diflferent ques- tions, taking care, however, that they contain the full sense of the respective answers. vu The definitions as well as all the other questions and answers are arranged as much as possible in a logical sequence and no attempt has been made to follow the order set forth by any particular Board of Local Inspectors. The applicant must be able to demonstrate pro- ficiency in the theoretical science of Navigation, as well as the practical solution of the problems set by the examiner. Any person with two years' experience in the deck department of a steam vessel is eligible for an Officer's License. Vlll Table of Contents PART L Definitions P^g^, Definitions in navigation and nautical astronomy. Description of the compass, variation and deviation, etc., etc., laws of storms, etc 1 to 47 PART 11. Chapter I. — Instruments Mariner's compass, parallel rulers, dividers or com- passes, log and logline, the log glass, ground log, patent log, pelorus, chronometer and sextant 50 to 56 Chapter 11. Compass error 57 Leeway and current 57 to 58 Chapter III. — The Sailings Plane sailing, spherical sailing, traverse sailing, parel- lel sailing, middle latitude sailing, mercator sail- ing, day's work 59 to 88 Chapter IV. Latitude by sun, moon, planets, pole star and other fixed stars 89 to 100 Chapter V. Logarithms 101 to 104 Chapter VI. Longitude by time sights of the sun. Longitude by equal altitudes of the sun, and longitude by sun- rise and sunset 105 to 115 Chapter VII. Amplitudes, Time Azimuth and Altitude Azimuth 116 to 1S9 Chapter VIII. The Tides 121 to 123 PART HI. Seanumship Page, Engine room bell and telegraph, lead and leadline, managing a vessel in heavy eea, and other nsefol questions relating to the handling of a vessel, etc., etc 125 to 137 Rules of the Road Lights, fog signals, whistles, international code flags, gun and rocket apparatus, etc., etc 139 to 160 Ship's Business Duties of masters and mates, rules for life^boats, lif^ rafts, rules for stowage of hay, oil, etc., etc 161 to 177 Appendix Rules and regulations governing examinations before the Board of Local Inspectors, etc., etc 179 to 196 Alphabetical Index TO PARTS I AND III A Page Aground, what to do 130 Alarm whistle 145 Altitude negative 37 Altitude observed 19 Altitude, true 19 Amplitude, definition of 20 Amplitude, deviation by 39 Anchor, how to bring a steamship to 131 Anchor lights, size of 141 Angles, right, oblique, obtuse, etc 2-3 Arc or angle, complement of 3 Arc or angle, supplement of 4 Arc, definition of 3 Azimuth, definition of 21 Azimuth, deviation by 39 B Beaufort Scale 177 Bell, engineer's 125 Bend in river or harbor, when approaching what to do 145 Bill of lading 175 Boat and fire drill 166 Bottomry 176 Cargo, prohibition of on board passenger steamers 166 Cargo, rules for stowing 137 Chain, how much to pay out in anchoring 132 Channels, what side for steamers to keep 148 Chart, compass diagrams, description of 29 Chart, compass diagrams, difference of 29 Chart, course and distance by 28 Chart, gnomic 22 Chart, Mercator's 21 Chart, nautical 21 Chart, polyconic 22 Charter party 176 Circle, great 4 Circle, small 5 Circle, vertical 5 Co-ordinates 15 xi Page Coastwise steamer, definition of 161 Code signals, international 155-159 Collision Threatened, how to act 134 Collision, what to do after a 135 Compass, compensation 26 Compass conrse, correction of 47 Compass, deviation of 24 Compass, how to place on hoard ship 42 Compass, mariner's, definition of 23 Compass, variation of 24 Conversion of degrees and points 45-46 Cross signalling 146 Cyclone, bearing of center 44 Cyclone, how to avoid center of 44 Cyclone, indication of 44 Cyclone, motion of 43 Dead reckoning latitude 29 Dead reckoning longitude 29 Declination, definition of 10 Departure, definition of 8 Deviation, definition of 24 Deviation, determination of 26 Deviation by distant object 41 Deviation by reciprocal bearings 40 Diagram for shaping course 42 Diagram of variation and deviation 25 Dip, definition of 17 Distress signal 149 Diurnal motions 21 Dock leaving, what to do 145 Dunnage 136 Ecliptic, definition of 14 Equator, definition of 6 Equator magnetic 23 Equinoctial, definition of 14 Fire alarm to engine room 151 Fire, what to do in case of 133 Fog bell 154 Fog, extra precautions 145 Fog signals 145 xii Page Getting under way J^^ Ground Tackle "J Gun and rocket apparatus l^'' H Hay, how to load 151 Heave to with disabled machinery ^^' Heave to in a gale 1*° High water and low water 38 Horizon, artificial *^ Horizon, celestial ^ Horizon, sensible ^^ Horizon, visible *~ Hour circles •^" International code of signals 155-159 L Latitude, celestial 15 Latitude, definition of w Latitude, parallels of ^ Latitude, difference of ° Latitude, by dead reckoning 29 Latitude by ex-meridian of the sun *2 Latitude by fixed stars — 34 Latitude by the moon • • • ^^ Latitude by planet 34 Latitude by Pole star 33 Latitude by sun at meridian 32 Lead line marking of 125 Leak, how to handle 132 Letters, character of 150 Letters, color of ISO Letters, measure of 150 Life boat, carrying capacity of 170 Life boat equipment 167 Life preservers, how to put on 167 Life preservers, material prohibited 173 Life preservers, test of 165 Life raft equipment 169 Life saving signals 159 Lights when aground 142 Lights when handling telegraph cables 142 Light for ocean steamers under way 139 Lights for sailing vessels 140 Lights and shapes shown by vessels not under way 142 xiii Page Lights for towing vessels 140 Lights unanthorized 153 Lights for vessels at anchor 140 Line carrying guns 171 Line-carrying guns, drill required 172 Line of no variation 26 Liquid, how to load 152 Logarithms • 35 Logarithms, advantage of 35 Logarithms, use of 35 Logline markings 43 Longitude, celestial IS Longitude, definition of 7 Longitude, dead reckoning 29 Longitude by equal altitudes 36 Longitude by sun 35 M Making land, what to do 135 Manifest 176 Masters and mates, duties of 162 Master, duties of when ship is under annual inspection 175 Masthead lights 153 Master's monthly report 175 Master's report to local inspector 163 Meridians, definition of 9 Meridians, magnetic 23 N Names on equipment 174 Names, how to paint 150 Navigation, definition of 1 Negative, altitudes 37 Ocean steamships, definition of 161 Octant and quadrant, definition of 30 Octant, adjustment of 30 Oil, inflammable, rules for 152 Parallax 18 Penalties for officers navigating water for which they are not licensed 175 Penalties for navigating a boat outside of waters for which she is licensed 175 Penalties for not keeping rules 163 xiy Page Pilot signals 149 Plane sailing 26 Poles, celestial 13 Polar — distance 10 Pole, elevated 13 Poles, magnetic 22 Poles, terrestrial 9 Propeller action of right-handed 129 Propeller action of left-handed 130 Protest 176 Quadrant and Octant, definition of 30 Quadrant, error of 30 R Racing of propeller 132 Radius 4 Range lights 144 Range light compulsory 154 Ranges for deviation of the compass 42 Range for screen board 154 Refraction 18 Reciprocal bearings 40 Right Ascension 11 River or sound steamer, how to load 151 Ring buoys 173 Rules of the road 139 Rules of the road inland 143 Rudder, lost 128 Sailings, plane 26 Sailings, parallel 27 Sailings, middle latitude 27 Sailings, mercator 27 Sailings, great circle 28 Sail vessels, approaching one another 148 Semi-diameter, augmentation of (moon) 18-19 Sextant, definition of 30 Sextant, error of 30 Sextant, adjustment of 30 Seamanship 125 Search light, rules for flashing 153 Semi-diameter 18 Short turn in narrow channels 131 Shapes and lights shown by vessels not under way 142 Sidereal time • • 11 Signals, misunderstanding of 148 Signal for pilot 149 XT Page Signal for distress 149 Solstitial points 15 Strain of cables, how to relieve 131 Stem light 143 Steamers, passing in the same direction 145 Steamers, meeting obliquely 146 Steam and sail vessel approaching one another 148 Stem, ship's name of, etc 151 Steam whistle, unnecessary sounding of 153 Storm warning signals 158 Station bill 163 Storm oil, rules for 174 Sun, apparent 11 Sun, mean 11 Sunrise and sunset 37 Sumners method 37 T Telegraph, engine room ■" *" Time, apparent li. Time, astronomical 13 Time, civil 13 Time, equation of 12 Time, mean 12 Tropics, definition of 9 V Variation 24 Variation and deviation^ how to apply 42 Vertex of a circle 6 W Wines and spirits, where to stow 166 Z Zenith and Nadir 5 Zenith — distance 20 Alphabetical Index PART II. C Chronometer 55 Chronometer Rates 108 Compass Error 57 Current 58 D Deviation of the Compass by Altitude-Azimuth 120 Deviation of the Compass by Amplitude 116 Deviation of the Compass by Time Azimuths using Azimuths Tables 118 Dividers or Compasses 52 G Ground Log 54 H High Water and Low Water 121 Instruments 50 L Latitude by Ex-Meridan of the Sun 93 Latitude by Meridian Altitude of a Fixed Star 94 Latitude by Meridian Altitude of the Moon 99 Latitude by Meridian Observation of the Sun 89 Latitude by Meridian Altitude of a Planet 97 Latitude by the Pole Star (Polaris) 95 Leeway 57 Log and Log-Line 53 Logarithms 101 Longitude 105 Longitude by Equal Altitude 113 Longitude by Sunset and Sunrise 115 xvii M Mariner's Compass 50 P Parallel Rulers 51 Patent-Log 54 Pelorus 55 Plane Sailing 59 R Rules and Formulas: Day's Work 82 Mercator Sailing 77 Middle Latitude Sailing 71 Parallel Sailing 67 Plane Sailing 62 Trarerse Sailing 65 S Sailings 59 Sounding Machines 55 Spherical Sailing 59 Tides 121 EXAMINATION QUESTIONS AND ANSWERS FOR MASTERS AND MATES OF OCEAN STEAMSHIPS The Master answers all the Questions and the Mates answer those Questions marked with an asterisk (*)» 1. — *What is Navigation? The Science that enahles us to determine our position at sea and to conduct the ship from place to place is in general terms called Navigation, it con- sists of two parts, Navigation and Nautical Astronomy. Navigation according to the first term enables us to determine our position by reference to the Earth and is further subdivided into a. Piloting or Coasting when position is obtained by reference to visible objects on the earth or from soundings of the depth of water and the nature of the bottom; b. Dead Reckoning in which the ship's position is deducted from courses steered and distances run from a given point of departure. 1 UTTMARK'S GUIDE Nautical Astronomy. This term is used for that part of the science which enahles us to determine the ship's position hy observations of the celestial bodies — ^the sun, moon, planets and fixed stars. 2.—*What is a Right Angle? A Right Angle is an angle of ninety degrees (90°) or the fourth part of a circle. All the angles in Fig. 1 are Right Angles. Fig. 1. 3. — *What is an Oblique Angle? An angle greater or less than 90° is called oblique. The angle BAG and BAD (Fig. 2) are oblique angles, c — Fig. 2. 4. — *What is an Obtuse Angle, also an Acute Angle? An angle greater than 90° is called obtuse; less than 90° is called acute. Fig. 3. The angle B A C is an obtuse angle. The angle C A D is an acute angle. 2 DEFINITIONS 5. — *What is a Spherical Angle? An angle formed by inter- section of two great circles is called a spherical angle. The angle C P D (Fig. 4) is a spherical angle. 6. — *What is an Arc? Fig. 4. A part of the circumfer- ence of a circle is called an arc. The curved line A B (Fig. 5) is an arc of the circle ABC A. Fig. 5. 7.—*What is Complement of an Arc or Angle? The difference between an arc or angle and 90° is called complement to that arc or angle. The arc C B (Fig. 6) is the complement to C D. The angle B A C is the comple- ment to C A D. The angle D A B is a right angle. 3 Fig. 6. UTTMARK'S GUIDE 8. — *What is the supplement to an Arc or Angle? The difference between an arc or caigle and 180° is called its supplement. The arc C B (Fig. 7) it J, the supplement to C D. The angle C A B is the Fiff 7 o* ' supplement to C A D. 9. — *What is a Great Circle? A circle whose plane passes through the center of a sphere is called a great circle. All the lines in Fig. 8 arc great circles. Fig. 8. 10.— *What is a Radius? A straight line drawn from the center of a circle to its circumference is called Ra- dius. The lines A B, A C and A D are radius to the circle in Fig. 9. Fig. 9 DEFINITIONS lh—*What are Small Circles? Circles whose planes do not pass through the center of the sphere are called small circles. AB, CD, EF and GH are small circles. (Fig. 10.) Fig. 10. 12. — *What are Zenith and Nadir? The point vertically overhead of the observer is called Zenith and the point vertically beneath is called Nadir. 13. — *What are Vertical Circles? Great circles passing through Zenith perpendic- ular to the Horizon are called Vertical Circles or Verticals, Z is the Zenith. is the place of the ob- server. H H' is the observer's hor- izon. Z V are all vertical circles or Verticals. (Fig. 11.) Kg. 11. UTTMARK'S GUIDE 14. — *What is the Vertex of a great Circle? The point of a great circle which is nearest the pole is called its Vertex, C D is a great circle. P is the Pole to the circle. V is the vertex of the circle C D. (Fig. 12.) 15. — *What is the Equator? Fig. 13. Fig. 12. The Equator is a great circle formed by the intersection with the Earth's surface of a plane perpendic- ular to its axis. The Equa- tor is equidistant from the poles. Every point of the Equator is 90 degrees from the poles. The great circle E Q is the Equator. (Fig. 13.) 16. — *What is Latitude? is the arc of the meridian in- tercepted between the Equa- tor and the given place. Lati- tude is reckoned from the Equator (Lat. 0) and ex- pressed in degrees, minutes and seconds North and South, up to 90° at the Poles. P is the Pole. E Q E is the Equator. ^ig- 1^. The Latitude of a place or position on the Earth L Q or L Q is the Latitude of L. (Fig. 14.) 6 DEFINITIONS 17. — *What are Parallels of Latitude? Parallels of Latitude are small circles formed by in- tersection of planes parallel to the Equator. E Q is the Equator. L U are Parallels of Lat- itude. (Fig. 15.) Fig. 15. 18. — *What is Longitude? The angle at the Pole contained between the meridians of any place or po- sition on earth and a certain meridian assumed to be the first or prime meridian. The Longitude is measured on the Equator and reckoned East or West up to 180°. The meridian passing through the observatory at Greenwich (England) is generally accepted as the first meridian. Fig. 16 illustrates East and West Longitude. 7 Fig. 16. UTTMARK'S GUIDE 19. — *What is Difference in Latitude? The di£ference of Latitude between the two places, A and B, is the arc of a meridian intercepted be- tween the parallels of Lati- tude of the given places and is named North or South ac- cording to the direction from one place to the other. The difference of Latitude between A and B is L L' p,. ^ reckoned South from A or ^^* North from B. (Fig. 17.) 20.— *What is Departure? ^ The Departure is the dis- tance East or West between the meridians of two places or positions and is reckoned in miles. We must note that this distance decreases as the meridians converge towards the poles. The Departure between the meridians of A and B is the distance A C in miles on the Latitude of A or the distance D B in miles on the Latitude of B. (Fig. 18.) 20a. — '^What is Difference of Longitude? The difference of Longitude is the angle between the meridians of two places intercepted at the pole and measured on the equator in degrees and minutes of arc. Fig. 18. 8 DEFINITIONS 21. *Whal; are the Terrestrial Poles? The Terrestrial Poles are the terminal points of the earth's axis around which the earth revolves. P represents the North Pole. P' represents the South Pole. The line P P' represents axis of the earth. (Fig. 19.) Fig 19. t ^ 22. — *What are the Meridians? Meridians are great circles passing through the Poles and cutting the Equator at right angles. The great circles P Q P' Q are all Meridians. E Q is the Equator. (Fig. 20.) Fig. 20. 2S.—*What are the Tropics? Fig. 21. The Tropics are small circles approximately 23^2° from the Equator and mark the extremities of the Sun's declination North and South. A B in the Northern Hemi- sphere is called the Tropic of Cancer. C D in the Southern Hemisphere is call- ed the Tropic of Capricorn. 9 UTTMARK'S GUIDE 24. — *What is Polar Distance? The Polar Distance of a celestial body is its distance from the elevated ^ pole of the observer meas- ured upon the circle of dec- lination passing through the center of the body. It is 90° plus declination if the Latitude of the ob- server and the declination of the body is of opposite name. Fig. 22. but 90° minus declination if of same name. P is the elevated Pole. P S is the Polar Distance of S. (Fig. 22.) 25. — *What is Declination? The Declination of a celestial body is the an- gular distance from the P equinoctial, measured upon the declination circle which passes through the center of the body, it is named North or South according to its direction from the Equi- noctial. E Q is the Equinoctial. S Q is the declination of S. Fig. 23. (Fig. 23.) 10 DEFINITIONS 26. — *What is Right Ascension? The Right Ascension of a celestial body is the angle at the Pole between the hour circle of the body and that of the first point of Aries. It is measured from the first point of Aries East- ward extending up to 360° or 24 hours. P is the Pole. A is the first point of Aries. A S is the Right Ascension of S. Fig. 24. (Fig. 24.) 27.~*What is Sidereal Time? Siderial Time is the hour angle of the first point of Aries. This point which is identical with the vernal equinox, is the origin of all co-ordinates and does not, like the Sun, Moon and the planets have, actual or apparent motion therein. It shares in this respect the properties of the fixed stars. We may therefore say that intervals of Sidereal Time are measured by the stars. 28. — "^What is Apparent Sun? The Apparent Sun is the real visible Sun. Its apparent movement in the ecliptic is irregular, ren- dering days of unequal length. 29. — *What is the Mean Sun? An imaginary Sun is supposed to move in the equinoctial with a uniform velocity equal to the 11 UTTMARK'S GUIDE mean velocity of the true Sun in the ecliptic. This Mean Sun is supposed to coincide with the true Sun at the vernal equinox or the first point in Aries. 30. — *What is Apparent Time? Apparent Time or Solar Time is the hour angle of the center of the Sun. An apparent or solar day is the interval of two successive transits of the Sun. It is apparent noon when the Sun's hour circle coincides with the celestial meridian. This is the most natural and direct measure of time, and the unit of time adopted by the Navigator at sea is the apparent solar day. Sl.—*What is Mean Time? Mean Time is the hour angle of the Mean Sun. A mean day is the interval between two successive transits of the ^ean Sun over the meridian or the mean of all the Solar days in the year. Mean noon is the instant when the Mean Sun's hour angle coin- cides with the meridian. Mean Time lapses uni- formly. At certain times it agrees with the apparent time, while at times it is behind and at other times in advance of the apparent time. Ordinary clocks, and chronometers for use in Navigation are regulated to this time. 32. — *What is Equation of Time? Equation of time is the difference between mean and apparent time. The amount and application may be found in the Nautical Almanac for any given day. 12 DEFINITIONS 33.~*jrAat is Civil Time? Civil Time is the time used in ordinary every- day life. It begins at midnight and ends the fol- lowing midnight, reckoning two periods, A. M. (ante meridian) and P. M. (post meridian) of twelve hours each. (Fig. 25.) ^Jl^ Fig. 25. 34. — *What is Astronomical Time? Astronomical Time is a continuous period of twenty-four hours, beginning at noon and ending at noon the following day. (Fig. 25.) 35. — ^What are the Celestial Poles? The extension of the poles of the earth into space, or the poles of the celestial sphere are called Celestial Poles. 36. — *What is the Elevated Pole? The pole which is above the horizon of the observer, or the pole of the earth of the same lati- tude as the observer, projected into the heavens. 13 UTTMARK'S GUIDE 37. — ^What is the Equinoctial? The Equinoctial or Celes- tial Equator is the great cir- cle formed by extending the Equator of the earth until it intersects the celestial sphere. E Q E is the Equinoctial. (Fig. 26.) Fig. 26. MABCH gljtf'J Fig. 27. 38. — *What is the Ecliptic? The Ecliptic is the great circle representing the path in which the sun, owing to the yearly revolu- tion of the earth, appears to move in the celestial sphere. The plane of the Ecliptic is inclined to that of the Equinoctial at an angle of 23° 27%'. This inclination is called the obliquity of the Ecliptic. C C represents the Ecliptic. (Fig. 27.) 14 DEFINITIONS 39. — *What are the Solstitial Points? The Solstitial points or Solstices are points on the ecliptic 90° from eqpiinoxes at which the sun reaches its highest declination in each hemisphere. They are called Summer or Winter Solstices, accord- ing to the time of the year. (Fig. 27a.) 40. — *What is Celestial Latitude? Celestial Latitude of any point in the heavens is its distance North or South from the ecliptic meas- ured on a great circle at right angles thereto. 41. — *What is Celestial Longitude? Celestial Longitude of any point in the heavens is its distance from the first point of Aries measured on the ecliptic eastward up to 360°. 42. — *What are Co-ordinates? A system of lines, angles or planes, or a comhina- 15 UTTMARK'S GUIDE tion of these used in determining the position of a point from some fixed plane or line adopted as a primary. 43. — *What are Hour Circles? Hour Circles, declination circles, or celestial meridians are great circles of P the celestial sphere passing through the poles. They are therefore at right angles to the equinoctial and may be considered formed by exten-^' tion of the terrestrial merid- ians until they intersect the celestial sphere. P A, P B, and P E are Hour Circles. (Fig. 28.) Fig. 28. 44.- -*What is the Visible Horizon? The Visible Horizon is a small circle limiting the ob- server's view at sea or the intersection of sea and sky. is the point of observa- tion. H H' H'' is the visible hor- izon of 0. (Fig. 29.) Fig. 29. 45. — *What is the Sensible Horizon? The Sensible Horizon is a plane at right angles to the plumb-line at the point of observation in Fig. 30. H H' is the Sensible Horizon. 16 Fig. 30. DEFINITIONS 46. — *What is the Celestial Horizon? The Celestial Horizon is the great circle formed hy a plane passing through the center of the earth at right angles to the zenith of the observer and extended until it intersects the celes- tial sphere. The plane of the Celestial Horizon is par- allel to the plane of the Sen- sible Horizon. H H' in Fig. 31 represents the Celestial Horizon. Fig. 31. 47. — What is the Artificial Horizon? Any liquid in a state of rest forming a reflective surface is an Artificial Horizon. Mercury being generally used for this purpose. 48. — *What is the Dip of the Horizon? The dip of the sea horizon is the angle of de- pression at the point of ob- servation due to the elevation of the observer's eye above the level of the sea, or the angle between the Visible and the Sensible Horizon. In Fig. 32, the angle H O H' is the Dip of the Horizon as seen from the point of ob- servation at O. 17 Fig. 32. UTTMARK'S GUIDE 49. — *What is Refraction? Refraction is the bending of a ray of light when passing through the atmosphere. It renders the observed altitude to appear greater than its real value. The angles S S' is re- fraction. (Fig. 33.) Fig. 33. SO.—*What is Parallax? Parallax is the angle of the earth's radius at the position of the observer as seen from the center of a celestial body. O is the position of the observer. C is the radius of the earth. S is the center of the Fig. 34. celestial body. The angle S C is the Parallax. (Fig. 34.) U PPER LI MB -^- LOWER LIMB 51. — *What is Semi-Diameter? Semi-diameter or half di- ameter is the angular meas- urement of the radius of a celestial object as seen from the observer's position. The angles SOL and S O L' are the Semi-diameters of Fig. 35. S. (Fig. 35.) 18 DEFINITIONS 52. — What is Augmentation of the Moon's Semi' diameter? The Augmentation of the Moon's Semidiameter is the apparent increase due to the decrease in dis- tance from the observer as the moon rises above the horizon. 53. — What is Observed Altitude? The Observed Altitude is the angular height above the horizon as measured by the sextant and expressed in de- grees, minutes and seconds of arc. The angle S O H is the Observed Altitude of S. (Fig. 36.) Fig. 36. 54. — "^What is True Altitude? Fig. 37. True Altitude is the angu- lar height of a point or the center of a celestial body above the rational horizon, as measured from the center of the earth. In Fig. 37. S H' is the True Altitude of S. 19 UTTMARK'S GUIDE 55. — What is Zenith Distance? Zenith Distance is the arc of a vertical circle between the object and the zenith of the observer, or its true alti- tude subtracted from ninety h degrees (90°— Alt.) Z S or the angle Z O S is the Zenith Distance of S'. (Fig. 38.) Fig. 38. 56. — *What is Amplitude? Amplitude is the angle at zenith between the prime vertical and the ver- tical circle passing through the center of the celestial body at the horizon while rising or setting. It is reck- oned from East while rising and from West while setting toward North or South, ac- cording to the declination of Fig. 39. the observed celestial body. Z is the zenith. w H— S' is a heavenly body. The angle E Z S' is the Amplitude of S'. (Fig. 39.) 20 DEFINITIONS 57. — *What is Azimuth? Azimuth is the angle at zenith between the meridian of the observer and the vertical circle passing through the center of the celestial body. It is gener- ally reckoned from North in North Latitude and from South in South Latitude up to 180°, East or West ac- cording to whether the body is East or West of the meridian. In Fig. 40, N S or the angle N Z S, is the Azi- muth of S. Fig. 40. 58. — *What are Diurnal Motions? The movements of the celestial bodies during the 24 hours are called Diurnal or Daily Motions. 59. — *What is a Nautical Chart? A Nautical Chart is a map representing a minia- ture portion of the sea, lakes or navigable rivers with coast lines, depths of water, nature of bottom, lights, lighthouses, buoys, currents and other useful information. There are three kinds, Mercator's^ Polyconic and Gnomic Projection. 60. — ^Describe the Mercator's Chart, On a Mercator's Chart the meridians are made parallel to one another, and the distance between the parallels of latitude is lengthened corresponding 21 UTTMARK'S GUIDE to the widening of the meridians. On this chart the earth is represented as a at surface and the track of the vessel is shown as a straight line. 61.-: — ^Describe the Polyconic Chart. On a chart constructed on the Polyconic projec- tion principle, the meridians converge toward the poles and are in reality curved lines, the degrees of Latitude and Longitude are projected according to their true value. A straight line on this chart rep- resents a near approach to a great circle and cuts all the meridians at a slightly different angle. 62. — Describe the Gnomic Chart. In a Gnomic, or Gnomonic, Chart, the straight line between any two points represents the arc of a great circle, and is therefore the shortest line between those two points. This chart is used in the polar regions where a Mercators Chart can not be con- structed. It is also used for finding the course and distance in great circle sailings. 63. — *What are the Magnetic Poles? All magnets have at each of their extremities, poles of different nature which we designate re- spectively as North and South Poles. The law of Magnetism is that poles of same name repel each other, and poles of different name attract each other. The earth may be considered as a huge magnet with two poles of opposite name. The one in the North- ern Hemisphere is called the magnetic North Pole, 22 DEFINITIONS and the one in the Southern Hemisphere is called the magnetic South Pole. The North Magnetic Pole is situated approximately in Latitude 70° 00' North and Longitude 97° West of Greenwich. The South Magnetic Pole is situated in Latitude 73° 30' South, and Longitude 147° 30' East of Greenwich. A magnetic needle freely suspended and allowed to come to rest unaffected by any local attraction, will do so in the magnetic meridian. 64. — *What are the Magnetic Meridians? The Magnetic Meridians are curved and some- what irregular lines extending between the magnetic poles. 65. — *What is the Magnetic Equator? The Magnetic Equator is the plane of a circle midway between the magnetic poles at right angles to the magnetic meridians. 66. — *What is the Mariner's Compass? The Mariner's Compass consist of a non-magnetic metallic bowl in the center of which is fixed a pivot. A magnetic needle, or generally several pairs of needles, parallel with one another, are so centered and balanced on the pivot that they can freely swing in the horizontal plane and undisturbed by proximity of iron will come to rest in the magnetic meridian. The ship's course is measured by this instrument, and bearings of objects on land as well as amplitudes and azimuths of the heavenly bodies are measured. 23 UTTMARK'S GUIDE 67. — *What is Variation of the Compass? Variation of the Compass is the angular differ- ence between the magnetic meridian and the true merid- ian. It differs in amount and name according to the ob- server's position on the globe. The variation is called West- erly if the North end of the magnetic needle points to the left of the true meridian, and Easterly if the same end of Fig. 42. the needle points to the right hand side of the true merid- ian. Fig. 42 indicates West Var- iation. Fig. 43 indicates East Var- iation. Fig. 43. 68. — *What is Deviation of the Compass? The Deviation of the Compass is the angular difference between the com- pass meridian (the compass North and South line) and the Magnetic Meridian. It is caused by iron in the con- struction of the ship or in her cargo, also by temporary local attraction. Fig. 44. 24 DEFINITIONS Diagrams Showing Variation and Deviation T C VARlAltON IS'WESTERt TOTAUIBROR d*tAaT£iay DEVIATION ;5*eAi7ERl.' C T TOTAL ERROR O'WCiTCIUY. VAJUATION 25 *W£3TEIUT. oEviATioNierwesiEter VAEIAtlON xvxfiaytstvt UTTMARK'S GUIDE Fig. 45. When the North end of the compass needle points to the left of the magnetic meridian the deviation is called Westerly and when the same end of the needle points to the right of the mag- netic meridian the deviation is called Easterly. It differs in amount and name accord- ing to the course the ship is steering. Fig. 44 indicates West Deviation. Fig. 45 indicates East Deviation. 69. — *How would you determine the deviation of the Compass? By amplitudes or azimuths of celestial bodies, by compass bearings of a remote object, by ranges and by reciprocal bearings. 70. — *How is deviation of the Compass Compen- sated? By the employment of artificial magnets placed on or under the deck near the compass, or within the Binnacle Stand. 71. — *What is the Line of No Variation? A line drawn through certain places on the sur- face of the earth where the compass needle points true North or South. 72. — ^Describe Plane Sailing. In plane sailing the curvature of the earth is 26 DEFINITIONS neglected and navigation is calculated on the assump- tion that the earth is an extended plane or flat surface instead of a globe. In plane sailing we consider only the course, distance, the difference of Latitude and Departure. When two or more courses are consid- ered the combination is callet Traverse Sailing. 13.—*Describe Parallel Sailing. Sailing along a parallel of Latitude East or West and converting departure into difference of Longitude is called Parallel Sailing. 74. — ^Describe Middle Latitude Sailing. Find the difference of latitude and the difference of longitude between the ship's place and the port bound to, then convert the difference of longitude into departure by the use of the middle latitude; next with the difference of latitude and departure find in the tables the true course and the distance to be sailed. To this true course apply the variation and deviation of the compass in order to obtain the compass course to steer. This may also be worked out by logarithms. 75. — ^Describe Mercator Sailing. Find the difference of latitude and the difference of longitude between the ship's place and the port bound to, then change the difference of latitude into meridional parts, with which and the difference of longitude find in the tables the true course. On the page of this course enter with the nautical difference of latitude in the latitude column, and opposite to the left in the distance column will be found the distance to be sailed. The variation and deviation of the 27 UTTMARK'S GUIDE compass must be applied to the true course in order to obtain the compass course to be steered. This may also be worked out by logarithms. 76, — Describe Great Circle Sailing. When the ship sails a course along a great circle, it is called great circle sailing. This is the shortest distance between two places and the only course on which the ship is continuously heading direct for the desired port or place. 77. — How do you find Course and Distance by Chart? Find the true course from point to point by the aid of the chart diagram compass and the parallel rules. To the true course apply the variation and deviation of the compass, and the answer will be the course to be steered by the ship's compass. Westerly variation and Westerly deviation are allowed to the right hand, and Easterly variation and Easterly devia- tion to the left hand when converting a true course into a compass course. To find the distance between the place of the ship and the place bound to, set the dividers to 60 miles (more or less according to the scale of the chart) on the side of the chart half way between the latitude of the two places, then see how many times this "set" is contained on the line of the course. On an inland chart, where the variation is practically the same over the whole surface, the cor- rect magnetic course may be found direct from the magnetic diagram compass, thus leaving only the deviation of the compass to be applied by the navi- gator. 28 DEFINITIONS 78. — *Do the Chart Compass Diagrams Represent True or Magnetic Directions? Often times the compass diagrams are double, the outside one being true, and the inside one magnetic. 79. — ^How do True and Magnetic Chart Compass Diagrams Differ? The North and South hue of the true compass diagram coincides with the true meridian; whereas the North and South line of the Magnetic compass diagram inclines at an angle from the true meridian; the angular difference is called Variation. 80. — *How Would You Find Latitude by Dead Reck- oning? Correct the compass courses for leeway, varia- tion, deviation, the send of the sea and current; and take the departure course into consideration. Against each course write the distance sailed and take from the nautical tables the corresponding difference of latitude and departure and apply the difference of latitude to the latitude left. 81. — *How Would You Find Longitude by Dead Reckoning? Using the middle latitude as a course, apply the departure in the latitude column, and find in the distance column to the left the amount of longitude made, which apply to the longitude left. 29 UTTMARK'S GUIDE 82. — *What is an Octant or Quadrant? An instrument of reflection for measuring alti- tudes of heavenly bodies, or angles in general. The arc is graduated in degrees and 15 or 20 minute divi- sions and its vernier in minutes and 15 or 20 seconds of arc. This instrument will read to at least 90 de- grees of arc. It is called an Octant because it is an eighth part of a circle, or a quadrant because and according to the law of reflection we can measure angles of double that amount or 90 degrees of arc. 83. — *What is a Sextant? An instrument of reflection for measuring alti- tudes of heavenly bodies and angles in general. Its arc is generally graduated in degrees and 10 minute divisions, and its vernier in minutes and 10 seconds of arc. It is a sixth part of a circle or 60 degrees and according to the law of reflection we can meas- ure angles of double that amount or 120 degrees of arc. 84. — *How Would You Detect Error in a Quadrant, Octant or Sextant? By going through the process of adjustment for the index mirror and the horizon glass. 85. — ^How Would You Adjust a Quadrant or Sex- tant? The first adjustment is to see if the index glass is perpendicular to the plane of the instrument; this is done by moving the sliding limb to the center of the arc; then note if the arc reflected in the index glass and the arc seen direct form one unbroken line. If 30 DEFINITIONS they do, the index glass is perpendicular, but if not, make this adjustment with the screw on the back of the index glass. The Second Adjustment is to see if the horizon glass is perpendicular to the plane of the instrument; this done by making the two zeros coincide with one another ; then holding the instrument at an angle slightly inclined from the horizontal plane and if the reflected horizon and that seen direct, form an un- broken line, the horizon glass is perpendicular, but if not, make this adjustment with the top screw on the back of the horizon glass. The Third Adjustment is to see if the horizon glass and the index glass are parallel to each other. To do this make the two zeros coincide, then hold the instrument vertically, and if the reflected horizon and that seen direct, form one unbroken line, the glasses are parallel, but if not, make this adjustment with the bottom screws on the back of the horizon glass. If this screw should be broken, or if by some other means this adjustment cannot be made, then make the glasses parallel, using the tangent screw, and the amount the zero of the sliding limb is moved on or off the arc will be the index error, subtractive if on the arc, but additive if off the arc. The Fourth Adjustment is to see that the axis of the telescope is parallel to the plane of the instru- ment. For this adjustment the inverting telescope is screwed in the collar of the instrument, and the tele- scope is turned until the parallel wires are parallel with the plane of the sextant. Two stars are then selected which are at least 90 degree apart, and an 31 UTTMARK'S GUIDE exact contact is made at the wire nearest the plane of the instrument. Next the sextant is moved so as to throw the objects on the other parallel wire, and if the angle remains the same, this adjustment is cor- rect, but if not perfect, the collar adjustment must be made by the screws on the back of the telescope collar. An error in this telescope adjustment always makes angles too great. 86. — *How do you find Latitude by the Sun at Meridian? Correct the observed altitude for dip, refraction, parallax, and semi-diameter, then obtain the zenith distance by subtracting the true altitude from 90 de- grees ; next correct the declination for the Greenwich time of observation, and apply same to the zenith dis- tance, adding, if of the same name, but subtracting, if of different names, and the answer will be the Lati- tude. 87. — How do you find Latitude by Ex-Meridian of the Sun? Observe an altitude as close to noon as possible, and note the time shown by chronometer, which cor- rect for its rate; then apply the equation of time for the given day, so as to obtain the apparent time at Greenwich. Next turn the ship's longitude into time, by the use of Table 7, and add same to the Greenwich time if the ship is in East longitude, but subtract if the ship is in West longitude, and the result will be the local apparent time at ship when the sight was taken. With the sun's declination and the lati- 32 DEFINITIONS tude by dead reckoning, select from Table 26 the change of the sun's altitude for one minute before or one minute past noon, and refer these given fig- ures to the side column in Table 27 ; then under the nearest time from noon will be found the augmenta- tion of the altitude. Correct the observed altitude for dip, refraction, parallax and semidiameter and add the augmentation to this altitude, the result will be the meridian altitude of the sun. Find the zenith distance and apply the declination in the usual way, the result will be the latitude of the ship at the time of sight. 88. — *How do you find Latitude by the Pole Star? Observe an altitude of Polaris at any hour of the night and correct for dip and refraction. Having noted the chronometer at sight, convert same into astronomical time. To this latter apply the ship's longitude in time, adding same if in East longitude, but subtracting if in West longitude, and the answer will be the astronomical time at ship. To this latter add the mean sun's right ascension for Greenwich noon next preceding the time of sight, also add the correction from Table 3 (Nautical Almanac) for the number of hours and minutes from Greenwich noon ; the result will be the local sidereal time. (L. S. T.) From the L. S. T. subtract the stars right ascension. The result will be the star's hour angle. With this hour angle enter the hour angle tables, Nautical Almanac, and find the corresponding correction. Apply this accordingly to its sign, plus or minus, to the star's true altitude. The result will be the lati- tude. Always North. 33 UTTMARK'S GUIDE 89. — *How do you find Latitude by a Planet? To the meridian altitude of the planet apply the corrections for dip, refraction and parallax, and subtract this true altitude from 90 degrees to obtain the zenith distance. Correct the planet's declination according to the time shown by chronom- eter at time of meridian passage, and apply same to the zenith distance, adding if of the same name, but subtracting between them if of different names, and the answer will be the latitude. 90. — How do you find Latitude by the Moon? Correct the observed meridian altitude for semi- diameter, dip, refraction and parallax, then subtract the true altitude from 90 degrees to obtain the zenith distance. Next select the moon's declination for the Greenwich hour at time of sight (expressed as- tronomically), and correct same for the minutes over the hour, which corrected declination is to be applied to the zenith distance, adding same if they are of the same name, but subtracting if of different names, and the answer will be the latitude. 91. — *How would you find Latitude by a Fixed Star? Correct the observed altitude for dip and refrac- tion, and subtract this true altitude from 90 degrees to find the zenith distance. From the Nautical Al- manac take out the declination of the star and ap- ply to the zenith distance following the same rules as for the other heavenly bodies. 34 DEFINITIONS 92. — *JFhat are Logarithms? They are numbers contrived to shorten the labor of multiplication and division by using in their place addition and subtraction. 93. — *How are Logarithms Used? In Navigation they are used the same as simple numbers, and are employed in cases of plane sailing and in working longitude by chronometer-altitude sights, etc. They are also used for extracting roots and raising numbers to any desired power. 94. — *What Advantage is Gained by their Use? They shorten the labor of multiplication or divi- sion of large sums, lessen the chances of mistakes, and enable us to work problems of higher mathemat- ics with ease and saving of time. 95. — *How do You Find Longitude by Morning and Afternoon Time Sights? Observe the altitude of the sun and note the time by the chronometer, correct the observed altitude and apply the chronometer rate, then add together the true altitude, the latitude of the ship by dead reckon- ing, and the sun's polar distance at time of sight; next divide this sum by two, and from this half sum subtract the true altitude and note the remainder. Then select from Table 44 the logarithms secant of latitude, cosecant of polar distance, cosine of the half sum and sine of the remainder. Add these four logs together. This sum represents the log haversine 35 UTTMARK'S GUIDE of the hour angle or the apparent time at ship when the sight was taken, and same will be selected from Table 45. Then apply to it the corrected equation of time so as to reduce it to the mean time at ship. The difference between this and the mean time shown at Greenwich when the sight was taken will give the longitude in time, and this converted into arc will be the longitude of the ship, named West if the G. M. T. is greater but East if G. M. T. is less than the ship's time. 96. — How Do You Find Longitude by Equal Alti- tudes of the Sun? Observe an altitude of the sun about half an hour before noon, and note the chronometer; then wait until the sun falls to the same altitude after noon, and again note the chronometer. Half way between these two chronometer times will be the mean time at Greenwich when it was apparent noon at the ship. Now turn the Greenwich time into apparent time by applying the corrected equation of time for the given day, then the difference between the apparent noon at ship and the apparent time at Greenwich will be the longitude in time, and the same converted into arc will be the ship's longitude. In the interval between the two sights if the ship has sailed towards the sun, the first altitude must be in- creased as many minutes of arc as the ship has sailed miles; but if the ship has sailed away from the sun, the first altitude must be decreased that many miles. If the ship has sailed bo as to alter her longitude, then 36 DEFINITIONS divide this by two and apply to the longitude by observation. This will be the longitude at noon. 97. — How Do You Calculate the Negative Altitude? Add the refraction and dip together and call the sum minus; then add the semidiameter and parallax together and call the sum plus. Now subtract be- tween the two quantities, and minus will result, which will be called the negative altitude for the lower limb. To obtain the negative altitude for the upper limb, add together the semidiameter, dip and refraction and subtract the parallax. 98. — How Do You Find Longitude at Sunrise and Sunset? Note when the sun's lower or upper limb touches the horizon at rising or setting, and observe the time shown at that instant by the chronometer; then add together the latitude by dead reckoning and the sun's polar distance; next subtract the negative altitude (approximately 21' for the sun's lower limb contact and 53' for the sun's upper limb contact) ; divide by two, and add the negative altitude. From this part of the problem the logarithms are selected and the example is worked in precisely the same way as for a regular chronometer altitude sight. 99. — Explain Sumner s Method. Sumner's Method is worked principally when the latitude by dead reckoning is uncertain. The rule is as follows : Assume two latitudes, one of them 30' or 1° greater; and the other the same amount 37 UTTMARK'S GUIDE less than the latitude by dead reckoning. Then observe a regular time sight of the sun and work it twice, using each time one of the assumed latitudes. Mark the two positions on the chart and connect them with a straight line. The ship will be somewhere on this line. Then wait until the sun changes its azimuth two or more points and take another time sight, which work twice as before with the same assumed lati- tudes. Mark these two positions on the chart also, and connect them with a straight line. The lines will cross and their intersection will show the position of the ship at the time of the first sight. If the ship has sailed a certain course after the first sight, then find the ship's position at the time of the second sight as follows: Project from the first position the true course and distance sailed, then draw a line through the point which will be parallel to the first line of position and where this line cuts the second line of position will be the place of the ship at the time of the second sight. 100. — How Would You Find the Time of High Water and Low Water at a Given Place? In the Bowditch Epitome will be found the longitude of the given place, and also the lunar in- terval or tidal constant for high and low water. In the Nautical Almanac, page , against the given date, find the meridian passage of the moon (upper transit) and correct this for the longitude of the given place, adding if the longitude is West or sub- tracting if the longitude is East. The result will be the time of the moon's meridian passage at the given 38 DEFINITIONS place. To this add the high water constant if high water is required or low water constant if low water is required. Should this result in a tide later than the one required, this will indicate that the moon's meridian passage must he taken out for the preceding day or the time of lower transit calculated and then proceed as hefore. 101. — *How Would You Find Compass Deviation by an Amplitude? Observe the sun's bearing by compass, then select its true bearing from Table No. 39 (Bowditch) ; the difference between these two bearings will be the total error of the compass. Plot the two bear- ings on a diagram, then if the true bearing is on the right hand side of the other the total error is Easterly, otherwise it is Westerly. Compare this with the variation given by the chart for the ship's position, and their difference will be the deviation of the com- pass for the course the ship was on when the sun's compass bearing was taken. To name this deviation, mark the total error and the variation on a compass card, and if the total error is to the right of the other, the deviation will be Easterly, but if to the left hand it will be Westerly. See also page 115. 102. — *How Would You Find the Deviation of the Compass by an Altitude Azimuth? Convert the observed altitude into a true alti- tude, then find the polar distance. Next add together the polar distance, true altitude and the latitude by dead reckoning, divide their sum by 2, and call the 39 UTTMARK'S GUIDE result the half sum, the difference between half sum and polar distance is called the remainder. Select the secant of the true altitude, secant of the latitude, cosine of the half sum, and the cosine of the remain- der. The sum of these four logs will be the log haver- sine. Refer same to Table 45 Bowditch. Read the degrees and quarter degrees from the top of the page, the minutes and seconds are taken from the left hand column, this is the supplement of the azimuth; sub- tract this from 180 degrees, the result will be the true azimuth. The azimuth is reckoned from North in North Latitude, from South in South Latitude over East or West according to whether the celestial body is East or West of the meridian. The rule is the same for the sun, moon, planet and fixed stars. Name total error as follows: refer both the com- pass bearing and the true bearing or azimuth to a compass card, and look at them from the center of the card, then, if the true bearing were seen to the right of the compass bearing, the total error would be Easterly; but if the true were seen to the left of the other it would be Westerly. To name the deviation, mark the total error and the variation on a compass card, and if the total error were to the right of the other the deviation would be Easterly, but if to the left hand it would be Westerly. 103. — *How Would You Find Deviation of the Com- pass by Reciprocal Bearings? To obtain deviation by reciprocal bearings, a compass known as a landing compass is carried on shore and set up in a place where it is free from mag- netic disturbance. A flag mounted on a staff is also 40 DEFINITIONS carried on shore, and this is used for signalling to the ship, and for allowing the observer on board to locate the shore compass as the ship is swung. When the vessel's head is steadied on a certain point the signal flag on board is displayed imme- diately over the compass, and the observer on board at that instant takes a bearing of the flag ashore situated over the landing compass. At the same time he observer at the landing compass takes a bearing of the flag over the ship's compass. After the swinging of the ship has been com- pleted the bearings are compared and the difference between them gives at once the deviation for the ship's head on the respective compass points. The shore bearings must have their signs re- versed before comparison is made. For example: If the bearing of the ship's compass from the shore was N. 10° E., the same would be converted into S. 10° W., etc. 104. — *How Would You Find the Deviation of the Compass by a Distant Object? Find the correct magnetic bearing according to the chart of the selected distant object, then swing the ship. The difference between the bearing of the ship's compass, will be the deviation for the ship's head. Refer the two bearings to a compass card, and if the bearing by chart compass were to the left hand of the other the deviation would be Westerly but if the bearing by chart compass were to the right hand the deviation would be Easterly. 41 UTTMARK'S GUIDE 105. — *What Ranges for Compass Adjusting or Find- ing the Deviation Could You Name in the Vicinity of New York and Other Familiar Waters? In the vicinity of New York use, for instance, New Dorp and Elm Tree Beacon in line, bearing N. 39° W. Mag., or Sandy Hook Light in line with South Beacon bearing S. 57* E. Mag. Sandy Hook Light and Sandy Hook Beacon S. 12° E. or 168° True. Waackaack Beacon in line with Pt. Comfort Beacon, true bearing S. 70° W. or 250° True. Conover Bea- con and Chapel HiU Beacon S. 6° W. or 186° True. 106. — *What is the Chief Thing to Guard Against When the Compass is Placed on Board Ship? A compass should be guarded against excessive deviation caused by proximity of any great amount of iron, such as funnels, masts, iron life-boats, life-rafts or movable iron objects. The Standard Compass should be placed so that the lubber lines fall in with the keel or center line of the ship. 107. — *By Which Chart Diagram Would You Shape the Course? By the magnetic diagram on the inland charts, allowing for deviation only, and the true diagram on ocean charts; for the latter allow for variation and deviation. 108. — *How Is Variation and Deviation of the Com- pass Applied? To convert a compass course into a true course, allow Westerly variation and Westerly deviation to 42 DEFINITIONS the left, Easterly variation and Easterly deviation to the right, assuming always that one stands in the center of the compass looking toward the circumfer- ence. 109. — *0n What Principle is the Log Line Marked? The length of line between the knots has the same proportion to a nautical mile as the number of seconds of the sand glass has to one hour. 110. — *Show the Calculation of the Length of One Knot as Represented by the Log Line, Using a 14 Second Glass. The Nautical Mile is 6,080 feet in length, the number of seconds in one hour is 3,600, the propor- tion therefore is as follows: 3600 : 14 = 6080 : X 14 X 6080 ^, . , « . , , Y = 2o leet, o inches, nearly. ^— 3600 ' 111. — *What Motions has a Cyclone? A cyclone revolves around a supposed calm cen- ter with an increasing velocity as the center is ap- proached. In the Northern hemisphere the progress of the center is along a line approximately W. N. W. until it reaches the vicinity of land when it generally turns in a Northerly direction and recurves towards N. E. and E. N. E., gradually expanding in diameter but decreasing in violence until it breaks up and disappears. 43 UTTMARK'S GUIDE 112. — *How Do You Find the Bearing of a Cyclone Center? In the Northern hemisphere face the wind and count eight points to the right; in the Southern hemi- sphere face the wind and count eight points to the left. This will give an approximate direction of the cyclone center. 113. — *How Could You Avoid the Cyclone Center? Look in the direction in which the storm is trav- elling in order to determine the semicircle in which you are. Then, if in the right semicircle in the Northern hemisphere, haul by the wind on the starboard tack, but if in the left semicircle, bring the wind on the starboard quarter, note the course, and keep to that course. In the Southern hemisphere, in the right semicircle, bring the wind on the port quarter, note the course and keep to it, but if in the left semicircle haul by the wind on the port tack. Whether in the Northern or Southern hemi- sphere, if obliged to heave to, then, in the right semicircle heave to on the starboard tack, but in the left semicircle heave to on the port tack. 114. — *What are the General Indications of an Ap- proaching Cyclone? Threatening appearance of the weather with a sultry atmosphere, rugged appearance of the clouds, rapidly moving detached tufts of clouds across the sky, and rapidly falling barometer. 44 DEFINITIONS Converting Points into Degrees and Vice Versa Points Old System New System North Nby E N 11° 15' E 11° 15' NNE N 22° 30' E 22° 30' NEbyN N 33° 45' E 33° 45' NE N 45° 00' E 45° 00' NEbyE N 56° 15' E 56° 15' ENE N 67° 30' E 67° 30' E by N N 78° 45' E 78° 45' East N/S90°00'E 90° 00' Eby S S 79° 45' E 101° 15' E S E S 67° 30' E 112° 30' SEbyE S 56° 15' E 123° 45' SE S 45° 00' E 135° 00' SEby S S 33° 45' E 146° 15' SSE S 22° 30' E 157° 30' SbyE S 11° 15' E 168° 45' South 180° 00' % point = 2° 48' 45" or approximately 3' ^2 point = 5° 37' 30" or approximately 6* % point = 8° 26' 15" or approximately 8* 45 UTTMARK'S GUIDE Converting Points into Degrees and Vice Versa Points Old System New System South 180° 00' Sby W S 11° 15' W 191° 15' s s w S 22° 30' W 202° 30' S Why S S 33° 45' W 213° 45' S W S 45° 00' W 225° 00' S Why W S 56° 15' W 236° 15' WS W S 67° 30' W 247° 30' Why S S 78° 45' W 258° 45' West S/N 90° 00' W 270° 00' WbyN N 78° 45' W 281° 15' WNW N 67° 30' W 292° 30' N Why W N 56° 15' W 303° 45' NW N 45° 00' W 315° 00' N WbyN N 33° 45' W 326° 15' N N W N 22° 30' W 337° 30' Nby W N 11° 15' W 348° 45' North 360° 00' Between and 90° the cour se is N and E Between 90' and 180° the coui se is S and E Between 180' and 270° the com se is S and W Between 270° and 360° the course is N and W 46 NAVIGATION PROBLEMS To convert a Compass course into a True course — Old System Assume we stand in center of compass looking toward the circumference. Allow Westerly Variation to the Left. Allow Westerly Deviation to the Left Allow Easterly Variation to the Right. Allow Easterly Deviation to the Right. Leeway for Starboard Tack to the Left. Leeway for Port Tack to the Right. To convert a True course into a Com,pass course reverse the above rules. To convert a Com,pass course into a True course — New System Westerly Variation and Westerly Deviation — Sub- tractive ( — ) Easterly Variation and Easterly Deviation — Addi- tive (+) Leeway for Starboard Tack — Subtractive ( — ) Leeway for Port Tack — ^Additive ( + ) To convert a True course into a Compass course reverse the above rules. 47 UTTMARK'S GUIDE 360* \^^^mmllm 84'21'30 an I' 15 90'00'oa srir/s 10° I lot' ilg. <%, 180* 48 NAVIGATION PROBLEMS UTTMARK'S GUIDE TO NAVIGATION AND NAUTICAL ASTRONOMY Part II Part II. contains a list and description of instru- ments used in navigation; it also furnishes the student with practical working examples for all the problems required to pass the examination before the Board of Local Inspectors, also the requirements for ex- aminations in the U. S. N. R. F. and U. S. Naval Auxiliary Service. The working rules for the problems are given as short as possible, bearing in mind the necessity of obtaining accurate results, using plain and com- prehensive illustrations, consistent with scientifically correct work. 49 UTTMARK'S GUIDE CHAPTER I. Instruments The necessary instruments, books, etc., used by the Navigator are as follows : Mariners' Compass, Charts for the Waters to be Navigated, Parallel Rulers, Compassses or Dividers, Log and Log-line, Log-glass, Lead and Lead-line, Sex- tant or Octant, Chronometer, Pelorus, Sounding Ma- chine, Binoculars, Barometer, Thermometer, Bow- ditch Useful Tables, Nautical Almanac, Azimuth Tables, Textbook on St. Hilaire Method and Utt- mark's Plotting Chart for Position-lines. The Mariner's Compass MARINER'S COMPASS, its construction and use is explained on page 23. The compass card is a circular disk, the periph- ery of which is divided into 360 equal parts called degrees, or 32 equal parts of 11° 15' each called points. These points are again subdivided into half points and quarter points. The compass card, page 48, shows the various systems. The process of naming the compass points in proper order is known as "boxing the compass." The newest and most con- venient way of numbering the degrees is from (North) increasing right-handed up to 360°. This system is now in use in the U. S. Navy, and if univer- 50 NAVIGATION PROBLEMS sally adopted would be of great benefit and conven- ience to all navigators. In the merchant marine, however, the older system still prevails. North and South are here con- sidered as (0°) marks. East and West as 90°. Inter- mediate degrees are read from the zero points, as, for instance, midway between North and East would be N. 45° E., midway between South and East, S. 45° E., etc. The oldest system which is still extensively used, on account of being most complicated should be memorized first of all. The card is divided into its thirty-two points with subdivisions. The four mean points. North, South, East and West are called the cardinal points. Each one is at right angle or eight points from the adjacent one. Midway between this are the intercardinal points which are named Northeast, Southeast, Southwest and Northwest. It is four points or 45° between each cardinal and the adjacent intercardinal points. Beginning with North, the thirty-two compass points are named as follows: North, North by East, North North East, North East by North, North East, North East by East, etc. In boxing the compass in half and quarter points it is the custom in the United States to refer to this as follows: North % East, North V2 East, North % East, North by East l^ East, etc. The three systems are shown in tabulated form, which also is conven- iently used in converting one system into another, see pages 45-48. On the inner side of the compass bowl are sometimes marked two, or sometimes four vertical lines called lubber lines. The compass should be placed so that the plane passing through 51 UTTMARK'S GUIDE two of these lines opposite to one another, falls in with, or parallel to the keel of the vessel. One lubber line always indicates the compass direction of the ship's head. There are two types of magnetic com- passes, the liquid or wet and the dry type. In the wet type the compass card nearly floats in a liquid composed of alcohol and water. The weight is partly taken off the pivot, minimizing friction and the compass works easier. The liquid has a tendency to decrease vibration of the card when the ship works its way through the water. The Mariner's or Nautical Chart, see page 21. The Mercator's Chart, see page 21. Gnomonic Projection Chart, see page 22. The Polyconic Chart, see page 22. Parallel Rulers These rulers are used for drawing lines parallel to one another in any direction and are generally used for transferring the course line (rhumb-line) on the chart to nearest compass or diagram in order to ascertain the course, or for laying off courses or bearings. They are generally made of hard wood, ebony or box wood being preferred. Dividers or Compasses These instruments consist of a pair of metallic legs movable about a pivot and so arranged that they may be opened and may be set at any desired angle. The points are generally made of steel, but one point may be replaced by a pencil or pen. The 52 NAVIGATION PROBLEMS instrument is called divider when used to measure distances, and compasses when used to draw circles or arcs. The Log and Log-Line The chip-log is used for measuring the speed of the vessel and consists of four parts, the log-chip, log- line, log-glass and reel. The log-chip is a triangular shaped piece of wood, weighed with an insertion of lead at one edge in order to keep it upright as it floats in the water. The log-line is generally about 150 fathoms in length (depending on the expected speed of the vessel), one end is fastened to the log- chip, the other end to the reel on which it is wound. About 20 fathoms from the log-chip end is fastened a piece of rag or bunting, sufl&ciently large (about 6 or 7 inches long) so it may be felt even on a dark cold night when gloves are used. The part of the line between the log-chip and the piece of rag or bunting is called stray-line and allows the chip-log to get sufficiently far away from the disturbed water in the wake of the ship. The remainder of the line when a twenty-eight second glass is used is divided into lengths of 47 feet, 3 inches, called knots. Short pieces of marling or fish line are inserted between the strands of the log- line. These intervals are marked one, two, three, four knots, etc., according to their numbers from the stray-line rag. Each knot is further subdivided into four equal parts, marked by a piece of plain line without any knots. When the fourteen-second glass 53 UTTMARK'S GUIDE is used the indicated speed must be multiplied by two. The calculations of the length of a knot is found and explained on page 43. The log-glass is a glass of the same shape or form as the old-fashioned hour glass. It is partly filled with sand. Two glasses are used, one indicates twenty-eight seconds of time and the other fourteen seconds of time. The first is generally used when the speed of the vessel is about four to five knots. At higher speed the fourteen-second glass should be used and the result multiplied by two. Use your watch or chronometer to determine from time to time if the glasses are correct. The Ground Log In shallow water where the direction of the ves- sel is influenced by tides or currents the log-chip may be detached and a lead attached to the end of the log-line. The lead is thrown overboard and the speed measured by the aid of the log-glass in the usual man- ner. The ship's course is opposite to the direction of the log-line. Use your compass to ascertain this. The Patent Log The patent log is a mechanical device to ascer- tain the speed of the ship. At one end is attached a rotator and the other end is fastened to an indicator which shows on a dial the number of knots the ship has traveled. Several different models are in the market. 54 Compensating Binnacle Compass and Shadow Pin Pelorus and Stand Patent Log Complete Log Dial Ihe Hand lype "E" Sounding Machine Aneroid Barometer Chronometer Ill f \ Vnrnllel Killers Mercurial Barometer Explanation of the various parts of the sextant A — Index glass B— Horizon glass C — Telescope collar D — Telescope ■D E — Shadeglasses F— Sliding limb G — Tangent screw H— Magnifying glass I— Handle J-Arc K — Vernier L— Frame of instrument M — Adjustment screws SEXTANTS NAVIGATION PROBLEMS The Lead (See page 49.) Sounding Machine There are several types of these machines in the market which are used instead of deep sea lead over which they have great advantage. Great depth may be measured quickly and accurately without stopping the ship. The Pelorus The Pelorus or dumb compass consists of a cir- cular disk revolving inside of a metallic ring mounted on gimbals upon a standard which may be placed in any convenient part of the bridge or ship where a clear view all around the horizon may be obtained. This instrument is used for taking land bearings of light-houses, peaks, points, etc., as well as for observ- ing amplitudes and azimuths of the heavenly bodies. The Ship^s Chronometer The chronometer is simply a carefully made clock so constructed as to keep reliable time. The aim of the makers is to produce a time-piece that will gain or lose at a small, uniform rate (an absolutely correct time-piece is not possible), so that the error at all times may be computed. Its chief feature is a variable level which enables the force of the main spring to act uniformly even when the chronometer is exposed to great variation of temperature such as would be experienced from extreme cold during a 55 UTTMARK'S GUIDE long voyage in the Arctic to extreme heat when cross- ing the Equator, or in tropical ports. The chronome- ter as used on board the ship is generally regulated to keep Greenwich time and used in calculating the astronomical longitude of the ship. 56 NAVIGATION PROBLEMS CHAPTER H The Compass Error For explanation of variation, deviation and other subjects pertaining to the compass and the magnetic poles, etc., see pages 24-26. Leeway Leeway is caused by wind and waves, setting the ship to leeward and may be defined as the angular difference between the ship's course by compass and her actual track through the water. FIG. A SHOWING LEEWAY FOR A VESSEL ON STARBOARD TACK The amount differs according to the strength of the wind and roughness of the sea. It is best esti- 57 UTTMARK'S GUIDE mated when standing in the after part of the vessel and looking at the wake of the ship. The angular difference between this and an imaginary line point- ing straight aft is the leeway, or, in other words, the difference between the line of the ship's keel and her actual track through the water. In correcting the course for leeway apply this when the ship is on her starboard tack to the left, or when the ship is on port tack to the right-hand side, assuming as before that we stand in the center of the compass looking toward the circumference. Current A body of water set in motion and carrying with it all that floats thereon is called a current. Among the best known is the Gulf Stream. This generates in the Gulf of Mexico, obtaining its greatest speed or force in the Strait of Florida, setting in a north and Eastward direction it crosses the North Atlantic, rendering mild temperature over and in waters ad- jacent to England, Ireland and Scotland. Even the northern part of Norway is influenced and therefore has mild winters with ice-free harbors all the year around. The direction in which the current flows is called the set, and the speed or velocity is called the drift. In calculating out the ship's position by Dead Reck- oning when a current has been experienced, consider the set of the current as an extra course and the drift or speed during the period as a distance run. If the set is taken from a magnetic chart or given magnetic in the sailing directories, correct for variation in order to find the true set. Deviation is not applied to a current. 58 NAVIGATION PROBLEMS CHAPTER III. The Sailings. In reference to the ship's position at sea relative to any other position either one that has been left or one to which the vessel is bound, or the difference between any two positions, five terms are involved, namely, the course or direction, the distance, the dif- ference of latitude, the departure, and the difference of longitude. The solution of the various problems in which the actual relations of the above terms are involved are called sailings and are as follows: Plane Sailing In this we consider the earth as a perfectly flat surface or plane. In plane sailing we can only con- sider the course and the distance, the difference of latitude and the departure. If two or more courses are involved, these are combined and the method is called traverse sailing. Spherical Sailing Whenever difference of longitude is involved the earth must be considered in its spherical form and therefore these sailings are called spherical sailings and include parallel sailing, middle latitude sailing, mercator sailing and Great Circle Sailing. 59 NAVIGATION PROBLEMS Rules and Formulas 61 UTTMARK'S GUIDE Plane Sailing As said before in plane sailing we take no con- sideration of the curvature of the earth, but prob- lems are solved by considering the sides and angles of a plane triangle. Let in triangle. Fig. B, the angle DEPARTURE T= ^ A A hi /s (f) A ^ / A i' /o 0/ 0/ 4/ Fig. B B A E (C) represent the course or rhumb line, the side A B the difference of latitude (D. Lat.), the side B E the departure (Dep.) and the hypothenuse A E the distance from A to E. We have thus the equa- tions Sin C Cos C Tang C Dep. Dist. D. Lat . Dist. Dep. D. Lat. 62 NAVIGATION PROBLEMS CO o M o o > etf O V PQ S M u **^ *2 CI CO 4iJ a eg .2 3 2-^ V .S 'o o a ^ a bD a eg uu .• U u u U u 4^ d 4- i u a A "^ a CO d c d tn d "^ 2 Q -a 8 55 4^ *s ea Q 'S Q 8 bD bD bD bD bD bD bD bD 1 bD bD bD bD O O l-H 1— 1 f. S -2 O 1-^ ^ C o l-H o o 1— 1 l-H O O F-H P-H + + 1 1 1 + 1 1 1 + 1 + OD 00 d< di H^ ij 9r ^ ^ ts ■IH -EH QQ 0) « Q Q Q Q Q Q Q Q V .FH Q Q bD bD f I bD bc bD bD bD bD bD bD O o ^ © O O O O O 1— 1 l-H P-H f^ ^ l-H l-H l-H l-H CS 1 II II II II II II 1 II II II 1 II >^ d. ^ d tg 1-5 " ^ 3 V d -S •p V • IH s «^ •§ Q i QQ 5 Q Q Q Q Q 8 Q (^ bO bD ta 5p bD bD bD bD bD bD bO bD o o o o C o O O o O ^>^ J J h^ ^ ^ 1-3 ►J tJ iJ 1-3 UU U d U s.s d C8 d O 00 ^ • *^ a CO S ^ ^ u "^ , . J . U 4^ 4^ OD ^ p. 1^ a. k3 r^lJ 0. p. ^ 1^ 4H -g d ■tt *i • l-( VE< V ^ "i^ d IB 8q V d « d •f4 'iH V OD OD QO Q QQ •pH QQ Q Q OD M 4J Q QQ QQQ II 1 ( 11 II J ' II 1 II II II 11 II % <0 .S ^ d ^ QQ \ H Q P 1 Q Q Q 6 Q Jo Q pa . oj • d 'C 5 : 'S . ns V •■a d • d h *j *i 4J >S CO C i a c ; 1 4. I— ( 4 c ' 93 c 1 . 'fH 4H rt P-H 3^ 3 - o .S 4i a 3 1^ to 3 ^ O V 1 <^ O 'fH QQ y Q c 3 Q C Q U Q U Q 1 d a V V CO TS n3 1 4 ^ .. t d 3 -S t ^1 ► m ■H V c a A c cd 4} o O ii t4 s 1 • c i 1 *s 1 i O «8 S i & Q C 3 c J c } Q CJ Q P ) Q c J o| o 63 UTTMARK'S GUIDE In the above table we have included all the various problems which may be solved by plane sail- ing, but the two first mentioned are most frequently used. The problems may be solved either by plane trigonometry, by construction, or by the use of traverse tables Nos. 1 and 2 Bowditch. The latter method is by far the most convenient and therefore generally used. Table No. 1 contains the difference of latitude and departure, corresponding to distances not exceed- ing 300 miles and to courses for every quarter point of the compass. Table 2 is of the same nature, with this difference that the difference of latitude and departure corresponds to every full degree of the compass and the distance extends to 600 miles. Example: A ship sails N. E. % E. true, the distance of 150 miles. Required the difference of latitude and de- parture made good. Enter Table No. I with a course 4% points, page 527 Bowditch Navigator. Opposite the distance 150 miles you will find the diff. latitude 89.4 and the departure 120.5 miles. NOTE: If you take the course from the top of the page, read the latitude and the departure from the top. If the course is taken from the bottom of the page, read latitude and departure from the bottom of the page. 64 NAVIGATION PROBLEMS Traverse Sailing When a ship sails on various courses her track will he irregular or zig-zag. This is called traverse, and the method of traverse sailing consists of finding the difference of latitude and departure correspond- ing to several courses and distances, combining them so as to reduce them to the equivalent of one single course and distance. This is done hy determining the distance in miles north or south and east or west made good on each course. Then add up all the northings, also add all the southings, subtract the lesser from the greater and call the remainder differ- ence of latitude made good. Then add together all the eastings and all the westings. Again subtract the lesser from the greater and call the remainder de- parture made good. To find the course and distance made good look in table No. 2 for difference of latitude in a latitude column and turn the pages over until you find the amount of departure to agree as near as possible. If the differ- ence of latitude is greater than the departure, the course will be found at the top of page, but if less than depar- ture it will be found at bottom of page and the distance in the column immediately to the left-hand side. Example No. 1 A ship sails the following true courses and dis- tances: N. W. by W., 10 miles; E., 20 miles; E. by S., 30 miles; W. 1/2 N., 40 miles; N. E. 1/2 E., 50 miles. Required the difference of latitude and departure made good, also course and distance made good. 65 UTTMARK'S GUIDE Solution True Course N. W. by W. East E. by S W. VaN N. E. Va E.. Dist. D. Lat. Dep. N S E W 10 5.6 8.3 20 — — 20.0 _— . 30 — 5.9 29.4 — 40 3.9 — — 39.8 50 31.7 — 38.7 — 41.2 5.9 35.3 5.9 88.1 48.1 40.0 48.1 Course made good N. 49° E. Distance made good 53 miles. Example No. 2 A ship having steered the following true courses, S. 14° E., 20 miles; S. 16° W., 80 miles; S. 9° E., 60 miles, N. 85° E., 25 miles, N. 39° W., 20 miles. Required the course and distance made good. In this example Table 2 is entirely used, but the rules for working are exactly the same as the foregoing example; 66 NAVIGATION PROBLEMS Solution True Course Dist. Latimde Departure N S E W S. 14° E 20 80 60 25 20 2.2 15.5 19.4 76.9 59.3 4.8 9.4 24.9 22.1 12.6 S. 16° W S. 9° E N. 85°E N. 39° W 17.7 155.6 17.7 137.9 39.1 34.7 4.4 34.7 Course made good S. 2° E. Distance made good 138 miles Parallel Sailing In the foregoing the earth has been considered as a plane surface and its spherical form has not been taken into consideration. The longitude or differ- ence of longitude has therefore not been possible to consider. Parallel sailing is the simplest form of such spherical sailings. It is the method of convert- ing the departure into difference of longitude or the reverse. It is used when the ship sails on a true east or west course or when the direction between two 67 UTTMARK'S GUIDE places is direct east or west. In fig. D let A and B represent two places of the same latitude, P the adjacent pole, A B the arc of the parallel of latitude, through the two places. D E the corresponding arc on the Equator intercept between the meridian P D Fig. D. and P E. R the equatorial radius of the earth F £ or F D. r the radius C B of the parallel A B and L the latitude of that parallel. Then since A B and D E are small arcs of two circles and are therefore proportional to the radius of the circles. We have the equations : A B C B Departure r .=x= or «= — D E E F Diflf. Long. R From the triangle F C B, r = R cos L, hence: Dep. R cos L or Diff. Long. ■= Dep. Sec. L or Diff. Long. R Dep. = Di£F. Long, cos L. 68 NAVIGATION PROBLEMS The foregoing explains the relation between minutes of longitude and miles of departure. Parallel sailing involves two cases; first, where the difference of longitude between two places on the same parallel is given to find the departure and second where the departure is given to find the difference of longi- tude. Solutions may be found by computation using logarithms or by inspection from the traverse tables. The latter method offers greater advantage as it is more convenient. The tables are based upon the following formula: Diff. of Longitude = Dist. Cos. Course (Dist. Cos. C.) Distance = difference of latitude Sec. C (D. Lat. Sec. C.) We may substitute for the column marked latitude in Table II the departure. For that marked distance, the difference of longitude and for the course at top or bottom of page, the latitude. Pig. {^. 69 UTTMARK'S GUIDE The tables then become very convenient for making the required conversions. Short rule for finding difference of longitude when the departure is given. Enter Table II with the latitude as a course, select the amount of departure from a latitude column, find the difference of longitude corresponding thereto in a distance column. For finding the departure when the difference of longitude is given, enter table II as before, take the amount of minutes or longitude into the distance column and find departure in a latitude colunm. Example A A ship in latitude 40° 50' North sails true West, 350 miles. Required the difference of longitude. Solution Enter Table II with 41° (this being the nearest full degree). Look for the distance 350 miles in a latitude column (you will find 350.2, this being the nearest). In the corresponding distance column will be found 464. This gives the minutes of difference of longi- tude and equals 7° 44'. Example B A ship sailing on the parallel of latitude 36° North has changed her longitude 5° 10'; how many miles has she sailed? Solution 5 X 60 = 300 minutes plus 10 = 310 minutes, this being the difference of longitude in minutes. Turning to 36° 70 NAVIGATION PROBLEMS in Table II. we find against 310 in the distance column: 250.8 in the latitude column. This is the number of miles the ship has sailed in order to change her longitude 5° 10'. NOTE: With expression miles, unless otherwise stated, we mean nautical miles or knots, which have the same length as a minute of latitude, or 6,080 feet. Middle Latitude Sailing If a vessel sails from a place A to a place B, sec Fig. F, it is evident that she alters her latitude as well as her longitude and the formula as given for parallel sailing must be modified. The course and distance from A to B of any two places may be found by Middle Latitude Sailing. Solving this prob- lem we need to know the latitude and longitude of the two places. Assuming latitude of A to be 40° 25' N. and longitude of A to be 72° 15' W., latitude of B 43° 15' N. and longitude of B 70° 30' W., proceed thus: 71 UTTMARK'S GUIDE Obtain the difference of latitude by subtracting the lesser from the greater if both places have latitudes of the same name but add if of different names; the result will be the difference of latitude expressed in degrees and minutes. Convert this into minutes of latitude or miles by multiplying the degrees by 60 and adding in the odd minutes. The difference of longitude is found by addition or subtraction following the same general rules as for latitude, namely, longitude of same name subtract, of different names, add. The result is the difference of longitude expressed in degrees and minutes of longitude. Convert this into minutes of longitude by multiplying the degrees by 60 and adding in the odd minutes. Example: Lat. A. 40° 25' N. Long. 72° 15' W. Lat. B. 43° 15' N. Long. 70° 30' W. Diff. of Lat. 2° 50' Diff. of Long. 1° 45' X 60 X 60 120 60 + 50 +45 Reduced to 170 miles Reduced to 105'of long. We have here one side of a triangle in miles and the other in minutes of longitude. These cannot be compared unless we convert the difference of longi- tude into departure or miles. If using the parallel of A (Fig. F) for conversion, we would on account of the meridians converging towards the pole, be using a parallel which would give us too great a number of miles as departure, or using the parallel of B would 72 NAVIGATION PROBLEMS give US too small a number of miles as departure. There must therefore, be a parallel between A and B which used for conversion would give us the cor- rect result; although not absolutely accurate, this will be midway between the two places or the middle latitude, which is found by adding the latitude of A and the latitude of B, if of same names, or subtract- ing if of different names; dividing the result by two gives us the middle latitude. Lat. A. 40° 25' N. Lat. B. 43° 15' N. Dividing by 2 83° 40' Gives middle lat. 41° 50' or 42° nearly. Having thus found the Middle Latitude and sub- stituting this for latitude in parallel sailing, see page 27 and Fig. G, we proceed exactly according to the III A ft /s> D M h A" Q[ /^ < /o a bJ ^ /f y / FIG.G. 73 UTTMARK'S GUIDE rules given there; with middle latitude of 42° con- sidered as a course and the difference of longitude 105 minutes as a distance we find the departure 80.4 in the latitude column. The departure is expressed in miles and therefore may be compared with the difference of latitude for finding the course 'and distance. Enter Table 2 with difference of latitude 170 and departure 80.4 we find latitude 170.4, departure 79.5 (this beini; the nearest we can find) and against this will be found true course N 25° E., distance 188 miles. Note. We name the course North because the point of destination B is to the North of A and East because the same point is to the Eastward of A. Examples for practice: (a) What is the true course and distance from A in latitude 40° 28' North, longitude 74° 00' West, to B in latitude 32° 10' North, longitude 64° 50' West? Answer, true course S. 42° E., distance 670 miles. (b) A ship sailed on the parallel 45° N. from longi- tude 75° 00' 00 " W. to longitude 00° 00' 00 ". What is the true course and distance. 74 NAVIGATION PROBLEMS < o o CO ^15 CO r-l 00 o CO + 5 - •r! "r! iM hf eS OS to 5)§ T? >^^ Q Q 75 00 o C : 0* ^^^ «'=''*- a ) *o < b 6 Longitude so Diflference o Degrees mult counted in Reduces sam Departure = 2.5 Ui z ^t. o b b V o b H oo o o O o o i2 O •* -«* o ^^.A-^ ■^ (A , 0} ^ 53 C •PH a 'O d s ! a V :i z e F-> : g : i ! ) > c 3 S ! .5 4 cc •s B a 1 A 3 4^ 4>> a i i \ 1 '^ a 1 8 •x3-:3 it 1 bbg n: 1 •: ''5 ^ S cH cd •!- ) s s ed •j:? "r* H M C 1 Q p: i •- 3i^ Q C > 76 NAVIGATION PROBLEMS Mercator Sailing In constructing a Mercator's chart an attempt is made to portray a globular form on a flat surface. The meridians are shown as straight lines parallel to one another and at right angles to the equatorial line or the base of the chart. As the meridians are shown as parallel instead of converging, the chart would show a distorted and very inaccurate image of the surface of the land and sea, unless the latitude scale of the chart is increased in the same proportion as the longitude scale is stretched out in order to allow the meridians to run parallel with one another. This is taken care of in the construction of an increas- ing latitude scale, where each degree or each minute of latitude is a little longer than the preceding one reckoned from the Equator towards the poles. The minutes of the Mercator's latitude scale are called "Meridional Parts" (m). The values of the meridional parts are computed in Bowditch Table 3. The course and distance between two points A and B may be measured on a Mercator's chart or be computed according to the formulas given on page 79. Given latitude of A 36° 40' North, longitude 60" 45' West, latitude of B 34° 10' North, longitude of 77 UTTMARK'S GUIDE B 63° 30' West. Required the true course and dis- tance. See Fig. H. DIFF. LONG. FIG.H. Obtain the difference of latitude and difference of longitude according to the same rules as for Middle Latitude sailing. From Table 3 Bowditch take out the meridional parts corresponding to the latitude of A also the meridional parts corresponding to the latitude of B. Subtract the lesser from the greater and call the remainder meridional difference of latitude (M. D. L.)* Example 1 (by computation) : Lat. B. 34° 10' N. m = 2170.4 Long. B. 63° 30' W. Lat. A. 36° 40' N. m = 2353.7 Long. A. 60° 45' W. Diff. Lat. 2° 30' M. D. L. 183.3 Diff. Long. 2° 45' X 60 X 60 120 4- 30 150 miles 120 + 45 165 min. of long. 78 NAVIGATION PROBLEMS Find the course according to the formula Diff. Long . 165 log = 12.21748 — 10 "^ M. D. L. "" 183.3 Iog= 2.26316 True Course S. 41° 59' 32'' W. log. tang. 9.95032 Find the distance according to the formula Di8t.=Diff. lat. secant Course (D. Lat. Sec. C.) Diff. Lat. 150 log = 2.17609 T. C. 41° 59' 32" log Sec = 9.12887 Answer, Dist. 201.8 miles.... log 2.30496 Same problem may be solved by inspection. Look in Table 2 Bowditch for the M. D. L. 183.3 in a latitude colunm. Search until you find the differ- ence of longitude 165 in a departure colunm next to the M. D. L., in this case (found on page 614) 183.6 in the latitude column and 165.3 in the departure column. This being the nearest, the course 42° is found at top of page, name the course S. 42° W., or 222°. Having found the course, consider the number of miiles of difference of latitude and look for same in the difference of latitude colunm, the distance will be found in the distance colunm immediately to the left of the difference of latitude. In this case 150 minutes being the nearest, the distance is found to be 202 miles. Both the course and distance differs very little from the result obtained by computation. Middle Latitude sailing may be used to best ad- vantage when the course is greater than 45°, Mercator sailing when the course is 45° or less. 79 UTTMARK'S GUIDE cj crs lo (N ■« irt esi I o to >^ fiQ z o H D »J O CO NAVIGATION PROBLEMS CM < X u X H OQ o o ;s s .9 i V 0) S) bb a a o o 00 t~- 00 CO ^ lO On bC s i •r<4 SO B B 1-^ i-:i B •i-i bO a o la Q o\ On UO ON o S r-t CO eo (—1 .2 e2 3 o •■4 e2 00 Ov o t- \fi CO cq © CO c5 bC bD o o IS ^ : to bb o o NO II H U H © o o 1/5 I-H II 11 II > i Q u H ^ -^ ^ u VO lo »-H rH ^ ^ CO V o 00 00 3 n o O CJ u H f M • o H H u UTTMARK'S GUIDE Day's Work Dead Reckoning is the mode of finding the posi- tion of the ship by courses steered and the distance run from some point or place the latitude and longi- tude of which is known, allowing for known current, leeway, set of the sea, variation and deviation. The day's work consists of summing up of courses and distances run during 24 hours ending at noon on any- given day during the voyage and obtaining the ship's position by Dead Reckoning at noon. As nearly al- ways a course steered by the ship's compass has to be corrected for its errors, the first part of the problem therefore consists in correcting courses. Leeway, deviation and variation have been explained in the previous chapter. The course may be steered using a compass card which is marked in points and quarter points. This arrangement is generally used in sailing vessels or in small steamboats or motor boats where it is more difficult to keep the vessel on an accurate course, or if the compass used has a small diameter. Larger vessels have generally a larger compass which is divided into degrees. The compass used in Mer- chant ships is divided into four quadrants, having North and South as Zero points and East and West named as 90°. In the U. S. Navy the arrangement is different and the compass in general use has a continuous increase of the degree and reads up to 360°, viz. : North being considered zero. East 90°, South 180°, West 270° completing the circle of 360° again at North. 82 NAVIGATION PROBLEMS The table on page 45 and compass card, page 48, illustrates the various systems of dividing the com- pass card, also rules for correcting courses will be found on these pages. 83 UTTMARK'S GUIDE es Ok u o v I— I I- M o o o CD a .>: • ph a o OS .S u I A P o © f^ ^ S V Esq O V u ♦J •hi s ft:; ^ o 01 u . S^ 3 o U t ^ 3 ^ % ' u H o 12; w 1^* c« ^ w ^ ^ s ♦J ** a, ■M ^* w u ft &i "^ Ph rH fH (N i::^ M O rH c^ a ^rt ft o o > ;I?;?2;^,H rH H W ^ ^ o .2 ^i *i 4i *i Ph ft ft ft ^^>^^ o N lO rH ^i *i *i *i ft ft ft ft o O lO rH rH 4) rH M >^ v^ ^ H tZ] H ^ I2i g IZi ^ i?^ 12; ;25 M ^ 9 6 W -^ W » a ^ J^ ^ S ^ h S o U ^ w ^ S o 84 NAVIGATION PROBLEMS Explanation of Table I and II Bowditch. Table I contains the Difference of Latitude and Departure corresponding to distances not exceeding 300 miles and for courses to every ^ point of the compass. Table II is of the same nature but for courses consisting of all degrees and including distances up to 600 miles. In Table I all courses from % point up to 4 points are found and taken out from the top of the page. Courses from 4 points up to 7% points are taken out from the bottom of the page. In Table II courses from 1° to 45° are found and taken out from the top of the page and courses from 45° to 89° are found and taken out from the bottom of the page. Note that the latitude and de- parture columns are reversed when looking from the bottom of the page. For full explanation of the tables see Plane Sailing, Middle Latitude Sailing and Mercator Sailing, pages 26-27. The tables may be employed in solving all the problems relating to right triangles. Dead Reckoning (Day's Work) Example 1. From latitude 39° 40' 50° N. and longitude 72° 40' 30" W. a vessel sails the following courses and distances: 85 UTTMARK'S GUIDE ITS O ift O CC "^ N M 4J 4J 4^ 4^ Pli On On &< ^^ o o <-• ** ©.Oh CI4 O4 P4 On HHHH CDC/3CO(/3 O H D O 1 < X ■rji On 0\ »J0 On CO -^ tc i-H CC i-H l> On in O «N M CO CNl rH 1/5 O 10 O CO "^ C^ C^ ^^^^ Tack ^j *.; 4J tJ &> Ph Oi CL, ^^ Oh Oh viinvixn A^ 86 ^ W ^ '- a o ^ rH in • IH o fl « cs O « ^ O^ ta a o § s •^ ^ "R fl 8t) g h-J Q H^l in ■73 O bD O bO (U « 'S 'S a a « 2 * O iSH U Q ^^ O (M \n i-H '^ CO 0\ CO ^ ^^ CO . o T3 es O CO \fi CO © 00 On 00 CO CO ■^ 01 V a ON r- 00 t^ CO bC •fH d o -^ »H 0) OS d M 4-> V a NAVIGATION PROBLEMS EXAMPLE II. From latitude 30° 20' 40" North and longitude 67° 43' 57" West, a ship sailed N. 5° W. by compass. Distance 180 miles. Variation 4° West. Deviation 7° East. For 10 hours the ship was in a current flowing N. 45° E. (magnetic) at the rate of 2 miles per hour. Variation of compass 5° West. For 6 hours ship was hove-to on the starboard tack, ship's head coming up to East and falling off to N 68° E. Leeway 20°. Variation 6° W. Deviation 4° W. Ship forged ahead at the rate of 1^/^ knots per hour. Required latitude and longitude of the ship; also true course and distance made good. 87 UTTMARK'S GUIDE Z o H D .J O X h (4 a u ^ ^ 1 1 CO W 1 o^ 00 f~: «^. ea s w 1 1 1 ^ On eC On On VO VO r-l pH rH O 5 b b ov CO (M u »i 3 o U V 3 u. o o o 2 w o o o > O o ■^ lO ^ n .2 V o c t- © Tj< (U >3 1 \h ^ i 1 lc« ( u CD Wi 3 3 M a a 5 »^ 12 P CO in d o ^t4 r- o in o en NO ^ o p to a •IH a o S "^ O rg 2^ bD a; O •IH 0) bO d o ^^ o ^ O r-l cq (M o en ^ Tj< 88 bD d •iH d o B £ P^ (U pO 4) q V d M d •PH tS •!-( Si H O • n3 ns o o o O bD <*« 0) "^ p^ C8 V h CO d +^ o.S 12^;^ ^ b vb b Ph o o O cfi CO CO bC d •FN d o -^ (0 u ns cs . >, f3 pA ns ^ (U n3 CO Q O NAVIGATION PROBLEMS CHAPTER IV. Latitude by Observation of the Heavenly Bodies, Sun, Moon, Planets, Pole Star and Other Fixed Stars INTRODUCTION: Latitude by a Circumpolar star. Stars, whose declination is greater than the observed altitude will never set but describe circles around the pole; these stars are called circumpolar stars and pass the meridian above and below the pole and above the horizon. Without knowing the name or declination of such stars latitude may be found in a very easy way by observing the altitude at the meridian passage above the pole, and again twelve hours later the altitude at the meridian passage below the pole. Correct the altitude for dip and re- fraction. Add these two altitudes together and di- vide by two in order to get the mean altitude. This mean altitude or elevation of the pole will be the latitude of the observer. Latitude by Meridian Observation of the Sun Measure the highest obtainable altitude by your sextant, note if the bearing is North or South, correct the altitude for index error (if any), adding if the error is off the arc, but subtracting if the error is on the arc. Then correct for dip. Table 14 Bowditch. This correction is always subtractive. The next cor- rection is for refraction, Table 20 A Bowditch, always 89 UTTMARK'S GUIDE eubtractive. Next correct for Parallax, Table 16 Bowditch, this correction is always additive. The final correction is for semi-diameter, the amount is found in the Nautical Almanac for every day in the year. Add this correction if the suns lower limb has been observed, but subtract if observation has been taken of the upper limb. The result will be the true central altitude. Subtract the true central altitude from 90°, the result will be Zenith Distance. Name same contrary to the bearing of the sun. From the Nautical Almanac take out the sun's declination for the nearest noon and correct same for the Greenwich time of observation. Apply the declination to the Zenith Distance, adding if Zenith Distance and declination have same name, but subtracting one from another if of different name, the result will be the latitude. Name the latitude according to the greater. Note: Always observe the lower limb unless this should happen to be obscured by clouds. Example for Practice. October 28, 1918, in longitude 75° 00' West of Greenwich, observed alti- tude of the sun's lower limb 40° 10' 10" bearing South. Index correction 1' 30" off the arc, height of eye 32 feet. Required the latitude. (See Diagrams, Page 92.) 90 NAVIGATION PROBLEMS O oo o o o o © o o in o 00 : + ^« «.§ J« 5 w CO O VO so t* O B s Xfi O VO CO O i-H "^ c 43 CO 0) (M On -^ CC CS| in csi ec O c^ o o o :^; ^ a §^ O P C<1 VO CO in a o •FN v p o a o *^ V h O a CO rH 00 VO CO in S + O §^ CS o CO ON en o o •IH O §1 0) O ,4 § •IH u Q Hi O CO CO CO ^CO b© rH 00 © en rt CO II in in CO © © V V CO © i-H VO t^ ON "<* CO © ^ ^ih vb ?H © V in MD ©l-H ^ Ov c CO "O to c^ O lO CO CO CO .2 S SH IT! ^ Q .2 ;h- M a o ^ o c^ Cv| o I— I Q O o a o u P4 cS I— I cs cs Oh 93 a CD 0) -^ 9 cs O 13 a . o +j On •IH <*< i«=i eS 2 "^ Hen C<> C 00 ^ (V ffl ^ CO o tJ o Oi±f to CO !>• in o o lo 00 cq ifi CO + a -23 a c^» CO lO CO © CO • <0 en H O CO i§.2 OCT! *3 O C £ ^ « O o O <5 CD « CD CO b b O to b e Correction for Declination 306" .64 Decl. for 17 Hours 19° 50' 24.9" N Corr. for 47.3 Minutes. — 5' 6.6" Decl. Time of Sight.... 19° 45' 18".3 N Horizontal Parallax = 58' 35" 100 NAVIGATION PROBLEMS CHAPTER V. Logarithms In order to abbreviate the tedious operations of multiplication and division with large numbers, a series of numbers, called Logarithms, was invented by Lord Napier, by means of which the operation of multiplication may be performed by addition, and that of division by subtraction. Numbers may be involved to any power by simple multiplication and the root of any power extracted by simple division. In Table 42 are given the logarithms of all num- bers, from 1 to 9999; to each one must be prefixed an index, with a period or dot to separate it from the other part, as in decimal fractions; the logarithms of the numbers from 1 to 100 are given in that table with their indices; but from 100 to 9999 the index is left out for the sake of brevity; it may be supplied, however, by the general rule that the index of the logarithm of any integer or mixed number is always one less than the number of integral places in the natural number. Thus, the index of the logarithm of any number (integral or mixed) between 10 and 100 is 1; from 100 to 1000 it is 2; from 1000 to 10000 it is 3, etc. To find the logarithm of any function of an angle. Table 44 must be employed. This table is 80 arranged that on every page there appear the logarithms of all the functions of a certain angle A, 101 UTTMARK'S GUIDE together with those of the angles 90° — A, 90°+ A, and 180° — A; thus on each page may be found the logarithms of the functions of four different angles. The number of degrees in the respective angles are printed in bold-faced type, one in each corner of the page; the number of minutes corresponding appear in one column at the left of the page and in another at the right; the names of the functions to which the various logarithms correspond are printed at the top and bottom of the columns. The invariable rule must be to take the name of the function from the top or bottom of the page, according as the number of degrees of the given angle is found at the top or bot- tom; and to take the minutes from the right or left- hand column, according as the number of degrees is found at the right or left-hand side of the page; or, more briefly, take names of functions and num- bers of minutes, respectively, from the line and column nearest in position to the number of degrees. The method of interpolating by inspection con- sists in entering that column marked "Di£f." which is adjacent to the one from which the logarithmic function for the next lower minute is taken, and finding, abreast the number in the left-hand minute column which corresponds to the seconds, the re- quired logarithmic difference; and the latter is to be added or subtracted according as the logarithms increase or decrease with an increased angle. Thus, if it be required to find log. sin 30° 10' 19'' find as before log. sin 30° 10' = 9.70115, then in the adja- cent column headed "Diff." and abreast the, number of seconds, 19, in the left-hand minute column will 102 NAVIGATION PROBLEMS be found 7, the logarithmic difference; add this, as the function is increasing, and we have the required logarithm 9.70122. If log. cosec 30° 10' W be sought; find log. cosec 30° 10' = 10.29885; then in the adjacent difference column, which is the same as was used for the sines, find as before the logarithmic difference, 7; and since this function decreases as the angle increases, this must be subtracted ; there- fore, log. cosec 30° 10' 19" = 10.29878. This method of interpolation by inspection is not available in that portion of the table where the logarithmic differences vary so rapidly that no values will apply alike to all the angles on the same page; on such pages the difference for one minute is given in a column headed "Diff. 1'," instead of the usual difference for each second; in this case the interpo- lation must be made by computation, the given dif- ference for one minute being D. In other parts of the table the interpolation by inspection may be lia- ble to slight error because of the variation in logarith- mic difference for different angles on the same page; but the tabulated values are sufficiently accurate for the calculations in navigation. 103 UTTMARK'S GUIDE Examples for practice: Answer No. 1 Log Secant 22° 20' 00''. = 10. 03386 No. 2 Log Cosine 92° 40' 00". =. 8. 66769 No. 3 Log Tangent 178° 10' 00". = 8. 50527 No. 4 Log Secant 60° 58' 50". = 10. 31416 No. 5 Log Sine 22° 13' 50". == 9. 57787 No. 6 Log Tangent 10° 10' 10". = 9. 25377 No. 7 Log Cosine 90° 10' 16". = 7. 47477 No. 8 Log Tangent 2° 04' 09". . = 8. 55786 No. 9 Log Cotangent 94° 54' 55". . == 8. 93450 TABLE 45: LOGARITHMIC AND NATURAL HAVERSINES The haversine is defined by the following rela- tion: Hav. A= y^ vers. A = V2 (1 — cos. A) = Sin^ V2 A It is a trigonometric function which simplifies the solution of many problems in nautical astronomy as well as in plane trigonometry. To afford the maxi- mum facility in carrying out the processes of solution, the values of the natural haversine and its logarithm are set down together in a single table for all values of angle ranging from 0° to 360°, expressed both in arc and in time. Log Haversine Example for practice: Solution No. 1 Log haver. 8.02066 P. M. Observ. = OOh 47m Ols No. 2 Log haver. 7.95418 A. M. Observ. = 23h 16m 278 Solution No. 1 177° 58' 00" Log. Hav. = 9.99986 No. 2 70° 44' 45" Log. Hav. = 9.52520 104 NAVIGATION PROBLEMS CHAPTER VI. Longitude The earth rotates on its axis once in 24 hours and as a complete circle contains 360 ° therefore 360 ° =24 hours; it necessarily follows that the distance East or West from any given point may be expressed in hours, minutes and seconds of time as well as in degrees, minutes and seconds of arc. At present the meridian which passes through Greenwich Observa- tory (England) is considered our prime or first meri- dian. If we have the means of finding the time at Greenwich, and at the same instant know the time on board ship or place, we can always find our longi- tude expressed in time by taking the difference be- tween the Greenwich and local time, converting this into arc which will give us the longitude required. The chronometer as used on board ship is regu- lated to Greenwich time. The ship's time at any given instance can be found by observations of the heavenly bodies, sun, moon, planets and fixed stars. The formula for finding the time or westerly hour angle (t) of any heavenly body is expressed as follows: • 2 1 / 1 ^^^ ^ ^^^ (S-h) Bin y2 = — ; — — transposmg we have cos L sin r hav. t = cos S sin (S-h) sec. L cosec. P where g^ h + L -f P 105 UTTMARK'S GUIDE h = true alt. of the heavenly body. L == Lat. of ship or place. P = Polar distance of the heavenly body. t = The westerly hour angle of the heavenly body. The best time for observation to obtain longitude by time sight is when the heavenly body is on or near the prime vertical, but care should be taken not to take observation when the object is too near the hori- zon. Eight to ten degrees should be the least altitude because the refraction is very great and uncertain when the body is below that altitude. Rules for Finding Longitude by the Sun, Ob- serve the altitude, note the time by chronometer, fol- lowing rules as given on page 35, paragraph 95. Always convert civil time into astronomical time because when using astronomical time the work be- comes simpler, and the problems clearer. 106 NAVIGATION PROBLEMS Example for Practice March 21, 1918, time at ship A. M. Observed altitude of the sun's lower limb 22° 13' 50'', index correction on the arc 1' 20". Chronometer at con- tact 2h 53m 58s A. M. Correction for chronometer error 7m 15s to be subtracted. Latitude by D. R. 10° 50' 10" S. Height of eye 25 feet. Required the longitude. SOLUTION Observed Alt. Sun's LL. 22° 13' SO" Index Correction — 1 20 Dip for 25 feet. 22 12 30 — 4 54 Refraction 22 07 36 — 02 22 22 05 14 Parallax + 08 22 OS 22 Semidiameter + 16 05 True Altitude 22 21 27 Latitude 10 SO 10 S Polar Distance 89 S2 23 Chr. at Sight Mar. 20d 14h 53m S8s Accumulated Rate. — 7 IS G. M. T Mar. 20dl4 46 42 Hourly DifJ. of Decl "1 59" Multiplied by the No. of \ 14.8 hours from Green. Noon J 873.2" Corr. for Decl. 14' 33" Decl. for Green, Noon... 0° 22' 10" S Correction *... — 14 33 Decl. at Time of Sight... 07 37" S Applied to 90° 89° 59' 60" Gives Polar Distance 89 52 23 Sum or 2S 123 04 00 J4 Sum or S 61 32 00 True Altitude Subtr 22 21 27 Remainder or (S— H) 39 10 33 Log. Secant 0.0O781 Log. Cosecant O.OOOOO Log. Cosine 9.67820 Log. Sine 9.80051 Hour Angle or A. T. S. . . 19 31 02 Equation of Time + 7 35 M. T. S. March 20 19 38 37 G. M. T. March 20 14 46 43 Longitude in Time 4 51 54 Longitude 72° 58' 30" E Log. Haversine 9.48652 Hourly Diff. of Equation 1 0.74Ssec Multiplied by the No. of \ 14.8 Hours from Green. Noon.. J Correction for Equation 11 sec Eq. T. Noon Mar. 20d 7m 46sec. Correction 11 Equation at Time of Sight. . . 7m 3Ssec 107 UTTMARK'S GUIDE CHRONOMETER RATES Example for Practice On July 19 the chronometer was slow 2m 1.8s and gained 1.7s daily. What will he the error on December 5 same year. SOLUTION July 19th, Chr 2m Ols.S slow Gained in 139 days 3m 56s.3 (gaining) Chr. error or rate Dec. 5 Im 548.5 fast Note. — ^From July 19th to December 5th same years is 139 days which multiplied by the daily rate of l.Ts gives 3m 56.3s. 139 1.7 97.3 139 60)236.3 (3 or 3m 56s.3 180 56 Example 2 On February 28 chronometer fast 7m 00 sec. and losing 2.8s daily. What will be the error on July 28 same year? SOLUTION Feb. 28th, Chr 7m OOs fast Lost in 150 days 7m OOs (losing) Chr. error or rate July 28. . Om OOs fast or slow 108 NAVIGATION PROBLEMS Note. — From February 28th to July 28th same year and not leap year, is 150 days which multiplied by the daily rate of 2.8s gives 7m OOs. 150 2.8 1200 300 60)420.0 (7m 420 000 LONGITUDE BY CHRONOMETER ALTITUDE SIGHT OF THE SUN (Backing and Filling Problems) Supposing we have had no observations during the night and we are taking an observation for time sight of the sun in the morning. In order to get a correct result in computing our longitude we must have the accurate latitude, but if we have had no astronomical fix since noon on the previous day our latitude is uncertain and we must therefore wait until noon in order to get our latitude by meridian obser- vation of the sun, and then work backwards in order to find latitude when we took morning observation. Rules for Working When the sun is at least eight or ten degrees above the horizon measure the altitude, note the time by chronometer, also the time at ship, log and course ship is steering. Correct the sun's altitude, obtain declination and equation of time from Nautical Al- pianac, then wait until noon and obtain your latitude. 109 UTTMARK'S GUIDE With the true course and distance run between morn- ing sight and noon obtain from table No. 2 Bowditch your difference of latitude and departure and convert your departure into longitude. To the latitude at noon apply your difference of latitude, naming this North if you have sailed South between morning and noon, or South if your course was in Northerly direc- tion. This will give you the latitude when you took A. M. sight. Then with the altitude, the correct lati- tude and polar distance obtain your longitude in the usual way and to this apply your difference of longi- tude ; East if you have sailed in Easterly direction or West if in Westerly direction. The result will be your longitude at noon. Note, longitude and latitude obtained by observation of sun or stars is called an astronomical fix. Example for Practice December 25, 1918, time at ship A. M. Ob- served altitude of the sun's lower limb 35° 40' 00". Index error 1' 30'' on the arc. The chronometer at time of contact Ih 03m 40s P. M. Log showing 10 miles. Height of eye 18 feet. Correction for chro- nometer rate to be figured out according to the fol- lowing: On September 10, 1918, chronometer was fast 10m 59s and losing 0.9 seconds daily. Between morning sight and noon the ship sailed N N W % W by compass, variation 1V2° W, devia- tion 9^2° E. Log showing 70 miles at noon. The meridian altitude of the sun's lower limb was then observed 48° 50' 10" S. Index error on the arc 1' 30". Longitude by D. R. 47° 15' W. Height of eye 18 feet. Required the latitude of the ship at noon and at time of morning sight, also the longitude of ship at time of A. M. sight and at noon. 110 NAVIGATION PROBLEMS SOLUTION Sept. 10th, Chron 10m 59a fast Lost in 106 days Im 35s.4 (losing) Chron. error or rate on Dec. 25 9m 23.6 fast From September 10th to December 25th same year = 106 days which multiplied by the daily rate of 0.9 sec. gives Im 35s.4. Ob. Alt. Sun's LL 48° SO' 10" S Index Correction — 1 30 48 48 40 Dip for 18 feet — 4 09 48 44 31 Refraction , — 51" 48' 43 40 Parallax + 6" 48 43 46 Semidiameter -f- 16 18 True Central Altitude... 49 00 04 S Subtract from 90° 89 59 60 Zenith Distance 40 59 56 N Declination 23 24 52 S Latitude at Noon 17° 35' 04" N App. Noon at Ship Dec. 25d Oh Om Os Longitude in Time W +.. 3h 09m 00s G. A. T Dec. 25d 3 09 00 Eq. Time — 3 G. M. T Dec. 25d 3h 08m S7s Hourly Diflf. for Declination 3.35 3.2 Multiplied by No. of Hours \ from Greenwich Noon j 670 lOOS Correction for Declination... 10.720 Declination at Gr. Noon 23° 25' 02.2" S Correction — 10.7 Declination at Sight.,.. 23"' 24' Sl.S* S 111 UTTMARK'S GUIDE Comp. Course . . . ...N. N. W. J4 W. = N. 31° W Deviation = 9° 30' E Magn. — N. 21° 30' W Variation = 1° 30' W True Course = N. 23° 00' W T. C. Dist. LAT. DEP. N S E W N. 23 W 60 SS.2 - - 23.4 Diff. of Long. = 24' 30" W. Latitude Left, Noon 17° 35' 04" N Difference of Latitude... 55' 12" S Lat. A.M..., 16° 39' 52" N Ob. Alt. Sun's LL 35° 40' 00" Index Cor — 1 30 Dip for 18 feet. Refraction 35° 38' 30" — 4' 09" 35° 34' 21" — 1' 21" 35° 33' 00" Parallax + 7" 35 33 07 Semidiamter + 16' 18" True Altitude 35° 49' 25" Longitude Left, A. M... 50° 53' 45" W Difference of Longitude. 24' 30" W Longitude at Noon 51° 17' 15" W Chr. at Sight, Dec. 2Sth Ih 03m 40s Accumulated Rate 9 23.6 [. T Dec. 2Sd Oh S4m 16.4s Hourly Difli or Decl 1 3.34 Multiplied by the No. of \ 0.9 Hours from Green. Noon J — — 3.015 Decl. for Green. Noon... 23° 25' 2" S Correction 3" Decl. at Time of Sight.. 23° 24' 59" Applied to 90° + 90 00 00 Gives Polar Distance 113 24 59 Latitude A. M 16° 39' 52" N Log. Secant 0.01863 Polar Distance 113° 24' 59" Log. Cosecant 0.03732 &im or 2S 165° 54' 16" J4 Sum or S 82° 57' 08" True Altitude Subtr 35° 49' 25" Remainder or (S— h).... 47° 07' 43" Log. Cosine , 9.0 Log. Sine 9.86503 Hour Angle or A. T. S.... 21h 30m 47s Log. Haversine 9.00982 Equation of Time — 06 Hourly Diflf. of Equation Mul- 1 1.24 tiplied by the No. of Hours [• 0.9 from Green. Noon J M. T. S Dec. 24d 21h 30m 41s G. M. T Dec. 25d 00 54 16 Longitude in Time 3 23 35 Longitude 50° S3' 45" W Correction for Equation 1.116 Equation for Green. Noon.... Om 06.8s Correction — 1.1 Equation at Time of Sight... Om 5.7s 112 NAVIGATION PROBLEMS LONGITUDE BY EQUAL ALTITUDE Occasionally in cloudy weather the sun may come out of the clouds when so near noon that an ordinary time sight cannot be taken. We can then avail ourselves of the equal altitude problem which is explained on page 36. Example for Practice July 28, 1918, in latitude by D. R. 18° 37' S, longitude 170° 48' W. Chronometer at first altitude 10 h 39m 57s P. M. Chronometer at second altitude llh 51m 29s P. M. Chronometer slow 14m 19s. Ship sails S by W true at a speed of 12 knots per hour. First altitude 52° 21'. Required longitude at noon and second sextant altitude. 113 UTTMARK'S GUIDE m o u 13 O M en i-H OC ?r 00 *« ^ Tj< C< >> 43 I— (fi »*^ ® *s ^ -«^r5 •5b vided h is from -5 11 0. •'1 '^ «^ a- 3 J J3 ^ 2 « a § •P" p V V O CO r-lt-3 O o i— I H 3 O en '^ ft 00 to «S CO u 9i g 4-> *-• 0) 0) a a o o a fl o o u h ^ M UU « -i{ ^^ in o o o ^ in o a o o bC o NAVIGATION PROBLEMS LONGITUDE BY SUNSET AND SUNRISE Quite often after a cloudy day it clears a little near the horizon and we may see the sun just before it sets, but too low to take an ordinary observation. We may then observe the upper limb at the instant it disappears from view, and obtain the longitude ac- cording to rules given on page 37, paragraphs 97, 98. Owing to the uncertainty of the refraction, too great reliance should not be placed on this, but is very useful in obtaining approximate position of the ship. The sunrise sights are seldom successful. Example for Practice On May 15, 1918, observed the sun's upper limb in contact with the horizon at setting. The chronom- eter showing 2h 49m 59s P. M. Correction for chro- nometer rate 9m 9s to be added. Latitude by D. R. 38° 50' 00'' N. Height of eye 52 feet. Required the longitude, SOLUTION Chronometer May ISd 2h 49m S9s Rate — 9 09 G. M. T May 15d 2h S9m 08s Latitude (L) 38° 50' 00" N Polar Distance (P) 71° 13' S3" Neg. Alt. (h). 110° 03' 53" . — 59' 15" Sum (2S) 109° 04' 38" Half Sum (S) 54° 32' 19" Neg. Alt. (h) + 59' 15" Remainder (S— h) 55° 31' 34" Decl. Green. Noon 18° 44' 19" N Correction for 2.8 hrs... + 01' 47.6" Declination at Sight. Apply to 90° 18° 46' 07" N 90 00 00 Polar Distance (P) 71° 13' S3" Eq. T. Green, noon 3m 48.5s Correction None Ey. T. at Sight 3m 48.5s L. Log. Sec 0.10848 P. Log. Cosec 0.02373 S. Log. Cos 9.76354 (S— h) Log. Sin 9.91612 A. T. S. (t) 7h 09m 05s Log. Hav 9.81187 Eq. T — 3m 49s M. T. S G. M. T May ISd 7h OSm 16s Obs. Alt. Sun's LL. May ISd 2h 59m C3s Dip. 52 feet Refr Longitude in Time 4h OSm 08s S. D Sum Parallax Longitude 61° 32' 00" E Neg. Alt. 115 = 00 00 00 = — 7' 04" = — 36' 29" = — 15' 51" = — 59' 24" + 9" = — 59' IS" UTTMARK'S GUIDE CHAPTER VII Deviation of the Compass by Amplitude This problem may be worked by the use of datas found in Bowditch Table No. 39. Explanation of this method is found on page 39 Guide Book. The problem is generally worked by the use of logarithms according to the formula Sin. A = Sec. L. sin. D where A is the amplitude of the heavenly body, L the latitude of ship or place and D the declination of the heavenly body. Rules for Working To the log. sec. of Lat. taken from Table 44 Bow- ditch add the log. sin. of the declination; the result is the log. sin. of true amplitude; name this North or South according to the declination; and East if the observation is taken when the object is rising, or West if the object is setting. Under this true ampli- tude write down the compass amplitude or bearing; subtract the lesser from the greater. The result is the total error. Name the total error as follows: Refer both the compass bearing and the true bear- ing or azimuth to a compass card, and look at them from the center of the card, then if the true bearing were seen to the right of the compass bearing, the total error would be easterly; but if the true bearing were seen to the left it would be westerly. To name the deviation, mark the total error and the variation on a compass card and if, when looking 116 NAVIGATION PROBLEMS from the center of the card, the total error were seen to the right of the variation, the deviation is Easterly, but if to the left hand, the deviation is Westerly. Example No. 1 June 22, 1918, chronometer 2h 11m 24s A. M. Chronometer error 24m 53s fast. Latitude of the ship by D. R. 42° 52' N. Sun's compass bearing at rising E. 2Sy2° N. Variation given by chart for the ship's position 5^° E. Required the deviation. SOLUTION Latitude 42" 52' N Log. Sec. Declination 23° 27' N Log. Sin.. True Amplitude E 32° 53' N Log. Sin.. Compass Bearing E 23° 30' N 0.13493 9.59989 9.73482 Total Error 9° 23' W Variation 5° 30' E Deviation 14° S3' W ytcar Example No. 2 February 21, 1918, G. M. T. llh 11m 12s A. M. Latitude of the ship by D. R. 40° 40' N. Sun's com- pass bearing at rising E. 2° N. Variation given by chart for the ship's position 5° W. Required the deviation. 117 UTTMARK'S GUIDE SOLUTION Latitude 40° 40' N Declination 10" 52' S True Amplitude E 14° 23' S Compass Bearing E 2° 00 N Total Error 16° 23' E Variation S° 00 W Log. Sec 0.12004 Log. Sin 9.27S37 Log. Sin 9.39S41 Deviation of the Compass by Time Azim,uths Using Azimuth Tables In working this problem we require the apparent time at ship, the position of the ship by D. R. Use the nearest degree of latitude. The declination of the heavenly body is taken from the Nautical Almanac; use the nearest full degree. The Azimuth tables consist of three parts. Part I is used on the equator. Part II when latitude and declination have same names. Part III when latitude and declination have different names. To name error and declination follow same general rules as for amplitude. Example No. 1 3:10 P. M. apparent time at ship. The sun bore by compass N. 135° W. Latitude by D. R. 25° N. Declination of the Sun 20° S. Variation 5° W. Required the deviation. 118 NAVIGATION PROBLEMS SOLUTION Latitude of the Ship to the Nearest Degree by Dead Reckoning 25° N Declination of the Sun to the Nearest Degree for the Given Day 20° S Corrected Local Apparent Time at Bearing . 3h lOm P. M. Bearing of the Sun according to Compass. . .N 135° 00' W True Bear, of the Sun as per Azimuth Table. N 129° 51' W Their Diff. is the Total Error of the Compass 5° 09' E Variation given by the Chart for the Ship's Position 5° 00 W Deviation of the Compass for the Ship's Head at the Time the Sun's Bearing was Taken . 10° 09' E Example No. 2 8h 05m A. M. Apparent time at ship. The sun bore by compass N. 92° E. Latitude by D. R. 35° N. Declination of the sun 10° N. Variation 15° E. Required the deviation. SOLUTION Latitude of the Ship to the Nearest Degree by Dead Reckoning 35° N Declination of the Sun to the Nearest De- gree for the Given Day 10° N Corrected Local Apparent Time at Bearing 8h 05m A. M. Bearing of the Sun according to Compass. . .N 92° 00 E True Bear, of the Sun as per Azimuth Table. N 100° 10' E Their Diff. is the Total Error of the Compass 8° 10' E Variation given by the Chart for the Ship's Position 15° 00' E Deviation of the Compass for the Ship's Head at the Time the Sun's Bearing was Taken. 6° 50' W 119 UTTMARK'S GUIDE Deviation of the Compass by Altitude-Azimuth This problem is fully explained on page 39, para- graph 102 (Guide Book). Example for Practice March 20, 1918, about lOh 00m A. M. at ship. Observed altitude of the sun's L. L. 34° 20'. Lati- tude by D. R. 40° 20' 00'' N. Long, by D. R. 45° W. Chronometer showing G. M. T. Ih 00m P. M. Sun bears by compass N. 125° E. Variation given by chart 7° E. Height of eye 16 feet. Required the deviation. SOLUTION Observed Altitude Correction 16 feet True Altitude .. 34° 20' . + 10' . 34° 30' 00" 51" 51" 09" 59" s Alt. Log. Sec Lat. Log. Sec S. Log. Cos (S— P) Log. Cos.... Log. Hav Sup. Azimuth True Azimuth Compass Bearing... Total Error Variation 0.08408 0.11788 9.10990 Decl. Greenwich Noon.. . 0° 22' 9.99601 180° 00' 53° 9.30787 Declination at Sight... Applied to 90° ....0° 21' .. 90° 10" s 00" 35' 00" Polar Distance True Altitude . 90° 21' . 34° 30' . 40° 20' 10" 51" 00" N .. N 126° 25' .. N 125° 00' 00 E 00 E Latitude 1° 25' 7° 00' E Sum (28) ..165° 12' 01" E Half Sum (S) . 82° 36' . 90° 21' 00" 10" 5° 35' W Polar Distance (P).... Remainder (S — P) . 7° 45' 10" i 120 NAVIGATION PROBLEMS CHAPTER VIII THE TIDES or Finding Time of High Water and Low Water at any given place See explanation in Guide Book, page 38, para- graph 100. Example for Practice No. 1 Required time of high water (a) A. M. and (b) P. M. at Boston, Mass. (Navy Yard flagstafif), on Sept. 19, 1918. From Bowditch Practical Navigator, page 282, under Maritime Positions and Tidal Data, we find Boston, Mass., Navy Yard flagstaff in long. 71° 03' W or approximately 5h from Greenwich. High water constant or Lunar Interval llh 27m. Low water constant or Lunar Interval 5h 17m. NOTE — High water and low water constants for any given port are found — see index to appendix No. 4 Bowditch Navigator, pages 279-318. Example No. 2 Required time of (a) high water and (b) low water A. M. at San Francisco Davidson Observatory on March 26, 1918. San Francisco, long. 122° 25' W (or approxi- mately 8 hours). High water constant 12 hours 7 minutes. Low water constant 5 hours 34 minutes. 121 UTTMARK'S GUIDE < 1 o H 3 O CD w i-t s e3 -« ji CO o r-l 1— 1 4J 4^ Oh Oh o; V en cn es 4-> 00 13 O •IH o o I a S .9 a a a (M rH ON rH •>* rH 00 g + C^ C^ 00 es ns CO Oh 0) cn X W5 .2 S) OS g *S 2 2 w M o i§ •IH :^ a a CO §^- ^ c^ O o csi ;H U Ot p u « a to "* Q ego. Thinking that this may be of interest to you, I am taking this opportunity of advising you that after having completed your course in navigation, I successfully passed the U. S. Local Inspector's examination for master of steam vessels of any ton- nage on the waters of any ocean. I also wish to say that I was very favorably impressed with the thoroughness of your methods of teaching and gladly recom- mend your school to anybody desiring to take a course in navi- gation. G. S. Spinney, First Officer, Steam Yacht "Cyprus." I am writing to thank you for the great interest you took in me while attending your school. I had no trouble in passing my examination before the Local Inspectors at New York and to-day I have received my license. o Wiilesen S. S. Floridian. At the completion of my term in your school I want to tender my sincere thanks for your kind, patient and never-ceasing work in helping me to finish my course. What I at first thought would be great difficulties were put before me so clearly through your kind efforts that I passed my examination with comparative ease. Richard Albrecht, 767 Forest Avenue, Bronx. Please accept my thanks for your great interest taken in me during my course of instruction at your school. I cannot speak too highly of your method of teaching navigaton, and greatly admire your patience and interest taken in those men wish- ing to study for their license. [i] TESTIMONIALS Having recently passed the Local Inspectors' Examination without trouble is proof of your ability as an efficient instructor in navigation. I can highly recommend you to anyone wishing to obtain a license. Fred W. Stehr, 3rd Mate, S. S. Sabine. I take great pleasure in writing you this letter to announce that I have passed the U. S. Local Inspectors and received the license for second mate on any ocean and any gross tonnage. I must say that when I was under your instruction for navigation I received the most excellet instruction from you. I will be very glad to reconmiend your school to anyone interested in navigation. Kindly accept my best wishes for a great success. H. A. WOLLENWEBER, U. S. N. A few lines from one of your former students to tell you that I have often been thankful for the course I took at your school last summer. It enabled me to get a chief quartermaster's rating in the Reserve. You will be interested to know that I have received my com- mission as ensign yesterday. I will always feel that your ad- mirable school did more for me than any other one thing. Tlie navigation I learned at your school has stood me in such good stead that I attribute my advancement in the Reserve largely to it. John T. Arms, Hotel Lorrane, Norfolk, Va. Mr. Lockwood wishes to join me in stating that the course of Practical Navigation we took in your school has helped us greatly in our work in the United States Naval Reserve Force. When diplomatic relations with Germany were broken a year ago last February, Mr. Lockwood and I decided that we wanted to get into the navy before war came. We applied at the Recruiting Office and were told that the rating of a first-class seaman was the best they could give us. Then we started your [g] UTTMARK'S GUIDE course of Practical Navigation in the middle part of April. The first of May we tried the Recruiting Office again, and were both enrolled as Boatswain's Mates, first-class, on the strength of our taking your course. We finished the course in June, and after being on duty at Newport, R. I., until December 1 applied for transfer to the Intensive Training School for Deck Officers in the United States Naval Auxiliary Reserve. We were told that oiJy men with college educations were accepted for this course, and also that we were slightly beyond the age limit. However, upon our telling them of the work done in your school, we were allowed to take the course. We were put on board a ship plying between here and a Southern port, and although we had never had any practical work in navigation, found that it came to us very easily. Mr. O. Berg, an ex-student of your school, was the Chief Mate on the boat we were on, and with our course with you, and a little coaching from him, it proved comparatively easy for us to take up the actual work. Ellsworth B. Doane, U. S. Naval Reserve Force, Pelham Ba}j, N. Y. Numerous other letters from satisfied students have been received and may be seen at the school. [h] LIST OF PUBLICATIONS 13 Uttmark's Guide to Elxamination for Masters and Mates, 4th Edition (complete in two parts) .... $3.50 H Uttmark's Nautical News 1 .00 H Uttmark's Textbook on Marc St. Hilaire Method . . . 2.50 13 Uttmark's Plotting Charts in pads of 25 charts (litho- graphed on strong ledger paper) , per pad 3.00 [^ Uttmark's Ready Reckoning pads, 75 sheets each. Marc St. Hilaire (Sun) 50 13 Uttmark's Ready Reckoning pads, 75 sheets each. Marc St. Hilaire (Stellar) 50 ^ Uttmark's Compass Card in colors 25 S Uttmark's Hour Angle and Right Ascension Card. . .25 All post paid in U. S. A. . — - □ Illustrated catalog of information in regard to instruction 1 1 C 6 in navigation mailed upon request. ' '• Please make checks or money orders payable to F. E. Uttmark. Mttmarka 8 State Street, New York City Facing Battery Park On the 'Bridge (c) Press Illustrat ng Service On the Bridge (c) Press Illustrating Service (c) Press Illustrating Service The Principal and some of the Instructors (c) Press Illustrating Service Instruction in the Use of Signals Office Socia. Room. Chart Work (c) Press Illustrating Service Chart Room (c) Press Illustrating Service Class Room TsTo. 3 Class Room IMo. 4 ^^ur%*. % THIS IS TO CERTUI' TILVT ylM,^„/„f/M',r„-OcEAi/> ■O-A-yj. 'S-^^t— ^^etM^^an/^yOMa^/t^rt/'^/t'/^ /e'/^lr/nj A^lf J,,,/, „yO '«./>' (jr^-A cS ' IcitT^tan^ Reproduction of one of the Diplomas Uiplomas for the various courses are issued to all students u^on graduation. "UTTMARK'S FOR NAVIGATION'