LIBRARY OK THE University of California. GIFT OF^ (AMlLsir Class -XlA 7, Bg Captmn Hcnrg l^aglor PubUstteft bg tfie Author S20 Qatterg Street 1904 Entered according to Act of Congress, in the year 1904, By Henry Taylok, In the office of the Librarian of Congress, at Washington, D. C. PRESS OF Walter N. Brunt 10^-104 Second Street, San Francisco, Cal. MARINER'S COMPASS. ^ ^H^ -yf rk^ ^ I UNIVc. TAI V^-— LES V IrmtS 3LE OF ANG NORTH POINTS M o 2 48 45 POINTS X SOUTH >o 5 37 30 }4 OK 8 26 15 ^ N.xE. N.xW. 1 11 15 1 S.xE. S.xW. 1 M 14 3 45 1 X 1 3-^ 16 52 30 1 }4 1 ^ 19 41 15 1 K N.N.E. N.N.W 2 22 30 00 2 S.S.E. s.s.w. 2Ji 25 18 45 2 X 2>^ 28 7 30 2 K 2% 30 56 15 2 X N.ExN. N.W.xN. 3 33 45 00 3 S.E.xS. S.W.xS. 3 M 3 K 36 33 45 3 X 39 22 30 3 }4 3M 42 11 15 3 h N.E. N.W. 4 45 00 00 4 S.E. S.W. 4M 47 48 45 4 '4 4K 50 37 30 4 K 4 % 53 26 15 4 g N.E.xE. X.W.xW. 5 56 15 00 5^^ S.E.xE. S.W.xW. 5 M 59 3 45 5 X 5 >^ 61 52 30 5 K 5^ 64 41 15 5 X E.N.E. W.N.W. 6 67 30 00 6 E.S.E. w.s.w. 6 K 70 18 45 6 X 6>^ 73 7 30 6 >^ 6 3^ 75 56 15 6X E.xN. W.xN. 7 78 45 00 7 E.xS. W.xS. 7 X 81 33 45 7 X 1 Yi 84 22 30 7 K 7 ^ 87 11 15 7 X East West 8 90 00 00 8 East West PREFACE. This book is devoted entirely to the subject of Navigation, Nau- tical Astronomy and Compass Adjustment, the object being so to simplify the problems involved, that no matter how limited a per- son's education, he may be brought from comparative ignorance to a high degree of efficiency as a navigator, the only requirement be- ing that the student must be able to read. There is almost an en- tire absence of algebraical signs. The first section, or opening part, is devoted to the first four rules of common arithmetic. This section is written in the sim- plest language so that any one having but a slight knowledge of English can understand, words of one syllable being used in pref- erence to longer words wherever practicable, but as the student advances, better language is introduced, yet simplicity is never lost sight of throughout the work. The arrangement is such that any part of the work may be re- ferred to with the greatest ease, and any desired problem found in a very short space of time. This is important, as the book is not only intended for beginners, but also as a work of reference for those that may have become "rusty." Special attention has been given to the requirements of the mod- ern navigator, whereby he can obtain the ship's position, at any time of the day or night, by single and double altitudes of the sun, stars and planets, but all problems relating to the moon have been entirely omitted, as they are not reliable, and are therefore obso- lete. The part relating to the finding of the deviation of the compass will be found to fit any case, no matter what the class of vessel. This section is important, owing to the use of iron and steel in the construction of modern vessels. This part also contains a de- scription of the different kinds of Pelorus and other instruments used in the taking of bearings, and azimuths, with rules for using the same, written in very plain language, — very necessary knowl- edge for the bridge officer. Chart-work and coast navigation has been thoroughly gone over, and many matters connected with the same, not generally known to seamen, have been introduced, especially those matters relating to the proper application and use of deviation when taking bear- ings and finding the course to steer. VI Preface Tides, and the time of their occurrence, are also given, with re- ductions to soundings, — very useful in finding the depth of water when crossing a shallow bar. Compass — Adjustment. — This difficult subject is given in an en- tirely different manner from that generally found in books of this description, all calculations being worked by addition, subtraction, multiplication and division. This part is illustrated by colored diagrams. By a very moderate amount of study any navigator should be able to compensate the vessel's compasses himself. The work, so far as practicable, is original throughout, and purely American, with special references to the numerous publica- tions issued by the United States Hydrographic Office for the benefit of navigators. This idea, it is to be hoped, will be duly appre- ciated, as there are so many seamen, at the present date of writing, who are totally ignorant of the existence of these useful publica- tions, and of the many advantages to be derived from studying them in preference to foreign works. Every problem is fully illustrated, and numerous examples are given for practice. The author feels assured that the book will fill a long-felt want, for it is the first of its kind ever published in the United States. ORDER OF STUDY. Take the first part of the book as far as "Day's Work," then fol- low the list: Latitude by Meridian Altitude of the Sun. Mercator Sailing. Amplitude. Longitude by Chronometer (Sun). NMien these are thoroughly understood, the student may study any part of the book that he prefers. TABLE OF CONTENTS. DIVISION 1. Page. Common Addition 1 Common Subtraction 1 Common Multiplication 2 Multiplication Tables 3 Common Division '^ Decimals 9 Addition — Degrees— Minutes — Seconds 14 Subtraction — Degrees — Minutes — Seconds 15 Multiplication — Degrees — Minutes — Seconds 15 Division Degrees — Minutes — Seconds 16 Logarithmic indices I'i' To correct Compass Course in points 18 To correct Compass Course in degrees 20 The Day's Work 22 DIVISION 2. The Sailings -±-t Use of Table 42 — Logarithms of Numbers 41 Use of Table 44 — Sines, Tangents, etc- 45 Mercator Sailing 46 Parallel Sailing 51 Mercator Sailing by Inspection 52 Difference of Longitude by Parallel Sailing 53 Middle Latitude Sailing 54 Great Circle Sailing 57 DIVISION 3. Latitude by Meridian Altitude of the Sun 59 Caution to the Eising Generation of Navigators 66 Special Table to correct Altitude 67 Latitude by Meridian Altitude of the Sun below the Pole 71 Table of Contents. Page. Latitude by Meridian Altitude of a Fixed Star "ii Rule to find the Time of Meridian Passage of a Fixed Star 74 Rule to find what star is approaching the Meridian 75 Rule to compute the Meridian Altitude of a fixed star 75 Latitude by Meridian Altitude of a planet 77 To correct the Planet's Declination 78 Latitude by Pole Star 81 DIVISION 4. Latitude by Ex-Meridian Altitude of the Sun, Epitome method. 87 Towson's method 88 Remarks on the method of finding the Latitude by Ex-Meridian Altitude 95 Latitude by Ex-Meridian Altitude of a Star 96 Latitude by Ex-Meridian Altitude of a Planet 97 DIVISION 5. Longitude by Chronometer 100 To correct the Chronometer Time 101 How to state Astronomically the Time shown by a chronometer. 110 To convert Civil Time to Astronomical Time Ill Rule to correct a Log Sine, Tangent and Secant to seconds. . . .115 To find the correct Latitude to work the sight 116 The Modern Method of working an A. M. sight 124 Remarks on Careless Navigation 133 DIVISION 6. Longitude by Fixed Stars 135 Longitude by Planet 138 Remarks in regard to Star and Planet observations when taken to find the longitude 1-11 What to do when crossing the Meridian of 180 degrees and other matters relating to the change of time 142 Little pointers, which, although not relating to the crossing of the 180° of longitude, still have considerable bearing on it. . 144 Table of Contents. Page. To set the wheelhouse clock so that it will indicate approxi- mately 12 hours when the Meridian Altitude js observed. .144 To find the length of a passage of an Ocean Greyhound 145 DIVISION 7. Sumner's Method 147 Latitude and Longitude by Double Altitudes 150 Chart illustrating the same 151 Eemarks on the Double Altitude problem 153 Johnson's Method 156 The Stars and how to find them 165 Latitude and Longitude by Double Altitude of Stars 169 Chart illustrating same 178 DIVISION 8. Deviation of the Compass 173 The Amplitude — Epitome Method 173 Short Method of Amplitude by Table 39 Bowditch Epitome 175 Short Method of working Amplitudes by the American Azimuth tables 177 The Altitude Azimuth 180 Time Azimuths 186 Method of Setting the Watch to Apparent Time Sufficiently near to work the Time Azimuth 187 To find the Apparent Time at ship when there is no chronome- ter on board 189 Time Azimuths by Stars or Planets 191 Napier's Diagram 194 Remarks on the finding of the deviation by Star Azimuths. . . .207 Eange Bearings 210 Reciprocal bearings 211 Instruments used on board of ships for taking bearings 212 The Pelorus 213 Methods of using the Pelorus 214 To use Field's Pelorus 215 The Shadow Pin 215 Good form for Recording the Deviations 217 Table of Contents. DIVISION 9. Page. Chart Work 218 The Parallel Euler 218 Field's Euler 218 The Transparent Protractor 219 The Three- Armed Protractor 219 Dividers 221 The Gnomonic Chart 221 The Polyconic Chart 221 Mercators Chart 221 To know if it is a TTue or Magnetic Chart 222 Variation and Dip Charts 222 Pilot Charts 223 To find the course between two places on a chart 225 To find the distance on a Mercators Chart 225 Ship's position by cross bearings 227 Ship's position by two bearings of one point 227 Chart illustrating the same 226 Ship's position by four point bearings or double the angle, with chart illustrating the same 228 Current Sailing 229 Diagram illustrating the same 230 To find the compass course to steer to make a Magnetic Course taken from a chart 231 Deviation Card 235 Remarks relating to the chart questions and other matters in regard to Coast Navigation 243 Listening for a signal during a fog 245 DIVISION 10. The Tides 247 Rule to find the time of high water by moans of tlio American Tide Tables 248 Use of the Tide Tables when taking soundings with the lead. .252 DIVISION 11. The Sextant 255 To select a good Sextant 255 Table of ConteiNts. Page. Color Shades 2^6 Bad Shade Glasses 256 Care of a good Sextant 257 To read the Sextant 258 Adjustment of the Sextant 259 To find the Index Error 261 To Measure the Altitude of the Sun 262 A Lead Line 262 To cast the Deep Sea Lead from a Sailing Ship 264 Thompson's Sounding Machine 264 The Log and Log Glass 266 To test a patent log to see if it registers correctly 267 Short and handy rule to measure the Log Line 268 To mark the Log Line 268 Definitions 271 DIVISION 12. Keeping the Chief Officer's Log Bool-: 284 DIVISION 13. The Official Log Book 288 The Meteorological Log or Weather Report 289 The Chronometer 298 Caution in Handling 299 Care on Board 299 More than one chronometer necessary 301 Winding the Chronometer 301 Eating the Chronometer 303 What to do if the Chronometer should break down 305 DIVISION 14. Mariner's Compass — Early History 307 The Lubber Line 308 Purchasing a Compass 309 Table of Contents. Page. Parsimonious Owners .' 310 Caution in regard to placing a compass and some incidents re- lating to the same 311 Bad position to be avoided 313 Magnetism 315 Chance for argument 317 First law of Magnetism 317 Magnetism in an iron ship 317 Magnetism contained in iron lying horizontal 330 Explanation of colored diagrams 321 Sorting out the Deviation 325 Quadrantal Deviation 327 Computation of the Co-efficients 329 Computing the value of each Co-efficient for every point of the compass 331 Table of Co-efficients 333 Placing the Compass 333 Caution in placing Magnets 335 Size of Magnets 335 Strength of Magnets 335 Care of Magnets 336 Prepare to adjust ship's Compass at sea 336 Eule to find the amount of Deviation due to vertical iron 337 To adjust 338 The Flinder's Bar 339 Table for correction of Quadrantal error 340 Eetentive Magnetism 341 Further information in regard to the Flinder's bar 342 Rule to find the direction of Ship's head when building 343 The heeling error 343 The heeling adjustment 345 Value of heeling adjustment 346 Johnson's Tables 348-349 Table for correcting Altitude 350 SIGNS AND ABBKEVIATIONS. ° degrees ' minutes of arc " seconds of arc i' Iioiirs ™ minutes of time » seconds of time -[- plus — minus A.T.S apparent time ship Accum. rate accumulated rate Ast. T astronomical time Amp amplitude Approx approximate A.M ante-meridian (morning) Az azimuth Alt altitude App apparent Cor. decl correct declination Civ. T civil time Chron. T chronometer time Co.-lat complement of latitude Co.-bearing complement of bearing Diif. of lat difference of latitude Diff. of long difference of longitude Dep departure Dist distance Decl declination D.E dead reckoning Dev deviation Equa. T equation of time G.M.T Greenwich mean time G.A.T Greenwich apparent time H.A hour angle I.E index error Lat latitude Long longitude L.L lower limb Mer. Alt meridional altitude Signs and Abbrp:viations. Mer. parts meridional parts Mer. d. lat meridional difEerence of latitude M.T.S mean time ship ]\[.T.G mean time Greenwich Mid. lat middle latitude Mer. Pass meridian passage Mag. CO magnetic course J^.A nautical almanac Obs. alt observed altitude Obs. az observed azimuth Obs. amp observed amplitude P.D polar distance P.M post meridian (afternoon) Parlx parallax R.A right ascension E.A. of Mer right ascension of meridian Eef refraction S.D semi-diameter S.T ship's time Sid. T sidereal time T. CO true course T. Alt true altitude T. Amp true amplitude T. Az true azimuth U.L upper limb Var variation Z.D zenith distance TAYLORS MODEETNAVIGATION. DIVISION I. ADDITION. Add the following numbers : 2' 6 5 5 4 3 7 15975323 4267 9 822 98564327 183724909 When adding any number of figures, commence with the column to the right, and whatever is over 10, 20, 30, 40, and so on, mark down under its own column, carry 1 to the next column if the num- ber is over 10 and less than 20, 2 if over 20 and less than 30, 3 if over 30 and less than 40, and 4 if over 40 and less than 50, and so on. This rule will be more easily understood if the foregoing example is followed. SUBTRACTIOX.— COMMOX NUMBERS. Example. From 260785421 Subtract 173098526 Ans. 87686895 When subtracting one number from another, proceed in the fol- lowing manner, as seen in the example. Thus, 6 from 1 I cannot, so I take 1 from the figure to the left and place it with the 1, mak- ing 11 of it ; now I say, 6 from 11 is 5, so I mark down the 5 ; next I say, 2 from 1, as I have borrowed 1 from the 2, making it now 1, and as I cannot take 2 from 1, I must borrow 1 from the 4, making it 3. and put this 1 with the other and make it 11 again; so I say, 2 Taylor's Mod. Nav. 1, Taylor's Modern Navigation. from 11 is 9; next, as I have borrowed 1 from the 4, it is now only 3, and as I cannot take 5 from 3, I borrow 1 from the 5 and place it with the 3, making 13 of it; so I say, 5 from 13 leaves 8; next, 8 from 5, but as I have borrowed 1, it is only 4, so 8 from 14 is 6 ; next, 9 from 8, but I have borrowed 1 here also, so 9 from 17 is 8; then as I have borrowed 1 from the 7, it makes it 6, so from 6 is 6 ; then 3 from I cannot, so I borrow 1, and say, 3 from 10 is 7 ; then 7 from 6, but here I borrowed 1, and so 7 from 15 is 8, and 1 from 1 leaves nothing. The question is then finished. Note. — Any problem in subtraction may be proved by adding the two lower lines together. The result will be equal to the top line. Examples. From 97B042379 Subtract 429076549 Ans. 546965830 From 9000423 Subtract 2000567 Ans. 6999856 MULTIPLICATION OF COMMON NUMBERS. When following these examples, the student should refer to the multiplication table if he is in doubt. Example. Multiply 69806 by 8 Ans. 558,448 The first figure, multiplied by 8, gives 48 ; so I mark down the 8 and hold on to the 4. Then I say, 8 times is 0, and add on the 4 ; so I mark down the 4. Next I say, 8 times 8 are 64 ; so I mark down the 4 and hold on to the 6. Then 8 times 9 are 72, and the G makes it 78 ; so I mark down the 8 and carry the 7. Next, 8 times 6 are 48, and the 7 will give 55. Multiplication. MULTIPLICATION TABLE. IX 1= 1 2X 1= 2 3X 1= 3 4X 1= 4 IX 2= 2 2X 2= 4 3X 2= 6 4X 2= 8 IX 3= 3 2X 3= 6 3X 3= 9 4X 3=12 IX i= 4 2X 4= 8 3X 4=12 4X 4=16 IX 5= 5 2X 5=10 3X 5=15 4X 5=20 IX 6=r 6 2X 6=12 3X 6=18 4X 6=24 IX "= 7 2X 7=14 3X 7=21 4X 7=28 IX S= 8 2X 8=16 3X 8=24 4X 8=33 IX 9= 9 2X 9=18 3X 9=27 4X 9=36 1X10=10 2X10=20 3X10=30 4X10=40 1X11=11 2X11=22 3X11=33 4X11=44 1X13—12 2X12=24 3X12=36 4X12=48 5X 1= 5 6X 1= 6 7X 1= 7 8X 1= 8 5X 2=10 6X 2=12 7X 2=14 8X 2=16 5X 3=15 6X 3=18 7X 3=21 8X 3=24 5X 4=20 6X 4=24 7X 4=28 8X 4=32 5X 5=25 6X 5=30 7X 5=35 8X 5=40 .5X 6=30 6X 6=36 7X 6=42 8X 6=48 5X 7=35 6X 7=42 7X 7=49 8X 7=56 5X 8=40 6X 8=48 7X 8=56 8X 8=64 5X 9=45 6X 9=54 7X 9=63 8X 9=72 5X10=50 6X10=60 7X10=70 8X10=80 5X11=55 6X11=66 7X11=77 8X11=88 5X12=60 6X12=72 7X12=84 8X12=96 9X 1= 9 lOX 1= 10 IIX 1= 11 12X 1= 12 OX 2= 18 lOX 2= 20 IIX 2= 22 12X 2= 24 ■9X 3= 27 lOX 3= 30 IIX 3= 33 12X 3= 36 9X 4= 36 lOX 4= 40 IIX 4= 44 12 X 4= 48 9X 5= 45 lOX 5= 50 IIX 5= 55 12X 5= 60 9X 6= 54 lOX 6= 60 IIX 6= 66 12X 6= 72 9X 7= 63 lOX 7= 70 IIX 7= 77 12X 7= 84 9X 8= 72 lOX 8= 80 IIX 8= 88 12X 8= 96 9X 9= 81 lOX 9= 90 IIX 9= 99 12X 9=108 '9X10= 90 10X10=100 11X10=110 12X10=120 9X11= 99 10X11 = 110 11X11 = 121 12X11=132 '.9X12=108 10X12=120 11X12=132 12X12=144 Taylor's Modern Navigation. Examples for Practice. Multiply 297654 by 7 Ans. 2,083,578 Multiply 897563 by 5 5 Ans. 4,487,815 Multiply 7098662 by 9 9 Ans. 63,887,958 Multiply 2907654873 by 6 6 Ans. 17,445,929,238 MULTIPLICATION BY TWO FIGURES. Multiply 542837 by 25 25 2714185 1085674 Ans. 13,570,925 Here we multiply by two figures; so, on the second line, when placing the first figure down, it must be put under the figure 8, as seen in the example; then the two lines must be added to get the proper answer. To read the answer, mark off, with commas, the first three figures to the right, then the next three, as seen above. The answer will then road, 13 million, 570 thousand, 9 hundred, and 25. Examples fur Practice. Multiply 926074 by 34 34 8704296 2778222 Ans. 31,486,516 Mil LT I PLICATION. Multiply 9765 by 78 78120 68355 Ans. 761,670 Multiply 492631 by 92 92 985262 4433679 Ans. 45,322,052' MULTIPLICATION BY THREE FIGURED Multiply 419678 by 247 247 2937746 1678712 839356 Ans. 103,660.466 Here we multiply by three figures, and it will be seen, in the ex- ample, that, each time we multiply, the result is placed one figure to the left; then the lines of figures are added as before. The re- sult, in words, is expressed in the following manner : 103 million, 660 thousand, 4 hundred, and 66. Examples. Multiply 827654 by 725 725 4138270 1655308 5793578 Ans. 600,049,150 Taylor's Modern Navigation. Multiply 256784 by 623 623 770352 513568 1540704 Ans. 159,976,432 Multiply 5006271 by 987 987 35043897 40050168 45056439 Ans. 4,941,189,477 Multiply 2709832 by 506 506 16258992 135491600 Ans. 1.371,174,992 It will be noticed here that there is a between the 5 and the 6 ; so, when multiplying by the second figure, simply place the under the second figure from the right, and proceed to multiply by the 5, as seen in the example. Note. — If there were more than one cipher, I would place as many ciphers as I was multiplying by under the other figures, let- ting the first cipher come under the second figure from the right, and then multiply as before. Thus, Multiply 98700234 by 5002 5002 197400468 49350117000 Ans. 493,698,570,468 To prove any question in multiplication, simply divide the result by the number used in multiplying, and the result will be the first row of figures. Division. SHOKT DIVISION.— COMMON NUMBERS. Example.— Divide 37062786 by 2. 2)37062786 Ans. 18,531,393 Here we say, 2 into 3 will go once and 1 over ; so, carry the 1 and place it before the 7, and we have 17 ; then 2 into 17 will go 8 times and 1 over; this 1 placed before the makes it 10, and 2 will go into 10 5 times even. Then, 2 into 6, 3 times; 2 into 2, once; 2 into 7, 3 times and 1 over; place the 1 before the 8 and make 18 of it; then 2 into 18 goes 9 times even, and 2 into 6, 3 times even. Example.— Divide 726987425 by 4. 4)726987425 Ans. 181,746,856, and 1 over. Four will go into 7 once and 3 over ; place the 3 before the 2 ; then 4 into 32, 8 times even ; then 4 into 6, once and 2 over ; place this 2 before the 9, and say, 4 into 29, 7 times and 1 over; place this 1 before the 8, and 4 into 18 goes 4 times and 2 over; then 4 into 27, 6 times and 3 over; then 4 into 34 goes 8 times and 3 over; then 4 into 22, 5 times and 2 over; then 4 into 25, 6 times and 1 over. Examples for Practice. Divide 956273 by 5. Ans. 191254, and 3 over. 100937 by 7. 14419, and 4 over. 1142879 by 8. 142859, and 7 over. To prove any answer on this page, multiply the answer by the figures used when dividing and add what is left over; and the re- sult will be the row of figures divided. Taylor's Modern Navigation'. LONG DIVISION, OE DIVIDING BY MORE THAN ONE FIGURE. Example. — Divide 542837 by 25. 25)542837(21711 50 178 175 33 25 87 75 12 Now we divide by two figures, and find that 25 will go twice into 54, with 4 as a remainder; so we bring down the 2 and then say, 25 into 42 once and 17 over; so bring down the 8, and say, 25 into 178 will go 7 times and 3 over; then bring down the 3, and 25 will go into 33 once and 8 over; bring down the last figure, 7, and then say, 25 into 87 will go 3 times and 12 over. This ends the exam- ple, and the 12 over is called 12-25 (twelve twenty-fifths). Example.— Divide 159976432 by 623. 623)159976432(256784 1246 3537 3115 4226 3738 4884 4361 5233 4984 2492 2492 Decimals. In this example we divide by three figures, and find that they will go into the first four figures twice and 353 over; so the 7 is brought down, making the number 3537 ; then G23 will go into it 5 times and 422 over; so we bring down the 6 and divide again, and continue in the same manner until all the figures are brought down, when the example will be finished. Tt will be noticed that there is no remainder here. Examples for Practice. Divide G00049150 by 725. Ans. 827,654. 4941189477 by 987. 5,006,271. 493698570468 by 5002. 98,700,234. DECIMALS. A decimal is a number which is a tenth, hundredth, thousandth, etc., of 1, or unity. A ivhole number is a number with the decimal point placed to the right ; thus, 2564. A decimal 7inmher is so called when the dot, or decimal point, is placed before it; thus, .276. A mixed number is so called when the decimal point is placed between two of the figures, as shown in the following number: 27.6 is 27 decimal 6. If the figures were placed like this, 2.76, then it would be 2 deci- mal 76. A number like this is 6 whole numbers, 6. A number like this is 6 tenths, .6 A number like this is 6 hundredths, .Ofi A number like this is 6 thousandths, .006 and the values decrease in the same manner, according to the num- ber of ciphers placed between the unit and the decimal point. Addition of Decimals. Example. 986.25 2.67 1493.14 65.04 Ans. 2547.10 There must be two decimal figures in the answer, because there are two decimals in the numbers added. 10 Taylor's Modern Navigation-, Example. 2.586 483.2 56.9152 Ans. 542.7012 Here it will be seen that decimals are placed under decimals ac- cording to their value, and also that the four figures to the right, in the answer, are decimals, because in one of the numbers there are also four decimal figures. Subtraction of Decimals. Example. From 2698.726 Subtract 523.973 Ans. 2174.753 Subtract in the same manner as common numbers, but count off to the right as many figures as you have decimals in the larger deci- mal number, and place the dot, or decimal point. Example. From 1090.263 Subtract 82.3 Ans. 1007.963 It will be noticed in this case that in one number there are three decimals and in the other only one; so you must point off three figures to the right. Example. From 26.000 Subtract .987 Ans. 25.013 Here one number is a whole number and the other entirely deci- mals; so it is necessary to place to the right of the 26 three ciphers, to enable you to subtract, borrowing one from the whole number, as seen in example. Multiplication of Decimals. Example. Multiply 26.58 by 4.2. 4.2 5316 10632 111.63G Decimals. 11 Multiply in same manner as common numbers, but point off from the result as many figures as are contained in the two num- bers. In this case there are three. Example. Multiply 89.73 by 41.26. 41.26 23838 7946 3973 15892 1639.2598 Here we point off four figures as decimals, because there are four decimals contained in the problem. Note. — Always cross off from the result as many figures as there are decimals contained in the two numbers. Eemember that it is very important that the decimal point be placed in its proper posi- tion. DIVISIO^ OF Decimals. When any number is divided by a lesser one, the result is a whole number. When any number is divided by a greater one, the result is a decimal number. It is not necessary, in the practice of navigation, to work deci- mals to more than two places. ^a:am/)Ze.— Divide 672.08 by 26.9. 26.9)672.08(24.9 538 1340 1076 2648 2421 227 Divide by same rule as for common numbers, and from the result point off one figure, because the number divided contains one more decimal figure than the divisor. Example.— DWidiQ 330 by 825. 825)330.0(.4 3300 12' Taylor's Modern Xavigatiox. Here one number is divided by a greater one ; so, annex a cipher to the right and divide. The result in this case is .4, or four tenths. ^a-am/;Ze.— Divide 2.5872 by 2.4. 2.4)2.5872(1.078 24 187 168 192 192 Here there will be three decimals, because the number divided has three more decimals than the divisor. If there should be a re- mainder, borrow a cipher and again divide until you have as many decimals as you may think are required. EuLE TO Convert a Fraction Into a Decimal. Bring the top figure down, annex a cipher to it, and divide by the lower. The result will be a decimal number equal to the frac- tion. If necessary, annex another cipher, or as many as may be, in the student's opinion, needed. In this case the number is .54, as per example. Thus, 27 50) 270 (.54 250 200 200 A Short Method to Reduce Minutes of an Hour to a Decimal OF AX Hour. There are fiO minutes in an hour, therefore 10 into 60 will go 6 times; so 6 minutes is one tenth part of an hour. So, to convert minutes into decimals, simply divide them by 6. This will give tenths. If there should be a remainder, annex n cipher to it, and again divide. The result will be hundredths. Example. 6)42 .7 (tenths). DECIMALS. 13 Example. 6) 51 (.85 (hundredths). 48 EuLE TO Convert Hours and Minutes of Time Into Decimals OF A Day. Divide the minutes by 6 and place the result to the right of the liours, then divide by 24. Example.— 2V' SG'". 24) 21.6 (.9 (tenths of a day). 21.6 Example— 18^ 24'". 24) 18.4 (.76 (hundredths). 168 160 144 EuLEs OF Three, or Proportion. If a ship sail 7.3 miles in one hour, how many miles will she sail in 24 hours? 7.3 24 2CK2 146 175.2 (175 miles and 2 tenths). If a ship is sailing at the rate of 18 miles per hour, how much v.-ill she make in 20 minutes? 1 hour. 60°^ : 20'" :: 18 miles. 20 60)360(6 miles. 360 14 Taylor's Modern Navigation. If a chronometer alter 26"' 40^ in 40 days, how much will it alter in one clay? 40 : 1 :: 26™ 40« 60 1600 1 40)1600(40^ per day. 160 ADDITION OF DEGREES, MINUTES, AND SECONDS. 60 minutes make 1 de- Sixty second s (■' ') make 1 minute (') gree (°) Add- 41° 21 15 ' 21' 41 14 41' 15 12 78° 17' 08" The sum of the seconds being 68", and as there are only 60" in 1', we must put down what is over the 60" and carry the 1' to the minutes; the sum of the minutes being 77', and as there are only 60' in 1°, we must put down what is over the 60' and carry the 1° to the degrees. Add— 20° 57' 50' 11 48 57 14 50 40 47° 37' 27" The sum of the seconds in this case is 147" ; this sum divided by 60" will give 2' and 27" ; carry the 2' to the minutes, and we get the sum of 157', which is 2° and 37'; carry the 2° to the degrees and add, and we get the sum of degrees. Examples for Practice. (1) 11° 57' 25" (2) 96° 10' 2" (3) 17° 59' 1" 13 16 29 60 15 57 1 23 74 52 18 7 4 59 108 58 59 SUBTHACTIOX MlLTU'LICATION. 15 (4) 13° 14' 15" (5) 41° 40' 50" (6) 11° 2' 59' 16 17 18 27 16 73 47 11 19 20 21 2 59 59 18 33 44 Answers. (1) 100° 06' 12" (2) 163° 30' 1" (3) 183° 59' 23" (4) 48° 51' 54" (5) 71° 56' 49" (6) 103° 23' 54' SUBTEACTION OF DEGREES, MI^^UTES, AND SECONDS. Example. 27° 20' 40" 19 30 50 7° 49' 50" As I cannot take 50" from 40", I must borrow 1' and add it to the seconds; now, as 1' is equal to 60". if I add it to the 40" it will make it 100", and I then say, 50" from 100" ; then, as we have taken 1' from the 20', we must say 30' from 19', and as we cannot, let us borrow a degree and add it to the minutes, which will make the minutes 79'; now we can take 30' from 79'; then, as we have borrowed 1°, we must say 19° from 26°. Examples for Practice. (1) 45° 29' 17" (2) 18° 59' 17" (3) 29° 51' 41" 27 43 24 17 58 43 17 22 52 (4) 120° 49' 59" (5) 91° 23' 1" (6) 23° 41' 15' 100 51 00 14 52 57 11 41 59 Answers. (1) 17° 45' 53" (2) 1° 00' 34" (3) 12° 28' 49" (4) 19° 58' 59" (5) 76° 30' 4" (6) 11° 59' 16" MULTIPLICATION OF DEGREES, MINUTES AND SECONDS. Multiply 47° 50' 40" by 2 2 95° 41' 20' 16 Taylor's Modern Xavigation. Twice 40" is 80" ; 80" is therefore 1' and 20" ; put down the 20" and carry the 1'; twice 50' is 100', and 1 more is 101'; 101' is 1° ard 41'; put down the 41' and carry the 1° ; then twice 47° and 1° are 95°. Multiply 19° 10' 59" by 3 2 38° 21' 58' Twice 59" is 118", which is 1' and 58"; put down the 58" and carry the 1'; twice 10' is 20' and 1' is 21'; put down this 21', be- cause it is less than 60'; then twice 19° is 38°. Examples for Practice. Multiply (1) 17° 58' 40"; (2) 59° 16' 52"; (3) 71° 59' 59"; (4) 89° 59' 14" by 2. Answers.— (1) 35° 57' 20"; (2) 118° 33' 44"; (3) 143° 59' 58"; (4) 179° 58' 28". Multiply 82° 42' 52" by 4 4 330° 51' 28" Four times 52" are 208", which is equal to 3' and 28" ; carry the 3'; then 4 times 42' and 3' are 171', which is equal to 2° and 51'; then 4 times 82° and 2° are 330°. Examples for Practice. Multiply (1) 9° 50' 41"; (2) 10° 17' 18"; (3) 19° 24' 30"; (4) 98° 42' 15" by 4. Answers.— {1) 39° 22' 44"; (2) 41° 9' 12"; (3) 77° 38' 00"; (4) 394° 49' 0". DIVISIOX OF DEGEEES, MINUTES, AND SECONDS. Divide 71° 53' 40" by 2. 2)71° 53' 40" 35° 56' 50" Indices. 17 Two will go into 71° 35 times and 1 over; carry this 1° and add it to the minutes; it will now be GO'; then 60' and 53' are 113'; then 2 into 113', and we get 56' and 1 over; carry this minute to the seconds, and we get 100" ; divide it by 2 and we get 50". Examples for Practice. (1) 2)27° IT' 14" (2) 2)89° 59' 50" (3) 2)17° 40' 18" (4) 2)5° 51' 58" (5) 2)120° 49' 57" (6) 2)89° 59' 16 " Answers.— (1) 13° 38' 37"; (2) 44° 59' 55"; (3) 8° 50' 9"; (4) 2° 55' 59"; (5) 60° 24' 58"; (6) 44° 59' 38". Divide 97° 50' 12" by 4. 4)97° 50' 12" 24° 27' 33" Four into 97° will go 24 times and 1 over; then, 1° being equal to 60', you must add 60' to the 50' and divide by 4; after dividing the minutes by 4 you find that you have 2' left ; add these 2' to the seconds, which will make 132", and divide again by 4. If, after you have divided the seconds, you have anything left over, let it go. Note. — In actual sea practice it is unnecessary to work to sec- onds of arc. Examples for Practice. (1) 4)89° 51' 20" (2) 4)13° 59' 18" (3) 4) 173° 20' 40 " (4) 4)101° 38' 42" (5) 4)50° 43' 50" (6) 4) 179° 1' " Answers.— (1) 22° 27' 50"; (2) 3° 29' 49": (3) 43° 20' 10"; (4) 25° 24' 40"; (5) 12° 40' 57"; (6) 44° 45' 15". LOGARITHMIC INDICES. ; As multiplication and division by logarithms are sufficiently ex- plained in Bowditch, I will not treat of them here, but will give a few illustrations of how the index of a number may be found. Tayi,or's Mod. Nav. 2. i8 Taylor's jModern Navigation. The index of a whole numher is always one less than the number of figures. For instance, if a number consist of six figures, the index will be five; expressed thus: 5. Examples to Illustrate. Whole Numb ers. 9. Index 0. 22. Index 1. 501. Index 2. 7983. Index 3. 82645. Index 4. 157867. Index 5. 2763948. Index 6. 82171619. Index 7. Mixed Numb ers. 1.9 Index 0, because 1 figure in whole number. 22.40 Index 1, because 2 figures in whole number. 80.7809 Index 1, because 2 figures in whole number. 896.32 Index 2, because 3 figures in whole number. 5680.276 Index 3, because 4 figures in whole number. 79648.9242 Index 4, because 5 figures in whole number. If the number consist of decimals only, the index is 9. when there are no ciphers following the decimal point, and one less for every cipher that follows the decimal point; thus: .2 Index is 9. .02 8. .002 1-! i . .0002 6. .00002 789 5. And so on. TO CORRECT COMPASS COURSE IN POINTS. Allow first the leeway, then the deviation, then the variation. Easterly variation and deviation always allow towards the right hand, and westerly towards the left hand, when finding the true course from the compass course. The student must always imagine himself standing in the center of the compass, looking towards the edge of the card. CoKRErnxG CoiusES. 19 Example. Course. Wind. Leeway. Dev. Var. N.E. N.N.W. 2 points. 1 point E. 3 points W. Now, as the wind is driving the ship's head more to the East, and as she is making two points leeway, it is easily to be seen that she must be making an E.N.E course. Now stand in the center of the compass and look at the E.N.E., then allow the 1 point easterly deviation to the right, and you will be at the E.XN. point. Now look at the E.XN". point, allow the 3 points westerly variation to the left, and you will find it to be N.E.. which is the true course. Example. Course. Wind. Leeway. Dev. Var. N.XW. W.XN. li points. 1 point W. 2 points E. Now, as the wind is driving the ship's head more N., and the lee- way being I14 points, it will be seen that the ship must be making a N.>4E. course through the water; face N.J^E., then allow the 1 point W. deviation to the left, and you will have N.VjW. ; face N.i/oW. and allow the 2 points E. variation to the right, and you will have N.XE.i^E., which is the true course. Example. Course. Wind. Leeway. Dev. Var. W. N.N.W. 1 point. U pts. W. 2^ pts. E. In this case the wind is driving the ship's head to the South, and she would be making a W.XS. course; then allow the 1% points W. deviation to the left, and we get S.W.XW.i/^W.; facing this point and allowing the variation 2^ points E. to the right, we have W.14S., which is the true course. Examples for Practice. '' Course. Wind. Leeway. Deviation. Variation. Answer. N.XE. E.XN. 1 pt. 2 pts. E. \ pt. W. N.XE.^E. S.S.E. s.w. 1^ pts. U pts. W. 2 pts. W. E.XS.iS. E.XS. S.XE. 2 pts. 3 pts. E. 5 pts. W. N.E.XE. S. E.S.E. 3 pts. 2^ pts. W. 4 pts. E. s.w.nv. w. N.N.W. ipt. \l pts. E. 2 pts. E. N.W.XW. E. N.N.E. Ipt. U pts. W. 3 pts. E. S.E.XE.fE N. E.N.E. 2 pts. \ pt. W. Ipt. W. N.W.I W. 20 Taylor's Modern Navigation. j^ote.—The X marked between the letters indicating the courses means the word "by"; thus, N-XW. means "north by west." TO COERECT A COURSE IN DEGREES AND MINUTES. First apply the leeway to the course, which is generally given in points; then turn the result into degrees by noting how many points and quarter-points the course is from the North or South, referring to the table of the angles given in first part of book; then apply the deviation and next the variation, easterly to the right and westerly to the left. Example. Course. Wind. Leeway. Dev. Var. S.W. S.S.E. U points. 10° E. 17° W. S. 59° 4' W. Dev. 10 E. S. 69 4 W. Var. 17 W. True course, S. 52° 4' W. The course being S.W. and the wind being S.S.E., it will be seen that the wind is driving the ship's head more to the West, and therefore she must be making a S.W.XW.I/4W. course by compass, which is 51/4 points from South. By referring to the table of the angles you will find 59° 3' 45" opposite 514 points; this will be S. 59° 4' W., nearly. Now stand in the center of the card and face towards this course, and allow the deviation 10° E. to the right, and you will see that you are going away from South (the point that you are reckoning from), and therefore you must add the 10° E. deviation. Now apply the variation 17° W., and allow it to the left, and you will be going towards the South this time; so you must subtract. The result will be the true course. Example. Course. Wind. Leeway. Dev. Var. N.XE. E. 2 points. 20° E. 14° W. The course after the leeway is applied is N.XW., which is one point from North; this, turned into degrees, is N. 11° 15' W.; Correcting Coursks. 21 then allow the deviation 20° E. to the right, hy subtracting the N. 11° 15' W. from the deviation 20° E., and you get N. 8° 45' E.; then allow the 14° W. variation to the left, and you must subtract the top from the bottom again in this case, and you will have N. 5° 15' W., which is the true course. Thus: Course, N. 11° 15' W. Dev. 20 00 E. N. 8 45 E. Var. 14 00 W. True course, N. 5° 15' W. Example. Course. Wind. Leeway. Dev. Var. W.XN. N. 1 pt. 19° E. Course, S. 90° 00' W. Dev. 19 00 E. S. 109 00 W. Var. 25 00 E. S. 134 00 W. 180 00 25° E True course, N. 46° 00' W. In this case, after allowing the leeway, the course will be West, which is 8 points from the South, and turned into degrees it is S. 90° 0' West. Allowing the deviation, 19° E., to the right, it is seen that we are going away from the South, which is the point we are reckoning from, and therefore we must add ; then allow the variation, 25° E., and as we are still going away from the South we must certainly add. We then have S. 134° W. ; now square this up by subtracting it from 180° and change the name of South to North, and the result is the true course. After a little practice, and by studying the compass-card, the reason why you subtract from 180° will be seen. 22 Taylor's Modern Navigation, Examples for Practice. Course. Winds. Leeway. Dev. Var. Answers. 1. N.N.E. N.W. n Pt. 10° E. 5° W. N. 55° 38' E. 2. W.N.W N. H " 5 E. 10 E. N. 69 23 E. 3. s.w.xw. s. i " 17 W. 2 E. S. 44 4 W. 4. s.xw. W.XS. ^ " 20 W. 17 E. S. 2 38 W. 5. S.S.E. E. \\ " 24 E. 21 E. S. 39 22 W. 6. E.iS. s. i " 11 W. 7 W. N. 74 49 E. 7. E.XN. S.S.E. \ " 27 E. 2 W. S. 81 52 E. The true course will never be more 1 than 90°; so if you have more after i illowing the I corrections, subtract it from 180° and change the name of North to South, or South to North, as the case may be. If you have just 90°, it will be due East or due West. Thus, suppose you had S. 90° 0' W., you would call it West; and suppose you had N". 90° 0' E., you would call it East; and so on. North is no degrees and South is no degrees; they are just plain North or South. THE DAY'S WORK, OE THE RULE TO FIND THE POSI- TION OF SHIP BY DEAD-RECKONING. The elements required to work this problem are the courses steered and the distances sailed on each. We must also know the deviation for each point, which must have been determined at some time before the working of the problem and noted in a compass- book kept for the purpose. Variation. — The variation of the compass will always be found (,n th'j chart of the locality that you happen to be in at the time. The Departure. — When leaving a port it is always the custom to take a departure from a certain point, the latitude and longitude of it being taken from the chart, or from the table of Maritime Posi- tions in the Bowditch Epitome. The bearing of the point by the compass and the distance oft' is then noted, also the deviation for the direction of the ship's head at the time. Now, as we have to reckon as if we had actually sailed from the point, it will be easily seen that we must turn the bearing right around; then apply the- deviation for the direction of the ship's head at the time the bear- ing was taken, and then the variation to get the true course, or de- parture course, as it is sometimes called. ])A\'S WOKK. 23 Example. — The bearing of a point of land being N.W.XW.I/4W., the opposite to it must be S.E.XE.l^E., this being 5i/4 points from South. Turned into degrees, it is S. 59° 4' E. The deviation and variation is then applied, easterly to the right and westerly to the left. We then have the true course, which is called the departure course. Correcting Course. — Then correct each course sailed, for the lee- way, deviation, and variation, as explained elsewhere. Current Course. — The current course, or the set and strength of a current, is taken from the chart or a book of sailing directions for that locality, and is given magnetic; therefore the only correc- iion to be applied is the variation, to get the true set. Rate of Current. — If the rate of the current is given at the rate per hour, all that you have to do is to multiply it by the number of hours in a day, and you will get the amount it will set in one day. 11 the set is given at so much per day, you have only to put the dis- tance given in the traverse table ; and if you want to know what is the rate per hour, divide by 24. Leeway. — The leeway is found by observing the ship's wake and noting the angle between it and the fore-and-aft line of the ship. ^Yhen studying these rules, follow the worked-out examples. Figure by figure. The departure bearing being E.XS. in this example, and the opposite point being W.XN., which is 7 points from North, and this, turned into degrees, being N". 78° 45' W., the deviation for the direction of the ship's head is then applied, and afterwards the variation, when we get the true departure course. (See Ex- ample.) Each course is then corrected for the leeway, then turned into degrees, and afterwards the deviation and variation is applied. Lastly, the current course is corrected for the variation only, as it is magnetic. All the courses being corrected, we now proceed to draw a traverse table, marking a column for the corrected courses, one for the distances sailed on each course, — one each for N., S., E., and W. The N". and S. columns are called the Differ- 24 Taylor's Modern Xavigation. ence of Latitude columns, the E. and W. the Departure columns. We now place each of the corrected courses to the nearest degree in its proper column, commencing with the Departure course and ending with the Current course, marking the distances sailed on each course alongside of the true courses, the distance oflE the point opposite the Departure course, and the amount of current opposite the Current course. Eefer to Table 2 of Bowditch and look for the degree of the first course, and you will find it at the foot of the page ; run your finger up the Distance column and find the distance; alongside of it will be found, in the Latitude column, 1.0, and in the Departure column, 6.9; put the 1.0 in the IST. column because the course is N., and the departure 6.9 in the W. column because it is W. ; then take each course and distance in its proper order and do the same. Now take the last course and look for it at the head of the page; run your finger down the Distance column and find the distance ; along- side of it will be found 18.5 in the Latitude column and 9.9 in the Departure column; put the 18.5 in the S. column because the course is S., and 9.9 in the W. column because the course is W. We will now suppose we have taken out the difference of latitude and departure for all the courses and distances. Next, add the N., S., E., and W. columns separately; subtract the IST. from the S. or the S. from the N". column, and the E. from the W, or the W. from the E., as the case may be. The difference between the IS', and S. columns will be the difference of latitude, and the differ- ence between the E. and W. columns will be the departure. To Fifiid the Latitude In. — Under the latitude left put the differ- ence of latitude, and if they are the same name, add, but if different names, subtract. The result will be the latitude in. In the example the difference of latitude is 58.9, or 59' nearly, because 9 lOths is nearly another mile, and it is named N. because the N. column is the greater. Now, as the latitude left is N. and the difference of latitude is N., we must add, because we are going away fiom the equator, and must therefore increase our latitude. The Latitude in is then 38° 59' N. To Find the Middle Latitude.— \M the latitude in to the lati- tude left and divide the sum by 2. The result will be the middle latitude. Day's Wouk. 25 To Find the Difference of Longitude.— Eniev Table 2 with the nearest degree of the middle Latitude as a course, and look in the Latitude column for the departure. When found, note the distance in the Distance column abreast of it. This distance will be the difference of longitude in minutes. If over 60', turn them into degrees and minutes by dividing by 60. In the example the middle latitude is 38°, so we must turn up 38° in Table 2 and look for the departure 100.5 in the Latitude column. It is then found abreast of 128 in the Distance column ; this 128 is therefore the difference of longitude in minutes, which divided by 60 gives 2° 8', to be named W. because the West column is the greater. To Find the Longitude /n.— Under the longitude left put the difference of longitude, and if they are the same name, add ; if different names, subtract. The result will be the Longitude in. to be named the same as the greater always. In the example the longitude left is 123° W., and as the difference of longitude is also W., it must be added to obtain the Longitude in. ]\rote.—U after applying the difference of longitude the result i> greater than 180°, subtract it from 360°, and change its name. To Find the Course and Distance made Good in a Straight Line. —Before starting to find the course and distance, see which is the greater, the difference of latitude or the departure, — as you must rpad difference of latitude and departure at the head of the page if the latitude is the greater, and at the bottom if the departure is the greater. Look in Table 2 until you find the difference of latitude and departure alongside of each other in their own columns, and when you have located them, the course will be found at the head of the page when the difference of latitude is the greater and at the foot of the page if the departure is the greater. The distance will be found in the distance column abreast of the difference of latitude and departure. In the example the difference of latitude and departure are found alongside of each other on the 60° page, because the departure is the greater, and the distance abreast is 116 miles. To Name the Course.— li the difference of latitude is N., name it N.; if S., name it S.; and towards the E. or W. according as you have made difference of longitude to the E. or W. In the example the course is N. 60° W. because the difference of latitude is N. and the departure is W. 26 Taylor's Modern Navigation. DAY'S WORK. Hours. Courses. Knots lOths Winds. Lee- way. Deviation. Remarks. Pts. 1 N.W.XW. 5 N.XE. 1| 20° W. A point, Pt. 2 5 Reyes, in lat. 3 5 38° N., long. 4 5 123° \V., bore by 5 N.N.W. 4 5 N.E. 2i 10° w. compass E. X 6 4 5 S., distance 7 7 4 miles. 8 4 9 West 4 5 N.N.W. 1 Ship's head 10 3 5 N.W.XW. 11 3 5 12 3 5 Dev. as per 1 W.N.W. 7 North. i 15° W. log. 2 3 4 i Var. 16° 30' 1 7 5 5 E. 5 N.W. 7 5 W.S.W. i 18° W. A current set 6 7 5 correct mag- 7 7 5 netic s.xw.. 8 7 5 distance 21 9 North 7 5 S.W. 2° E. miles, from the 10 6 5 time dep. was 11 6 5 taken to the end 12 6 5 of day. study the above example, and at the same time study the rules. Day^s Work. 27 Examples. Dep. CO. E. XS. Opposite W.XN. N. 78° 45' \V. Dev. 20 00 W. N. 98 45 W Var. 16 30 E. T. dep. CO. N. 82° 15' W. 1st CO. N. 75° 56' W. 4th co. N. 70° 19' W. Dev. 20 00 W. Dev. 15 00 W. N. 9^56' W. N. 85° 19' W. Var. 16 30 E. Var. 16 30 E. T. CO. N.79^'W. T. CO. N. 68° 49' W. 2d CO. N. 47° 49' W. 5th co. N. 39° 23' W. Dev. 10 00 W. Dev. 18 00 W. N. 57° 49' W. N.57°23'W. Var. 16 30 E. Var. 16 30 E. T. CO. N.4T°l9'W. T. CO. N.40°53'W. 3d CO. B. 78° 45' W. 6th co. N. 0° 00' Var. 16 30 E. Dev. 2 00 E. S.95^'W. N. 2°00'E. 180 00 Var. 16 30 E. T.co. N.il^'W. T.co. N.18°30'E. Current CO. S. 11° 15' W. Var. 16 30 E. T. current co. S. 27° 45' W. 28 Taylor's Modern Navigation. TRAVERSE TABLE. Corrected Courses. Distance. Difference of Latitude. Departure. N. s. E. W. N. 82° W. 7 1.0 6.9 N. 79 W. 20 3.8 19.6 N. 41 W. 17 12.8 11.2 N. 85 W. 15 1.3 14.9 N. 69 W. 29 10.4 27.1 N. 41 W. 30 22.6 19.7 N. 19 E. 27 25.5 8.8 S. 28 W. 21 18.5 9.9 '7.4 L8.5 58.9 N. 18.5 8.8 109.3 8.8 Diff. of lat. Lat. left, 38°00'N. 59 N. Dep. 100.5 Long, left, 123° 00' W. Diff. of long. 2 8 W. Lat. in 38° 59' N. 38 00 N. Long, in, 125° 8' W. 2)76° 59' Mid. lat. 38° 29' With difference of latitude 58.9 and departure 100.5, the course is N. 60° W., and distance IIG miles. Day's Wokk. 29 DAY'S WORK. Hrs. Courses. Knots. lOths Winds. Ia-c- Peviiition. Remarks. 1 N.N.E. 14 7 East Pts. 2i 47° E. A point in 2 12 3 lat. 59° 57' 3 10 S., long. 0° 5' 4 10 W., bore by 5 s.xw. 8 E.XS. 11 21° W. compass N. 6 7 W.XW.^W., 7 4 distance 21 8 3 miles. 9 W.^N. 4 5 N.N.W. ^ 29° E. Ship'shead 10 4 5 N.N.E. 11 4 5 12 4 5 Dev. as per 1 E.S.E. 4 N.E. 2f 47° W. log. 2 4 Var. 18° 3 4 5 47' W. 4 5 6 7 8 9 10 11 12 N.W.XW.^W. 4 5 6 6 7 9 13 14 15 5 S.W. 1 22° E. A current set correct magnetic W. X S. i S. 29 E.iS. S.XE. i 19° W. miles from the time dep. was vaken to end of day. 30 Taylor's Modern Xavigation. TRAVERSE TABLE. Dep. CO. Opposit N.W.XW.^W. e S.E.XE.|E. S. 61° 53' E. 47 00 E. Corrected Courses. Dist. Diff. of Lat. Departure. N. s. E. w. Dev. S. 34° E. N. 23 E. S. 9 E. N. 80 W. N. 78 E. N. 47 E. N. 52 E. S. 57 W. 21 47 22 18 17 24 51 29 43.3 3.1 3.5 16.4 31.4 17.4 21.7 15.8 11.7 18.4 3.4 16.6 40.2 Var. S. 14° 53' E. 18 47 W. T. CO. 1st CO. Dev. S. 33° 40' E. N. 5°38'W. 47 00 E. N.41°22'E. 18 47 W. 17.7 17.6 24.3 Var. 97 7 54 9 90 3 59 6 T. CO. 2d CO. Dev. N. 22° 35' E. S. 30° 56' W. 21 00 W. 54.9 59.6 Diff. of lat. 42.8 N. Dep. 30.7 E. Var. S. 9°56'W. 18 47 W. S. 8° 51' E. N. 90° 00' W. 29 00 E. Lat. left, 59° 57' ^ "^ ■■ - -^ -.-Tr 43 ». -Long, ieit, u^ D w . N. 1 1 E. S. Long, in, 0° 56' E. L 5' T. CO. 3d CO. Dev. Lat. in, 59° 14 2)119 1] Mid. lat. 59° 3. Var. N.61°00' W. 18 47 W. With difference of latitude 42.8 and departure 30.7, the course is N. 36° E. and distance 52 miles. T. CO. N. 79° 47' W. S. 36° 34' E. 47 00 W. 4th CO. Dev. 6th CO. S. Dev. S. Var. S. T. CO. N. Current CO. i^ Var. T. CO. f 90° 00' E 19 00 W Var. S. 83° 34' E. 18 47 W. 109° 00' E 18 47 \\ S. 102° 21' PI 180 00 127° 47' E 180 00 T. CO. 5th CO. Dev. N. 77° 39' E. N. 50° 38' W. 22 00 E. 52° 13' E v75° 56' W 18 47 ^\ Var. N. 28° 38' W. 18 47 W. T. CO. N. 47° 25' W. ^.57° 09' W Day's Work. 31 DAY'S WORK. Hrs. Courses. Knots. lOths Winds. Lee- way. Deviation. Remarks, Etc. Pts. 1 s.w. 2 3 8.S.E. 2^ 20° W. A point in lat. 2 2 3 48° 23' N., long. 3 2 B 124° 44' W., bore 4 2 8 by compass East, 5 6 7 s.s.w. 4 West 1 10° W. distance 11 miles. 10 Ship's head S. 8 10 W. 9 S.XE. 10 S.W.XW. 2 2° E. 10 8 Dev.as per log. 11 7 12 4 Var. 23° 20' E. 1 S.E. 2 5 s.s.w\ ^ 17° E. 2 1 5 A current set 3 5 correct magnetic 4 5 N.N.W. 27 miles 5 W^est. 2 8.S.W. i 27° W. from the time the 6 5 dep. was taken to 7 6 the end of the 8 6 day. 9 W.XS. 7 8.xw^ 1 24° W. 10 7 11 8 12 8 Correct the departure course for deviation and variation; com- pass courses steered for leeway, deviation, and variation; current course for variation. Find the latitude and longitude in, and the course and dis- tance made good by inspection. Answers. Dep. CO. K 87° W. 11; S. 7G° W. 10; S. 25° W. 30; S. 8° E. 29; S. 10° E. 5; N. 88° W. 19; S. 87° W. 30; N. 1° E. 27. D. lat. 36.5 S. Dep. 77.0 W. Lat. in, 47° 46' N. D. long. 115' W. T. CO. S. 65° W. Dist. 86 miles. Long, in, 126° 39' W. 32 Taylor's Modern Navigation. DAY'S WORK. Hrs. Courses. Knots. lOths Winds. Lee- way. Deviation. Remarks, Etc. Pts. 1 East. 14 West. 2° W. Position noon yes- 2 12 terday lat. 51° 50' S., 3 11 5 long. 178° 10' E. 4 10 5 5 North. 7 6 E.N.E. \ 20° W. Dev. as per log. 6 7 4 7 7 4 Var. 0° 0'. 8 f7 6 9 E.N.E. 10 8 North. H 8° W. A current set cor- 10 11 2 rect magnetic N.N. 11 11 W. 10 miles during 12 12 3 the day. 1 S.E. 8 2 s.s.w. 2 12° E. 2 7 2 3 6 4 4 6 , 5 S.S.E. 5 East. 1| 15^° E. 6 5 7 5 8 5 9 West. 3 N.N.W. 8 10 2 11 2 12 1 Find the latitude and longitude in, and the course and distance made good by inspection. Answers. 1st CO. N. 88° E. 48, N. 26° W. 30; N. 74° E. 46; S. 56° E. 26; S. 13° W. 20; South 8; N. 23° W. 10. D. lat. 8.6. Dep. 93.2. Lat. in, 51° 41' S. Long, in, 179° 20' W. D. long. 2° 30' E. T. co. N. 85° E. Dist. 93 miles. Day's Work. 33 DAY'S WORK. 10 11 12 S.S.W South. West. N.XE, East. E.XS. (> r) 6 5 (i 5 5 5 5 5 5 ry 5 5 5 4 4 4 1 1 1 1 2 5 5 2 8 Lee way. S.E. E.S.E. S.S.W N.W. N.N.E. N.E. Pts. 4| 18^° W 10° W H 51 A point, Yaquina Head, in lat. 44° 40' N., long. 124° 5' W., bore bv compass N.xE., distance 17 miles. 30° W 12° E. 40° E. 10° E. Remarks, Etc. w Ship's head S.S. Dev. as per log. Var. 20° 40' E. A current set the ship N.xE. correct magnetic 3 miles from the time the departure was taken to the end of the day. Find the latitude and longitude in, and the course and distance made good by inspection. Answers. Dep. CO. S. 13^ W. IT; S. 78° W. 27; S. 44° W. 22; N. 88" W. i:; X. 52° E. 4, S. 12° E. 13; S. 17° W. 30; N. 32° E. 3. D. lat. 83.(3 S. Dep. 61. 7 W. Lat. in, 43° 16' N. D. long. 86. Long, in, 125° 31' W. T. co. S. 36° W. Dist. 104 miles. Taylor's Mod. Nav. 3. 3-i Taylor's Modern Navigation. DAY'S WORK. Hrs. Courses. Knots. lOths Winds. Lee- way. Deviation. Remarks, Etc. Pts. 1 West. 11 E.XS. 2° E. A point in lat. 2 11 37° 42' N., long. 3 10 123° 00' W.,bore 4 8 by compass E.X 5 W.S.W. 7 5 N.W. li 10° E. S.^S, distance 20 6 7 5 miles. 7 7 5 8 7 5 Ship's head 9 South. 7 W.S.W. If 27° E. West. 10 7 11 7 Dev. as per log. 12 7 1 N.W. 5 W.S.W. i 11° W. Var. 16° 10' E. 2 4 3 4 A current set 4 4 correct magnetic 5 N.XE. 4 5 N.W.XW. 2 30° W. W.S.W. 22 miles 6 5 5 from the time the 7 6 5 departure was 8 4 5 taken to the end 9 East. 5 S.S.E. 6 2° W. of the day. 10 5 11 5 12 5 Find the latitude and longitude in, and the course and distance made good by inspection. Answers. Dep. CO. N. 55° W. 20; N. 72° W. 40; S. 80° W. 30; S. 23° W. 28; N. 34° W. 17; N. 20° E. 21; N. 37° E. 2. Current co. S. 84° W. 22'. D. lat. 26.0 N. Dep. 117.8 W. Lat. in, 38° 8' N. D. long. 149. Long, in, 125° 29' W. T. co. N. 771/2° W. Dist. 120 miles. Day's Work. 35 DAY'S WORK. Hrs. Courses. Knots. lOths Winds. Lee- way. Deviation. Remarks, Etc. Pt,s. 1 E.^N. 2 5 N.XE. i 27° E. A point in 2 2 5 lat.O°0',long. 3 4 0° 0', bore })y 4 5 compassEast, 5 W.iS. 7 6 S. X W. 1 29° W. distance 14 6 8 8 miles. 7 8 8 8 8 8 Ship's head 9 8 7 E.^N. 10 8 3 11 N.|E. 7 5 E.XN. ^ 12° E. Dev. as per 12 6 5 log. 1 6 5 2 6 5 Var. 1° 52' 3 E.XS.fS. 6 South. 1| 19° E. E. 4 4 5 4 A current 6 4 set South cor- 7 N.W.XW4W. 6 3 N.^E. 2i 31° W. rect magnetic 8 6 n 1 12 miles from 9 6 8 time dep. was 10 6 8 taken to end 11 6 8 of day. 12 6 6 Find the latitude and longitude in, and the course and distance made good by inspection. Answers. Dep. CO. N. 61° W. 14; S. 64° E. 14; S. 68° W. 51; N. 17° E. 27; S. 69° E. 18; S. &Q° W. 40. Current co. S. 2° W. 12. D. lat. 27.4 S. Dep. 59.1 W. Lat. in, 0° 27' S. Long, in, 0° 59' W. T. CO. S. 65° W. Dist. 65 miles. It will be noticed in this example that the latitude is practically zero; so whenever the latitude or middle latitude is less than 1°, the departure will be the difference of longitude. 36 Taylor's Modern Navigation. DAY'S WORK. S.E4S. N.E.XE. E.^N. E.4S. S.XE.^E. Winds. 1^^^; Deviation E.N.E. N.XW, N.XE. N.N.E. E.XN. u H 10° w 18° E. Remarks, Etc. E. 29° E. 5° W. Sandy Hook light-ship, in lat. 40° 29' N., long. 73° 49' W., bore by compass N., distance 2 miles. Ship's head S. E.|S. Dev. as per log. Var. 9° 20' W. A current set correct magnetic N. E. X E. 11 miles from the time the dep. was taken to the end of the day. Find the latitude and longitude in, and the course and distance made good by inspection. Answers. Dep. CO. S. 19° E. 2; S. 53° E. 38; N. T3° E. 38; S. 64° E. 20; S. 42° E. 50; S. 5° W. 15. Current co. X. 47° E. 11. D. lat. 67.1 S. Dep. 125.5 E. Lat. in, 39° 22' S. D. long. 164'. T. CO, S. 62° E. Dist. 142 miles. Day's Work. 37 DAY'S WORK. Hrs. Courses. Knots. lUths Winds. Lee- Way. Deviation. Remarks, Etc. rts. 1 N.W. 4 5 N.N.E. 1| 2°E. Cape Men- 2 4 5 docino, in 3 4 5 lat. 40° 26' 4 4 5 N., long. 5 WA N. 3 5 N.N.W. i 14° E. 124° 24' W., B 3 5 borebycom- 7 3 5 pass E.S.E., 8 3 5 distance 6 9 W.S.W. 4 5 N.W. 2i 17^° E. miles. 10 6 5 Ship's 11 6 5 head N.W^ 12 5 5 Dev. as 1 2 3 4 S.W.XW.iW. 5 4 3 3 5 3 5 N.^v.^w. U 18° E. per log. Var! 18° O'E. 5 N.XW. 3 W.XN. 1 11° W. A current 6 3 set correct 7 9 magnetic N. 8 3 W. i mile 9 N.W.XN.IN. 5 2 South. 7° W. from time 10 6 5 dep. was ta- 11 7 3 ken to end 12 8 of day. Find the latitude and longitude in, and the course and distance made good by inspection. Answers. Dep. CO. N. 48° W. 6; N. 45° W. 18; N. 58° W. 14; S. 78° W. 23; S. 84° W. 17; N. 7° E. 11; N. 14° W. 27. Current co. N. 27° W. 12. D. lat. 65.3 N. Dep. 79.1 W. Lat. in, 41° 31' N. D. long. 105 W. Long, in, 126° 09' W. T. co. N. 50° W. Dist. 103 miles. 38 Taylor's Modern Navigation. DAY'S WORK. Hrs. Courses. Knots. lOths Winds. Lee- way. Deviation. Remarks, Ktc Pts. 1 s.xw. 5 5 w.x.s. i 15° E. Nantucket New 2 5 5 SouthShoallight, 3 5 in lat. 40° 46' N., 4 5 long. 69° 56' W., 5 s.w.xw. 4 5 North. 27° E. bore by compass 6 4 5 N.W., distance 7 7 4 5 miles. 8 4 5 9 S.E.iE. 8 6 E.N.E. 2 3°E. Ship's head S. 10 12 8 xw. 11 12 8 12 12 8 Dev. as per 1 East. 7 N.N.E. ^ 17° W. log. 2 6 3 6 Var. 13° 0' W. 4 8 5 S.XE. 14 5 E.XS. 1 29° W. A current set 6 14 5 correct magnetic 7 14 W.XS. 10 miles 8 14 from the time the 9 North. 3 W.N.W. 31 19° E. departure was ta- 10 2 ken to the end of 11 1 the day. 12 1 Find the latitude and longitude in, and the course and distance made good by inspection. I ^ ; - ; '. •■•"M 1 • Answers. Dep. CO. S. 43° E. 7; S. 10° W. 21; S. 70° W. 18; S. 35° E. 47; N. 66° E. 27; S. 42° E. 57; N. 48° E. 7. Current co. S. 66° W. 10. D. lat. 101.3 S. Dep. 70.2 E. D. long. 1° 32' E. Lat. in, 39° 05' N. Long, in, 68° 24' W. T. co. S. 35° E. Dist. 123 miles. Day's Woi?k. 39 DAY'S WORK. Hrs. Courses. Knots. lOths Winds. Lee- way. Deviation. Remarks, Etc. 1 S.46°E. 12 Northerly. 2° 5° E. Lat. left, 47° 2 12 57' N.; long, left, 3 12 177° 14' E. 4 12 5 12 Var. 28° 20' 6 12 E. / 12 8 12 9 12 5 10 12 5 11 12 5 12 12 5 1 12 5 2 12 5 3 12 5 4 12 5 5 12 5 6 12 5 7 12 5 8 12 5 9 12 5 10 12 5 11 12 5 12 12 5 Find the latitude and longitude in, and the course and distance made good by inspection. Answers. T. CO. S. 11° E., 296 miles. D. lat. 290.6 S. Dep. 56.5 E. Lat. in, 43° 06' N. Mid. lat. 45° 31'. D. long. 81' E. Long, in, 178° 35' E. 40 Taylor's MeoERN Navigatiox. DAY'S WORK. His. Coursfs. Knots. lOths Winds. Lee- way. Deviation. Remarks, Etc. Pts. 1 South. 7 9 E.S.E. 3 29° E. Position yesterday- 2 / 2 noon, lat.in, 48°10'S., 3 7 2 long, in, 0° 10' E. 4 7 4 5 East. 6 2 N.N.E. n 10° W. Var. 18° 20' W. 6 5 1 7 5 2 A current set true 8 5 2 South 21 miles from 9 5 3 the time the departure 10 5 was taken to the end of 11 5 the day. 12 5 1 West. 6 s.s.w. 5i 14° E. 2 6 3 6 4 6 5 5 6 5 6 North. 6 8 E.N.E. 1 30° W. 7 6 / 8 5 6 9 5 9 10 4 7 11 5 3 12 5 Find the latitude and longitude in, and the course and distance made good by inspection. Answers. Dep. CO. S. 44° W. 29; N. 87° E. 42; N. 32° W. 31; N. 60° W. 40; South, 21. D. lat. 6.6 N. Dep. 29.2 W. Lat. in, 48° 3' S. D. long. 44' W. Long, in, 0° 34' W. T. co. N. 78° W. Dist. 30 miles. 1)ay"s \Voi;k. 41 DAY'S WORK. Hrs. Courses. Knots. lOths Winds. Lee- way. Deviation. Remarks, Kte. Pts. 1 East. ;; 5 N.N.E. 2 42° W. Cape Charles 2 3 5 light-vessel, in 3 3 5 lat. 37° 12' N., 4 o 5 long. 75° 42' 5 3 W., bore by- 6 3 compass W.X 7 N.XE.iE. 3 2 N.W. u 23° W. N., distance 18 8 3 2 miles. 9 3 4 10 3 fi Ship's head 11 3 6 East. 12 s.^w. 3 5 E.S.E. ^ 5° E. 1 3 5 Dev. as per 2 3 2 log. 3 3 2 4 3 2 Var.4°55'W. 5 3 9 6 3 2 A current set 7 s.w.xs.^s. 9 6 W.N.W. 3i 27° E. N. 1 E. correct 8 1 4 magnetic 18 9 1 miles from time 10 1 departure was 11 1 taken to end of 12 1 day. Find the latitude and longitude in. and the course and distance made good by inspection. A ns IV CIS. Dep. CO. X. 54° E. 18; N. Q6° E. 20; Xorth IT; S. 11° W. 23; S. 14° W. 8. Current co. N. 2° W. 18. D. lat. 23.3. Dep. 26.0. D. long. 33' E. Lat. in. 37° 35' N. Long, in, 75° 09' W. T. co. X. 49° E. Dist. 35 miles. 43 Taylor's Modern Navigation. DAY'S WORK. Hrs. Courses. Knots. lOths Winds. Lee- way. Deviation. Remarks, Etc. 1 N.XE.fE. 8 5 East. Pts. 2| 40" E. A point in lat. 2 8 5 20° 47' S., long. 3 8 5 179° 59' E., bore 4 8 5 by compass E. | 5 S.XE. 6 E.XS. U 27° E. S^, distance 12 6 4 miles. 7 4 8 4 Ship's head N. 9 W.| N. 5 N.XW. 3^ 52° E. E.|E. 10 6 11 7 Dev. as per 12 8 log. 1 East. 12 5 N.N.E. i 48° W. 2 13 5 Var. 57° W. 3 14 5 4 14 5 A current set 5 S.S.E. 16 5 8.W. 29° E. correct magnetic 6 16 5 S. X E. 1 E. 2| 7 16 miles per hour 8 16 from the time the 9 W.XS.fS. 5 South. 11 49° W. departure was ta- 10 2 ken to the end of 11 2 the day. 12 1 Find the latitude and longitude in, and the course and distance made good by inspection. N. 28^ W . 34 ;S . 27 = E. 18; S. 54° w E. 65; S. 16° E. 10. Current CO S. 77° Dep. CO. S. 81° W. 12: 26; N. 12° W. 55; S. 51' E. 66. D. lat. 14.7 S. Dep. 65.5 E. Lat. in, 21° 02' S. D. long. 70' E. Long, in, 178° 51' W. T. co. S. 77° E. Dist. 67 miles. In this example the longitude will be greater than 180° after the difference of longitude is applied, so we must subtract it from 360° to get the desired answer. Da.y's Work. 43 DAY'S WORK. Hrs. Ctmrses. Knots. ... \Vin(l^^. wiiy. Doviatiou. Remarks, Etc. ins. 1 N.E. 14 5 N.N.W. 24 10° w. No Sima, Japan, 2 14 5 in lat. 34° 53' N., 3 14 long. 139° 54' E., 4 13 bore bv compass N. 5 E.N.E. 12 5 North. 4i 21° W. W., distance 19 6 12 miles. 7 12 8 12 5 Ship's head N.E. 9 East. 13 5 North. 3 27° W. 10 13 5 Dev. as per log. 11 13 5 12 13 5 Var. 6° 20' E. 1 S.E. 10 5 E.N.E. 2i 10° E. 2 8 A current set cor- 3 7 5 rect magnetic E.N. 4 3 E. 2:^ miles per hour 5 West. 2 S.S.W. 6 35^ E. from the time the 6 1 5 departure was taken 7 1 3 to the end of the 8 2 2 day. 9 N.W. 3 6 N.N.E. ^ 25° E. 10 3 8 11 3 8 12 2 8 Find the latitude and longitude in, and the course and distance made good by inspection. Answers. Dep. CO. S. 49° E. 19; N. 69° E. 56; S. 79° E. 49; S. 77° E. 54; S. 3° E. 29; N. 19° E. 7; N. 19° W. 14. Current co. N. 74° E. 54. D. lat. 8.1 S. Dep. 218.4 E. Lat. in, 34° 45' N. D. long. 4° 27' E. Long, in, 144° 21' E. T. co. S. 88° E. Dist. 219 miles. DIVISION II. THE SAILINGS. The tables required to work the problems contained in this sec- tion of the book are Table 3, Meridional Parts; Table 43, Loga- rithms of Numbers; and Table 44, Log. Sines, Tangents, and Secants. So, before proceeding with the problems themselves, it will not be amiss to explain the use of the above tables. For the sake of illustration, suppose we wish to find the Meridi- onal Parts for 59° 27'. First turn up Table 3 and look along the head or foot of the pages until the required number of degrees is found, namely, 59° ; then under the 59° and abreast of the 27' (which we look for on the side) will be found 4442'.!. Example. — Eequired the Mer. Parts corresponding to 37° 19'. Ans. 2402'.6. Note. — The foregoing is required in the first part of Mercator's Sailing. To Use Tasle 42, Logarithms of Numbers. The index of a number is one less than the number of figures; for example, if the number contain two figures, the index is 1 ; if three figures, the index is 2 ; if four figures, the index is 3, and so on. Therefore, before entering the table, mark down the index, with the decimal to the right. If you look at the first part of the table when it begins at one figure, you will notice that when there is one figure there is a for the index, but when there are two figures there is 1 for the index, and abreast of 100 there is 2. of an index; after this you are supposed to know how to find the index yourself, according to the rule given above. Example. — Eequired the log. corresponding to 4976. Here we have four figures, so the index is three, expressed thus, 3. Then search for the first three figures on the left, namely, 497, and abreast of them, under the fourth figure, which is 6, take out the log. and mark it down; thus, 3.69688. Example. — Eequired the log. for 293. Here there are three figures only, so abreast of the number 293, in the first column, you will find 2.46687, to which you must prefix the figure 2, because 2 is the index of three figures. If the number consist of more than four figures, proceed by the rule given on pages 184-185, Bowditch Epitome, edition of 1903. Sailings. 45 After learning the foregoing the student must next understand how to take out of Table 42 a number corresponding to a given logarithm. Example. — Find tlie number corresponding to log. 2.58070. Here you must search in the body of the table until the number 58070 is found, then note the figures to the left and the figure on top of the column; in this case it will be found abreast of 380 and under the 8 ; mark down all four and point ofE one figure, namely, the 8, because there are two in the index, for the reason that the number found must always be one more than the index of the log. The answer will then be 380.8. If tihere be only one for index, then point off two figures; thus, 38.08. If only a cipher, then point off three; thus. 3.808. But if there be three for index, then place the point to the right of all four, and the answer will be 3808. of a v\-hole number. To Use Table 44, Log. Sines, Tangents, and Secants. When entering this table to take out a log., there are two ways of reading it ; namely, from the top and from the bottom. If you read degrees on the top. read the names on the top, and minutes from the same side, under the degrees; but if you read degrees from the bottom, read the names from the bottom, and minutes above the degrees. Example. — Eequired the log. sine of 30° 27'. Look on to]) of page for the 30°, then under the 30° look for the 27', and take out the log. from the sine column abreast, which is 9.70482. E.vample. — Required tlie log. tangent of 67° 55'. Here we must look for the degrees on the bottom of the page, because they are more than 45°, and when found, run up the minute column until we see 55', then abreast of it, and in the tangent column, reading from the bottom, we find the log. 10.39177. Example. — Required the log. cosecant of 112° 45'. Look for 112° on the bottom of page and for the 45' above it. Abreast of the 45° will be found, in the cosecant column, 10.03517. 46 Taylor's Modern Navigation. To Find the Degrees and Minutes Corresponding to a Log. — Search in the required column until the log. is found, and note the degrees on the top and the minutes to the left if the name is taken from the top, but if the name is taken from the bottom, read the degrees from the bottom, and the minutes to the right. Example. — Eequired the degrees and minutes corresponding to log. tangent 10.47213. Here we search in tangent column, looking from the bottom whenever the index of log. tangent is 10. or more, and from the top when the index is 9. or less. We find in this example the log. abreast of 22' on the 71° page, so we mark down 71° 22'. Note. — It is unnecessary in the sailings to work logs, to seconds, but it is in some of the higher problems, and will be explained when necessary. MERCATOR'S SAILING. Mercator's sailing is the method used to find the true course and distance between two places when the latitude and longitude are known. For the theory of this problem, see page 49, articles 124 and 125, also page 19, article 63, Bowditch Epitome, edition of 1902. Rule. Mark down the latitudes and longitudes under each other, as seen in the example. Find the difference of latitude by adding the latitudes together if they are of different names, and by subtracting if the same name. Bring the sum, or remainder, into minutes by multiplying by 60. The result will be the diff. of kit. in minutes. Next find the difference of longitude by adding the longitudes- together if they are of different names, and by subtracting if the- same name. Bring the sum, or remainder, into minutes by multi- plying by 60. The result will be the diff. of long, in minutes. To Find the Meridional Difference of Latitude. — Take out of Table 3 the Mer. Parts for both latitudes. Thus, look on the top of the page for the degrees, and on the sides for the minutes. Run your finger across from the minutes, and under the degrees will be- Sailings. 47 found the Mer. Parts. Mark these Mer. Parts under each other, and add or subtract them, according as you add or subtract the latitudes. The result will be the mer. diff of lat. To Find the Course. — Mark down the diff. of long, and under it the mer. diff. of lat., always adding 10 to the index of* the diff. of long. Take out of Table 43 the log. of the diff. of long., always subtraeting from it the log. of the mer. diff. of lat. Now look for the remainder in the tangent column of Table 44, and when found, note the degrees on the top and the minutes to the left, if you read tangent from the top ; but if you read tangent from the bottom, note the degrees at the bottom and the minutes to the right. In either case the degrees and minutes will be the course. To Name the Course. From a S. lat. to a N. lat. the course is N. From a N. lat. to a S. lat. the course is S. From a N. lat. to a greater N. lat. the course is N. From a N. lat. to a smaller X. lat. the course is S. From a S. lat. to a greater S. lat. the course is S. From a S. lat. to a smaller S. lat. the course is N. From a w long. to an E. long. the course is E. From an E. long. to a W long the course is W From an E. long. to a greater E. long. the course is E. From an E. long. to a smaller E. long. the course is W From a W long. to a greater W long. the course is W From a W long. to a smaller \\ long. the course is E. If the sum of the two longitudes be greater than 180°, subtract it from 360° and reduce the remainder to minutes. The result ■will be the diff. of long. In this case, name the course the same name as the longitude from. To Find the Distance.— Take out of Table 44 the secant of the ,course and add the log. (Table 42) of the diff. of lat. to it. The .sum, rejecting 10 from the index, will be the log. of the distance (Table 42). The number of figures required in the distance will always be •one more than the index of the sum of the logs. ; that is, if the in- dex is 1, two figures will be required; if 2, three figures; if 3, four :figures, etc. 48 • Taylor's Moderj^ Xavigatiox. Lat. A, 38° 00' N. Lat. B, 34 29 N. 2454.1 2193.6 3 31 Mer. Part, 260.5 60 Diff.oflat. 211 Examples. (Tables required: Meridional Parts, Table 3; Common Loga- rithms, Table 42; Log. Sines, Tangents, and Secants, Table 44.) Example. — Find the course and distance from A to B. Long. 18° 15' E. Long. 20 40 W. 38 55 60 Diff. of long. 2335 To Find the Course. Log. of diff. of long. 2335 =13.36829 (Subtract always.) Log. of Mer. Parts, 260.5= 2.41581 Tangent, 10.95248 Course S. 83° 38' W. To Find the Distance. Secant of course, 83° 38' = .95510 (Add always.) Log. of diff. of lat. 211 = 2.32428 Log. of distance, 3.27938 Dist. 1903 miles. The index of the diff. of long, is 3, but as 10 must always be added to the index of diff. of long., the index must be 13. The in- dex of the Mer. Parts is 2, because there are only three whole numbers in it. When looking for the tangent in the question, you must read from the bottom of the page and note the minutes to the right; the secant is found abreast of the tangent. The log. of the distance is found abreast of 190 and under 3. To Name the Course. — From North to less North latitude the course is South ; from East to West, the course is West. Example. — Find the course and distance from A to B. 1112.1 Long. 178° 12' E. 674.9 Long. 168 12 \\\ Mer. Part, 1787.0 316 24 360 00 Lat. A, 18° 20' N. Lat. B, 11 29 60 15 35 S. Diff. of lat. 1775 13° 36' 60 Diff. of long. 816 Sailings. 4J> To Find the Course. Log. of diff. of long. 816 -=12.91169 (Subtract always.) Log. of Mer. Parts, 1787.0= 3.25212 Tangent, 9.65957 Course S. 24° 33' E. To Find the Distance. Secant of course, 24° 33'= .04115 (Add always.) Log. of diff. of lat. 1775 =3.24920 Log. of distance, 3.29035 Dist. 1952 miles. In this case the sum of the longitudes is greater th<\n ISO"^, and therefore must be subtracted from 360° and the remainder reduced to minutes. When this occurs, name the course the same name as the first longitude or longitude from. The number of figures required in the distance is always one more than the index calls for. Examples for Practice. Xo. 1. Find the course and distance from Point Eeycs. in latitude 38° 00' jST., long. 123° 0' W., to No Sima, Japan, in latitude 34° 53' N., long. 139° 54' E. From lat. 38° 00' N". Long. 123° 00' W. To lat. 34° 53' X. Long. 139° 54' E. Answer.— D. lat. 187'; mer. D. lat. 231.5; D. long. 5826'; tan- gent 11.40082; T. co. S. 87° 43' W.; log. of dist. 3.67151; dist. 4694 miles. No. 2. Find the course and distance from Cape Beale to Cape Arago. From lat. 48° 48' N. Long. 12-5° 14' W. To lat. 43° 21' N. Long. 124° 23' W. Answer.— D. lat. 327'; mer. D. lat. 470.4; D. long. 51'; tangent 9.03510; T. co. S. 6° 12' E.; log. of dist. 2.51710; dist. 328.9 miles. No. 3. Find the course and distance from Honolulu to Auckland. From lat. 21° 18' N. Long. 157° 52' W. To lat. 36° 50' S. Long. 174° 49' E. Answer.— D. lat. 3488' ; mer. D. lat. 3666.6 ; D. long. 1639 ; tan- gent 9.65027; T. co. S. 24° 5' W.; log. of dist. 3.58213; dist. 3821 miles. Taylor's Mod. Nav. 4. 50 Taylor's Modern Navigation. No. 4. Find the course and distance from Auckland to Sydney. From- lat. 36° 50' S. Long. 174° 49' E. To lat. 33° 50' S. Long. 151° 18' E. Answer.— D. lat. 180'; mer. D. lat. 219.7; D. long. 1411'; tan- gent 10.80770; T. co. N. 81° 9' W.; log. of dist. 3.06818; dist. 1170 miles. No. 5. Find the course and distance from Auckland to Cape Horn. From lat. 36° 50' S. Long. 174° 49' E. To lat. 55° 59' S. Long. 67° 16' W. Answer.— D. lat. 1149'; mer. D. lat. 1686.7; D. long. 7075'; tan- gent 10.62261; T. co. S. 76° 35' E.; log. of dist. 3.69477; dist. 4952 miles. No. 6. Find the course and distance from Cape Horn to St. Helena. From lat. 55° 59' S. Long. 67° 16' W. To lat. 15° 55' S. Long. 5° 44' W. Answer.— D. lat. 2404; mer. D. lat. 3091.9; D. long. 3692; tan- gent 10.07702; T. co. N. 50° 3' E.; log. of dist. 3.57331; dist. 3744 miles. No. 7. From lat. 12° 4' S. Long. 77° 16' W. To lat. 20° 13' S. Long. 70° 12' W. Answer.— Tangent 9.92236; T. co. S. 39° 54' E. ; log. of dist. 2.80442 ; dist. 637 miles. No. 8. From lat. 17° 42' S. Long. 71° 23' W. To lat. 20° 12' S. Long. 70° 11' W. Answer.— Tangent 9.65867; T. co. S. 24° 30' E.; log. of dist 2.21707; dist. 164.9 miles. No. 9. From lat. 56° 17' N. Long. 176° 59' E. To lat. 40° 18' S. Long. 101° 50' E. Answer.— Tangent 9.82690; T. co. S. 33° 52' W.; log. of dist. 3.84380; dist. 6980 miles. Sailings. 51 Xo. 10. From lat. 60° 27' S. Long. 179° 59' W. To lat. 1° 15' S. Long. 179° 20' E. Answer.— T. co. N. 00° 32' W.; dist. 3552 miles. Xo. 11. From lat. 0° 2' X. Long. 153° 40' W. To lat. 10° 15' S. Long. 153° 40' E. Answer.— T. eo. S. 78° 59' W.; dist. 3224 miles. Xo. 12. From lat. 38° 50' X. Long. 50° 38' E. To lat. 00° 00' Long. 00° 00' Answer.- T. co. S. 50° 21' W.; dist. 3G51 miles. Xo. 13. From lat. 75° 15' S. Long. 108° 22' E. To lat. 42° 59' S. Long. 10° 20' W. Answer.— T. co. X. 59° 43' W.; dist. 3839 miles. Xo. 14. From lat. 25° 16' X. Long. 00° 20' E. To lat. 48° 18' X. Long. 15° 29' W. Answer.— To. co. X. 28° 33' W.; dist. 1573 miles. Xo. 15. From lat. 58° 58' X. Long. 75° 40' W. To lat. 40° 15' X. Long. 0° 2' E. Answer.— T. co. S. 68° 50' E.; dist. 3110 miles. Xo. 16. From lat. 10° 16' S. Long. 88° 51' W. To lat. 17° 20' X. Long. 40° 50' W. Answer.— T. co. X. 59° 57' E.; dist. 3310 miles. PAEALLEL SAILIXG. To Find the Distance Between Two Places ^Yhen Their Latitudes Are the Same. EULE. To the cosine of the latitude add the log. of the diff. of long. The sum, rejecting the 10 in the index, will be the log. of the distance. 52 Taylor's Modern Navigation. Exantples. From lat. 38° 00' X. Long. 123° 00' W. To lat. 3S° 00' X. Long 179 59 W. 56° 59' 60 3419 Cosine of lat. 38° 00' N. -9.89653 Log. of diff. of long. 3419 =3.53390 3.43043 = 2694 miles. Lat. 10° 12' X. Long. 45° 50' E. Lat. 10° 12' X. Long. 18° 20' E. List. 1624 miles. Lat. 27° 52' X. Long. 89° 10' W. Lat. 27° 52' X. Long. 20° 15' E. Dist. 5804 miles. Lat. 34° 5' S. Long. 100° 10' W. Lat. 34° 5' S. Long. 74° 45' W. Dist. 1263 miles. Lat. 12° 16' S. Long. 176° 21' E. Lat. 12° 16' S. Long. 176° 21' W. Dist. 428.0 miles. MERCATOK'S SAILIXG BY IXSPECTIOX (SHORT METHOD). Find the diff. of lat.. mer. diff. of lat., and diff. of long, as in the longer method. Point off to the right one figure of each, making them small enough to enter the tables. With a tenth part of the mer. diff. of lat. as lat., and a tenth part of the diff. of long, as dep., enter Table 2 and search for them in their own columns until they are found alongside of each other. When found, note the degrees on top of page if lat. is the greater, and on bottom if dep. is the greater. The result will be the course, to be named by the same rule as in the longer method. Sailings. 53 To Find iJic Dlstanvc. — Kcej) on ^ame page and search in the lat. column for one tenth j)art of the proper clifE. of lat.. and when found, note the distance al)reast in the distance column, annex a cipher to it. and the result will he the distance. If a tenth part of the element recpiired is too large for the tal)le, take one half or one third, and enter the tables as before; but when finding the distance, multiply the result by whatever figure was used to reduce the elements. This method is correct for short distances only, and should be used only for finding the distance between position of one day and the next. Thus, suppose diff. of lat. to be 129' ^., nier. diff. of lat. 140', and diff. of long. 89' W. Find course and distance by inspection. The diff. of long., 8.1), in de}). column, } ^- , ^ ^ roo ly Mer. diff. of lat., 14.0, in lat. column, S ^ ^ ' and 12.9, in lat. column, gives 24, in the distance column abreast, wdiich, multiplied by 10, gives 240 miles. TO FIND THE DIFFEKEXCE OF LONGITUDE BY PAEALLEL SAILING. This method may Ije put to ]iractical use when finding the diff. of long, in day's work. Rule. Take the secant of the middle latitude from Taljle 44 and add the log., Table 42, of the departure to it. The sum. rejecting the 10 from the index, will be the log. of the diff. of long.. Table 42. Example.— lA\t. 49° 54' N., dep. 134.G. Required the diff. of long. Secant of lat. 49° 54' = 10.19103 Log. of dep. 134.6 = 2.12905 2.32008=209.0 diff. of long. We found the sum (nearly) of these logs, abreast of 209, and under 0, therefore we mark down 2090; and because the index is 2, we must have three figures in the answer, therefore we put the deci- mal point before the last figure and get 209.0, which is the diff. of long. 54: Taylor's Modern Xavigation. Examples for Practice. Lat. 2° 27' S.; dep. 59.6. Required the diff. of long. Answer. — 59.66. Lat. 19° 51' N.; dep. 181.6. Required the diff. of long. Answer. — 193.1. Lat. 19° 51' X.; dep. 320.5. Required the diff. of long. Answer.— 340.8. Lat. 82° 10' S.; dep. 10.9. Required the diff. of long. Answer.— 79.98. MIDDLE-LATITUDE SAILING. (Extract from Lieutenant Raper's Epitome of Navigation, pages 103, 104.) (This valuable book should be in the lil)rary of every navigator, or those interested in navigation.) "The diff. of long, found by mid. lat. is true at the Equator, and very nearly true for short distances in all latitudes, especially when the course is nearly East or West. In hig*h latitudes, when the distance is great and the course oblique, the error becomes considerable, but the result may be made as accurate as we please by subdi-^iding the distance run into small portions and finding the diff. of long, for each portion separately. "The diff. of long, deduced by mid. lat. sailing is too small; an estimate of the error for places on the same side of the Equator may be formed with the help of a few cases. Suppose the course 4 points, or 45°, and the D. lat. 10°, or 600 miles; then if this D. lat. is made good in any lat. below 30°, the error of the D. long, will not exceed 2'; if made good between the parallels of 40° and 50°, the error will be about 3'; and between 60° and 70°, about 19', or one third of a degree. For smaller distances the errors will be much less, and for greater distances much greater, as they vary in much more rapid proportion than the distances. "It is proper to remark that when the course is large, that is, nearly seven or eight points, the diff. of long, should be found by mid. lat. in preference to Mercator's sailing; because, although the latter is mathematically correct in principle, yet a small error in the course may, when the course is large, produce a considerable error in the diff. of long. Sailings. 55 "The reason of this is easily shown. In mid. lat. sailing we convert the departure into D. long. The process increases the dep. in a proportion which is less than 2 to 1 in all latitudes below 60°, and exceeds 3 to 1 in latitudes beyond 70°. The error of the dep., increased in the same proportion, becomes thus the error of the D. long. Now, when the course is nearly East or West, the dep. is nearly the same as the distance, and an error of some de- grees in the course does not affect the dep. sensibly ; hence in this case the error of the D. long, depends on that of the dist. alone. "But in Mercator's sailing, on the other hand, we convert the Mer. diff. of lat. into diff. of long., and the process, when the course is large, converts a given Mer. diff. of lat. into diff. of long, much greater than itself; and thus increases the error of the Mer. diff. of lat. in the same proportion. Thus, for example, at the course 80° the D. of long, exceeds the Mer. diff. of lat. in the pro- portion of 6 to 1; at the course 85° this proportion is 11 to 1. Now, when the course is large a slight change in it sensibly affects the D. lat., and also the Mer. diff. of lat., which is deduced directly from it. "In high latitudes the Mer. Parts vary rapidly, and the error of the D. long, is aggravated accordingly; hence the precept more especially demands attention in high latitudes." Middle Latitude Sailing is a method to find the true course and distance betwei'n two places when both latitude and longitude are given. There are quite a number of different cases, but only one will be given here, as it will be sufficient for the ordinary practice of navi- gation. The method is not exact in all cases, but may be used with abso- lute confidence when the distance is small and the ship is in a high latitude, also when latitudes have same name, and for larger distances if the latitude is low and the course greater than 45°, — the nearer 90°, the better. If the latitudes have different names, the two portions of the track on the opposite sides of the Equator should be calculated separately. Rule. Mark down on the left-hand side of the page the two latitudes under each other, and a little to the right mark down the same lati- tudes again, and on the right-hand side of page mark down the two longitudes as seen in the examples. 56 Taylor's Moderx Xavigation. To Find the Difference of Latitude. — If the latitudes have the same name, subtract the lesser from the greater; but if different names, add and bring the result into minutes by multiplying by 60. To Find Middle Latitude. — If latitudes have same name, one half the sum will be the mid. lat., but if different names, and are nearly equal, one half the greater lat. will be the mid. lat. ; then multiply by 60 to obtain the minutes. These rules may be assumed to be correct for short distances and for ordinary purposes, but they are not really so, since the true mid. lat. will always be a little nearer to the Pole. There is a table given in the Bowditch Epitome, computed by Workman in 1805, whereby the true mid. lat. may be found, but it is not necessary unless great accuracy is required. To Find the Difference of Longitude. — If longitudes have same names, subtract the lesser from the greater; but if different names, add, and bring the result into minutes by multiplyiug by 60. The computation will then be as follows : To Find the Course. — To the log. of the diff. of long, add cosine of mid. lat. and suijtract from the sum the log. of the diff. of lat. The remainder will be the tangent of the course. iSTame the course by same rule as in Mercators sailing. To Find Distance. — To the secant of the course add the log. of diff. of lat. The sum. rejecting 10 from the index, will be the log. of the distance. Example. — Find the true course and distance from A to B by middle-latitude sailing. Lat. A, 20° 38' N. 20° 38' N. Long. A, 156° 22' W Lat. B, 27 06 N. 27 06 N. Long. B, 142 11 E. 6 28 2)47 44 "298""33 60 Diff. of lat. 388 Mid. lat. 23° 52' 360 00 61 27 60 Diff. of long. 368^ Sailings. 57 To Find the Course. To log. of diff. of long. 3687'= 3.56667 Add cosine mid. lat. 23° 52'= 9.96118 From sum, 13.52785 Subtract log. diff. of lat. 388'= 2.58883 Gives log. tangent of course, N. 83° 26' W. = 10.93902 To secant of course, X. 83° 26' W. = 10.94173 Add log. D. lat. 388'= 2.58883 Log. of dist. 3.53056 = 3393 miles. Answer.— N. 83° 26' W. Dist. 3393 miles. Example. — Find the true course and distance from A to B by middle latitude sailing. Lat. A, 38° 00' N. 38° 00' N. Long. A, Lat. B, 34 29 N. 34 29 N. Long. B, , 18° 15' E. , 20 40 W, 3 31 2)72 29 60 _I1 Mid. lat. 36° 14' D. lat. 211 D. long. Log. I), long. 2335'= 3.36829 + Cosine mid. lat. 36° 14'= 9.90667 38 55 60 2335 Sum, 13.27496 -Log. D. lat. 211'= 2.32428 -Tangent of course, S. 83° 36' W. = 10.95068 Secant co. S. 83° 36' W. = 10.95285 + Log. D. lat. 211'= 2.32428 Log of dist. 3.27713 = Answer.— S. 83° 36' W. Dist. 1893 Miles. = 1893 miles. GREAT-CIRCLE SAILIXG. A great circle is an imaginary line drawn around the world. which, if the world were cut through on this line, woulil divide it into two equal parts, the knife passing through the center. It is gen- erally defined thus : A great circle is a circle whose plane passes through the center of any sphere. All true meridians are great circles; so, also, is the Equator a great circle. 58 Taylor's ]\Iodern Xavigatiox. The preceding methods, namely, Mercator's and middle lati- tude sailing, give the true course and the distance from one place to another, but this is not the shortest distance, although if you steer on this course it will eventually bring you to your destination. By plotting the course by Mercator's or middle-latitude sailing on a Mercator's chart, it will be noticed that the course makes the same angle with each meridian it crosses; but if you go to a globe and stretch a thread between two places, like San Francisco and Yokohama, Japan, it will be seen that the thread cuts each true meridian at a different angle. It is therefore very evident that the Mercator or the middle-latitude course will not take you the shortest distance, for the reason, as before remarked, that the course is always the same, whereas on the great circle the course is always changing. If the course between two places is Xorth or South, or if both places are on the Equator, where the course would be East or West, it is obviously unnecessary to consider the problem of great-circle sailing, as, under such circumstances, we should be sailing on the Equator or on a true meridian, which are both great circles. The computation of the problem is a very lengthy one, and is rarely used. It involves the calculation of the Vertex, maximum separation of the latitude, etc., but the United States Hydrographic Office comes to the rescue of the navigator by publishing the Great Circle or Gnomonic Chart. On the monthly Pilot Charts (which may be obtained free of charge from the local Hydrographic officials) the principal great- circle tracks are printed, but if the one desired is not found thereon, recourse must be had to the Great Circle Chart itself. EULE. Lay a straight-edge over the two places and draw a straight line, and mark off the latitude for every five degrees of longitude, trans- fer these positions to a Mercator's track chart, and calculate, by either Mercator or middle-latitude sailing, the true course and the distance between each position. This rule will be sufficiently correct for all practical purposes, but if greater accuracy is desired, mark off the latitude for each two and a half degrees of longitude, instead of five as before ex- plained. The student is advised to procure a chart and follow the instructions and examples given thereon, especially the rule given to find the track beyond the limit of the chart. DIVISION III. LATITUDE BY MERIDIAX ALTITUDE OF THE SUN. The Observation. — A few minutes before noon bring down the sun's image to the horizon and make the lower edge, or lower limb, touch it very nicely. Watch the sun as it rises, and each time a space is seen between the sun's lower limb and the horizon, make them touch again by means of the tangent-screw. As the sun approaches the meridian it moves in altitude very slowly; so, watch it closely until the lower limb is seen to overlap the horizon, but do not bring it up again, because the last altitude observed will be the Meridian Altitude. Read what is on the sex- tant, and proceed to work the problem according to the following rules : Mark down the day of the month on the left-hand side and the longitude of the ship on the right-hand side of the page. Convert this longitude into time by multiplying by 4 and dividing by 60, or use Table 7. Place this time under the ship's date, and subtract it from the ship's date if ship is in East long, and add if in West long. This will give the Greenwich Apparent Time (G.A.T.). To Correct the Declination for the G.A.T. — Take out of the Nautical Almanac, for apparent noon, the sun's declination and its difference for one hour, abreast of the Greenwich date. Mul- tiply the difference for one hour by the hours and tenths of hours of the G.A.T., crossing off from the product as many figures as you have decimals in the question. The remainder will be sec- onds, which must be converted into minutes and seconds by dividing by 60, if the remainder should be more than 60. The result will be the correction for the declination, to be added to the declination if declination is increasing, but subtracted if declination is decreas- ing. To Correct the Altitude. — Mark down the observed altitude, and place, at some distance to the right of it, the sign of + and of — . Place the index error (I.E.) under the -f" or — sign, as the case may be. Then turn up Table l-l, and with the height of the eye in feet above the level of the sea take out the dip and place it always 60 Taylor's Modern Navigation. under the — sign. Xext enter Table 20 with the degrees of alti- tude in the altitude column and take out the Refraction and place it always under the — sign. Then enter Table 16 with the de- grees of altitude and take out the Parallax, and place this always under the -\- sign. Now enter the Nautical Almanac on page 1, and take the sun's semidiameter from abreast of the Greenwich date. Place this under the + sign if the lower limb (L.L.) of the sun is observed, and under the — sign if the upper limb (U.L.) of the sun is observed. Take the sum of the -\- column and the sum of the — column and subtract the lesser from the greater. This will give the correction for the altitude, to be added to the altitude if the -|- column be the greater, and subtracted if the — column be the greater. The result will be the True Altitude of the Sun. Subtract this True Altitude from 90°, and the remainder will be the sun's Zenith Distance (Z.D.), to be named opposite to the sun's bearing. Now apply the corrected declination to this Z.D., adding if of the same name, but subtracting if of contrary names. The result will be the Latitude, which must be named the same name as the greater. If the True Altitude be greater than 90°, subtract 90° from it. The remainder will be the Z.D., to be named the same as the bear- To Find the TeutJts of Hours. — The number of times that 6 will go into the minutes will give the tenths of hours. The method given in these rules to correct the declination is the best for a beginner, but there is another method very much in use among experienced navigators, namely, that of correcting the declination for the longitude in time, or from the nearest noon. If the student wish to correct his declination for the longitude in time, he must work in the following manner: Convert the longi- tude into time, as usual, and take out the declination for the ship's date, and multiply the difference in one hour by the hours and tenths of hours of the longitude in time. This will give the cor- rection for the declination, and when applying this correction go by the following rules : If in East longitude, and the declination is increasing, subtract the correction; but if the declination is de- creasing, add the correction. If in West longitude, and the declina- tion is decreasing, subtract the correction, and if increasing, add the correction. This method of correcting the declination must be used only in the problem of latitude by sun's Meridian Altitude. Meridian Altitude. 61 To Find ike Greenwich Apparent Time {G.A.T.). Convert the longitude into time by the preceding rule, and if in East longitude, subtract from tlie ship's date; but if in West longi- tude, add to ship's date. Example.— 189^, May 21st, in longitude 145° 10' E. Required the G.A.T. Mark down May 21^ 0" 0"' 0^ Long. 145° 10' E. Sub., because E. long., 9 40 ^ 4 G.A.T. 20^ 14'^ 19"^ 20« 60)580 4Q_ Long, in time, 9^^ 40^" 40« In this example we subtract, because the longitude is East; so we must say, 40^ from 60^ leaves 20^ ; then, as we have borrowed 1 minute, we must take 40°^ from 59°^, which leaves 19™; then take 9^ from 23^ and we get 14^, and as we have borrowed 1 day, the date will now be the 20th. Example.— 1S94:, June 1st, in long. 92° 17' E. Required the G.A.T. Mark down June 1'' 0^^ 0"^ O'' Long. 92° 17' E. - 6 9 8 E. 4 G.A.T. May 31'' 17'^ 50"^ 52« 60) 369 08 Long, in time, 6*^ 9"^ 08' ^ote.—Jn this case we have to borrow a day. Example.— 1S94:, August 27th, in long. 115° 27' W. Required the G.A.T. Mark down Aug. 27^10" 0'» 0« Long. 115° 27' W. Add, because W. long. 7 41 48 4 G.A.T. Aug. 27ni^ll^48« 60)4 61 48 Long, in time, 7^ 41"^ 48» Note.— In West longitude wo always add. 63 Taylor's Modern Xavigation. To Correct the Swi's Declination for the G.A.T. Example.— ISdi, November 21st, in longitude 49° 59' E. Re- quired the G.A.T., and thence the declination. Nov. 21"^ 0^ O''^ 0^ Long. 49° 59' E. -3 19 56 E. 4 G.A.T. 20*1 20*^ 40'» 4^^ 60)199 56 Long, in time, S'^ 19"^ 56* Now look in the Nautical Almanac for the declination, which is found abreast of November 20th, and when found, mark it down, also take out the diff. in 1 hour, found abreast of the declination. Multiply this diff. in 1 hour by the hours and tenths of hours of the G.A.T. Decl. for Nov. 20=19° 46' 04" S. Diff. in 1 hour, 33".80 Decl. increasing, +1136 20.6 Correct decl. 19° 57' 40" S. 20280 67600 60)696.280 11' 36" As 6 minutes are one tenth of an hour, and 6 goes into 40 6 times, 6 must be the tenths of hours. Note. — Cross off as many figures from the product as there are decimals in the question. 696 divided by 60 gives 11' 36", the correction for the declina- tion. Example.— 1894, March 20th. in longitude 179° 10' W. March 20'^ 0'^ 0'" 0« Long. 179° 10' \V. + 11 56 40 4 G.A.T. 20*^ IP 56'"40« 60)716 40 Long, in time, 11'' 56'" 40« Meridian Altitude. 63 Decl. March 20th, 0° 2' 50" S. Diff. 1 hour, 59".22 Decl. decreasing, —11 44 11.9 Cor. decl. 0°1)8' 54" N. 53298 5922 5922 60)704.718 11' 44" Note. — In this case the sun is about to cross the Equator; so, subtract the declination from the correction, and the remainder is the corrected declination, of an opposite name. Examples Complete. 1894, February 28th, in longitude 120° W. Observed meridian altitude of sun's lower limb, 29° 32' 15", bearing South. Index error, —4' 11". Height of eye, 30 feet. Find the latitude. Feb. 28*1 00^^ 00°^ 00« + 8 00 00 G.A.T. Feb. 28'' 8^ 00"" 00« Decl. 7° 51' 12" S. -7 34 Cor. decl. 7° 43' 38" S. Obs. alt. 29° 32' 15" S. + 5 03 29 37 18 90 00 00 60 22 42 N. 7 43 38 S. T. alt. Z.D. 60 22 42 N. + 5' 03" Cor. decl. Lat. 52° 39' 04" N. Long. 120° W. 4 60)480 gh Qm Diff. J Eor 1 hour, 56".78 8. 60)454.24 7' 34" + S.D. 16' 11" Parlx. + 08 + 16 19 -11 16 LE. 4' 11' Dip, 5 22 Ref. 1 43 -11' 16' The longitude in time is 8 hours West, and is added to the ship's date to obtain the G.A.T. In correcting the declination it will be noticed that there are only two decimal figures used, therefore fil Taylor's Modern Navigation. only two are crossed olf from the product. The correction for the declination is subtracted, because declination is decreasing. It will also be noticed that the Z.D. and declination are of con- trary names, and therefore one is subtracted from the other to ob- tain the latitude, and the latitude is named North, or same name as the greater. NERiDiAN Altitude Example No. 1 Let N Z S n represent the plane of the celestial sphere. Z Zenith, N S Horizon, n Nadir, P P Poles, Q Q Equator, X Sun, obs. Observer. The student must imagine himself standing in the center of the sphere, at the point marked obs., the upper part of the circle being light and the lower part darkness. Eequired to find the arc P N, namely, the elevation of the Pole. which is always equal to the arc Z i}. Either one being equal to the latitude. X S Sun's Altitude. Q X Declination. X Z Zenith distance. Meridian Altitude. 65 Therefore, X S subtracted from 90° (which is the arc Z S), gives the Zenith distance X Z, so X Q subtracted from X Z gives the arc Q Z, which is the angle between the celestial equator and the zenith, and is equal to the latitude, or, in other words, equal to the elevation of P above X. The name of the latitude in this case is Xnrth, because the Pole is elevated above the Xorth Horizon. 1894, September 23d, in long. 179° 50' E. Obs. mer. alt. of Sim's U.L. 72° 45', bearing S. I.E. +20' 10". Height of eye, 21 feet. Find the latitude. Sept. 23^' 00'^ 00"^ 00^ Long. 179° 50' E. -11 59 20 4 G.A.T. Sept. 22" 12*^ 00°^ 40« 60)719 20 IV 59™20« Decl. 0° 13' 15" N. Diff. 1 hour, 58".46 -11 41 12. Cor. decl. 0° 1'34" S. N. N. I.E. Pari 20' X. + 10" 3 11692 5846 Obs. alt. 72° 45' 00" -33 60)701.52 TimT" Dip, Kef. T. alt. 72 44 27 90 00 00 + 20' 13" S.D. Z.D. 17 15 33 + 20 46 20 13 Cor. decl. 1 34 N. -00' 33' Lat. 17^17' 07" N. The longitude in time is subtracted from ship's date to obtain G.A.T., because longitude is East. In this case the upper limb being observed, the semidiameter is placed in the — column. Taylor's Mod. Nav. 5. t)6 Taylor's Modern Navigation. Examples for Fracticc. 1894, December 21st, in long. 53° 40' E. Obs. mer. alt. of sun's I..L. 89° 58' 00", bearing S. I.E. +2' 00". Height of eye, 20 feet. Find the latitude. Dec. 'il'i 00" 00'" 00« 3 34 40 Long. 53° 40' E. 4 G.A.T. Dec. 20"^ 20" 25" 24 00 3" 35" 20' 60)214 40 Long, in time, 3" 34"' 40" (time from nearest noon). Here it will be noticed that the hours being 20, it is more correct to work from the nearest noon, namely, the 21st, when taking out the sun's declination; so, subtract the hours and minutes from 24 and use the result to correct the declination ; but as we are working backward, note if the declination is increasing or decreasing, read- ing backwards from the 21st. Decl. 23° 27' 18' - 1 Cor. decl. 23° 27M7" G (It IS reaUy 17". 6, but we call it 18", because the decimal is more than 5.) 0.40 hourly diff 3.6 nearly. 240 120 1".440 correction. Obs. mer. alt. L.L. 89° 58' 00" S. I.E. 2' 00' T. alt. Z.D. Cor. decl. Lat. + 13 55 90 11 55 90 00 00 00 11 55 23 27 17 23° 39' 12" S. S.D. 16 18 Parlx. 00 + 18 18 - 4 23 + 13"'^' Dip, Ref. 4' 23' 00 4' 23' In this case the true altitude is greater than 90° ; so, subtract 90° from the true altitude, and keep the name of the bearing for the Z.D. Caution to the Rising Generation of Navigators. We address these remark,-; especially to young men. Lecky, in his valuable book entitled Wrlid-Irs in I'mclical Navigation, Meridian Altitude. 67 directs the attention of seamen to the hizy and criminal habit of some old and so-called experienced navigators, whereby they find the latitude by subtracting the sun's altitude from the constant, 89° 48'. It is ivrong, very wrong, and the master or officer doing so lazy a thing is not fit to hold his position. Some of them say, "I know it is not right, but it comes out near enough." Young men, do not allow any old Sindbad or Billie Ringbolt to advise you that it is near enough, for the following reasons : 1. The correction for height of eye is governed by the number of feet that the observer is elevated above the sea-level, but the lazy man with his lazy method does not take this into consideration, but uses the same correction, no matter if he is standing on the top of his deck-load, on the deck awash, or on the bridge of a high- sided steamer. 2. The refraction is governed by the amount of the sun's altitude as seen by inspecting the table, but the lazy man does not take even this into consideration, but uses the same old cor- rection, no matter if the sun is right above his head or only a few degrees above the horizon. The difference between the working of the correct and incorrect methods amounts to but few figures, but it may give, under certain conditions, an error amounting to more than six miles, which, from the lazy man's point of view, m.ay not be considerable, but from a good navigator's point of view, is more than considerable, for the reason that if the sight to ascer- tain the longitude is worked up with this wrong latitude a very large error will be made in the longitude, according to the sun's true azimuth at time of sight. The amount and condition will be fur- ther discussed under the head of longitude. Special Table to Correct Altitude. At the end of this book will be found a table for the correction of the sun's altitude, lower limb, w-hich may be used with ab- solute confidence for practice at sea. It is simply a mean of the corrections used, namely, Semidiameter, Dip, Refraction, and Parallax, with a small correction to be applied according to the time of year, and may be entered in the following manner : Look on top of page for the height of eye above the level of the sea in feet, and on the left-hand side for the altitude, then under the feet and abreast of the altitude will be found the correction, to Uq added to the altitude ahcaijs. The correction is given in minutea, and tenths of minutes; so, to convert the tenths into seconds^ simply multiply them by 6. ^_^^ 68 Taylor's Modern Navigation. Practical Illustration of IJoiv to Work the Meridian Altitude Problem at Sea. — Short hut Correct Method. 1894, December 20th, in long. 170° 10' W. Obs. mer alt. of sun's L.L. 52° 20' 18", bearing S. I.E. +2' 20". Height of eye, 26 feet. Find the latitude. Dec. 20th, decl. at noon, 23° 2(i' 54" S. Added, because decl. is increas- j _l 1 Q AH ing and ship is in W. long. <, -(- io UU decl. 23° 27' 12" S. Long. 170° 10' W. By Table 7. 170° = 11^^ 20"' 00^ 10' =00 00 40 Long, in time, 11^' 20"' 40^ Obs. alt. L.L. 52° 20' 18" S. Cor. T. alt. Z.D. Cor. decl Lat. Note.- + 12 38 52 32 56 90 00 00 37 27 04 23 27 12 N. S. 13° 59' 52" N. + LE. 2' 20" Diff, .Ihi ■. 1".58 Cor. + 10 18 11.3 + 12' 38" 474 158 158 17.854 (18' ' nearly.) This work may be still further abbreviated in practice by omitting the seconds and working to the minutes of arc only. Also, it is not necessary to use the longitude in time, but instead, simply read the chronometer hours and minutes, applying, of course, its correction and using this time to correct the declination, using the mean page of Almanac because the chronometer shows Green- wich mean time. Meridian Altitude. No. 1. 1894, September 23d, in long. 150° 10' E. ; obs. mer. alt. of sun'< L.L. 75° 40' 20", bearing S. ; I.E. +5' 40" ; eye 14 feet. Required the latitude. Answer.— G.A.T. 22-^ IS'^ 59"' 20^; cor. decl. 0° 0' 24" S. ; T. alt. 75° 58' 6"; lat. 14° 1' 30" X. No. 2. 1894, February 22d, in long. 100° 42' E. ; obs. mer. alt. of sun's L.L. 40° 40', bearing S. ; I.E. +12' 12" ; eye 24 feet. Required the latitude. Answer.— Cor. decl. 10° 11' 17" S. ; T. alt. 41° 2' 35"; lat. 38° 46' 08" N. Meridian Altitude. 69 No. 3. 189-4. January IGtli. in long. 52° 49' W. ; obs. nier. alt. of sun's L.L. 50° 10' 10", bearing S.; I.E. —5' 40"; eye 30 feet. Required the latitude. Answer.— Cor. decl. 20° 51' 22" S.; T. alt. 50° 14' 42"; lat. 18° 53' oG" X. No. 4. 1894, March 2nth, in long. 170° 50' E; obs. mer. alt. of sun's L.L. 60° 20' 10". bearing X. ; I.E. +2' 10" ; eye 12 feet. Required the latitude. Answer.— Cor. decl. 0° 14' 5" S.; T. alt. 60° 34' 31" ; lat. 29° 39' 34" S. Xo. 5. 1894, August 20th, in long. 170° 10' E.; obs. rom-. alt. of sun's L.L. 39° 49', bearing X. ; I.E. —7' 40" ; eye 26 feet Required the latitude. Answer.— Cor. decl 12° 32' 04" X.; T. alt. 31° 51 09"; lat. 37° 36' 47" S. Xo. 6. 1894, March 21st, in long. 179° 59' E. ; obs. mor. alt. of sun's L.L. 89° 50' 40", bearing X. ; I.E. —10' 16" ; eye 32 feet. Required the latitude. Answer.- Cor. decl. 0° 9' 1" X.; T. alt. 89° 50' 54": lat. 0° 0' 5" S. Xo. 7. 1894, March 17th, in long. 92° 40' E.; obs. mer. alt. of sun's L.L. 89° 54' 10", bearing S. ; I.E. +2' 10" ; eye 22 feet. Required the latitude. Answer.— Cor. decl. 1° 20' 2" S.; T. alt. 90° 7' 50"; lat. 1° 27' 52" S. 70 Taylor's Modern Navigation. No. 8. 1894, August 12th, in long. 45° 40' W.; obs. mer. alt. of sun's L.L. 48° 50' 10", bearing S.; I.E. +5' 10"; eye 18 feet. Required the latitude. Answer.— Cor. decl. 14° 52' 26" N.; T. alt. 49° 6' 16"; lat. 55° 46' 10" N. No. 9. 1894, September 22d, in long. 101° 42' W. ; obs. mer. alt. of sun's L.L. 47° 21' 00", bearing S. ; I.E. +4' 10" ; eye 30 feet. Required the latitude. Answer.— Cor. decl. 0° 6' 38" N.; T. alt. 47° 34' 59"; lat. 42° 31' 39" N. No. 10. 1894, October 1st, in long. 68° 14' E. ; obs. mer. alt. of sun's L.L. 49° 15' 10", bearing S.; I.E. —5' 40"; eye 18 feet. Required the latitude. Answer.— Cor. decl. 3° 12' 52" S.; T. alt. 49° 20' 37"; lat. 37° 26' 31" N. No. 11. 1894, January 15th, in long. 97° 15' W.; obs. mer. alt. of sun's L.L. 54° 20' 30", bearing N. ; I.E. +15' 20" ; eye 10 feet. Required the latitude. Answer.— Cor. decl. 21° 1' 25" S. ; T. alt. 54° 48' 26"; lat. 56° 12' 59" S. No. 12. 1894, July 1st, in long. 98° 10' E. ; obs. mer. alt. of sun's U.L. 89° 59' 40", bearing S.; I.E. +2' 10"; eye 18 feet. Required the latitude. Answer.— Cor. decl. 23° 7' 40" N.; T. alt. 89° 41' 55"; lat. 23° 25' 45" N. Meridian Altitude. 71 No. 13. 1894, May 1st, in long. 109° 10' E.; obs. mer. alt. of sun's ILL. 48° SO' 10", bearing N. ; I.E. +1' 10" ; eye 22 feet. Required the latitude. Answer.— Cor. decl. 15° 8' 57" N.; T. alt. 48° 00' 04"; lat. 26° 50' 59" S. No. 14. 1894. March 21st, in long. 104° 15' E. ; obs. mer. alt. of sun's U.L. 41° 50' 00", bearing N. ; I.E. +10' 15" ; eye 8 feet. Required the latitude. Answer.— Cor. decl. 0° 10' 00" N.; T. alt. 41° 40' 26"; lat. 48° 9' 34" S. Note. — The examples for practice here given are all worked for every second ; but if the student use the table for the correction of the altitude, the result will be within one mile of the above answers, with the exception of the upper-limb sights, the table being in- tended for lower-limb sights only. LATITUDE BY MERIDIAN ALTITUDE OF THE SUN BELOW THE POLE. (Midnight Sun.) Very Useful for Seamen Navigating in the Polar Regions. Rule. Mark down the date, and to the right of it mark 12^^ O"" 0% as seen in example. Convert the longitude into time, and apply it to the ship's date, etc., adding if ship is in West longitude and sub- tracting if in East. The result will be the G.A.T. Next enter the Nautical Almanac and take out the declination from the apparent page, correcting it for the G.A.T. Correct the observed altitude for I.E., Dip., S.D., Ref.. and Parlx., and obtain the true altitude. Subtract the corrected declination from 90°. The remainder will be the Polar Distance. To the Polar Distance (P.D.) always add the true altitude. The result will be the latitude, which will be named the same as the declination. The sun is 12 hours later coming to the Meridian helow the Pole ; so the apparent time at place must be 12"^ O"" 0^ When the sun Taylor's Modern Xavigation. is approaching the Meridian above the Pole, it moves from East to West, but when approaching the Meridian below the Pole, it moves from West to East. Example. — 1894, July 20th, at midnight, the ship being in long. 175° 20' W.; the altitude of the sun's L.L. below the Pole 9° 48' 00" ; I.E. 00' 00" : lieiglit of eye 24 feet. Find the latitude. July 20*^ 12^^ 0'" O'' Long. 175° 20' W. + 11 41 20 4 G.A.T. 20 23 41 20 60)701 20 2^ 00 "TlMl^O^ 00^ 19"^ from July 21st, at noon. Decl. 21st, 20° 26' 34" N. Diff. 1 hour, 29".16 - 9 _.3_ Sub. always, 20 26 43 N. 8.748 90 00 00 (9" -nearly.) P.D. 69° 33' 17" Obs. alt. L .L. 9° 48' 00" + 5 44 N. + S.D. 15' 47" Parlx. 9 Dip, 4' 48" Ref. 5 24 True alt. P.D. 9 53 44 69 33 17 + 15 56 -10 12 + ^44" -10' 12" Lat. 79° 27' 01" The same result will be obtained if, instead of finding the polar distance (P.D.), 90° is added to the true altitude and the declina- tion subtracted from the sum. It may not be amiss for the student to understand the following short rule: If the P.D. of a celestial body be less than the latitude, it will not set, but will pass the meridian twice in 24 hours; hence the name, circum polar. This should be remembered when studying the problem of latitude by a fixed star, in the following section. Meridian Altitude. 73 Example below the Pole 2 P Required, the arc P S. N S Horizon, I' V Poles, Q Q Equator. X Sun, Z Zenith, obs. Observer. X S Sun's Altitude. X Q Declination. P to Q 00° : therefore, if X Q i? subtracted from it the ]).)lar dist- ance is found X P, now if the arc X P is known and also the Alti- tude, or arc X S, to obtain the arc P S, the sum of X S and X P must be taken to obtain the elevation of the Pole. This illustration will give South latitude because the Pole is elevated above the South Horizon. 74 Taylor's Modern Navigation. LATITUDE BY MERIDIAN ALTITUDE OF A FIXED STAR It is generally advisable for those who wish to observe the stars to supply themselves with a star-chart, so that they can pick out at sight the particular star required at any time. They should com- mence, when learning the stars, to locate the principal constella- tions, such as the constellation of Orion or of the Great Bear, and from these, by striking lines and angles, to locate others. It be- comes necessary, before making the observation, to know at what time the star will pass the meridian ; then, when this is ascertained, the observer should bring the star down to the horizon by means of the sextant, according to the rule given in the chapter relating to the sextant, watching the star until it arrives at its greatest altitude and using this altitude to find the latitude by the rule given here. Observations of stars should be taken during twilight, as far as possible, as the horizon is well defined at that time, but if the true place of the horizon is doubtful, take one observation from the North and one from the South, and the mean of the two will bo the lati- tude, very nearly. Rule to Find the Time of Meridian Passage of a Fixed Star. From the Nautical Almanac, and for the nearest day, take out the star's Right Ascension, under the heading of fixed stars. From the Nautical Almanac, page 2 of the month, take out the Sidereal Time, which is the Right Ascension of the mean sun. Then subtract the Sidereal Time from the star's Right Ascension,, borrowing 24 hours if necessary. The remainder will be the ap- proximate mean time of the star's passing the meridian. This will give the mean time of the Star's Meridian Passage, sufficiently near for the ordinary practice of navigation. If the apparent time is required, apply the equation as given on page 2 of the numth. Example.— J -a^nuKTy 1, 1894, the time of the Meridian Passage of the star a Piscis Australis (Fomalhavt) was required. Jan. 1st, right ascension of star, 22'' 51'" 4^" Sid. time, or right ascension of mean sun, 18 44 25) (subtract.) 4 7 19 M.T.S. Equation of time, —3 53 App. time of star passing meridian, 4'' 3"^ 26« A.T.S., p.m. If the result is greater than 12 hours, reject 12. The remainder will be the time in the morning. Meridian Altitudb. 75 Rule to Find What Star is Approaching the Meridian. In quite a number of epitouios a table is given for A.T.S. of star's passiug the meridian, but if not given, the following is a good rule to tell what star is near the meridian. Add the Sidereal Time to the Astronomical M.T.S., rejecting 24 hours if necessary. The result will be the approximate Right Ascension of the Meridian (R.A. of Mer.). Turn to table of Fixed Stars in Nautical Almanac and look for this approximate R.A. of Mer., and when found, take the name of the star abreast. The difference between the star with less R.A. and the R.A. of Mer. will give the star West and falling, and the differ- ence between the star with greater R.A. and the R.A. of Mer. will give the star East and rising, which will be the star to observe for latitude. If the decl. mid lat. are same name — In North lat. the star will bear Xorth if decl. is greater than lat. and South if less. In South lat. the star will bear South if decl. is greater than lat. and North if less. If lat. and decl. are contrary names, the star will bear North if decl. is North, and South if decl. is South. Declination is Celestial Latitude. Stars whose declinations are greater than the colat. when lat. and decl. are different names, will not rise above the horizon. RULE TO COMPUTE THE MERIDIAN ALTITUDE OF A FIXED STAR. It frequently occurs at sea that star-charts are not available, or that the observer has very little knowledge in regard to the posi- tion of the different stars. In such a case proceed as follows : Find the latitude of the ship, by dead-reckoning, as accurately as pos- sible, and subtract it from 90°. The result will be the colatitude. To the colatitude, retaining the name of the latitude itself, ap- ply the star's declination, adding when of same name and subtract- ing when contrary names. The result will be the approximate meridian altitude, to be reckoned from the southern horizon when latitude is North, and from the northern when latitude is South; "but when the sum is greater than 90°, subtract it from 180°, and nckon from the North in North latitude and from the South in j5outh latitude. T.ii'LOR's ]\10DERX XaVIGATIOX. Xow jjlace the altitude on the sextant and direct your sight to the northern or southern horizon, according to the name of the al- titude. Then on or near the horizon the star will be seen. Make it touch the horizon nicely by means of the tangent-screw, watch- ing it until it has obtained its greatest altitude. This will give you the meridian altitude of the star required. Example. — Find the approx. raer. alt. of star Sirius, lat. of ship by dead-reckoning 40° 20' S. Lat. 40° 20' S. 90 00 Colat. 49 40 S. Decl. 16 34 S. Approx. alt. bearing N. 66° 14' Rule lo Find the Latitude. — Mark down the altitude, and to the right of it place down the + and — signs. Mark down the I.E., if any, under the sign corresponding to its name. Take out the dip for the number of feet and place it under the — sign. Next take out the refraction for the altitude, and mark it down under the — sign also. By taking the sum of each column and subtracting the lesser from the greater, will be obtained the correction for the al- titude, to be subtracted from the altitude if the — sign is the greater, and added if the -f sign is the greater, the same as when working meridian altitude of tlie sun. (S.D. and Parlx. are not required in this problem.) This will give the true altitude of the star, to be subtracted from 90° to get the Z.D., which is to be named opposite to tlie bearing of the star. Now enter the Nautical Almanac with the name of the star, and take therefrom the star's declination, which may be used as it stands, because the declination of a star, as may be seen by reference to the column of annual variation, changes but very little in a whole year. A — sign is invfixed when the declination is South, and a -f sign is prefixed wlien the declination is North. Apply this declination to the Z.D.. adding if same name, and subtracting if contrary names. The result will be the latitude, to be named the same as the greater. iiVr///////r'.— October 20, 1894, mer. alt. of star a Piscis Australis {Fomalhaut) was 30° 10' IG", bearing South. F.E. 00' 00". Hei^rht of eye 18fe<'t. ° Meridian' Altitude. 77 Obs. alt. 30° 10' 16" S. Dip, 4' 09" - 5 50 Ref. 1 41 T. alt. 80 04 26 90 00 00 -5' 50" Z.D. 59 55 34 N. Decl. 30 11 2 S. Lat. 29° 44' 32" N. Examples fur Practice. 1894, Feb. 3d. obs. mor. alt. of .itar « Bootis {Arctwus) 80° 22' 00", bearing S. ; I.E. +2' 10"; eye 16 ft. Find the latitude. Answer.— Latitude 29° 23' 59" N. 1894, March 8th, obs. mer. alt. of star a Virginis (Spka) 61° 30' 00", bearing ^.; I.E. —6' 30"; eye 21 ft. Find the latitude. Answer.— Latitude 39° 18' 00" S. 1894, April 20th, obs. mer. alt. of star a Crucis 9° 34' 00", bear- ing S. ; I.E. +12' 50" ; eye 18 ft. Find the latitude. Answer.— Latitude 7° 52' 12" X. 1894, May 15th, obs. mer. alt. of star « Canis Majoris {Sirius) 43° 51' 00", bearing X. ; I.E. 0' 00" ; eye 10 ft. Find the latitude. Answer.— Latitude 62° 47' 22° S. 1894, Dec. 16th, obs. mer. alt. of star a Canis Minoris {Procyon) 50° 16' 40", bearing X.; i.K. 00' 00"; eye 12 ft. Find the latitude. Answer.— Latitude 34° 17' 46" S. 1894, July 31st, obs. mer. alt. of star /? Scorpii 30° 40' 16", bearing S. ; I.E. —2' 30" ; eye 8 ft. Find the latitude. Answer.— Latitude 39° 55' 44" N. LATITUDE BY MEEIDIAX ALTITUDE OF A PLAXET. The observation is made similarly to that of a star, by either bringing the planet's image down to the horizon by means of sex- tant or by computing the altitude and setting the sextant thereto as already explained in the preceding chapter on stars. When correcting the altitude the same method may be used as for a star. Although there is a sensible semidiameter to the planets TAiLOR's Modern Xavigation. Yenus and Jupiter, \vith Mars aud Saturn it is very small. For sea practice, however, both S.D, and parallax may be entirely ignored. It is generally supposed among seamen that planets can be ob- served at night only. This is not so in the case of Venus, for a very good result may be obtained from this planet, sometimes, dur- ing the morning hours. Thus, suppose that by reference to the Nautical Almanac, under the planet's name, and abreast of the date, the time of its meridian passage should be found to be lO*' a.m. Then with the lat. by dead-reckoning and its decl. compute the approximate mer. alt. Set this mer. alt. on the sextant and direct the sight to either the North or South points off the horizon, and on or near it will be seen the planet's image. Watch it as it rises and note the greatest altitude, and proceed to work the problem. To be a successful observer it is very necessary that a good sex- tant be used, with the silvering in excellent condition. It should also be fitted with a good star-finder or star-telescope. When making the contact with a star or planet and the horizon, endeavor to measure from its center, especially if it is the intention to ignore the S.D. If the planet's parallax in altitude is used, reference must be made to Table 17 of Bowditch, but, as a rule, it is so small that no attention need be given it. The student, after reading the foregoing, will no doubt discern that a knowledge of the time of the planet's passage ■ over the meridian will be very essential, so that he may know about what time to observe. This will be found by simply referring to the Almanac, under the heading of meridian passage, and may be taken out at sight for ordinary practice, but if greater accuracy is de- sired, correct it for the longitude of the ship. To Correct the Planet's Declination. Mark down the astronomical date and time of meridian passage and apply the longitude in time, adding if West and subtracting if East. The result will be the M.T.G., corresponding to the merid- ian passage at ship. With this mean time at Greenwich enter the Nautical Almanac and take out the decl. and multiply the var. of decl. in one hour by the hours and tenths of hours, and obtain the correction. Add to or subtract from this correction the decl. according as it is in- creasing or decreasing. The result will be the cor. decl. Meridian Altitude. 79 To CoiujEcT THE Altitude. Apply the I.E., if any, also the clip and ref. same as for star al- titude, and find the true altitude of the planet. Subtract the true altitude from 90° and obtain the Z.D., and name it opposite to the bearing. To FixD the Latitude. If the Z.D. and decl. have same name, add them together, but if contrary names, subtract. The result will be the latitude, to be named always the same as the greater. Example. — 1894, Xovember ITth, a.m. at ship, in long. 43° 20' E.; the obs. mer. alt. of planet Jupiter (center) was Vi° Id' 10", Ix'aring North ; height of eye 12 feet. Find the latitude. Nov. 16^' 14'> 39'" 00-^ mer. pass. - 2 53 20 WW 45"' 40^ M.T.( Decl. 23° 2' 36" N. + 08 Cor. decl. 23° 2' 42" N. Central alt. 27° 10' 10" - 5 17 X. T. alt. 27 4 53 90 00 00 Z.D. 62 55 7 s. Decl. 23 2 42 N. Lat. 39° 52' 25" ' S. Long. 43° 20' 4 E. 60)173 20 211 53"^ '20^ 0".69 11.7 483 069 069 08.073 Dip, 3' 24" Ref. 1 53 5' 1- Examples for Practice. 1894, March 31st, a.m. at ship, in long. 112° 17' E.; obs. mer. alt. of planet Mars (center) 60° 2?' 10", bearing North; height of eye 18 feet. Find the latitude. 80 Taylor's Modern Navigation. It is always necessary to work with astronomical time; so, as it is A.M. at place, the meridian passage and date must be taken from the day before; namely, the 30th. March 30^ 19'^ 43'" 30^ mer. pass. - 7 29 08 long, in time. Loi ig. 112° 17' E. 4 30d 12^^ 14"" 22« M.T.G. 60)449 08 Planet's decl. March 30th =20° 49' 9" - 4 13 7h 6C 29'" 08« 20'.77 12.2 Cor. decl. 20° 44' 56" 4154 4154 2077 1)253.394 4' 13" Central alt. 60° 27' 10" N. - 4 43 T. alt. 60 22 27 90 00 00 Z.D. 29 37 33 S. Decl. 20 44 56 S. Lat. 50° 22' 29" S. Dip, 4' 09" Ref. 34 -4' 43" 1894, January 26th, p.m. at ship, in long. 30° 23' W. ; obs. mer. alt. of the planet Venus (center) 47° 10' 20". bearing South; height of eye 35 feet. Find the latitude. Jan. 26'' 2'^ 00"' 00^ mer. pass. + 2 1 32 M.T.G. 26M»' l'"32« Decl 5° 7' 14" -2 11 ' S. Cor. decl. 5° 5' 03" ■s. Long. 30° 23' W 4 60)121 32 2h pn 328 32".83 4 60^13732 2' 11' Meridian Altitude. 81 Central alt. 47° 10' 20" - 6 42 ■s. T. alt. 47 3 38 90 00 00 Z.D. 42 56 22 N. Decl. 5 5 3 S. Lat. 37° 51' 19" N. Dip, 5' 48' Ref. 54 -6' 42' LATITUDE BY OBSERVED ALTITUDE OF THE POLE- STAR WHEN OUT OF THE MERIDIAN. The Pole-star is not situated exactly at the pole, but is revolving around it at a distance of about lyi °. It is the nearest circum- polar star, and in the United States never sets. If the Pole-star were situated exactly at the pole, its altitude would always be equal "to the observer's latitude. For example, if the observer were on the Equator, the Pole-star would be on the horizon, but if he advanced 10° to the North, the Pole-star would be 10° above the horizon and the observer in 10° North lat.; there- fore the elevation of the pole is always equal to the latitude of the place. It will, no doubt, be noticed that twice during its revolution around the pole the Pole-star will be at the same height as the pole itself, and also that twice it will be on the meridian, namely, above and below. The Observation. — The best time to observe the Pole-star is during twilight, the same as any other star, but the following is a good illustration. Supposing that it is the intention to observe the Pole-star to obtain the latitude some time during the early hours of the morning. Proceed as follows: About the time that the first appearance of dawn is seen in the sky, bring the Pole-star down to the horizon and clamp the sextant. Then wait until daylight, and with the sextant direct the sight to the same part of the horizon, and on or near it will be seen the star, although perhaps there may be so much light in the sky that the star will not be visible. Make the contact between the star and horizon very nicely, read the altitude, and note the time on board of ^hip or the time by chronometer (G.M.T,). You then proceed to find the latitude by the rule here given, which is the same as that given on the last page of the American Nautical Almanac. Taylor's Mod. Nav. 6. 82 TAYLOifs Modern Xavigatiox. EuLE. — Mark down the ship's tiiiie^ and if it be a.m. add 12 to the hours, but if p.m.^ let it stand as it is. This will give the astronomical time at ship. Enter Table 3 of the Nautical Almanac (which is a table for converting mean solar or sun's time into sidereal or star time)^. with the hours of the astronomical time on the top of the page and the minutes on the side. Under the hours and abreast of the minutes will be found the mean time interval, which must always be added to the astronomical time at ship. Next, from the Nautical Almanac, on page 2 of the month and abreast of the Greenwich date, take out the sidereal time, or right ascen- sion of the mean sun, for the nearest day. Add this also to the ship's time. It is sometimes considered necessary to correct the sidereal time for the number of hours, but from a practical point of view it is not required, owing to the Pole-star not changing its altitude very rapidly. We will therefore not consider this correction in this rule, but will assume that the sidereal time taken out abreast of the date is the correct one to be used. Now convert the longitude into time, and with this time enter Table 3 of the Nautical Almanac, with the hours on the top of the page and the minutes on the side. Under the hours and abreast of the minutes will be found the interval, to be applied to the ship's time. Subtract this interval when in East longitude and add when in West longitude. This rule, when followed out, will give you the local sidereal or star time at ship. To Find the Star's IIour-Anglc. { less than P 20"M, subtract it from P 20"M; If the sider- J between 1^^ 20"M, and 13'^ 20"M, subtract 1'^ 20"M, eal time is j from it; l^ greater than 18'^ 20'".1, subtract it from 25" 20'". 1 ; and the remainder is the hour-angle of the Pole-star. Now correct the observed altitude of the star the same as in cor- recting the altitude of any star, namely, by applying the LE. of the sextant, the refraction, and the dip. Then enter the table here given, with the hours on the top of the page and the minutes on the side, and take out the correction,, which must be applied to the altitude according to the sign pre- fixed to it, adding when the -|- sign is prefixed and subtracting when the — sign is prefixed. This will give the latitude, to be named. North always. ]\Iehidiax Altitude. 83 The table of hour-angles given here is only for working the questions contained in this book, and for the observations taken during the year of 1894. When making ohservations for yourself, use the table of hour-angles given in the American Nautical Al- manac of the current year. The reason for this is that the con- stant numbers change from vear to vear. TABLE lY.— 1894. Hour- Angle. 0" 1'^ 2" 8" 4" 5'' m 5 10 15 20 25 30 35 40 45 50 55 60 115.3 0.2 113.6 113.2'-' -112.S'-' -112.8;, 112.4 111-9 ■ 111.4"-j' -110.8''' 110-2 • 1 9.B 1 8.9"-' 0.7 "\ !?:; m 1.11 -} Ik -057.4]'[, 56.4 -'; 55.2 ■; 54.1 ■' 52.9- -0 52.9.,', 51.7 •: 50.5 •; 49.3 -0 48.0 1' 46.7 • 45.4 - 44.1'-' 1.4 -0 42.7,, 41.3 • 39.9 ■' 38.5,-^ 037.1" -0 37.1 ;^ 35.6 •, 34 2; 32.7'-' -031.2''^ 29.7- 28.2 -^ 26.6'-' 1.5 -0 25.1 ^ 23.5 • 21.9- 20.3 -' -018.7'-*' -018.7 '^ 017.1 • 015.5 • 013.9 1.6 -012.3,. 010.7- 9.0 • 7.4'-' 1.6 -0 5.8,^ 4.1 ■ 2.5 • -0 0.8 • 0.8'-' Hour- Angle. 6'^ 7h 8" 9" 10" IV' m 5 10 15 20 25 30 35 40 45 50 55 60 +0 0.8 '. 2.5 -;. 4.1 5.7|-;: 9.0 -^ 010.7 -' 012.3'-' i.fi +013.9^, 015.5 017.1 ■ 018.7 - +0 20.3 -0 20.3 '^ 21.9 -' 23.4 - 25.0^-' 1.5 -0 26.5 , , 28.1 - 29.6 ■! 31.1 -' ^0 32.6]'; 34.0 ! 35.5 •; 36.9 •' 38.3 : 38.3,' 39.7 -' 041.1 -, 42.5 '- +0 43.8[t 45.1 •; 046.4 i 47.7'-;; -0 49.o'"| 50.2 -; 051.4 ':, 52.6 ■" -0 53.7'-' 53.7 '„ 54.9;; 56.0 - 057.1'-' 1.0 4 58.1,^ 59.1 • 1 0.1 -" 1 1.1 ;^^ '1 2-1 11 1 III- i ^ 1 7.8 - 0.7 4-1 8.5^^ 1 -:: 110.4"-; ■i 12.9" -112.9;, 113.3- 113.7 • 114.0"-' 0.3 ^ 114-3 OS 114.6- 114-8-.^ 1 15.0 " 0.1 .1 15.1 ^, -lit!" 84 Taylor's Modern Navigation. Example.— ^ovemhev 10, 1894, at 9^ 29"^ 29« p.m., M.T.S.; long. 29° E.; T. alt. Pole-star 29° 29' 00". Find the latitude. Mean time ship, 9'^ 29'" 29« Sidereal interval. Table 3, N.A. + 1 34 Sidereal time, or R.A. of mean ) ^^ -j^g g-j^ sun, page 2 of month, ' Long. 29" E. 49 34 4 60)116 1'^ 56™ (From Table 3.) -19 00 49 15 1 20 06 Hour-angle Pole-star, 0'^ 30'" 51« T. alt. Pole-star, 29° 29' 00" (Cor. for dip and ref.) Cor. from table, -1 14 48 Lat. of ship, 28° 14' 12" N. The above question is taken from the Nautical Almanac for 1894. Exaiu ph.— ^OYvmhei 12, 1894, p.m. at ship; long. 35° 28' W.; chron. November 12*^ 13^ 40"^ 10^ M.T.G. ; obs. alt. Pole-star 64° 28' 30"; I.E. 00' 00"; height of eye 25 feet. Find the lati- tude. Chron. Nov. 12'^ 13'^ 40'" 10^ M.T.G. Long. 35° 28' W - 2 21 52 4 12 11 18 18 M.T.S. 60)141 52 Sidereal interval, + 1 51 (Table 3.) 2'' 2P" 52^ R.A., or sidereal , +15 30 21 N.A. time nearest day, ) Interval for W. long. + 23 Sidereal time at ship, 2 50 53 - 1 20 06 Hour-angle, 1" 30"' 47« Obs. alt. 64° 28' 30" - 5 22 Dip, 4' 54' Ref. 28 T. alt. 64 23 08 -1 09 30 —5' 22' Latitude, 63° 13' 38" N. Meridian Altitude. 85 Examples. 1894, February 6th, 1'' -iy"" a.m., M.T.S.; long. 45° 26' W. ; obs. alt. Pole-star 56° 5i)' 40"; I.E. —1' 15"; eye 12 ft. Find the lati- tude. Answer. — 57° 55' 53" j^. 1894, January 22d, 2^ 10°^ a.m., M.T.S.; long. 52° W.; obs. alt. Pole-star 48° 54' 00"; I.E. -f20' 10"; eye 10 ft. Find the latitude. Answer.— 50° 03 55" X. 1894, April Tth, p.m. at ship; long. 150° E.; chron. April 1^ 1^ 40'" 16^ M.T.G.; obs. alt. Pole-star 46° 59' 50"; I.E. 00'; eye 24 ft. Find the latitude. Answer.— 48° 08' 44" X. 1894, November 22d, 7'^ 50™ p.m., M.T.S. ; long. 160° 10' W.; obs. alt. Pole-star 57° 48' 10"; I.E. 00'; eye 20 ft. Find the lati- tude. Answer.— 56° 32' 29" X. 1894, December 25th, 7^^ 10"" 12« p.m., M.T.S. ; long. 18° 40' E. ; obs. alt. Pole-star 35° 10' 20"; I.E. 00'; eye 14 ft. Find the lati- tude. Answer.— 33° 49' 53" X. Pole ^tar Probleh Let be place of observer. X S observer's horizon, Z observer's meridian. 86 Taylor's Modern Navigation. Z Zenith, and the circle A C B D the path of the Pole-star, P the Pole itself. As the elevation of the Pole is equal to the latitude of the place, the following will enable the student to understand it. By studying the diagram it will be evident that twice during the day the Pole-star's altitude will be the same as the Pole itself, namely, when it is at the points A and B, in either of these posi- tions, its correct altitude is equal to the latitude. When at D it is on the meridian below the Pole, and when at C on the meridian above it. If the star is in the lower semicircle, viz. : B D A, the correction must always be added to the altitude to obtain the latitude, but when in the semicircle A C B, it must be subtracted. For the solving of this problem, see rule. DIVISION IV. LATITUDE BY EX MERIDIAN ALTITUDE OF THE SUN, OH DEDUCTION TO THE MERIDIAN. When the sun is obscured at noon by reas^on of cloudy weather, it is impossible to find the latitude by meridian altitude. In such a case the latitude must be found by the reduction to the meridian method. The Observatipn. — Within one hour of noon at ship (the nearer to noon, the better) observe the sun's altitude and note the time by chronometer, or the correct apparent time at ship ; then proceed by the following rule. EULE. First Case. — To find Greenwich time if ship's time is given. To the time by watch apply the error for apparent time at ship ; add if slow, subtract if fast. Then apply the difference of longitude in time; add if East, subtract if West. The result will be the A.T.S., to which apply the longitude in time; if East, subtract; if West, add. The result will then be the Greenwich apparent time (G.A.T.). Second Case. — If G.M.T. is given. To the time by chronometer apply the error, if any. This is the G.M.T. Convert the longitude into time ; adding if East, subtracting if West. The result will be the ship's mean time (S.M.T.). Take the equation of time from the Nautical Almanac, page 2, and correct for the G.M.T. and apply it to the S.M.T., as stated on top of the column. The result will be the apparent time at ship (A.T.S.). To Find the Time from Noon. — If p.m. at ship, tlie minutes and seconds of A.T.tS. will be the time from noon. If a.m. at ship, sub- tract the hours, minutes, and seconds of A.T.S. from 24 hours, and the remainder will be the time from noon. Correct the declination for the Greenwich time, and correct the altitude. To Find the Approximate Meridian Altitude (Approx. Mer. Alt.). — Mark down the correct declination, and under it put the latitude by account. If they are different names, add; if the same name, subtract. Then subtract the result from 90°. The remain- S8 Taylor's Moderx Xavigatiox. der will be the approx. mer. alt. Under the approx. mer. alt. put the T. alt. Add them, and divide the sum by 2. The remainder is the half-sum of the approx. mer. alt. and the T. alt. The Worhing. — Add together the cosine of the latitude by ac- count, cosine of the correct declination, twice the sine of the time from noon, taken from the p.m. column always, and the secant of half the sum of the approx. mer. alt. and the T. alt. The sum is the sine of one half the correction, to be added to the T. alt. to obtain the mer. alt. Then subtract the corrected altitude from 90°. The remainder will be the Z.D., to be named opposite to the suns bearing. Under the Z.D. put the correct declination, adding if same name, sub- tracting if different names. The remainder is the latitude, to be named the same as the greater. Reduction to the Meridiax by Towson^s Method. This method is immensely superior to any other, for the reasons that it is extremely simple, and that it is independent of the lat- itude by account. But there is a limit to it, when the altitude and declination are both large; that is. when the sun is on the same side of the equator as the observer; but as it is winter when the navigator needs this problem the most, he need not worry about the limit. If, when working Towson's method, you find that you are outside the limit of the table, you must fall back upon the Bowditch rule. Towson's Rule. — Correct the altitude and declination and find the time from noon, as in the Bowditch method. Enter Table 1 with the declination on top, and the time from noon in the hour-angle column, and take the correction abreast of it and add it to the corrected declination always. Take the index number abreast of the correction and mark it down. Then enter Table 2 with the altitude on top and the index number at the side, and under the altitude abreast of the index number will be found the correction, to be added to the T. alt. always. Subtract the in- creased altitude from 90° and find the Z.D. Name the Z.D. opposite name to the bearing. Apply the increased declination and find the latitude by the same rule as in the meridian altitude. The latitude found will be the latitude of the sliip at the time of observation, noi for noon, unless the ship has bei'n standing still between the observation and noon. Meridian Altitude. 89 Example— 1S94. August 5t>a. r.M. at ship, in lat. 44° 00' X. and long. 119° 40' W. by ace; obs. alt. of sun's L.L. 57° 20' 00", bearing S. ; I.E. — 12' 10": height of eye 20 feet; time by chron. August 22'^ S^ 20'" 40«, which was 2"^ 8'' fast of G.M.T. Requin-d the latitude. Chron. Aug. 22" 8" 20'" 40« - 2 8 G.M.T. 22 8 18 32 Sub., because W., - 7 58 40 S.M.T. Cor. equa. S.A.T. 22" 0'^ 17"^ 14^ Long. 119° 40' W. 4 60)478 40 Long, in time, 58"^ 40« 22 19 52 2 38 Equa. N.A., p. 2 of month. 2"^ 43^27 0.632 H.D. -5 .24 8.3 Equa. of time cor. for G.M.T. — 2"^ 38^.03 1896 5056 -5^2456 Decl. 11° 42' 43" N. - 6 59 Cor. decl. 11° 35' 44" N. 50".56 H.D. S.3 (hrs. and tenths of G.M.T.) 15168 40448 60)419.648 6' 59" Obs. alt. 57° 20' 00" S. Parlx. 0' 4" LE. 12' 10' - 1 15 S.D. 15 52 Dip, 4 23 Cor. alt. 57° IS' 45" + 15' 56" Ref. 38 -17 11 + 15 56 1' 15' 90 Taylor's Modern Navigation. Lat. by ace. =44'' 00' 00" N. Cor. decl. =11 35 44 N. Approx.mer.alt. = 57 35 44 Sine for 17'" 12% as it Cor. alt. =57 18 45 is nearest to 17"M4% 32 90 24 16 00 00 .=57 = 57 35 44 18 45 })114 54 29 :8.57421 X2 Rejecting 10, ,-7.14842 Half-sum of alts. = 57° 27' 14" Cosine lat. by ace. 44° 00' N. = 9.85693 Cosine cor. decl. 11 36 N. = 9.99104 Twice sine time from noon, 17"^ 14^ = 7.14842- Secant half-sum of alts. 57° 27' =10.26919 Rejectingthetens,thesum isthesineof half- ) reduction, ) 7.26558 = 6' nearly X2 Reduction, to be always added to cor. alt. +12' Cor. alt. 57° 18' 45" bearing S. Reduction, + 12 00 Reduced alt. 57 30 45 90 00 00 Z.D. 32 29 15 N. Cor. decl. 11 35 44 N. Latitude, 44° 04' 59" N. This example is worked to nearest minutes of arc only, in the logs. Same Problem by Towson's Ex Meridian Tables. The A.T.S, must be found, to obtain the hour-angle, or time from noon; also, the decl. and alt. must be corrected as in the Epitome method. /Give 1' 59" (from Table 1), to ,, _ \ be added to cor. decl., and H.A 1,- 14» = nearest 17»9' ^^^^^^^ ^^ ■ ;„ ^j,,^ ^„i. Cor. decl. 11° 35'=nearestl2° „^„_ ;, j„„,;,, „,, i„j^, I number, namelv, 35. Mekiuian Altitude. 91 Cor. decl. 11° 85' 44" N. + 1 59 Augmented decl. 11° 37' 43" N. Alt. 57° 30' ) Give, when interpolating, 14' 35" (from Index number, 35 i Table 2), to be added to the cor. alt. Cor. alt. 57° 18' 45" S. + 14 35 Augmented alt. 57 33 20 S. 90 00 00 Z.D. 32 26 40 N. Augmented decl. 11 37 43 N. Latitude, 44° 04' 23" N. Example— 1894, September 16th, a.m. at ship, in lat. 20° 10' S. and long. 140° 2' E. by ace; obs. alt. of sun's L.L. 66° 50', bearing N. ; I.E. 00' 00" ; height of eye 29 feet ; time by watch Sept. 15"^ 22^ 40™ 50% which has been found to be slow V S*" 10« on A.T.S. ; diff. of long, made to the West was 16' since the error on A.T.S. was determined. Required the latitude by reduction to the meridian. ' '' Sept. 15-^ 22^^ 40'" 50^ D. long. 16' W. Long. 140° 2'E Slow of A.T.S. + 1 2 10 4 4 Decl. Cor. decl. =2° 42' 17" N 15 23 43 00 4 60)64 60)560 8 - 1 1- 4« g*' 20'" 8» S. 15 23 41 56 24" 00"^ 00« - 9 20 8 23 41 56 A.T.S. G. 15^ U^ 21" M8« Igm 4s (xi^g fj.on-j noon.) 57".79 H.D. 14.4 23116 23116 5779 2° 56' 09"X. 60)832.176 13 52 13' 52" 92 Taylor's ^Modkrx Xav aOATIOX. 8.D. Pari. Obs. alt. 66° 50' 00' + 10 19 T. alt. 67° 00' 19" 15' 57" 4 + 16 01 - 5 42 Dip, 5' 17' Ref. 25 -5' 42' 10' 19" Lat. ace. Cor. decl. 20° 10' 8. 2 42 N. 22 52 90 00 Approx. mer. alt. 67 T. alt. 67 Sine 18" 4« =8.59395 X 2 Half- sum alts. 67° 04' Cosine lat. ace. Cosine cor. deel. 2 X sine time from noon, 18'" 4^^ 20° 10' S. 2° 42' N. 2Xsine =7.18790 9.97252 I 9.99952 I Secant half-sum alts. 67° 04' T. alt. 67° 00' 19" N. + 26 = 7.18790 = 10.40931 7.56925=13' X_2 Reduction, 4-26 67 26 19 90 00 00 Z.D. 22 33 41 Cor. decl. 2 42 17 Latitude, 19° 51' 24" 8. Sainc Problem by Towsons Method. H.A. 18'» 4-^ Cor. decl. 2° 42' 17" N. + 23 Index number 41. T. alt. 67° 00' 19" N. + 25 44 2° 42' 40" N. 67 26 03 90 00 00 Z.D. 22 33 57 8. Cor. decl. 2 42 40 N. Latitude, 19° 51' 17" S. Meridian Altitude. 93 Exam pies, fur Practice. 1894, August (Uh, a.im. at ship, in lat. 47° 50' S. and long. 85° 15' W. by ace; sun's obs. alt. L.L. Ji5° 25' 00'', bearing N.; I.E. — 5' 40"; eye 23 ft.; time by chron. (S'^ 5" 47"" 50% which was Ifi"" 47^ fast of G.M.T. Find the latitude by reduction to the merid- ian. Answer.— G.M.T. August G'l b"" 'dV" 03«; S.M.T. 5^' W 50"' 03*; A.T.S. Q^ 23" 44'" 22^; ct. 46° 04' 06" S. Outside the limit of Towson's Tables. 1894, March 30th, p.m. at ship, in lat. 42° 29' N. and long. 140° 40' E. by ace; sun's obs. alt. L.L. 50° 57' 20", bearing S.; I.E. —1' 10"; eye 20 ft.; time by chron. March 30^ 1^ lO'" 15% which was 51"" 2« fast of A.T.S. ; diff. of long, made to the East 17' since the error on A.T.S. was found. Find the latitude by reduction to the meridian. Answer. — Time from noon 20™ 21^; cor. decl. 3° 43' 39" N.; T. alt. 51° 07' 04", corrected by table; sine 7.36622; lat. 42° 20' 35" N". Answer by Towson's.— Lat. 42° 20' 35" N. 1894, May 22d, a.m. at ship, in lat. 53° 50' S. and long. 179'* ]8' W. by ace; sun's obs. alt. L.L. 15° 28' 10", bearing N.; I.E. +5' 15"; eye 12 ft.; time by chron. May 22'» 5^ 47™ 30% which was 6^ 10™ 10« fast of A.T.S.; diff. of long, made to the East 12' since the error on A.T.S. was determined. Find the latitude by reduction to the meridian. Answer.— Time from noon 21™ 52«; T. alt. 15° 42' 37"; cor. decl. 20° 32' 08" N.; lat. 53° 36' 15" S. Answer by Towson's.— Lat. 53° 36' 27" S. 1894, November 1st, a.m. at ship, in lat. 42° 18' X. and long. 51° 10' W. by ace; sun's obs. alt. L.L. 33° 2' 30". bearing S.; I.E. 00' 00"; eye 16 ft.; time by chron. Nov. 1'^ 1^ 10™ 50% which had been found to be V 47™ 10« fast on A.T.S.; diff. of long, made to West 17' since the error on A.T.S. was determined. Find the latitude by reduction to the meridian. Answer.— Lat. 41° 33' 56" X. by Bowditch. Lat. 41° 32' 36" X. by Towson's. 1894, October 30th, p.m. at ship, in lat. 28° 49' S. and long. 166° 50' W. by ace ; sun's obs. alt. L.L. 75° 4' 10", bearing N. ; eye 26 ft. ; time by watch October 30<^ 11^' 16™ 5% which was fast 10^ of G.M.T. Find the latitude by reduction to the meridian. Answer.— Lat. 27° 39' 41" S. Meridian Altitude. 95 1894, July 12th, p.m. at ship, in lat. 3(i° 49' S. and long. 174° 20' E. by ace; "^ sun's obs. alt. L.L. 30° 54' 10". bearing X.; I.E. —3' 10"; eye 30 ft.; time by chron. July ll'> 12" 40'" 8", which was IB-" 40^ slow of G.M.T. Find the latitude by reduction to the meridian. Answer.— Lat. 36° 30' 53" S. 1894, June 11th, a.m. at ship, in lat. 47° 20' S. and long. 120° 4' E. bv ace; sun's obs. alt. L.L. 19° 22' 30", bearing N. ; I.E. +7' 20" ; eye 20 ft. ; time by chron. June 10^ 15^ 40"" 10«. which was I'" 41^ slow of G.M.T. Find the latitude by reduction to the meridian. Answer.— Lat. 47° 9' 49" S. 1894, May 28th, p.m. at ship, in lat. 49° 20' N. and long. 100° 20' E. bv ace; sun's obs. alt. L.L. 61° 52' 10", bearing S. ; LE. H-3'"l0" ; eye 12 ft. ; time by watch May 28<^ &' 40™ 10% which had been found"^ to be 6" lO"" 5^ fast of A.T.S. ; ditf. of long, made to the East 20' since the error on A.T.S. was determined. Find the latitude by reduction to the meridian. Answer.— Lat. 48° 38' 42" N. KEMAEKS OX THE METHOD OF FIXDIXG THE LATITUDE BY EX MERIDIAX ALTITUDE. * It is very necessary for the student to understand thoroughly that the latitude found by any of the rules in this section is the latitude of the ship at the time the sight was taken, and if the latitude be required for some other time, it must be corrected for the difference of latitude the ship has made on the true course and the distance the ship sailed in the interval. It will be noticed that the times given are somewhat different, and as a correct knowledge of the time is very important, we will here give an explanation. First Case.— When error is given on apparent time at ship with a difference of longitude. Suppose it is the intention to observe the sun's altitude to ob- tain the latitude by reduction to the meridian. Find the error of the chronometer on apparent time at ship in the following manner, previous to the sight : Calculate the longitude the ship will be in at the intended time of observation, convert it into time, and mark it minus ( — ) if West longitude, and plus ( + ) if East longitude. Xext, take from 96 Taylor's Modern Xavigation. page 2 of the Nautical Almanac the equation of time and correct it for G.M.T. and mark it + or — , according to the sign on top of column; then take the sum of the longitude in time and the corrected equation if they are both 4- or both — , or the differ- ence if one is + and the other — . The result in either case will be the error of the chronometer or watch on apparent time at ship, to be applied to the noted time by chronometer or watch according to its sign, to obtain the A.T.S. at observation. Now, if the sun be not observed at the time intended, this A.T.S. must be again corrected for the diff. of long, the ship made between this time and the time of actually taking the observation to obtain the correct apparent time at ship, and thence the hour-angle, or time from noon. Second Case. — When the time by chronometer is noted, and, by the way, this is the easiest method to understand. Measure the sun's altitude, and note time by chronometer, and proceed to find the A.T.S. by the rule given. For Practice at Sea. — Set your watch to A.T.S. for noon, com- pare watch with chronometer, and mark down the times. Turn long, of ship by D.R, into time, and add it to correct G.M.T. if in East longitude, and subtract if in West longitude. The result will be M.T.S. Take the equation of time from page 2 of the Nautical Almanac and correct it for G.M.T., then apply the cor. equa. to M.T.S. according to its sign, and the result will be A.T.S. at instant of comparing the watch with chronometer. Set the watch ahead or back according to whether slow or fast. You will then have A.T.S. on your watch. Make the observation and note the time by watch. This will be the A.T.S. at time of observation. If it is an a.m. sight, subtract what the watch shows from 12 hours, and the remainder will be the time from noon; but if P.M., the minutes and seconds will be the time from noon. These wrinkles, we opine, will, in conjunction with the rules, enable the student to put the method into actual practice. LATITUDE BY EX MERIDIAN OF A STAR. The working of the problem is essentially the same as the sun problem, with the exception of determining the star's hour-angle. Rule to Find the Hour-Angle. Mark down the astronomical mean time at ship if given, omit- ting the date. Meridian ALTiTiibEV ^^ ' V' l ; : ^t;/ T Y ^7 If (i.M/r. is given, namely, time by clirouometer, apply to it the longitude in time, adding if East, subtracting if West. The result will be the M.T.S. From page 2 of the Nautical Almanac take out the sidereal time, iiiean- noun, and correct it for the M.T.G. by using Table 3 of the Xautical Almanac for converting mean solar into sidereal time. Add this corrected sidereal time to the astronomical mean time at ship. The result will be the right ascension of the meridian (R.A. of mer.). Take the difference between the R.A. of mer. and the star's R.A. (which is found abreast of the star's declination under the lieading of Fixed Stars, in the Nautical Almanac, correcting it for the annual change if it is large, but ignoring it entirely if small). The remainder will be the star's hour-angle (H.A.). Correct the altitude as in other star problems. Take out the star's declination. Compute the approximate meridian altitude, and finish the problem the same as when working latitude by ex meridian of the sun. LATITUDE BY EX MERIDIAN ALTITUDE OF A PLANET. The problem is worked the same as a star problem, with the ex- ception of correcting the planet's declination and right ascension. Example.— 1S94:, April 8th, a.m. at ship, in lat. 20° 30' N. and long. 115° 50' E. by D.R.; obs. alt. star Vega 71° 25' N.; I.E. +5' 20"; dip 22 feet; time by chronometer April 7^ 9^* 26°^ 0% which was slow 2^" 15^ for G.M.T. Required the latitude by ex meridian altitude. April 7.1 gh 26'" 0« + 2 15 G.M.T. 9 28 15 + 7 43 20 S.M.T. + 17 11 35 From N.A. + 1 2 59 1 + 1 33 R.A. of mer. 18 16 07 R.A. starVega, 18 33 21 Star's-hour angle, 17" 1 14s Taylor's Mod. ] SlAV. 7. Long. 115° 50' E. 4 60)463 20 71, 43m 20« 59 sid. time mean noon. 1 33 (Interval, Table 3, N.A., for M.T.S.) Taylor's Moderx Xavigatiox. Lat. by D.R. 20° 30' 00" N. Star's obs. alt. 71° 25' 00" Dip, 4' 36' N. + 24 Ref. 20 Star's decl. 38 41 6 18 90 11 6 00 00 App. mer. alt. True alt. 71 71 48 54 25 24 2) il43 14 18 T. alt. 71° 25' 24" -4 56 I.E. + 5 20 + 0' 24' Half-sum alt. 71° 37' 9" Cosine lat., by D.R. 20° 30' 0"N.= 9.971591 Cosine decl. 38° 41' 6" -= 9.89243 I Logs, corrected to 2 X sine H. A. 17'^ 14« = 7.15010 j seconds. Secant half-sum alt. 71° 37' 9" - 10.50124 I Sine 7.51536 Nearest 7.50512 =11' Changeinj^^ 3^. 3 1024 =^6' log. for 1 \^^ Reduction, Star's T. alt. 71° 25 24 N. 360 I79 180 Z.D. 18 12 04 S. N. Change for l' = 63)1024(16 Lat. 20° 29' 02" S. 11 16 2 22 32 . 71° ' 25 24 71 47 56 90 00 00 18 12 04 38 41 06 394 378 This example is worked to seconds throughout, but it is not necessary in practice. Example.— 1894:, July 10th, a.m. at ship, in lat. 29° 45' N, and long. 175° 45' W. by D.R. ; obs. alt. of star Fomalhaut, when out of the meridian, 30° 5' 30", bearing S.; I.E. —3' 20"; height of eye 24 feet; time by chronometer July lO-^ 4:^ ^'^ 25% which was IB"" 10^ fast for G.M.T. Required the latitude by ex meridian alti- tude. Meridian Altitude. 99 July 10" 4" 7"' '25« Long. 175° 45' W. - 13 10 4 G.M.T. 10 3 54 15 60)703 - 11 43 00 IP 43°^ S.M.T. 16 11 15 Sid. time, 7 13 35 Table 3, N.A. 38 R.A. of mer. 23 25 28 R.A. of star, 22 51 48 Star's hour-angle, 33™ 40« Star's decl. 30° 11' 02"S. Lat. by D.R. 29 45 00 N. 59 56 02 90 00 00 Approx. alt. 30 03 58 T. alt. 29 55 41 2)59 59 39 Half-sum, 29° 59' 49" Star's obs. alt. 30° 5' 30" I.E. 3' 20" - 9 49 Dip, 4 48 T. alt. 29° 55' 41" Ref. 1 41 -9^" Cosine lat. 29° 45' 0" N. = 9.93862 Cosine decl. 30 11 2 S. = 9.93673 2 X sine H. A. 33™ 40« =7.73290 Secant half-sum, 29° 59' 49" =10.06245 Sine 7.67070=16' 2 Reduction, 32' Star's T. alt. 29° 55' 41" + 32 S. 30 27 41 90 00 00 Z.D. 59 32 19 N. Decl. 30 11 02 S. Lat. 29° 21' 17" ■N. DIVISION V. LONGITUDE BY CHRONOMETER. The Observation. — Station an officer at the chronometer. Take your sextant, bring the sun's image down to the horizon, and then clamp it; call to the officer to stand by, then with the tangent- screw make the lower limb of the sun touch the horizon very nicely, and immediately call out, "Stop." The officer will then note the hours, minutes, and seconds shown by the chronometer at that instant, and the observer will read the sun's obs. alt., which must be marked down abreast of the time by chronometer. If the horizon be not very well defined, take four or five sights, and get the mean of them by adding the altitudes together and dividing by the number taken; then add the chronometer times together and divide by the same number. Example. — Suppose the following number of sights were taken when the horizon was not very clear. Alt. 18° 15' Chron. time, 8'^ 40"^ ^ 20« 18 40 8 41 13 18 42 8 41 18 •18 52 8 42 10 4)74 29 4)34 45 01 :ean of obs. alt. 18° 37' 15" Mean of chron. time, 8'' 41'" 15« If the horizon be clear and the sun bo seen plainly, one sight is as good as a dozen. In actual sea practice the error of the chro- nometer is known for every day, so that the rating is required only at long intervals. At the examination, however, the candidate will be required to find the error of the chronometer given in the question to find the longitude. Longitude. If^l EULE. To Correct the Chronometer Time.— To the time by chronome- ter apply the second error, adding if slow, subtracting if fast. Next, write down to the right, under each other, the two errors; if both should be slow or both fast, subtract, or if one be fast and the other slow, add; convert the sum, or remainder, into seconds by multiplying by 60, and divide the result by the number of days between the dates of the two errors. The result will be the daily rate, viz., what the chronometer is gaining or losing in one day. To Know if the Daily Bate is Losing or Gaining. From fast to less fast, dnily rate is losing. From fast to more fast, daily rate is gainin.. From slow to more slow, daily rate is losing. From slow to less slow, daily rate is gaining. From slow to fast, daily rate is gaining. From fast to slow, daily rate is losing. To Find the Accumulated Eate.—Y'md the number of days and tenths of days between the date of the second error and the day of chronometer time and multiply by the daily rate, crossing off from the product as many figures as there are decimals contained in the question. The remainder will be seconds, and is called the accu- vnilaied rate. Convert these seconds into minutes and seconds if more than GO. Add this accumulated rate to the chronometer time if daily rate is losing, but subtract if it is gaining. The re- sult will be the correct Greenwich Mean Time (G.M.T.). To Find Tenths of Daijs.—^lavk down the hours and tenths of hours of the chronometer time and divide by 24. The result will be tenths of a day. It is not necessary to carry it to more than one place of decimals. Correct the declination for G.M.T., the same as it is done in Mer. alt. and amp. problems. To Find the Polar Distance.— li the latitude and declination are of the same name, subtract the declination from 90°, but if of different names, add the declination to 90°. The result in either case will be the Polar Distance (P.D.). 102 Taylor's Modern Xavigatiox. To Correct the Equation of Time. — Take from page 2 of the Nautical Almanac the equation of time for the Greenwich day and its difference for one hour. Multiply this difference for one hour by the hours and tenths of hours of the G.M.T., and cross off from the product, to the right, as many figures as there are decimals in the question. The figures that are left will be seconds, to be added to the Equation if it is increasing, and subtracted if it is decreas- ing. The result will be the corrected equation of time. Take the sign of addition or subtraction to or from apparent time from the top of page 1 and prefix it to the corrected equation. Correct the sun's obs. alt. as usual for I.E., dip, S.D., parlx., and ref. The Computation. — Mark down the T. Alt., Lat., and P.D. un- der one another and add them, divide the sum by 2 and call the result the half-sum, subtract the T. Alt. from the half-sum, and call the result the remainder. Take out of Table 44 the secant of the latitude, cosecant, P.D., cosine half-sum. and sine of the remainder, throw away the index when it is 10, add these four logs., and divide the sum by 2. This half-sum is the sine of the Apparent Time at Ship (A.T.S.), Table 44. Look for the half-sum in the sine column, and if it cannot be found exactly, take the next less log. and note the hours, minutes, and seconds abreast of it in the a.m. column if it is a.m. at ship, but in the p.m. column if it is p.m. at ship ; take this next less log. and mark it down under the half-sum of logs., subtract them, and look in the little table at the bottom of the page for the difference abreast of A. Take the nearest, and note the seconds above it; add these seconds to the '^ ™ ® if it is v.^i. at ship, and subtract if a.m. at ship. The result will be the civil A.T.S. If it is a.m. at ship, add 12 to the hours of this civil time, and put the ship's date one day back ; if p.m. at ship, put the ship's date in front of the !> ™ « The result in both cases will be the astronomical apparent time at ship (A.T.S.). Under the A.T.S. put the correct equation of time, and add or subtract it according to the instructions on top of the equation column on page 1 of the Nautical Almanac. The result will be the mean time at ship (M.T.S.). LoXGnTDE. 103 UiukT the M/r.S. put the correct G.M.T.. and subtract the lesser from the greater. The remainder will be the longitude in time. Convert this longitude in time into longitude by multiplying by GO and dividing by 4. To Name the Longitude. Greenwich time best longitude West. Greenwich time least longitude East. . Example for Practice. Time by chronometer :\Iarch 21^ 20'' 35"^ 10% which was 4°^ 20" fast on January 3d. and on February 2d was 7°^ 5^ fast. Required the correct G.M.T. March 21" 20" 35'" 10^ 1st error, Jan. 3d, 4"' 2(>^ fast. - 7 .") 2d error, Feb. 2d, 7 05 fast. Approx. 21 20 28 5 2 45 - 4 23 BO G.M.T. 21" 20'' 23'" 42^ 30)165(5^5 (daily rate 150 gaining.) 150 150 From Feb. 2d to end of month, 26 days. 20*' 28" Up to and including March 21st. 24) 20.5 (.8 (tenths of 5.5 192 a day.) 2390 2390 60)262.90 Accuni. rate, —4'" 23** It will be noticed that the second error is subtracted from the chronometer time because it is fast, the result being the approxi- mate G.M.T. The errors are subtracted because they are of the same name, and the result is divided by the number of days between the two dates to obtain the dailv rate, gainins; in this case because the sec- 104 Taylor's Modern JSTavigatiox. ond error is more fast than the first. Next, the days are counted between the date of the second error and day of chronometer time, and the tenths are also fonnd; these days and tenths are multi- plied by the daily rate. The result is, then, the accumulated rate, to be subtracted from the approximate G.M.T. because daily rate i.:- gaining. The final result is then G.M.T. Example.— Time by chronometer March 24*^ IS^^ 56°^ 10% which was fast l"" 29^ on January 19th, and on March 10th was 2™ 13^ slow. Required the correct G.M.T. March 24M5^56'"10« 2d error, + 2 13*^ 24 15 58 23 Accum.rate, +1 4 G.M.T., 24^5'^ 59"^ 27« 1st error, Jan. 19th, I'" 29« fast. 2d error, March 10th, 2 13 slow. Days, 50 3 42 60 50)222(4^4 (daily rate 200 losing.) ~^0 Number of days between date of 2d error and day of chronometer time is 14''.66 24)16'\0(.66 (decimals Daily rate, 4.4 144 of days.) leo 144 5864 5864 60)64.504 1"^ 4^= accumulated rate; to be added to the chronometer time because daily rate is losing. In this case we must add the second error to the chronometer time because it is slow; and as one error is fast and the other slow, we must add them and bring the sum into seconds; we then di- vide by 50, the number of days between the errors; as 50 will go 4 times into 222, 4 is a whole number; we then borrow a cipher and let 50 go into it again 4 times; this is a decimal because we had to borrow a cipher to lot 50 go into it. In finding the decimals of days we generally put down the hours and tenths of hours and divide by 24, but, in this case, 16 hours is nearer than 15 hours and nine tenths, therefore we divide 16 hours by 24 and get .(i(i; we then multiply the days and decimals Longitude 105 of days between the 2d error and the chronometer time by the daily rate, and as we have three decimals in the question, we must cut off three figures from the product, which, in this case, leaves 64 seconds, to be added to the chronometer time because daily rate is losing. Example. — Time by chronometer November 11*^ 1^ 20™ 5^ which on April 30th was 6'" 2^ fast and gaining 10^ daily. Eequired the correct G.^^LT. Nov. 11" 1" 20'" 5« April 00 (Nothing in April.) The only error, - 6 2 May 31 mnL4 3 j"!"^® 30 Accum.rate, - 32 30 J^^^ '^^ 24)1\ 20t(.05 (decimals Aug. 31 G.M.T. ll^OMl-33^ Sept. 30 Oct. 31 Nov. 11 1 .20 of days.) 195.05 10. 60)195.050 32"^ 30^ accum. rate. As 2-1: will not go into 1.2, we borrow a cipher and put this cipher in the dividend; then it wall go .05 times. In this case we have only one error, but the daily rate is given, therefore we have only the accumulated rate. The number of days between April 30th and November 11th is 195.05, which mul- tiplied by the daily rate gives 32'" 30% to be subtracted from chronometer time because daily rate is gaining. Examples in Correcting the Equation of Time. Example.— March 21*^ 201^ 23"° 5G^ G.M.T. Eequired the cor- rect equation of time. March 21st, equa. of time, =7"^ 13^8 Sub. cor., because equa. is decreasing, — 15.5 Correct equa. of time, + 6'" 58^3 106 Taylor's Modern Navigation. To be added, because it says so on the top of the column on page 1, Nautical Almanac. Diff. for 1 hour, .759 20.4 3036 15180 15.4836 As there are four decimal figures in the question, we must cross off four ; but take the first one and apply it to the equation, as seen in example. Exainple.— March. 24"* lo^^ 59™ 27^ G.M.T. Eequired the cor- rect equation of time. March 24th, equa. of time =6"^ 18^82 Equa. is decreasing — 12 .28 Correct equa. of time to be ^ lAm aTTT added to app. time ) Diff. for 1 hour =.768 16 hours is nearest 16. 4608 768 12.288 Example.— Becemhei 2^*^ lli^ 20°^ 50^ G.M.T. Eequired the cor- rect equation of time. Dec. 24th, equa. of time =0'" 8\72 Diff. 1 hour=- 1".250 - 14.12 1P.3 Cor. equa., to be added } ^^T^q 3750 to app. time, ) 13750 14.1250 In this case the correction is greater than the equation, there- fore we must subtract the equation from the correction; and the remainder must be added to apparent time because we have crossed the black lino. (See top cohunn in Nautical Almanac.) Longitude. 107 Example. — 'June 13*^ rect equation of time. Vi"' dS" G.M.T. Required the cor- June 13th, equa. of time=0'" 12\00 Decreasing, — 12 .27 Cor. equa., to be added ) ~ to app. time, ^ Diff. 1 hour= .51! 23.7 00«.27 3626 1554 1036 12.2766 The equation is decreasing, therefore we must subtract, and as the correction is greater, the equation must be subtracted from it. The remainder will then be on the other side of the black line, and must be added to apparent time. (See top of column in Nautical Almanac.) Example.— 1894, May 2d, p.m. at ship, in lat 31° 17' N.; the observed altitude of the sun's L.L. was 27° 1110"; I.E. +4' 3"; height of eye 12 feet; time by chronometer May 1^ 201^ 57"^ 20^ which was 10"" 6^ fast on March 17th, and on April 1st was 10°^ 40« fast. Required the longitude. May 1^20" 57'" 20nst error, Mar. 17th, 10'" 6^ fast. 2d error, — 10 40 2d error, April 1st, 10 40 fast. Approx. 1 20 46 Accum. rate, — 1 30^9 40 11 G.M.T. Id 20^ 45'" 29« Daily rate, 2.3 "927 618 15)34(2^3 (daily rate 30 gaining.) 45 60)71.07 Accum. rate, 1"^ IV Decl. 15° 9'31"N. + 15 36 N. Diff. 1 hr. 45.24 20.7 Cor. decl. 15 25 07 90 00 00 24)20.8 (.9(tenths of days.) 21.6 Diff.lhr. 3'" 2^77 0.305 + 6 .31 20.7 3'" 9^08 2135 6100 6.3135 Equa. Sub. from app. T P.D. 53" 60)936.448 15' 36" 108 Taylor's Modern Xavigation. ] 1 ..L. 27° 11' 10" -^•14 48 [.E. 4' 3" ^.D. 15 54 ^arlx. 8 Obs. alt. I + 20 05 - 5 17 + 14' 48" True alt. Lat. P.D. 27 25 58 31 17 00 74 34 53 sec .06823 cosec .01591 2)133 17 51 Half-sum, T. alt. 66 38 55 27 25 58 cos 9.59808 Remainder, 39° 12' 57" sine 9.80089 Dip., 3' 24' Ref. 1 53 -5' 17' 2)19.48311 9.74155 sine of A.T.S. 4h 27m 44s p_M. 9.74151 next less log. 2 4A=:2« May 2^ 4 27 46 astronomical A.T.S. Equa. 3 9 (to be sub. from apparent time.) May 2 4 24 37 mean time ship. May 1 20 45 29 M.T.G. long, in time. Long. 114° 47' 00" E. Xever say "miles of longitude": it is not correct; say "minutes." The longitude in time may be converted into longitude by Table 7, or by multiplying the hours by 15 because there are 15° in one hour of time, and dividing the minutes by 4 because there are 4 minutes in a degree of longitude, and the seconds by 4 because there are 4 seconds in a minute of longitude ; thus : 7'' 39"^ 08^ 15 2^ 4 27 3 46 9 2 4 24 1 20 45 37 29 7 39 60 08 180 4)459 188 105 45 00 ■ 9 2 Long. 114° 47' 00" LONOITUDK 109 Exam pic— ISdi, December 5th, A.M. at ship, in lat. 39°20' N.; the obs. alt. of suivs L.L. was 7° 6' 00"; no index error; height of eye 24 feet ; time by chronometer December 5^ 7^^ 54™ 3% which was S"" 10** fast of G.M.T. Required the longitude at time of sight; and supposing the ship sailed S.S.W. true, distance 36 miles, from time of sight to noon, what is the position of ship at noon? Dec. 5*' 7^^ 54'" 3^ Fast - 9 10 Diff. 1 hr. Decl. 22° 25' 18" S. 18".74 + 2 24 7.7 Dec. 5'^ 7'' 44"' 53« G.M.T. Cor. decl. 22 27 42 S. 13118 90 00 00 13118 Diff. 1 hr. Equa 9"' 8^76 1.045 P.D. 112° 27' 42" 60) 144.298 - 8.04 7.7 2' 24" Cor. equa. 9"' 0^72 7315 7315 8.0465 Obs. alt. L.L. 7° 6' 00" + 4 19 True alt. 7 10 19 Lat. 39 20 00 P.D. 112 27 42 sec cose cos ' sin( + S. D. 16' 17" Parlx. 9 + 16 26 -12 07 Dip, 4' 48' Ref. 7 19 -12' 07' + 4' 19" .11156^ ?c .03428 y log. 9.26131 j ^^" 3 9.97898. 2)158 58 01 Half-sum, 79 29 00 T. alt. 7 10 19 to nearest utes^of arc. Remainder, 72° 18' 41' 2)19.38613 Sine 9.69306 Next less 9.69301 5A 110 Taylor's Moderx Navigation. 12^ 0- ■ 2« 8 3 36 A.M. Dec. 4'^20 3 34 ast. A.T.S. Equa . - 9 1 Dec. 4 19 54 33 M.T.S. Dec. 5 7 44 53 M.T.G. IP 50« ^ 20^ long, in time. 60 120 4)710 140 Long. 177° 35' 00" W. at sight. T. CO. S.S.W. 36 = D. lat. 33'.3 S.; dep. 13'.8 W. Position of ship at sight, lat. 39° 20' N.; long. 177° 35' W. D. lat. 33 S.; D. long. 18 W. Position of ship at noon, lat. 38° 47' N.; long. 177° 53' W. Before proceeding any further with the chronometer observa- tion, it will be necessary for the student to understand that the face of the chronometer has only 12 hours marked on it, the same as any ordinary clock, and the time read from it is simply civil Greenwich mean time. Therefore, as civil time is reckoned from midnight to midnight, it is all-important that a thorough knowledge of handling this time be possessed by the navigator, so that he may convert the civil into astronomical time when working a time sight. Ignorance of this subject will cause the navigator to make a very large error in his position ; so we will endeavor to explain. How to State Astronomically the Time Shown by a Chronometer. If the observer is in East longitude, his time is always ahead of the time at Greenwich to the amount of his longitude in time. If in West longitude, his time is behind Greenwich to the amount of his longitude in time. If it is A.M. at Greenwich on tbe same civil date as at ship, add 18 to the hours shown on face of chronometer and place the ship's date one day back. If it is A.M. at Greenwich on next civil date, add 12 to the hours and keep the ship's date. If it is P.M. at Greenwich on same civil date as at ship, simply prefix the ship's date to the chronometer time. Longitude. Ill If it is P.M. at Greenwich on the day before ship's civil date, prefix yesterday's date to chronometer time. In either of the above cases the result will be the chronometer time expressed astronomically. To Convert Civil Time to Astronomical Time. The astronomical day commences at noon and ends the follow- ing noon, and is reckoned from to 24 hours. Example.— li it is May 22d at 2'' IG'" 00« p.m., mark the date and time down as it stands, for p.m. civil time coincides with astronomical time, but if it is May 22d at 2'* 16" 00« a.m., then 12 must be added to the hours, and the date placed one day back, to reckon from the last noon that has passed. The reason is very obvious, because 2" 16"^ 00^ a.m. is the time from midnight, and midnight is 12 hours from noon of the preceding day. Again, supposing it to be lO'^ p.m., we should simply call it 10 hours, but if 10'' a.m., we must call it 22 hours from yesterday noon. It it be l'^ A.M., it would be 13 hours; if 2^' a.m., 14 hours; if 3" A.M., 15 hours; if 2'* p.m., only 2 hours; if 3^ p.m., 3 hours, and so on. ^a;amj3Ze.— Supposing we looked at a chronometer when it showed 8^ 40"^ 10^ when the date at ship was March 20th, at 9^ A.M. by ship's clock, and the long, by D.K. w^as 180° W. Now, 180° converted into time equal 12 hours, and as it is West, Greenwich time must be 12 hours ahead of ship's time; so 12 hours ahead of 9^ a.m. will be d^ p.m. for G.T., and by comparing this with the chronometer time it will, no doubt, be seen that the chronometer is showing p.m. at Greenwich ; therefore, simply place the ship's date in front of it ; thus, IMarch 20'^ 8^ 40»" 10% astronomi- cal time at Greenwich. Same Example. — Supposing the long, to be East instead of West. In this case the ship's time would be 12 hours ahead of Greenwich time; therefore, to obtain G.T. we must go back 12 hours from ship's time, which would give p.m. of yesterday at Greenwich; so, place yesterday's date in front of the chronometer time; thus, March ig'' 8»^ 40"^ 10«. Example.— July 10th, at about 10 o'clock A.^^r. at ship, a chro- nometer showed 1^ 42^" 40^ when the ship was in long. 125° E. by D.E. Ecquired the chronometer time, expressed astronomically. 112 Taylor's Modern Navigation. Long. 125° E.= 8^ 20"^ in time; as it is East, ship's time is ahead of Greenwich time that amount; so, count back from 10 a.:m. 8'' 20°^, and we shall have I'' 40°* a.m., and by comparing this with the chronometer time it will be noticed that the chronome- ter is showing a.m. at Greenwich on the same civil date ; so, to con- vert this civil time into astronomical, 12 must be added to the hours, and the date placed one day back. The answer, then, will be July 9^ 13^* 42"^ 40^ Example. — July 20th, p.m. at ship, in long. 150° E. by D.K., a chronometer showed 6^ 29°* 58^ Eequired the chronometer time, expressed astronomically. It will be noticed, in this example, that the time by ship's clock is not given, but it is easily found, as will be seen. Long. 150° E. =: 10^ of time, and as it is East, the time at ship will be 10^ ahead of what the chronometer shows; therefore, count 10^ ahead from chronometer time, and we have 4 p.m. as the ap- proximate time at ship at the. instant of looking at the chronometer. Then, if it was 4** p.m. at ship, and this time is lO*" ahead of chronometer time, it is very apparent to the student that the chronometer is showing a.m. at Greenwich on the same civil date as at ship ; therefore, add 12- hours to the hours and reckon from yesterday's date; the answer will then be July 19^ 18^ 29"^ 58^ Example. — August 1st, p.m. at ship, in long. 165° W. by D.K., a chronometer showed 2'' 17™ 21^. Required the chronometer time, expressed astronomically. Long. 165° W. = ll""; therefore ship's time is behind G.T. 11**; count back from the chronometer these 11 hours, and we have 3^ the approximate time at ship. Now, as G.T. is ll"" ahead of ship's time, it will be noticed that chronometer is showing a.m. of next civil date at Greenwich, therefore 12 must be added to the hours and the date, for the chronometer time will be the same as the ship's. Answer.— August 1*^ 14^ IT"* 21^ We advise the navigator to learn how to reason the time out as given, but in case of his not being able to do so, the following rule will be of use, providing the time by ship's clock is known. If it is a.m. at ship, add 12 to the hours shown by ship's clock, and put ship's date one day back. If p.m. at ship, let ship's date and time stand. In either case the result will be the approximate astronomical time at ship. LONOITUDE. 113 To this astronomical time at ship apply the long, in time, adding if West lov.g.. subtracting it East long. The result will be the ap- proximate astronomical time at Greenwich. Compare the astronomi- cal time at Greenwich with the chronometer time, and if there are more than 12^ add 15'' to the chronometer time, but if less than Iv^'', let the chronometer time stand as it is, and in either case pre- fix to the chronometer time the same date as that found in the ap- proximate time. Example. June 14'' 10'' a.m. at ship. Long. 75° E. 12 ^ 4 13 22 60)300 - 5E. June 13'^ 17'' approx. G.T. 5" 0" Chron. 4'' 54'^' 34« 12 June 13^ 16" 54'" 34-^ Here 12 is added to the hours because approximate time is more than 12. Examjjie. Aug. 18th, 9 A.M. Long. 96° W. 12 4 17 21 60)384 + 6 24 \V. 18" 3" 23'" approx. G.T. Ans.— Chron. 18** 3" U"" 45=^ 6" 24' In this case let time stand, because hours in approximate time are less than 12. Examples for Practice. 1. June 3, P.M.atship, inlong.ll5°W.,achron. showed 10" 57'"21" 2. Oct. 31, P.M. 3. May 15, a.m. " ' 4. Feb. 19, 8 a.m. 5. July 16, 4 P.M. 6. Oct. 23, A.M. State chronometer time astronomically. rAYt.OR's Mod. Nav. S. 179 W., 3 19 14 180 W., 8 32 48 53 W., 11 21 40 145 E., 6 29 58 135 E., 6 41 114 Taylor's Modern Navigation. Answers. Answers.— 1. June 3^ lO'^ 57"^ 2V 2. Oct. 31, 15 19 14 3. May 15, 8 32 48 4. Feb. 18, 23 21 40 5. July 15, 18 29 58 6. Oct. 22, 12 6 41 Example.— 1S94, April 7th, 3^ 34°^ p.m. at ship, in lat. 47° 54' N.; long, by ace. 140° W.; alt. of sun's L.L. 36° 40' 00"; a chro- nometer showed 12'* 34™ 50% which was 15'° 26« fast of G.M.T. on March 26th, and gaining 3^ daily ; height of eye 20 feet. Eequired the longitude. April 7" 3'^ 34'" p.m. Long. 140° W. Long, in time, + 9 20 4 April 7^ 12^* 54'" approx. G.T. 60)560 9^ 20°^ It will be noticed that the approximate time is a little more than 12^ so the chronometer must be the same, and the 7th day is pre- fixed, as it is 12** 34" 50^ from noon of April 7th. April 7^ 12'^ 34'" 50« Mar. 5'* Fast - 15 26 April 7 7 12 19 24 12.5 — 38 3. (daily rate gaining.) G.M.T., April 7'' 12^ 18'" 46^ 37.5 (when the decimal is .5 or more, increase the whole number by 1.) Decl. 6° 55' 54" N. 56".32 Equa. 2'" 6«.56 0^708 + 11 33 12.3 - 8.70 12.3 Cor. decl. 7 07 27 N. 16896 +P^57«.86 2124 90 00 00 11264 1416 P.D. 82° 52' 33" ^^^^ _0708_ 60)692.736 08^7084 11' 33" Longitude. 115 + _ S.D. 16' 00" Dip, 4' 23" Parlx. 7 Ref. 1 18 + 16 07 -5' 41" Obs. alt. L.L. 36° 40' 00" - 5 41 + 10 26 + 10' 26" T. alt. 36 50 26 Lat. 47 54 00 sec .17365 P.D. 82 52 33 cosec .00336 2)167 36 59 Half-sum, 83 48 29 cos 9.03288 T. alt. 36 50 26 Remainder, 46° 58' 03" sine 9.86390 2)19.07379 sine 9.53689 Nearest 9.53682 Diff. 'A = 2« 2* 2^^ 4im 4 April 7 2 41 6 A.T.S. Cor. equa. + 1 58 7 2 43 04 M.T.S. 7 12 18 46 M.T.G, 9 35 42 60 180 4)575 222 120 Long. 143° 55' 30" W. at time of sight. Rule to Correct a Log. Sine, Tangent, and Secant to Seconds Take the difference between the two logs, and multiply it by the seconds and divide by 60. The result will be the correction, to be added or subtracted, according as the log. is increasing or decreas- ing. The same may be done by inspection, thus : Search under S' on left-hand side of page until the required num- ber of seconds is found, and abreast of it, in the difference column, nearest to the required log., will be the correction, to be applied to the loff. as before. 116 TAYLOifs Modern Xavigation. In actual practice it is not necessary for the navigator to work logs, to seconds of arc. There is still another wrinkle to learn* before putting the longi- tude by chronometer problem into actual practice, which the fol- lowing explanation will enable the reader to understand: The sight to obtain the longitude must be worked with the lati- tude the ship is in at time of sight, and as the latitude is obtained at noon by meridian altitude, or near noon by ex meridian, the lati- tude at those times must be reduced to observation by using the true course and distance the ship has sailed between sight and noon when it is an a.m. sight, and from noon to sight when p.m. Work back the latitude from noon when it is a.m.^ and work ahead from noon when P.M., and the longitude found in both cases by using the reduced latitude will be the longitude of ship at time of sight. Bring this longitude forward from sight to noon, if it is A.M., by using the diff. of long., and work back the long, to noon if it is P.M., and the result in either case will be longitude of ship at noon. Example. — Take a sight to find long, as usual, and note the true course and distance the ship gailed between the time of observation and noon. Enter Table 2 with the true course and distance and take out the diff. of lat. and dep. and mark them down. To Find the Correct Latitude to Work the Sight. — If it is an a.m. sight, reverse the name of the D. lat. made good, and work the noon lat. back to sights. Example. — Suppose the true course and distance from an a.m. sight to noon was JST.XE. 27 miles, and the lat. by observation at noon was 46° 50' N. Required the latitude of the ship at the time of sight. Course N.XE. 27=D. lat. 26.5; dep. 5.3. Lat. at noon, 46° 50' N. Diff. of lat. 26^ S. (opposite of N.) Lat. at sight, 46° 23^ N. Tlie course the ship actually steered was X.XE. true, but we must reckon the diff'. of lat. South, because we are working hack- wards from the noon lat. to obtain the lat. of the ship at time the sight was taken. In this case the proper lat. to work the sight would be 46° 23' 30" N. LoXGITUnE. 11' After working the sight and obtaining the long., bring it for- vrard to noon by the diff. of long, the ship has made since the sight was taken. In this example the dep. is 5.3, which is equal to 8' of long., and must be applied to the eastward of the long, at sight, because the ship sailed East since the sight was taken. To Find the Correct Latitude to Work a P.M. Sight.— Bv'mg the lat. found at noon forward to the time of sight, by the true course and distance the ship has sailed since noon. Enter Table 2 with the true course and distance as before, and take out the diff. of lat. and dep. Apply the diff. of lat. to the noon lat. in the ordinary way, and you will have the correct lat. to work a P.M. sight. After w^orking the sight and finding the long., work it back to noon, by applying the diff. of long, the ship has made since noon in the opposite direction to what she made it; that is, if the ship sailed East, allow it to the West of the long, at sight, and if West, allow it to the P]ast, to obtain the long, of the ship at noon. Example. — Supposing it is a p.m. sight, and the true course and distance between noon and sight was S. 69° W. 49 miles, the lat. by observation at noon being 38° 10' S. Find the latitude to work sight. T. CO. S. 69^ W. 49=D. lat. 17.6; dep. 45.7. Lat. at noon, 88° 10' 00" S. D. lat. 17 36 S. (6X6=36) Lat. at sight, 38° 27' 36" S. (working ahead.) And supposing the long, at sight to be 116° 17' W., what is the long, at noon? Long, at sight, 116° 17' W. Dep. 45.7 = diff. of long. 58 (working back.) Long, at noon, 115° 19' W. Example. — Supposing it is an a.m. siglit, true course S. 73° W., distance 39 miles; lat. at noon 29° 37' S. Find latitude at sight. T. CO. S. 72° W. 39=D. lat. 12.1; dep. 37.1. Lat. at noon, 29° 37' 00" S. D. lat. 12 6 N. (worked back.) Lat. at sight. 29° 24' 54" S. 118 Taylors Modern IS^avigation. And supposing, also, that the long, at sight is 172° 22' E. Find long, of ship at noon. Long, at sight, 172° 22' E. Dep. 37.1 = D. long. 42^ W. (worked ahead.) Long. 171° 39i' E. at noon. Example. — 1894, November llth, a.m. at ship ; obs. alt. of sun's L.L. was 21° 28' 00"; height of eye 10 feet; time by chronometer IC* 42" 28% which was 42™ 23'' slow for G.M.T. ; lat. of ship at noon 47° 08' S.; compass course between sight and noon N. 46° W., distance 45 miles; deviation 7° E.; variation by chart 5° E.; approximate long, at time of sight 108° E. by D.E. Required the position of ship at noon. Nov. 11*^ 8^^ a.m. (the 10th day must be prefixed Long. 108 12 to the chronometer time because 4 10 20 it is showing p.m. of yesterda}' 60)432 _ Y 12m at Greenwich.) 7^ 12^ 10<^ 12^^ 48" Chron. Nov. lO"^ 10'^ 42-- 28^ Decl. 17° 14' 09" S. 41".97 + 42 23 +7 58 11.4 G.M.T. lO-i IP 24"" 5P 17 22 07 16788 90 00 00 4197 P.D. 72° 37' 53" 4197 60)478.458 7' 58' Equa. 15"^^ 56^54 0.257 -02 .92 11.4 1028 Cor. equa. -15'" 53\62 0257 0257 02^9298 Longitude. 119 Obs. alt. 21° 28' 00" + 10 47 + S.D 16' 12" Dip, Parlx. 8 Ref. 8' 06" 2 27 T. alt. 21° 38' 47" + 16 20 - 5 33 -5' 33" + 10' 47" Comp. Dev. CO. N. 46° W. 7 E. Lat. at noon, 47° 08' D. lat. 37 00" S. 18 S. Mag. Var. N. 39 W. 5 E. Lat. to work sight, 47° 45' 18" S. T. CO. N. 34° W. 45 = D. lat. 37.3; Dep. 25.2. T. alt. 21' Lat. 47 P.D. 72 = 38' 45 37 '47" 18 sec .17243 53 cosec .02026 2)142 01 58 Half-sum,71 T. alt. 21 00 38 59 cos 9.51227 47 49' = 22' ' 12" sine 9.88020 2)19.58516 sine 9.79258 79256 2A = P 12" 6 53 20 Nov. 10M8 Equa. — 53 15 19 A.T.S. 54 10 18 10 11 37 24 25 M.T.S. 51 M.T.G. 7'^ 60 12'" 34« 4)432 34 120 Long, at sight, 108 D, long. 8 30 E. 38 00 W. Long, at noon, 107*^ ) 30' 30" E. 120 Taylor's Modekx Xavigatiox. Example.— 18\) 4:. August 21st. o p.m. at ship, the obs. alt. o\ sun's L.L. was 2.2° 14' 41"; dip 36 feet; time by chronometer IQh 4^m 55s^ which was fast 16™ 9^ for G.M.T. ; lat. of ship at noon, by observation, 47° 23' IST. ; course by compass between noon and sight S. 36° W., distance 47 miles; deviation 3° W.; variation 10° E.; approximate long. 86° W. by D.R. Required the position of ship at noon. Aug. 2V' 10'^ 47" Fast 10 ' 55^* 09 Decl. 12° 2' 51" - 8 46 N. 50".09 10.5 G.M.T. 21^' 10'^ 31" ^ 46'' Cor. decl. 11 54 05 90 00 00 P.D. 78° 05' 55" 25045 50090 60)525.945 8' 46' Equa. Cor. equa. +2™ 51 2"^ 58^23 - 06 .44 0.614 10.5 3070 06140 06».4470 Comp. CO. S. 36° W. Dev. 3 \V. Lat. at noon, 47° 23' 00" N. D. lat. 34 24 S. Lat. at sight, 46° 48' 36" N. Mag CO. S. 33 W. Var. 10 E. T. CO. S. 43° W. 47 = D. lat. 34.4; dep. 32.1 = D. long. 47'. Obs. alt. 22° 14' 41" + 7 45 T. alt. 22° 22' 26" + — S.D. 15' 51" Dip, 5' 53' Parlx. 8 Ref. 2 21 + 15 59 -8' 14' - 8 14 + 7' 45' LOXGITUDE. 121 T. alt. 22° 22' 26" Lat. 46 48 36 sec .16468 P.D. 78 05 55 cosec .00944 2)147 16 57 78 38 28 cos 9.44972 22 22 26 sine 51° 16' 02" 9.89213 2)19.51597 9.75798 5« ' 28 Next less, 9.75787 4h 39,.: 11 21 4 39 + 2 33 52 A.T.S. 21 4 42 21 10 31 25 46 M.T.S. M.T.G. 11A=5« 5 49 21 60 60 4)349 81 Long. 87 20 15 W. at sight. 47 00 E. (worked back.) Long. 86° 33' 15" W. at noon. Examples for rractice. 1894, January 7th, p.m. at ship, in lat. 5° 21' N. ; long, by ace. 163° E. ; obs. alt. of sun's L.L. 17° 20' 00" ; I.E. —1' 2" ; eye 21 ft. ; time by chron. 5^ 48'° 39^ which on November 22d was G'" 10^ fast and on December 25th was 4™ 5^ fast. Eequired the longitude by chronometer. Answer. — Daily rate 3^8, losing; accum. rate 48^; G.M.T. Jan- uary 6^ 17'' 45"^ 22-^; cor. decl. 22° 22' 42" S.; P.D. 112° 22' 42"; cor. equa. -ffi"' 29M5; T. alt. 17° 27' 49"; sum of logs. 19.50203; S.A.T. 7*5 4»' 34'" 29«; M.T.S. 7'^ 4^' 40'" 58^ long. 163* 54' E. 1894, March 3d, 4" 36'" p.m. at ship, in lat. 31° 14' N.; long, by ace. 174° W.; obs. alt. of sun's L.L. 16° 49' 00"; I.E. +3' 40"; eye 17 ft.; time by chron. 4^ 12"" 10% which was fast 2"^ 10^ on January 21st, and on March 1st was 2"^ 40^ slow. Eequired the longitude by chronometer. 122 Taylor's Modern Xavigatiox. Answer. — Daily rate 7^4, losing; accum. rate 20^; G.M.T. March 3'i IG^ IS'" 10«; cor. decl. 6° 27' 02" S.; cor. equa. +11°^ 54^59; T. alt. 17° 01' 46"; sum of logs. 19.46761; S.A.T. 2^ 4"^ 22"^ 25^ M.T.S. S^ 4:^ 34'" 20«; long. 175° 12' 30" W. 1894, March 20th, 8" 25"" a.m. at ship, in lat. 21° 38' N. ; long, by ace. 156° W.; obs. alt. of sun's L.L. 31° 23' 10"; I.E. —0' 20"; eye 36 ft.; time by cnron. 6^ 48™ 46®, which had been found to be fast O"" 26« on January 20th, and on February 27th it was 0"^ 3^ slow. Eequired the longitude by chronometer. Answer. — Daily rate .8% losing; accum. rate 17^; G.M.T. March 2od Qh 49m gs. cor. decl. 0° 3' 53" IST.; cor. equa. +7'° 26^84; T. alt. 31° 31' 26"; sum of logs. 19.34028; A.T.S. 191 20" 16-" 49®; M.T.S. 19<^ 201^ 24'" 16®; long. 156° 12' 30" W. 1894, April 14th, p.m. at ship, in lat. 48° 21' N.; long, by ace. 170° W.; obs. alt. of sun's L.L. 29° 59' 00"; I.E. —00' 00"; eye 30 ft. ; time by chron. 2^ 58'" 43®, which on December 25, 1893, was 6"^ 30® fast, and losing 1®.9 daily. Required the longitude by chronometer. Answer.— Daily rate 3"" 30®; G.M.T. April 14^ 14'' 55"' 43®; cor. decl. 9° 43' 44" N.; cor. equa. +0"' 4^33; T. alt. 30° 08' 00"; sum of logs. 19.32850; A.T.S. 14"^ 3" 39"' 55®; M.T.S. 14* S'' 39"' 59®; long. 168° 55' W. 1894, June 4th, at 7" 30-" a.m. at ship, in lat. 17° 20' N. ; obs. alt. of sun's U.L. 31° 10' 10"; I.E. —1' 2"; eye 20 ft.; time by chron. June 3*^ 22*' 40"* 15®, which was fast 5"* 10® on February 1st, and on April 10th was 0"" 10® slow. Required the longitude by chro- nometer. Answer. — Daily rate 4®.7, losing; accum. rate 4™ 18®; G.M.T. June 3** 22" 44"' 43®; cor. decl. 22° 27' 46" N.; cor. equa.. — 1"" 56®.04; T. alt. 30° 47' 20"; sum of logs. 19.43822; A.T.S. 3^ 19" 47"' 20®; M.T.S. 3'^ 19" 45'" 24®; long. 44° 50' 15" W. 1894, August 10th, 10 o'clock a.m. at ship, in lat. 46° 31' S.; long, by ace. 135° W.; obs. alt. of sun's L.L. 18° 20' 30"; I.E. + 4' 15" ; eye 16 ft. ; time by chron. 7" 18"' 40®, which was slow 3"' 4® on March 11th, and losing 0®.7 daily. Required the kmgitude by chronometer. Answer.— Accum. rate 1"' 47% losing; GM.T. August lO'* 7" 23"' 31®; cor. decl. 15° 24' 59" N.; cor equa. +5"' 7^48 ; T. alt. 18° 34' 3"; .sum of logs. 19.05930; A.T.S. 9'' 21" 21"' 41®; M.T.S. 9^ 21" 26"' 48®; long. 149° 10' 45" W. Longitude. 123 1894, September 24th, p.m. at chip, in lat. 38° 02' S.; long, by aec. 120° 10' E.; obs. alt. of sun's U.L. 11° 34' 40"; I.E. +10' 5"; eye 12 ft. ; time by ehron. September 23'^ 18^ 20°» 5% which was 1" 3" slow on January 20th and on August 1st was 11™ 43^ slow. Ee- quired the longitude by chronometer Answer. — Daily rate 3^3, losing; accum. rate 2™ 57*; G.M.T. September 23^ 18'» 34°^ 45*; cor. decl. 0° 28' 16" S.; cor. equa. — T°» 57*.94; T. alt. 11° 20' 47"; sum of logs. 19.57791; A.T.S. 24 59'" 29*; P.D. 96° 29' 20"; equa. +11™ 56*; T. alt. 17° 33' 24"; lat. at sight 40° 31' 48" X.; A.T.S. 3^ 19'^ 59™ 8*; long, at noon 93° 26' 45" E. I'^i Taylor's Moderx Xavigation. 1894, December 23d, p.m. at ship; lat. of ship at noon 47° 26' S. ; obs. alt. sun's L.L. 26° 48' 00" ; I.E. —6'; eye 28 ft. ; time by chron. S"" lO'" 6% which on July 21st was slow 6"° 13* for G.M.T., and on Xovember 3d was 4"" 49** slow for G.M.T. ; compass course between sight and noon X. 28° W., dist. 44 miles; var. 16° W.; dev. 12° E. ; long, of shij). by D.L*., East. Required the longitude of ship at noon. Answer.— G.M.T. December 22"^ 20'' 14°* 15«; P.D. 66° 33' 13"; cqua. — 0-" 43■^; T. alt. 26° 51' 20"; A.T.S. 231 gh Qm 20^; long, at noon 131° 54' 30" E. THE MODERX METHOD OF WORKIXG AX A.M. SIGHT. The preceding rules anent the finding of the longitude by chro- nometer are all very well in their places, but they involve tedious waiting for the noon latitude, and consequent delay in ascertaining the ship's longitude at both time of sight and noon. The following, we hope, will be of use in the actual practice of navigation, — in fact, the rule is, and has been for a number of years, in use on large ocean liners, and has been used by the writer daily when at sea. It will be noticed, when working the previous method, that the observer must wait until noon to obtain the latitude, and that this latitude must be reduced backwards to time of sight before it is possible to work it out to obtain the longitude at time of sight ; then this longitude must be brought forward to noon by D.R., as before explained, to obtain the ship's position at noon, involving consider- able delay after the noon observation before place of ship is deter- mined, specially if the navigator is a little slow, causing consider- able comment among the wise ones of the ship's company. It is not necessary to wait until noon before working the sight, as will be seen by perusing the following very carefully. As soon as the sight is taken in the morning, work it out, using the latitude by D.R. The result will be the approximate position at time of sight. Xcxt enter the Sun's True Bearing or Azimuth Tables with the A.T.S. , Latitude, and Declination contained in the sight, and take out the Sun's True Bearing or Azimuth, which must be always reckoned less than 90°. being careful to give it the proper name, according to tlic instructions on bottom of each page of the tables; subtract this True Azimuth from 90°, and name the result the Co- J I oaring. LON'GITUDE. 12.; The navigator has all the forenoon to do this work, which is a great boon to slow men. Xow. a few minutes before noon, let us say about fifteen minutes, bring the approximate position at time of sight ahead to noon by using the True Course and Distance the ship has sailed in the in- terval. This will give an approximate position at noon, but will not be the correct one unless the correct latitude was used to work the sight ; but read on a little further. Xext correct the sun's declination for the approximate longitude for noon, and we are all ready to take the noon sight to obtain the latitude. Eemember. all this work is done before noon. Xow take the noon sight and obtain the latitude, and if it does not correspond with the approximate latitude brought forward, then the approximate longitude is not correct, but we may correct it, without working it all over again, by the following rule: Eule to Correct tJie Longitude for an Error in tlie Latitude. Turn up Table 2 in Bowditch Epitome and enter it with the Co- bearing as a course; look in the latitude column for the difference between the correct latitude at noon and the approximate one; when found, note the dep. abreast of it, convert this dep. into diff. of long, by the rule used in the day's work, and the result will be the cor- rection, to be applied to the approximate longitude at noon to ob- tain the correct longitude at noon. Eule to Apply the Correction. — Mark down the name of the Sun's True Azimuth, and under it the opposite, then that letter which is diagonally opposed to the name of the correction for the latitude will be the name of the correction for the longitude; thus supposing the name of the Azimuth to be X.E., under it mark S.W., and supposing the correct latitude is to the Xorth of the approxi- mate one. then place the pencil on X. and draw a line to W., and \V. will be the name of the correction. This method of working may be still further improved by work- ing the probhni of latitude by ex meridian altitude about five min- utes before noon, anticipating the meridian altitude ; then leaving an officer to take the meridian altitude as a check, it is possible to ob- tain the ship's position before the last tap is out of the bell at noon. I'iij Taylor's Modern Navigation. We confidently expect that these rules will be of great benefit to the modern navigator, and he is requested to j^rove them for him- self, by working a few sights by the old-fashioned method as a test. We do not expect the old Xoahs to try, as it is hard to teach an old sea-dog new tricks. This modern method of working the sight may be plotted on a chart, provided it is of a sufficiently large scale. After working the observation and obtaining the approximate position of the ship and also the Sun's Azimuth, proceed as follows: Mark down on the chart the approximate latitude and longitude the ship is in at time of sight, draw a line through this position at a right angle (90°) to the Sun's True Bearing; the result will give a line of position, and the ship i« somewhere on this line at time of observation. From anywhere on this line lay off the true course and distance the ship sailed between sight and noon, and draw another line through the end of the course and distance line, parallel to the first line of position, and call this last one the pro- jected line ; the ship is now somewhere on this line at noon. Xext lay down the latitude the ship is in at noon and draw a line through it until it crosses the projected line, and the point where the pro- jected line cuts the latitude line will be the ship's position at noon. The above is simply half a Sumner's Method worked with a com- mon meridian altitude problem. LoxGiTroK. 127 A P.M. sight may be worked by this method also. Thus, suppos- ing a sight was taken about four o'clock in the afternoon, and worked up with the latitude by D.E. as before, and supposing, also, that the correct latitude was ascertained by observing a fixed star or planet about nine p.m., then the latitude and longitude being brouglit forward as before, and the latitudes not corresponding, the longitude may be corrected for the error in the latitude and ship's position correctly determined at nine p.m. Example. — 1894, February 12th, 10'' 40"^, a.m., when ship was in lat. 38° 00' N". and long. 160° E. by D.R., the following sight was taken to ascertain the longitude, and worked up immediately: Chron. 12'^ 35'" 00^ which was ll"* 26" fast of G.M.T.; obs. alt. of sun's L.L. 35° 43' 00" ; height of eye 26 feet. True course of ship from sight to noon X. 28° W., distance 12 miles; cor. lat. at nooii by observation 37° 52' X. Find ship's correct position at noon by modern method. Feb. 11-^ 12'^ 35"^ 00« Decl. Fast - 11 26 lid 12" 23'" 34'' G.M.T. 13° 55' 34" S. 49".53 - 10 14 12.4 13 45 20 S. 19812 90 00 00 9906 103° 45' 20" 4953 60)614.172 10' 14" Equa. 14"^ 26^91 0.14 + 14"" 26^77 .012 12.4 048 024 012 0.1488 + S.D. 16' 14" Pari X. 7 + 16 21 - 6 21 + 10' 00" Obs. alt. 35° 43' 00" S.D. 16' 14" Dip, 5' 00" 10 00 Parlx. 7 Ref. 1 21 True alt. 35° 53' 00" +16 21 —6' 21" 128 Taylor's Modern Xavigation. T. alt. 35° 53' Lat. D.R. 38 00 sec .10347 P.D. 103 45 cosec .01263 2)177 38 Half-sum, 88 49 cos 8.31495 T. alt. 35 53 Rem. 52° 56' sine 9.90197 2)18.33302 sine 9.16651 9.16631 20A=2« 12'^ 00™ 2« 10 52 32 .T.S. ll'J 22 52 30 + 14 27 [.T.S. 11 23 06 57 t.T.G. 11 12 23 34 10 43 23 4 60 180 )643 203 A.T.S. 10'^ 52-^ Lat. 38° N. Decl. 14° S. Approx. long, at sight, 160° 50' 45" E. ■ ) T. az., N. 160° E. ) . 180 s7^ E. 90 Cobearing, 70° T. CO. X. 28° W., 12 miles; D. lat. 10.6 N".; dep. 5.6 W. Approx. position at sight, Lat. 38° 00' N. Long.l60°50'45" E. D. lat. UN. 7 00 W. Approx. position at noon, 38 11 N. 160 43 45 E. Correct lat. at noon, 37 52 N. Cor. 1 6 00 W. Error in lat. 19' 159°37'45"E. Cobearing 70° as course and error 19' in lat. column give 52.6 dep.=D. long. 6Q' (correction for the long.). S.. E. N. W. LOXGITUDE. 129 The corroct latitude being more to the South, West must be tlie correction for the longitude. Example.— ISd A, March 4th, a.m. at ship, in lat. 40° 12' N. and long. 92° E. by D.K., the following observation was taken to ascer- tain the longitude: Obs. alt. of sun's L.L. 17° 29'; I.E. +2' 10"; height of eye 30 feet ; time by chron. I'' 4'" 51^ which was 56°» 38« slow. True course between sight and noon S. 36° E., distance 40 miles; cor. lat. at noon 39° 57' X. Find ship's position at noon, by modern method. Ih 4m 5p Decl. 6° 19' 41" S. 57".8 + 56 38 9 38 10. 2 01 12 29 6 29 90 P.D. 96° 29' 0.5 10. 05.0 + I.E. 2' 10" S.D. 16 10 Parlx. 8 + 18 28 - 8 25 + 10' 03" 19 S. 19" 60)578.0 9' 38 March 3^ U"" Ol'" Equa. 11'" 50« 5 29«M.'r.G. + 11'" 55^ Alt. 17° 29' 00' + 10 03 Dip, 5' 22" Ref. 3 3 T. alt. 17° 39' -8' 25" T. alt. 17° 39' Lat. DR. 40 12 sec .11702 P.D. 96 29 cosec .00279 2)154 20 Half-s um, 77 10 cos 9.34658 T. alt. 17 39 Rem. 59^ • 31' sine 2) 9.93539 19.40178 sine ! 9.70089 72 17A = 6^ Taylor's Mod. Nav. 9. 130 Taylor's Modern Navigation'. 12" 0"' 7 58 6^ 56 A.T.S. 7" 59™ Lat. 40° N. Decl. 6° S. A.M. \ N.115°E. VT.az. 180 S. 65 E. 3^ 19 58 + 11 50 A.T.S. 55 3 20 10 3 14 01 45 M.T.S. 29 M.T.G. 90 Cobearing, 25° 6 9 15 90 2 15 4 16 Long. 92° 19' E. approx. at sight. T. CO. S. 36° E. 40; D. lat. 32.4 S.; dep. 23.5 K Approx. position at sight, Lat. 40° 12' N. D.lat. 32^ S. Approx. position at noon, 39 39^ N. Correct lat. at noon, 39 57 N. Long. 92° 19' E. D. lonf r. 31 E. 92 50 E. 10 E. 93° 00' E. ,0= =D. long. 10' E. Error in the lat. 17yN. Cobearing 25° and D. lat. 17 V-' give dep. 8.0 Name of sun's true azimuth, S. yE. Opposite N.^ W. Correct latitude being more to the Xorth. East must be the name of the correction, to be applied to the longitude. The ship's true position at noon is therefore lat. 39° 57' N. ; long. 93° 00' E. Example.— 1894:, April 27th, 8*^ a.m. at ship, in lat. 35° 47' N. and long. 153° W. by D.E., the following sight was taken to ascer- tain the longitude: Obs. alt. of sun's L.L. 39° 33'; heiglit of eye 20 feet; time by chron. 5"^ 22°^ 34^ which was 34'" 22« slow. True course S. 72° W. ; distance 16 miles, between siglit and noon; cor- rect lat. at noon 35° 18' N. April 27'' 5^^ 22"^ 34« + 34 22 Decl. Cor. decl. P.D. 13° 55' 12" + 4 41 N. N. 47".6 5.9 G.M.T. 27" 5" 56"^ 56 13 59 53 90 00 00 76° 00' 07" 4284 2380 60)280.84 4' 41" Longitude. 131 Equa. 2'" 29^ 0.4 Alt. 29° 33' 00" 2 5.9 + 9 58 + S.D. 15' 55" Parlx. 8 Dip, 4' 23" Ref. 1 42 - -2'" 31^ 2.36 T. alt. 29° 42' 58" + l(i 03 — (; 05 -6' 05" + 9' 58" T. alt. 29° 43' Lat. D.R. 35 47 sec .09085 P.D. 2) 76 00 cos( JC. . ,01310 141 30 Half-sum , 70 45 cos 9. 51811 T. alt. 29 43 Rem. 41° 02' sin( 2 ? 9.81723 )19. 43929 sine 9. 71964 71952 ^5' 12A = 12'^ 0"^ 5*^ 7 47 4 A.M. A.T.S. equa. M.T.S. A.T.S. Lat. Decl. 7*^ 47"^ A.M. -j T. az. 26^ 19 46 - 2 26 19 44 59 31 28 36° N. [ N. 94° E. 14 N. ) 180 S. 86 E. 90 Cobearing, 4° 27 5 56 56 M.T.G. 10 12 28 15 150 3 7 Long. 153° 7' W. approx. at sight. T. CO. S. 72 ° W., 16 miles ; D. lat. 4.9 S. ; dep. 15.2 W. Approx. position, Lat. 35""' 47' N. D. lat. 5 S. Approx. position at noon, Lat. 35 42 N. Correct lat. at noon, 35 18 N. Error in lat. 24' Long. D. long. 153° 7'W 19 W Long. Corr. 153 26 W. 2 W. 153°28'\V, 132 Taylok's Modern Navigation, Cobearing 4° as course, with D. lat. 24' in lat. column, gives d(-p. 1.7, which is equal to 2' D. long., to be applied to the approx. long, at noon to obtain the correct long, at noon. Name of sun's true azimuth, S. E. Opposite, N. W. And as the correct latitude is to the South of the incorrect one. West must be the name of the correction for the longitude. The ship's true position at noon is then lat. 35° 18' N.; long. 153° 28' W. This section would not be complete without a general considera- tion of the best times to observe and the errors likely to arise from certain causes. It will, no doubt, be remembered that, under the head of "Caution to the Eising Generation of Navigators," the seaman was introduced to the "extremely reprehensible habit" (Lecky) of finding the lati- tude by subtracting the observed altitude from 89° 48', not with the hope or intention that he would become too familiar, but to quote, 89° 48' "is a monster of so dreadful mien As, to be hated, needs but to be seen," ^nd, understood, to be avoided. But to return to the original proposition, — the effect of an error in the latitude, and the best times to observe. An observation to find the longitude ought to be taken when the sun is rising or falling rapidly ; namely, when it is about half-way between the horizon and the greatest altitude it is likely to attain on the particular day of observation. Do not take the observation too near noon, because the sun moves more slowly in altitude as it approaches the meridian, and when very near it, its altitude will not change to any appreciable extent in one minute of time, and as one minute of time is equal to 15' of longitude, the chances are that there wall be a considerable error in longitude if the observation to find the longitude is taken too near noon. Do not take the sight when the sun is very low (unless you have no other alternative), as tlie refraction is a very doubtful quantity, and very large when the sun is near the horizon, but take it when the sun is on or near the Priinc Verficnl — in other words, when East or West true. LOXGITUDE. 133 It is not always possible to take a sight when the sun bears East or West, as it entirely depends on the latitude of the observer and the declination of the sun, but the observer should, if possible, al- ways take the sight when the sun is on or near the Prime Vertical. This may be determined in the following manner, with the as- sistance of the American Azimuth tables : EULE. Open the tables to the nearest degree of latitude, being careful to notice if the latitude and declination have the same name or contrary names; look under the nearest degree of declination until 90° is found, then note the time abreast in either the a.m. or p.m. columns at the sides; this will give the time of the sun's passage over the Prime Vertical, which is the best time to take a sight to find the longitude; but if 90° cannot be found, take the time abreast of the nearest number of degrees, and this will be the best time to observe, under the circumstances. The object of taking the sight when the sun is on the Prime Ver- tical is, if there is an error in the latitude, it produces no error in the longitude, and if it is not possible to get a Prime Vertical sight, take one as near to it as possible, for the reason that the nearer the sun's bearing approaches the true East or true West, the smaller will be the error in the longitude produced by an error in the latitude. By referring to the three modern a.m. sights worked out in full, these conditions are exemplified, for one of them has a large cor- rection to be applied to the longitude because the bearing at time of sight was a long way from East or West true. The other is a Prime Vertical sight, nearly, and has only a very small correction to be applied. These examples were selected on purpose to illustrate the facts herein stated, and may be proven by working the old- fashioned method. It therefore behooves the navigator to be careful to use the cor- rect latitude, and not the lazy 89° 48' proposition to obtain it. The lazy method of finding the latitude is most dangerous during the winter months, as during this season the sun does not come any- where near the Prime Vertical, and does not rise very high ; re- fraction will be large and of a doubtful quantity, and an error in the latitude at this time, when used to find the longitude, may pro- duce, under certain conditions, as much as 28' or 30' of an error in the longitude. The mischief does not stop here, for if the navi- gator is steering in for the land with the intention of making a cer- 134 Taylor's Moderx ^s'avigation. tain point, he may find liis vessel considerably out of her intended position, and he may consider himself lucky if he keeps her afloat, by the extraordinary vigilance of the lookout-man, provided, of course, the weather is^ clear, so that a good lookout can be kept. The navigator (God save the mark !), of course, would blame, for any accident that might occur, bad steering, inattention of the deck- officer, or some sudden change in the deviation of his compass, or ur known current, but we, behind the scenes, know the reason, and he ought to. DIVISION YI. LONGITUDE BY FIXED STAKS. To the time shown by chronometer apply the error, if any, and obtain the G.M.T. the same as for the sun. Correct the star's ob- served altitude for index error, if any, and for dip and refraction. Enter the Nautical Almanac and take from page 2 of the month (at Greenwich Mean Noon), abreast of the Greenwich date, the sidereal time or right ascension of mean sun. Correct this sidereal time by entering Table 3, at the end of the Nautical Almanac, with the hours and minutes of G.M.T., and take therefrom the mean time interval, which must always be added to the sidereal time at noon to obtain the reduced sidereal time. Next enter table of fixed stars, and abreast of star's name take out and mark down its right ascension (R.A.), and let it stand as it is. Now take the star's declination and mark it North if -{-, but South if — , and find the polar distance by the usual rule. Mark down the true alt., lat., and P.D., add them, divide the sum by 2, and subtract from the half-sum the true alt. Next take the secant of lat., cosecant P.D., cosine half-sum, sine remainder, add these four logs., and divide the sum by 2 ; this half-sum of logs, will be the log. sine of the sidereal time at ship. If the star observed is West of the meridian, take the time from the P.M. column ; but if East of the meridian, take the time from the A.M. column and add 12 hours to it. In either case the result will be the sidereal time at ship. To this sidereal time at ship add the right ascension (R.A.) of the star, rejecting 24 hours if necessary. The result will be the right ascension of the meridian (R.A. of mer.). From the R.A. of mer. subtract the reduced sidereal time, borrow- ing 24 hours if necessary. The result will be the M.T.S. If the hours of the M.T.S. are fewer than 12, prefix the civil date; if more than 12, prefix yesterday's date. The result will be the astronomical mean time at ship. Now take the difference between the M.T.S. and M.T.G. The result will be the longitude of the ship in time, which must be con- verted into longitude by the rule used in any of the preceding ex- amples when finding the longitude. All star and planet observations here given are worked to nearest minutes of arc only, which is sufficiently near for all practical pur- poses. 136 T-VYLOirs Moderx Xavigatiox. Longitude by Altair. Example. — 1894, May 21st, 1 o'clock a.m. at ship, in lat. 27° 5' X. ; long. 146° 7' W. by D.R. ; obs. alt. of star Altair East of merid- ian 40° 48'; I.E. — 2' lU"; height of eye 20 feet; time by chron. 10*^ SO"" 25^ which was fast lO'" 50« for M.T.G. Find the longi- tude at time of sight. Mav 20"^ 22'^ 30«^ 25^ R.A. 3'^ 52"> 3P 10 50 + 3 40 (Table 3, N. A.) 20*^ 22^ 19™ 35^ G.M.T. 3" 56"' IP red. sid. time Star's obs. alt. 40° 48' 00" I.E. 2' 10" - 7 40 Dip, 4 23 T. alt. 40° 40' 20' Ref. 1 7 7' 40' Star's decl. 8° 35' 19" N. 90 00 00 N. P.D. 81° 24' 41" Star's R.A. 19^ 45™ 37^ T. alt. 40° 40' Lat. 27 05 sec .05044 P.D. 81 25 cosec .00489 2)149 10 Half-sum, 74 35 cos 9.42461 40 40 33 55 sine 9.74662 2)19.22656 sine 9.61328 = 20'^ 46 20" 46™ 07« sid. T.S. -19 45 37 Rejecting 24 hours, 16 31 44 R.A. of mer. 3 56 11 red. sid. time. May 20" 12 35 33 M.T.S. May 20 22 19 35 M.T.G. 9 44 02 long, in time. 15 135 11 00 30 l.oiitr. 146° 00' 30" \V. at sight, LOiNGlTUDli. 137 J^OXGITIDE BY VeGA. Example.— 1S94, April 25th, at 10 p.m. at ship, in lat. 34° 55' N.; long. 143° 30' E. by D.R.; obs. alt. of star Vega 24° 28' East of meridian; I.E. —1' 30"; height of eye 30 feet; time by chron. 1" 15'" 55% which was fast 12'" 20-^ for G.M.T. Find longitude of ship at time of sight. April 25" 1" 15'" 55^ Sid. time 2" 13'" 57« Fast - 12 20 + 10 (Interval, Table 8, N. A.) April 25** P 03'^^ 35^ M.T.G. 2*^ 14"" 07« red. sid. time. Star's R.A. 18" 33"' 2P. Star's decl. 38° 41' 6" N. dO 00 00 P.D. 51° 18' 54" Star's obs. alt. 24° 28' 00" I.E. 1' 30" 8 00 Dip, 4 23 T. alt. 24° 20' 00" ^^^- 1^ - 8' 00" T. alt. 24° 20' Lat. 34 55 sec .08619 P.D. 51 19 cosec .10756 2)110 34 Half-sum, 55 17 cos 9.75551 T. alt. 24 20 Rem. 30° 57' sine 9.71121 2)19.66047 sine 9.83023 = 6" 19'" 28^ 138 Taylor's Modern Navigation. 6" 19'" 28^* 12 18 19 28 sid. time at ship. + 18 33 21 R.A. of Vega. Rejecting 24 hours, 12 52 49 R.A. of mer. — 2 14 07 red. sid. time. April 25 10 38 42 M.T.8. April 25 1 03 35 M.T.G. 9" 35>" 07« long, in time, 15 135 8 45 1 45 Lons. 143° 46' 45" E. at time of sight. LONGITUDE BY PLANET. Correct the planet's declination. Open the Nautical Almanac under the planet's name, at the end of the Almanac. Search for the month on top and the date at the side, and abreast of the date take out the planet's declination, and its variation for one hour, multiplying it by the hours and tenths of hours of G.M.T., the same as when correcting the sun's declination. Correct the planet's right ascension in same manner. The remainder of the problem is identical with that of a star. Longitude by Planet Jupiter. Example. — 1894, November iSth, ()'' 20™ a.m. at ship, in lat. 25° 26' N.; long. 126° W. by D.R.; obs. alt. of planet Jupiter (center) 45° 24' 50" West of meridian; I.E. —2' 00"; height of eye 26 feet; time by chron. 3*^ 19"" 30% which was fast ll'" 30^ for M.T.G. Find longitude of ship at time of sight. Nov. (i" 3" 19" ' 30« Dec! 1. 23^ 00' 12" N. 0".55 14 30 r.(;. Cor. (brl -[- 1 3.1 Nov. <•)'• 3" 05" ■ 00^ M.' . 23 00 13 050 90 00 00 150 P.I). 6B° 59' 47" 1".550 Longitude. 139 Planet's R.A. (i" 2(V" 17^(i7 0.506 Sid. time, 15'' 2'" 45^ 1 M 3.1 Sid. interval, +30 Cor. R.A. (5" 26"' 16M1 0506 Red. sid. T. 15" 3'" 10« 1518 1.5686 Obs. alt. 45° 24' 50" I.E. 2' 00" - 7 58 Dip, 5 00 True alt. 45° 16' 52' Ref. 58 7' 58' T. alt. 4.5° 17' Lat. 25 26 sec .04427 P.D. 67 00 cosec .03597 2)137 43 Half-sum, 68 51 cos 9.55728 T. alt. 45 17 sine Rem. 23° 34' 9.60186 2 ) 19.23938 sine 9.61969 1« 9.61966 3'^ 16'" 56 3A = p S^ 16°' 57** hour-angle, or sid. time at ship. + 6 26 16 cor. R.A. of Jupiter. 9 43 13 R.A. of Mer. — 15 3 15 red. sid. time. Nov. 5 18 39 58 M.T.S. Nov.' 6 3 05 00 M.T.G. 8 25 02 15 140 6 15 30 Long. 146° 15' 30" W. at time of sight. 140 Taylor's Modern Navigation. Examples for Practice. 189-i, May 22d, 5*^ 20°^ a.m. at ship, in lat. 24° 5' N.; long., by D.R., 152° 30' W.; obs. alt. of planet Venus East of meridian 28° 12'; I.E. +3' 20"; eye 26 ft.; time by chron. 3"^ 25°^ 30% which was fast 14™ 35^ for M.T.G. Find the longitude of ship at time of sight. Answer.— Decl. 4° 54' 28" N.; E.A. 1^ 5°^ 54^; sid. T. 4h Qm 55s. rp ^^^_ 28° 8' 51"; long. 152° 47' W. 1894, April 28th, O'' 10"° a.m. at ship, in lat. 33° 34' 20" X. ; long. 164° 20' E. by D.R. ; obs. alt. of star Eegulus West of meridian 26° 15' 00"; I.E.— 2' 10"; eye 19 ft.; time by chron. 1" 6°^ 30% which was slow 2'" 20^ for M.T.G. Find the longitude at time of sight. Answer.— Decl. 12° 29' 6" X.; T. alt. 26° 6' 36"; E.A. 10*^ 02'" 44«; sid. T. 2^ 22"" OP; long. 164° 45' 45" E. 1894, August 9th, a.m. at ship, in lat. 24° 5' 50" X.; long., by D.E., 156° 24' W.; obs. alt. of star Eigel East of meridian 32° 35' 00" ; I.E. +3' 40" ; eye 20 ft. ; time, by chron. 3"^ 15"^ 20% which was fast 7"^ 40^ for G.M.T. Find the longitude at time of sight. Answer.— Decl. 8° 19' 28" S.; T. alt. 32° 32' 46"; E.A. 5^^ 09°» 27«; sid. T. 9»^ 12°^ 23% long. 156° 16' 15" W. 1894, January 16th, 5 a.m. at ship, in lat. 30° 15' N. ; long., by D.E., 145° 10' W.; obs. alt, of planet ^Mars (center) East of merid- ian 16° 48' 00"; I.E. +3' 40"; eye 22 ft.; time by chron. S^ 6"^ 53% which was 7°* 13« fast for M.T.G. Find the longitude of ship at time of sight. Answer.— P.D. 111° 55' 55"; T. alt. 16° 44' 00"; planet's E.A. 16^ 36™ 07; red. sid. T. 19»^ 44"" 08% E.A. of mer. 13'' Ol"" 55% long. 145° 28' 15" W 1894, March 11th, 5'' 40^" a.m. at ship, in lat. 12° 20' N. ; long., by D.E., 166° 15' E.; obs. alt. planet Saturn (center) 34° 10' 50" West of meridian; I.E. +3' 20"; eye 21 ft.; time by chron. 6" 40°» 10% which was slow 5°' 12^ for M.T.G. Find the longitude of ship at time of sight. Answer.— P.D. 96° 48' 33"; planc't's E.A. 13'> 33°^ 12'; red. sid. T. 23'' 13"' 41% T. alt. 34° 8' 16"; E.A. of mer. 17" 04"' 2(1%; long. 166° 20' 30" E. 1894, October 22d, 5'' 30"' a.m. at ship, in lat. 21° 26' 00" N. ; long., by D.E., 160° 10' W. ; obs. alt. of star Aldt'barnn West of Longitude. 141 meridian 4(J° 15' U" ; eye 25 ft.; J.E. +;}' 2(»"; time by chron. 4'' 2'" 1U^ which was slow 7'" 5^ for M.T.G. Find the longitude of ship at time of sight. Answer.— P.D. 73° 42' 15"; E.A. of star 4" 29'" 50«; sid. T. 14h 4m i8«; E.A. of Mer. 7" 34"> IT**; T. alt. 4()° 12' 30"; long. 159° 48' 45" W. Remarks ix Regard to Star and Planet Observations avuen Taken to Find the Longitude. Many seamen are of the opinion that observations of stars and planets, when used to ascertain longitude, involve a very lengthy and therefore tedious calculation, requiring an exceedingly pro- found knowledge of mathematics and trigonometry. This is not so, for any one that can work a sun-sight can also work a stellar observation if he is willing to learn ; and, by the way, a word in the ear of those that are not very fond of work; star-sights have fewer figures than sun-sights, and are extremely easy to learn. Seamen will, no doubt, remember numerous instances when it was not possible to observe the sun, by reason of cloudy or foggy weather, but when night came on and the weather cleared, quite a number of good navigational stars were visible to choose from, whereas if dependence is placed entirely on "t)ld Sol," he may be obscured at the most desirable time, and the navigator would then have to calculate by dead-reckoning, which is bad, even at its best. There are plenty of stars always visible on a fairly clear night, which may be observed for both latitude and longitude, but there is only one sun to observe during the day. The following case in point, relating to the usefulness of star- observations, will, no doubt, be duly appreciated. The run between sight and noon, or noon and sight, according as it is an a.m. or p.m. observation of the sun, may be almost en- tirely dispensed with when the stars are observed, for it is possible to select a star to the Xorth or South for latitude, and another to the East or \Yest for longitude. Make the latitude observation first and the longitude second, and as nearly simultaneous as possible; thus: Have two sextants, and an assistant "standing by" the chronometer. Measure the meridian altitude of a star nicely and lay the sextant down; you have plenty of time to read it afterwards. As soon as this is done, pick up the other sextant and observe a star for longitude, and note the chro- nometer time; work up the latitude, then the longitude, and the 142 Taylor's Moderin Xavigatiox. ship's true position is found, with the doubt in regard to the true course and distance entirely eliminated. This pointer will, of itself, be a sufficient recommendation of the value of star-observa- tions. The best time to observe is when the horizon is well defined and when the object is on or near the prime vertical. As before ex- plained, good results will be had if the observer is persistent and does not expect too much at first; for practice will make him per- fect in measuring the altitude. WHAT TO DO WHEN CROSSING THE MERIDIAN OF 180°, AND OTHER MATTERS RELATING TO THE CHANGE OF TIME. It is presumed that the student is by this time thoroughly fa- miliar with the various methods of determining the longitude by chronometer, yet he would, no doubt, become confused in their practical application if the following were omitted: There are 360° of longitude in all,— 180° of East and 180° of West longitude. — both of them meaning one and the same place, namely, the opposite meridian to that of Greenwich. 360° divided by 24 hours gives 15°; therefore 15° is equal to 1 hour of time, and 1° equals 4 minutes of time. It will be remembered that when a ship is in East longitude her time is ahead of, and when in West longitude her time is behind, that of Greenwich, always to the amount of her longitude in time. Now, it must be understood that as a vessel moves to the East or to the West her time will change according to the amount of dif- ference of longitude she makes good, gaining if traveling to the East, losing if traveling to the West, as will be seen. A vessel going East moves towards the sun, and the sun moves towards the ship. This is not theoretically correct in regard to the sun, but we will assume it is so, for the sake of illustration. Now, this vessel, for every 15° she moves to the East, meets the sun one hour earlier each day ; that is, the sun would rise earlier and arrive at its meridian altitudo earlier by one hour for every 15° the ship sailed to the East. If the ship sailed West, the contrary wouhl be the result; namely, for every 15° she sailed West it wouhl take the sun one hour longer to catch up with the ship. Now, suppose the ship sailed from New York to the l^'ast 15°; Longitude. 143 her time would be one hour ahead of New York time; that is, if it was 9 A.M. at New York it would be 10 a.m. at ship. Hut if she sailed 15° to the West, then her time would be one hour behind New York time; that is, if it was 9 a.m. at New Y'ork it would be 8 a.m. at ship. It will therefore be very evident that as the ship sails East her days become shorter, and if she continues sailing to the East until she has made the entire circle of the world, when she arrives at New York it will be found by those on board that they have gained one whole day, or 24 hours. The ship's date would then be one day ahead of the Xew Y^ork date, that is, if it was Sunday, March 17th, at New York, it would be Monday, March 18th, according to the reckoning of those on board. Now, if it were possible that this ship had sailed to the West in- stead of to the East, and made also a round turn of the world, she would find on her arrival at New York that her date would be one day behind; that is, if it was March 17th at New Y^ork, it would be March 16th with those on board. These two cases are what might occur to any one not changing the date w^hen crossing the 180th meridian. Thus a vessel after sailing East and arriving at 180° of longitude would find her time to coincide with Greenwich time; but with this difference, her time would be 12 hours ahead of Greenwich ; that is, if it was noon at ship it w^ould be midnight of last night at Greenwich ; but if she had sailed West, her time would coincide with that of Greenwich again, but 12 hours behind; that is, if it was noon at ship it would be midnight of next night at Greenwich. The word coincide means that the ship's clock time would be the same as chronometer time. It is therefore very necessary for the navigator to attend to liis date when crossing the 180th meridian, and the following is the rule : If sailing to the eastward and arriving at 180°, hold the date one day back; thus if the ship arrive at the meridian at 10 a.m. on Sunday, May 3d, call the next day Sunday. May 3d. also. If she is sailing to the West, jump over a day ; thus if ship arrives at meridian some time on Saturday, May 2d, call tlie next day :Mon- day. May 4th. Now, it must not be supposed that the time has been changed 24 hours, for such is not the case in reality ; only the date changed, for the vessel, sailing to the East, has gained 12 hours, and by holding the date one day back, the effect of gaining one day 144 Taylok's Modern Navigation. when making the circle of the world is counteracted by the time sho arrives at the place of departure. The result when sailing West is the contrary of the above, as by the time the ship arrives at 180° she must have lost 12 hours, and the result, in this case, of a vessel making the circle of the world would be that of losing one day ; therefore this is counteracted by jumping over a day. Little Pointers, which. Although not Relating to the Crossing of the 180th Degree of Longitude, still have Considerable Bearing on it. Bule to Set Ship's Wheelhouse Clod so that It will Indicate Ap- proximately Twelve Hours when the Meridian Altitude is Observed. — On board of sailing-ship, most seamen have noticed a consider- able discrepancy in the time shown by the clock and the moment of striking eight bells; this is all very well for the windjammer, al- though the cook and steward may kick about the dinner being spoiled, but it will not do for an ocean steamer, for there are too many people to be considered; therefore clocks on board must be set at some time when it will least inconvenience those on board. To proceed, suppose that we are bound from San Francisco to China, and therefore sailing to the West. The ship would be losing time each day, according to the amount of difference of longitude in time she makes between noons of two consecutive days. If she made 7° of diff. of long., she would have lost 28 minutes, and her actual running time between noon of yesterday and to-day would be actually 24^ 28™, and if the ship's clock had not been altered, which it ought to have been, it would indicate 28 minutes past 12 when the sun was on the meridian. Now, if this ship had been sailing East this 7° (from China to San Francisco), she would have gained 28 minutes, and the actual running time between noon of yesterday and to-day would be 23*' 32™. In this case, if the ship's clock had not been attended to, the navigator would be 28 minutes too late for the meridian altitude. The preceding remarks will direct the attention of the student to the fact that there is something to be done to the clock, and the following is the rule: Rule. The bridge-officer having the watch from 8 to 12 p.m. must, a lit- tle before midnight, calculate approxinuitcly, by D.K., tlie amount Longitude. 145 of diff. of long, in time the vessel will make from last noon to next day at noon, and if sailing to the East he must put the clock ahead this amount, but if going West he must put the clock back this amount, dividing the time between his watch and the next. After being relieved at eight bells he must proceed to the saloon and set the clocks there, then to the engine-room and inform the engineer on watch, who will set the engine-room clock so that it tallies with the deck time, the bridge-officer entering in the wheelhouse log-book tlie amount of change, and the engineer entering it in the engine- room log-book. If the above is properly carried out, all clocks on board will indi- cate 12, very nearly, when the sun is on the meridian. To Find the Length of Passage of an Ocean Greyhound. Xote the civil date and time at the instant of departure, and state it astronomically. Note the civil date and time at arrival, and state it astronomi- cally also. , Take the difference between the two by subtracting one from the other. The result will be the apparent length of passage. Find the difference of longitude between the place of departure and that of arrival and convert it into time. Add this difference of longitude in time to the apparent length of passage if ship has sailed to the West, but subtract if she has sailed to the East. The result in either case will be the mean length of time the ship occupied on the passage between the port of de- parture and that of arrival. The reason why the difference of longitude in time is subtracted when the ship sails East is that there is actually less time than 24 hours in each day, because of her gaining time ; and the reason why the difference is added when sailing West is because, losing time, her apparent days are more than 24 hours long. When sailing East, her apparent length of passage is too great, and when sailing West, too small. Example. — Passed Fort Point, San Francisco, in long. 122° 29' W., on January 16th, at 6** 20°* a.m. Arrived at Honolulu, Ha- waiian Islands', in long. 157° 22' W., on January 22d, at 1^ 40'' P.M. Eequirod the mean length of passage. Taa'LOR's Mod. Nav. 10. 146 TAYLOifs Modern Xavigation. Fort Point, ast. timf, Jan. Honolulu, ast. time, Jan. , 15*^ 1 2U" 22 7 40 ' U0« 00 Long. 122° 29' Long. 157 22 34 53 4 W W. A pp. length of passage, Diff. of long, in time, 6 13 20 + 2 19 00 32 Mean length of passage, 6** 15'' 39°' 32« 60)139 32 2'M9'"32« Example. — Passed Sandy Hook light-ship, in long. 74° W., on April 21st, at 10'' 32°' a.m. Arrived off the Fastnet Rock, in long. 9° 36' W., on April 27th, at 2" 5"' a.m. Required the mean length of passage. Sandy Hook, ast. time, April 20'' 22" 32"' 00^ Long. 74° 00' W. Fastnet Rock, ast. time, April 26 14 5 OU Long. 9 36 W. App. length of passage, 5 15 33 00 64 24 Diff. of long, in time, — 4 17 36 4 Mean length of passage, 5" 11" 15"' 24-^ 60)257 36 4" 17"^ 36« DIVISION Ml. SUMNER'S METHOD OF FINDING THE LATITUDE AND LONGITUDE. Like many other useful discoveries, tliis method was actually stumbled upon by Captain Sumner, an American ship-master, and a very lucid account of the occurrence is given in the Bowditch Epitome, which we advise the student to read. The Ohsercation. — Take two chronometer observations, one in the forenoon and one in the afternoon, or both in the morning or both in the afternoon if they are not too close together, being careful to note the true course and distance sailed between sights. Select two latitudes, one on each side of where you think the ship is. The Computation. — Work the first observation with these two latitudes, and mark them A and B. Next work the second observation with the same two latitudes, and mark them C and D. Then select a chart having the proper latitudes, and mark on it the first two longitudes, A and B, on their respective latitudes; draw a line of indefinite length through them, and name this line the First Line of Position, and the ship will be somewhere on this line at time of taking the first sight. From any part of this first line of posipon lay off the true course and distance the ship sailed between sights, and through the end of this course and distance line draw another, parallel to the first line of position, and name it the Projected Line. Now mark on the chart the second two longitudes on their re- spective latitudes and draw a line of indefinite length through them. This last line is called the second line of position, and as the ship is somewhere on this line, and also somewhere on the pro- jected line, at the instant of taking the second sight, the point where they intersect or cross each other will be the position of the ship. The second and projected lines must always cross, but if tliey do not, extend them until they do. A very important item to renu'inl)cr in relation to the lines of position is that the sun's true bearing may be found by striking a right angle to either one of them, to the east if an a.:m. sight, and tii the West if a p.m. sight; therefore if at the time of taking the 148 Taylor's Modern Navigation. observations the observed bearing of tlie sun and the direction of the ship's head has been noted, the deviation may be found, as well as ship's position. Example for Practice. 1894, September 25th 7 a.m. at ship, and uncertain of my posi- tion; a chronometer showed 1^ 6"" S** G.M.T., and at same instant the sun's obs. alt. L.L. was 10° 49' 20= ; the ship then sailed S. 62° E. true, 27 miles, when the following sight was taken: At 3 p.m. at ship, same day, chronometer showed 2>^ 00™ 30^ G.M.T., when the obs. alt. sun's L.L. was 26° 46' 40", and height of observer's eye at both observations 10 feet. The ship, by D.R., was estimated to be between the latitudes of 46° 58' J^T. and 46° 20' N., and long., by D.R., about 179° E. Required the latitude and longitude of ship at time of taking the second observation, and the sun's true azimuth at both first and second sights. First Observation. 1894, Decl. Sept. 24^ 7 0° 33' 41" + 6 55- s. s. 2^ G.M.T. Cor. 58".53 7 .1 Ecius equa. I. 8"" 3« 0.8 6 7.1 -8"^ 9^ 5.68 Obs. alt. 10° 49' 20" Cor. +8 32 Decl. 40 36 90 00 00 5853 40971 T. alt. 10° 57' 52" P.D. 90° 40' 36" 60)415.563" 6' 55" T. alt. 10° 58' T. alt. 10° 58' Lat. 4') 58 sec .16595 Lat. 46 20 sec .16086 P.D. 90 41 cosec .00003 P.D. 90 41 cosec .00003 2)148 37 2)147 59 Half-sum 74 18 cos 9.43233 73 59 cos 9.44078 T. alt. 10 58 10 58 Rem. 63° 20' sine 9.95116 63° 01' sine 9.94995 2)19.54947 2)19.55162 sine 9.77473 sine 9.77581 9.77575 6A 3^^ Double Altitudes. 149 Sept. 24" 19'^ 07'" 44^ A.T.S. Sept. 24" 19" 06"> r)3« A.T.S. Equa. - 8 9 - 08 09 24 18 59 35 M.T.S 24 7 6 02 M.T.G 11 53 33 15 165 13 15 8 15 178° 23' 15" E. 24 18 58 44 M.T.S 24 07 06 02 MT.C 11 52 42 15 165 13 10 30 Long. A, 178° 10' 30" E. Long. B, First Line of Position, N. 12^ E. and S. 12° W.; Sun's True Bearing S. ?8° E. Second Observation. 1894 Sept. 24" 15'^ 00 ^^ 30= M.T.G. Equ a. 8™ 3« 0.8 12 15. Cor. Equa _Sm 15^ 12.0 Decl 0° 33 41' S. 58".53 Obs. alt. 26° 46' 40' + 14 38- s. " 15. Cor. T. a t. + 11 26° 57' 07 48 19 29265 47 90 00 00 5853 P.D. 90° 48' 19' 60)877.95 14' 38' T. alt. 26° 58' T. alt 26° 58' Lat. 46 58 sec .16595 Lat. 46 20 sec .16086 P.D. 90 48 cosec .00004 P.D. 90 48 cosec .00004 2)164 44 2)164 06 Half-sum^2 22 cos 9.12331 82 03 cos 9.14085 T. alt. 26 58 26 58 Rem. 55°^' sine 9.91547 55° 05' sine 9.913&1 2)19.20477 2)19.21556 sine 9.60238 sine 9.60778 9.60215 9.60761 23 A 6« 17 A 5« 150 TAYLOir.s Modern Navigation. Sept. 25"^ 03" Equa. 08"' - 8 46« 15 A.T.S. M.T.S. M.T.G. E. W. 25*^ 03" 11"^ - 8 17^ A.T.S. 15 25 03 24 15 00 00 31 30 25 03 25 15 03 00 02 M.T.S. 30 M.T.G. 12 15 00 01 12 15 180 180 360 02 "30 8 38 00 32 180 360 00 00 15 00 30 Long. D, 179° 59' 45" 30 E. 00 Long. C, 179° 21' 30" W. Second Line of Position, N. 35° W. and S. 35° E.; Sun's True Bearing S. 55° W. Position at second observation, Lat. 47° 40' N. ; Long. 179° 17' E. LATITUDE AND LONGITUDE BY DOUBLE ALTITUDES. This section of the book is one of the most important, and the application of these modern methods enables the navigator to as- certain his position at any time of the day or night, whenever celes- tial objects are visible. Those methods of Double Altitudes whereby the Latitude only is found are obsolete, and may, with the Lunars, be relegated to the dust-bin — in fact, they are so very much out of date that mention of them at all is questionable. It is a great wonder that the methods here given have not been more generally used on board of American vessels, for when we consider that the latitude, longitude, and sun's true azimuth are all found with one Avorking, the great benefit to be derived is enough to convince the most skeptical among the seafaring class. The working of a Sumner Method is simply a repetition of a common chronometer sight, and is extremely easy to learn, but it is long, tedious, and cumbersome, because the approximate posi- tions found must be plotted on a chart of a sufficiently large scale before the desired result is arrived at; still, although with the be- fore mentioned defects, it is of the greatest utility in navigation, for it is possible to navigate a vessel with this method alone, without bavins: resource to a bitilude observation. DouiJLE Altitudes. 151 The problem illustrated on Chart attached to this section, is an extreme case, but extreme cases are always best for illustra- tion, for the reason that the subject is brought more forcibly before the student. Projection o/^JuMN£R'5iiETHuu 178 £ I78'£ ' I790E ' 180* In practice it is rarely necessary for the lines of position and projection to be extended beyond the parallels of the latitudes used in the question yet it may occur at any time, and if it should, the problem should again be computed by selecting a latitude beyond 152 Taylor's Moderx Xavigation. the point of intersection of the lines, rejecting as inaccurate the previous calculation. The rule, when selecting the two assumed latitudes wherewith to compute the longitudes, is as follows : Find the latitude by D.R., and allow about 20' to 30' on each side of it for the two assumed latitudes, and as a rule, in actual practice, the ship will always be found between these parallels. It should be remembered that latitude gives the position on a parallel, or small circle, and that longitude gives the position on a meridian, or groat circle, the point of their intersection being posi- tion of place. It is always possible to determine the ship's place on a part of a circle, as will be seen. If the declination is equal to the latitude of the place, the sun will be in the zenith at noon, and there is always some place on the earth's surface where the sun is vertical, or overhead, and there is always a circle on this earth, surrounding the spot where the sun is vertical, whereon is the observer. Take for instance a flag-pole, and draw a circle, say, 100 feet from its base. Each one on this circle having the same height of eye, and measuring the angle between its summit and base, would have the same angle. Advance towards the pole, and the angle increases ; retreat from the pole, and the angle decreases. This is true, also, in regard to the sun ; for of any number of ob- servers on any part of the same circle, observing the sun at the same instant, each and every one would have the same altitude. If these circles were drawn on a globe they would be true circles. but when drawn on a Mercator chart they are elliptical figures, f^wing to the apparent increase in the size of the degrees of latitude, caused by representing the earth as a plane instead of as a sphere. In actual practice, only small parts of circles are required, but if it is the desire of the student to obtain the whole circle, posi- tions must be computed for every 5° of latitude. In the case of the sun, the first observation gives only a position oil one circle, and although a knowledge of this is very valuable, still, it does not, of itself, give the position of the ship ; therefore, after waiting about one and a half hours, so as to allow the sun to change its position, or to become vertical to some other place, a second observation must be taken, giving another circle, whereon the observer is also; and supposing the ship not to have changed her position, these two circles would be seen to cross each other twice, Double Altitudes. 153 if plottiil oil a chart, but at widely different places on the earth's surface; and as cither one of these positions will give the ship's place, it is hardly necessary to state how easy it is for the naviga- tor to discern the proper one, his D.R. being his check, and we feel assured he will know the D.R. inside of a handful of degrees. If the ship has changed her position between the two observa- tions, it will be necessary for the first circle, or line, to be advanced according to the direction and distance. This matter of shifting the first circle along is the greatest draw- back to the method being applied to the sun, as there is always a considerable element of doubt in correctly estimating the true course and distance sailed. But here the stars and planets come to the rescue, for by them it becomes possible to take simultaneous observations of two celestial bodies in widely different directions, namely, one body ob- served to the East and the other body to the West, and the cir- cles, or lines as they will hereafter be called, when plotted on the chart, will give at their point of intersection the ship's place, en- tirely doing away with D.R. This method of using the stars may still further be improved, if there is any doubt in regard to the true place of the horizon, by observation of a third star or planet, and plotting this line on the chart. All doubt will then b^' entirely eliminated. All lines of position should cut each other at any angle between 60° and 120° to insure a good result; if the angle is less or greater, the intersection of the lines is not well defined, and an error amounting to several miles may arise in the desired result. A good observer — and remember, it is the "man behind the gun" that tells — ought to be sure of the observed altitude inside of 2', provided he has a good sextant, well-silvered glasses, and a good star-telescope. It will be seen, therefore, that the whole object of the problem is to locate the line whereon the ship will be at the time of taking an observation. By the rule given for the sun, this is found by working the sight with two latitudes, plotting the positions found on a chart, and drawing a line through them; but by reference to the rule it will be found that the assertion is made anent the sun's true bearing being at a right angle to the line of position. This is illustrated on the chart. jSTow, if the sun's true bearing, or azimuth, is at a right angle to the line of position, it stands to reason that the line of position is 154 Taylor's Moder^t Navigation. at a right angle to the sun's bearing. This is a very valuable point to know; for if it is possible to obtain the sun's true-bearing, it is certainly possible also to obtain the line of position from it. Contained in every chronometer sight, when worked out, is the A.T.S., latitude, and declination. These three elements given, with the assistance of American Azimuth Tables the sun's true bearing at time of sight may be found by inspection. Therefore, work the sight only once with the latitude by D.E., and with the elements as before mentioned procure the sun's true bearing, and either add or subtract 90°. The result will be the line of position, as correct as if the operation had been performed iwice. It is not necessary to use the latitude brought forward from the first sight to work the second, but it is more correct. These lines of position, when extended and drawn on a chart, will exhibit the bearing of the land, and the navigator may shape a course along them with absolute confidence in his eventually ar- riving at the point indicated by the line dr.iwn. provided he is ihoroughly acquainted with the errors of his navigating compass, and provided, as soon as the land is sighted, he takes a bearing of some prominent object, like, for instance, a mountain. The inter- section of the line of bearing with the line of position will give the ship's place, or if the land is not visible, and recourse is had to the lead, the ship's place may be determined with tolerable accuracy, provided soundings are taken at frequent intervals as ship ap- proaches the land. In a preceding part of this book, relating to the modern a.m. sight, a small diagram is given, proving the problem by graphically drawing it. it will be noticed that the sun's true azimuth is an important element. An ordinary sight worked with the approximate latitude gives only an approximate longitude, yet these approximations may be utilized by striking a right angle to the sun's bearing at time of sight, through the approximate position, giving a line whereon is the ship, but on what part is not known. With the course and distance between sight and noon bring posi- tion forward, and obtain the projected line, whereon the ship will be at noon. At noon determine the latitude, and tbe point whore it cuts the projected line will be the position at noon, provided that true course and distance have been correctlv estimated. DoiBLE Altitudes. 155 Sumner's Method. tJ.ni III pics fur rraciice. 1894, August 15th, 8'' 5'" a.m. at ship, the sun's true alt. was 32° G^ O0",-chronometer showing (S^ 2°^ 48*^ G.M.T. and after sailing IS'. 11° W. true, distance 35 miles, a second observation was taken at 4'^ 30™ P.M., chronometer showing 2^ 32°^ 48^ G.M.T., the sun's true alt. being 23° 37' 00" ; ship's position, by D.R., was lat. 47° 7' N. and long. 147° W. at time of first sight; assumed lats. to work both sights, 46° 50' N. and 47° 25' N. Eequired the ship's posi- tion at time of second observation, trend of lines of position, and Sim's true azimuth at both sights. Answers. — First observation, lat. 46° 50' X., long. 147" 15' \V.. lat. 47° 25' X., long. 146° 59' 30" W.; second observation, lat. 46° 50' N., long. 147° 05' 30" W., lat. 47° 25' X., long. 147° 10' 30" W. Ship's position, lat. 47° 50' N., long. 147° 14' W. ; first line of position N. 15° E. and S. 15° W., T. az. S. 75° E. ; second line of position, N. 5° W. and S. 5° E., T. az. S. 85° W. 1894, May 23d, 3^^ 20°^ p.m. at ship; the chronometer showed 1** 20™ 00^ G.M.T., when the sun's true alt. was 40° 23' 00" ; ship then sailed JST. 3° W, true, distance 20 miles, when a second sight was taken at 5^^ 30™ p.m., chronometer showing 3"^ 30™ 00^ G.M.T. ; sun's true alt. 18° 21' 00"; ship's position, by D.E., lat 46° 53' N. and long. 148° W., assumed lats. to work both sights 4(i° 38' X. and 47° 8' N. Eequired the ship's position at second observation, lines of position, and sun's true azimuth. Answers.— First observation, lat. 46° 38' X.. long. 148° 1!)' W.. lat. 47° 8' X., long 148° 30' W. ; second observation, lat. 46° 38' X., long. 148° 28' 30" W., lat. 47° 8' X., long. 148° 20' W. Ship's position, lat. 47° 02' 30" X., long. 148° 21' W. ; first line of posi- tion, X. 13° W. and S. 13° E., T. az. S. 77° W.; second line of position, X. 11° E. and S. 11° W., T. az. X. 79° W. 1894, June 28th, 7" 30™ a.m. at ship; a chronometer showed 5'^ 38™ 00« M.G.T., when the sun's obs. alt. was 34° 20' 53" ; the ship then steamed X.X.E., distance 18 miles, when, at 9'' 40™ a.m. on same day, a chronometer showed 7'' 43™ 00** M.G.T., the obs. alt. of sun's L.L. being 54° 46' 10"; no instrumental errors; height of eye 30 feet at both sights. The ship was supposed to be, by D.E., in lat. 46° 31' X^. long. 147° 40' \A^ The two assumed latitudes to work the sights are 16' on either side, namely, 46° 15' X. and 46° 156 Taylor's Modern Navigation. 47' N. Eeqiiired the position of the vessel at time of second sight. trend of lines of position, and sun's true bearing or azimuth. Answer.— First observation, lat. 46° 15' N., long. 147° 30' W.. lat. 46° 47' N., long. 147° 29' W.; second observation, lat. 46° 15' N., long. 147° 57' W., lat. 46° 47' N., long. 147° 30' W. First line of position, N. 2° E. and S. 2° W., sun's true bearing, E. 2° S. ; second line of position, N. 30° E. and S. 30° W., sun's true bearing S. 60° E.; position of ship, lat 46° 36' 30" N.^ long. 147° 39' 30" W. (This problem is worked to nearest minutes of arc.) 1894, January 1st, 9** 30™ a.m. at ship ; chronometer showed 7'' 36°! 28« M.G.T., when the sun's true alt. was 14° 03' 10" ; ship then steamed E.N.E. true, distance 49 miles, when a second obser- vation was taken at 2^ p.m., chronometer showing 12*^ 02™ 28' M.G.T., the sun's true alt. being 14° 21' 00"; ship's position, by D.E., lat. 46° 30' N., long. 146° 20' W.; assumed lats. to work sights 46° 12' N. and 46° 48' N. Kequired the ship's position at time of second sight, trend of lines of position, and sun's true bear- ing at each observation. Answer. — First observation, lat. 46° 12' K., long. 147° 47' W., lat. 46° 48' N., long. 146° 23' W.; second observation, lat. 46° 12' N., long. 145° 44' W., lat. 46° 48' N., long. 147° 10' W. Ship's position, lat. 46° 33' N., long. 146° 33' W.; first line of position, N. 58° E. and S. 58° W., sun's true bearing S. 32° E.; second line of position N. 59° W. and S. 59° E., sun's true bearing S. 31° W. JOHNSON'S METHOD. We have pretty well thrashed out our old friend Sumner; so it is time Ave modified him somewhat. This may be, or we ought to say is, done by substituting the method called "The Double Chro- nometer, or Latitude and Longitude in Cloudy Weather," by Pro- fessor Johnson, to whom all honor is due for simplifying many mt :th- ods now in every-day use on board of ships at sea. The work is pub- lished in pamphlet form, and contains but one table that we wish to use here. (See end of book.) The method is entirely correct, and may be proven liy working Sumner's, by both methods, or by actual test when at sea. The great value of Johnson's Method lies in its extreme sim- plicity, brevity, and accuracy, working each sight only once (instead of twice, as in the older but longer methods), with a very short but convenient and easy calculation by division and multiplication of decimals at the latter part; but in this part of the problem there Double Altitudes. 157 is contained an item not found in any other question in naviga- tion, and that is, when it is finished we can tell if we are right or v/rong in the working. Do not misunderstand this assertion, how- ever. When it is said we can tell if the answer is right or wrong, what is really meant is, we can tell if Mr. Johnson's method is worked correctly; but it does not prove that the observations are correct. This is very important for the navigator to understand. It will also be noticed that there is not any clumsy plotting to perform on a chart, the same as in Sumner's, with always a considerable element of doubt in determining the exact point of intersection of the lines drawn, especially when they do not cut distinctly; and, by the way, it is quite a difficult operation to draw a line straight if the vessel is rolling and pitching in a sea- wa}', making it a difficult matter to keep your legs, let alone the drawing of a straight line; therefore this is another reason why this method should be used in preference to old Sumner's. And, as a final word, we wish to state that there is no method in existence to-day that is of so much value to navigators as 'Johnson's, therefore the seaman may use it with the most absolute confidence, and any errors he may discover are his own, not John- son's. We speak in this forcible manner because there is a tendency among a certain class of seamen to decry it as a fancy method, good enough for boys to amuse themselves with, but not for us old seamen, who crawled through the hawse-pipes and worked our- selves aft. For such this book is not written. The Rule. Take two ordinary chronometer observations, with an interval between of about an hour and a half or two hours, to allow the sun's true bearing to change at least two points. The reason for allowing the sun to change its bearing sufficiently has already been explained under the head of Sumner's. Work the first observation with the latitude by D.E. the ship was in at the time of first sight ; the result will be the approximate latitude and longitude at time of first sight; bring this approximate position forward to time of second sight by using the true course and distance the ship sailed in the interval between sights; the result will now be the approxi- mate position of ship at time of second sight. Call the longitude brought forward No. 1. Now work the second sight with the latitude brought forward 158 Taylor's Moderx Xavigatiox. from the first, and call the resulting longitude No. 2 ; next enter the American Azimuth Tables with the A.T.S., lat., and decl. contained in each sight, and take out the sun's true bearing for each sight and mark them down; then mark down the- latitude used to work the second sight on left side of page, as seen in examples, then No. 1 longitude and No. 3 longitude, and abreast of their re- spective longitudes mark down the azimuths. Next enter Table No. 2 in Johnson's Latitude and Longitude in Cloudy Weather, and with the nearest degree of latitude on the top and the nearest degree of the first azimuth on the side, abreast, and underneath take out the corresponding number, interpolating if the degrees are not even, and mark this number down abreast of the first azimuth and call it a; then do the same with the second azimuth, and call the number h ; add these two numbers, a and h, if the bearings have different names, but subtract if same name. Find the difference of longitude between No. 1 and No. 2 and divide it by the sum or difference of a and l. The result will be the correction for the latitude. Multiply this correction for the latitude by a, and the result will be the correction for the first longitude. Multiply the same correction by h, and the result will be the correction for the second longitude. Bule to Apply the Correction for the Longitudes. First Case. — When the bearings are in the same or opposite quar- ters of the compass, allow both corrections to the East, or both to the West, in such a manner as to make the two longitudes agree. Second Case. — When the bearings are in adjacent quarters of the compass, allow the easterly longitude towards the West, and the westerly longitude towards the East, in such a manner as to make the longitudes agree. If they do not agree, the corrections have been wrongly applied, and herein there is a safeguard against error, peculiar to this method only. To Apply the Correction to tlic Latitude. Under No. 1 longitude or No. 2 longitude mark down the name of the azimuth belonging to it, and under it again mark down the opposite bearing; then if the correction to the longitude was W. tliat letter which is on the opposite corner to W. will be the name of the correction for the latitude. Double Altitudes. 15!) Johnson's Method. Example. — ISD-I, January 1st. 7'' 3()'" a. ii. wln'ii ship was in !at. 46° 30' X. and long. 146° 30' W. by D.K., the following sight was taken : Chronometer showing 7" 36°^ 38« M.T.G. ; sun's true alt. 14° 03' 10". The ship then steamed E.N.E. true, distance 49 miles, when another sight was taken at 2*" p.m., chronometer show- ing 12^ 02'° 28^ M.G.T. ; sun's true alt. 14° 21' 00". Find latitude and longitude of ship at time of second obsirvation, by Johnson's Method. First Observation. Jan. 1" 07^ 36'" 28« Decl. 22° 59' 23" S. M.T.G. 12".7 7 .6 Equa. 3'" 53^ 1.2 9 7.6 -1 36 + 4'" 02« 72 22 57 47 S. 90 00 00 762 889 84 9.12 P.D. 112° 57' 47" 96.52 T. alt. 14° 03' 10" 1' 36" T. alt. 14° 03' Lat. D.R. 46 30 sec .16219 P.D. 112 58 cosec .03587 2)173 31 86 454 cos 8.75242 14 3 72° 42' sine 9.97989 2)"l8.93037 sine 9.46518 9.46511 7A V ATS 9'' 44'" A ^r "^ A.I.&. J -14 A. M. I .^, _^_^ j^. ^^^o j^ Lat. 47° N. y 1<^0 ' T. az. S. 32° E. Decl. 23° S. J ICO Tayloij's Modern Xavigatiox. T. CO. E. N.E., 49; D. lat. 18.8; Dep. 45.3. 12^^ V 9 44'" 16 Dec. 31 21 44 15 A.T.S. + 4 02 equa. Dec. 31 21 48 17 M.T.8. Jan. 1 7 36 28 M.T.G. 9^ 48"" IP 135 12 2 45 Approx. post'n first sight, lat. 46° 30' N. Long. 147 2 45 W. 19 N. 16 Approx.post'n sec'nd sight, lat. 46° 49' N. 145° 56' 45" W. ( 1 ) Second Observation. Jan. 1*^ 12^ 02™ 28^ M.T.G. Equa. 3" 53« 1.2 14 12. Decl. 22° 59' 23" S. 12.7 + 4"^ 07^ 14.4 - 2 32 12. 22 56 51 S. 254 90 00 00 127 T. alt. 14° 21' 00" P.D. 112° 56' 51" 152.4 2 32 T. alt. 14° 21' Lat. brought forward 46 49 sec .164/3 P.D. 112 57 cosec .03581 )174 07 87 03^ cos 14 21 8.71030 72° 42' sine 9.97989 2)18.89073 9.44536 44516 20A 4"' Double Altitudes. IGI A.T.S. 2'. lO- P. M. ^ ^g^. Lat. 47° N. y N. 149 W. Decl. 23° 8. J ^- -• ^- ''' ^^- Jan. I'l 02" 09'" 32« A.T.S. + 4 07 Jan. 1 02 13 39 M.T.S. Jan. 1 12 02 28 M.T.G. 9 48 49 135 rox. Ion 12 12 15 App g. 147° 12' 15" W. at second sight (2) Lat. 46° 49' N. (1) 145° 57' W. S. 32°E. a 2'.30 16 (2) 147 12 W. S. 31° W. N. 1 15 b 2.44 46° 33' 4'.74 60 4.74)75.00(15'.82 474 2760 2370 3900 3792 1080 948 (1) 145° 57' W. 15'.82 (2) 147° 12' W. 15'.82 36 W. 2.30 39 E. 2.44 146° 33' W. 47460 146° 33' W. 6328 3164 6328 3164 W. 38'.6008 )'.3860 N. W. N. E. Johnson's Method. Example.— 1S94, June 28th, at ?•> 30'« a.m., when ship was in lat. 46° 31' N. and long. 147° 40' W., by D.R., a sight was taken, when chronometer showed 5^ 38'" 00« G.M.T.; sun's obs. alt. L.L.34° Taylor's Mod. Nav. 11. 162 Taylor's Modern JSTavigation. 20' 53"; and after steering N.N.W. 18 miles another sight was taken at 9"^ 40"^ a.m., chronometer showing '7^ 43°^ 00^ M.T.G., the obs. alt. sun's L.L. being 54° 46' 10". Find ship's position at time of second observation, by Johnson's Method. First Observation. June 28*^ 05^^ 38'" 00^ M.T.G. Decl. 23° 17' 05" N. 7.2 - 40 5.6 + 3 5.6 + 3 02 2.80 Cor. Decl. 23 16 25 N. 432 90 00 00 360 Obs. alt. 34° 20' 53" P. D. 66° 43' 35" 40.32 + 9 12 T. alt. 34° 30' 05" Alt. 34° 30' Lat. D. R. 46 31 sec .16232 A.T.S. 7^ 45'" A.M. ) T.az. N.92°E. P. D. 66 44 oosec .03684 Lat. 47° N. [ 180 2)147 45 Decl. Half-sum 73 52 cos 9.44385 T. alt. 34 30 23° N. 1 T.az.S.88°E. Kem. 39° 22' sine 9.80228 2)19.44529 sine9.72264 W 2« 9.72259 7 45'" 04 A.M. 5A2« 27 19 45 02 A.T.S. '. CO. N. N.W. 18; D. lat. 16.6; Dep. 6.9 + 3 02 equa. 27 19 48 04 IVLT.S. 28 05 38 00 M.T.G. 9 49 56 15 135 12 15 14 Approx. position Lat. 46° 31' N long. 147 29 00 W. 17 N. 10 00 W. Approx. position at j -^^r^, 147° 39' 00" W. second sight . . ^ Double Altitudes. 16S Second Observation. June 28" 07'^ 43"' 00« M.T.G. Decl. 23° 17' 05" N. 7.2 Equa. 2"» 59" .5 55 7.7 4 7.7 Cor. decl. 23 16 10 N. 504 +3 03 3.85 90 00 00 504 P.D. 66° 43' 50" 55.44 Obs. alt. 54° 46' 10" + 10 00 T. alt. 54° 56' 10' T. alt. 54° 56' Lat. brought forward 46 48 sec .16460 P.D. 66 44 cosec .03684 )168 28 84 14 cos 9.00207 54 56 29° 18' sine 9.68965 2)18.89316 9.44658 .44646 12 A 2^ 12^ 2^ A.T.S. 9*' 50™ ) T. az. N. 120° E. 9 50"° 08 Lat. 47° N. Decl. 23° N. [ 180 A.T.S. 27 21 .50 06 ) T. az. S. 60° E. Equa. + 3 03 M.T.S. 27 21 53 09 M.T.G. 28 07 43 9 49 15 135 12 15 12 00 51 45 Long. (2) 147° 27' 45" W. 164 Taylor's Modekx Xavigatiox. Lat.brt.fwd.46°4'8'N. (1) Long. 147° 39' W. S. 88° E. o 0'.05 9 S. (2) Long. 147 28 W. ^. BO E. b \ .21 Lat. in, 46°37'N. 1.16)11.00(9'.48 IMG 10.44 560 464 928 39' W. 9'.48 Long. (2) 147° 28' W. h 9'.48 a .05 11 W. 1 .21 .4740 147° 39' W. 948 S. E. 1896 948 11'.4708 N. W. Ansiver—Lat. 46° 37' N.; Long. 147° 39' W. Examples fur Fvactifc. 1894, August 15th, 8^^ 05-^ a.m., when ship was in lat. 47° 7' N. and long. 147° W. by D.E., the sun's true alt. was 32° 6' 00", chronometer showing &" 2"^ 48^ G.M.T, ; the ship then steamed X. 11° W. true, distance 35 miles, when a second observation was taken at 4'> 30°^p.m., chronometer showing 2*' 32"^ 48^ G.M.T., sun? true alt. being 23° 37' 00". Find ship's position at time of second sight, by Johnson's Method. Answers. — First approximate position, lat. 47° 41' N. and long. 147° 17' W.; same brought forward, lat. 47° 41' N. and long. 147° 17' W. Second approximate position, lat. 47° 41' N. and long. 147° 13' W. 1st az. S. 65° E.; 2d az. S. 85° W., a 0.32., h 0.12; diff. 0.44; difP. of long, 4'; corr. for lat. 9'.09; corr. for 1st long. 3' E.; corr. for 2d long. 1' W. Ship's position lat. 47° 50' N. and long. 147° 14' W. 1894, May 23d, 3*^ 20-" r.M., when the ship was in lat. 4G° 53' X and long. 148° W. by D.R., a chronometer showed l'^ 20'" 00* G.M.T., when the sun's true alt. was 40° 23' 00" ; ship then steamed N. 3° W. true, distance 20 miles, when a second observation, at 5^ 30'" P.M., was taken, chronometer showing 3'' 30'" 00^ G.M.T., gun's true alt. 18° 21' 00". Find ship's position at time of sec- ond sight, by Johnson's Method. The Stars. 165 Answers. — First approximate position, lat. 4()° 53' N". and long. 148° 24' W.; same brought forward, lat. 47° 13' N. and long 148° 25' W. Second approximate position, lat. 47° 13' N. and long. 148° 18' W.; 1st az. S. 77° W.; 2d az. N. 79° W.; a 0.33; h 0.28; corr. for lat. 11' S.; corr. for 1st long. 4' E.; corr. for 2d long. 3' W.; ship's position, lat. 47° 2' N. and long. 148° 21' W. THE STARS, AND HOW TO FIND THEM. It is absolutely necessary, before proceeding, for the student to supply himself with a set of good star-charts. These the United States government has published at the ridiculously small sum of ten cents each. There being only two charts, the ambitious naviga- tor can fit himself out for exactly twenty cents. We think, however, that it would be much better if the Hydrographic Office charged more, for then the agents would try to sell them, instead of keep- ing them in the background and showing to the purchaser only those whereon a decent profit is made. There are other very excellent star-maps. The very best of these, from the writer's point of view, are published by Prof. J. M. Kelly of San Francisco, California. These comprise a set of seven maps, one being a map of the comparative sizes of the sun, the planets and their satellites. We wish, also, to direct the student's attention to a most excel- lent work, entitled Popular Astronomy, by Professor Simon Xew- comb, who was superintendent of the American Nautical Almanac at the time of its publication. It is hardly necessary to state that stars are seen only at night, for the reason that, the sun's light being so strong, they are ob- scured; therefore the stars we see are those that occupy that half of the celestial sphere opposite to that occupied by the sun. As the earth moves in its path around the sun, we are on different sides at different seasons; and if it were possible to see beyond him, we should see the stars change. But what is not possible dur- ing the day is possible at night; and if the stars behind the sun change, those in the opposite part of the celestial sphere must also change. It is therefore very evident that the earth, in its annual revolu- tion around the sun, will have each part of the visible celestial sphere in turn exposed to view. This, however, will depend en- tirely on the observer's latitude and the declinations of the stars ; the rule being that stars whose declinations are greater than the 166 Taylor's Moderx Xayigation. colatitiide, when latitude and dfclination are of different names, will not rise above the horizon. The total number of stars visible to the naked eye is about five thousand, but this depends a great deal on the atmosphere and the eye's training. Herschel and Struve estimated that about twenty million were visible with Herschel's twenty-foot telescope, but since their time telescopes have been much improved, and although no reliable estimate has been made since then, yet the number visible with the present facilities must be about double Herschel and Struve's estimate. Stars are classified according to their brightness, which is termed magnitude, and this is indicated by numbers; for instance, Sirius, Altair. and Aldebaran are of the first magnitude, but the Pole-star is only of the second magnitude. Sometimes a decimal is used for greater accuracy, and is expressed thus, 1.2, meaning a magnitude between the first and second. For the purposes of navigation, there are catalogued, in the American Nautical Almanac, 150 stars, 19 being of the first mag- nitude, 50 of the second, 72 of the third, and 9 of the fourth. Stars of lesser magnitude have no practical use in navigation. Stars visible with the largest and best telescopes are of about the sixteenth magnitude, but the system of measurement in use at the present time is far from being perfect. The earliest catalogue known is found in the Almagest of Ptolemy, supposed to be that of Hipparchus. dating as far back as 150 years before the Chris- tian era, and with it we find that the position of the stars then and now is practically the same. There is a small discrepancy, but the best astronomers attribute it mostly to errors in cataloguing. Stars were divided into groups, or constellations, by the an- cients, but it is very hard to discern any likeness to the men, women, animals, and reptiles whose names they applied to the groups, although on many school celestial globes, and in books, these names are still given, the system being popular among the people, but on modern maps it is entirely disregarded. The matter of naming the stars is one of considerable difliculty. The ancients, in naming the groups, applied to them such names as the Great Bear (Ursa Major), Little Bear (Ursa Minor), Grea* Dog (Canis Major), Little Dog (Canis Minor), etc. The Arabs adopted the plan of giving special names, or borrowed names from the Greeks. The Stars. 167 The modern luetliod of naming the stars is that of using the let- ters of the Greek alphabet, after which are given the names of the constellations, the CI reek being the Christian name, and the con- stellation appellation the family name, and when the Greek alpha- bet is exhausted, recourse is had to the Latin alphabet with a sys- tem of numbers. The student, when learning the stars, should, with the assist- ance of the star-maps, before mentioned, endeavor to locate some of the most prominent. In the northern hemisphere the first one to locate is Ursa Major, popularly known as the Great Bear, or Dipper. This group consists of seven stars; three, almost in a line, are called the Bear's tail, the other four forming the body ; the two in the shoulder and fore leg are called the pointers (on the map they are marked with an arrow pointing towards the Pole-star), and are famous for their usefulness in assisting the observer to find the Pole-star, or Polaris. This useful star is nearly always above the liorizon in north latitude, and is situated at the end of the tail of the Little Bear, or Ursa Minor, a group which is almost an exact counterpart of Ursa Major, only much smaller and not so bright. After locating these two groups, the identification of the others is easy if the following instructions are carried out : Glue the map on a smooth board and glaze it so that it may be washed if it gets soiled by handling; have a bull's-eye lantern handy, with some one standing by to throw a light on the chart, as it will take both hands to hold it. Face the North, hold the clu^rt above your head, with the con- fctellations of Ursa Major and Ursa Minor in same position as seen on the sky itself; you will then see on the cliart the various groups v.'ith their names attached to them. Now, suppose Ursa Major to be to the left of the pole, but a little below it; then about the same distance to the right of the pole will be seen Cassiopeia, the throned woman, which is easily recog- nized by the four comparatively bright stars in a broken line at right angles to one another. Next in order comes Perseus, a brilliant constellation, situated in the Milky Way, and a little farther from the pole than Cassio- peia. It may be recognized by a string of good stars stretching along the Milky Way. It contains the variable star Algol. It will now bo necessarv to locate another constellation ; and the ITiS Taylor's Modern Navigation. observer should bear in mind that it depends on the time of year and the time of night when certain stars can be seen. We will therefore next select the beautiful constellation of Orion. This should be easy, because of the brilliancy and peculiar grouping of the stars, there being three of the second magnitude close together and in a straight line, called the Belt of Orion; four other good stars will be found — two above and two below — the two upper ones representing the shoulders of Orion, and the lower ones the knees. All of these stars may be used in navigation. A line drawn through the Belt of Orion will pass close to the star Sirius, the brightest star in the heavens, situated in the con- stellation of Canis Major, or Great Dog. A line drawn from Sirius through the shoulders of Orion will pass close to Aldebaran, commonly called by seamen the Bull's-eye. It is easily recognized, for it is the brightest of tive stars forming the letter V. A line drawn from Aldebaran to Ursa Major, passing through Taurus, will pass close to Capella. Numerous other examples of finding the stars could be given, but we think the above will be sufficient to show how to use the map. It will be noticed, however, that there are many stars on the map with no name attached. We will therefore show how the names of those stars used in navigation may be marked on the map for easy reference. On the outer edge of the map is marked the right ascension in Eoman numerals. The inner circles represent the declination for every ten degrees. By inspecting these circles it will be noticed that stars having declinations not exceeding 30° S. are given, as well as all those having North declinations. Now open the Nautical Almanac under the head of fixed stars and take the first one, with its right ascension and declination, lay a straight-edge over the pole and the right ascension on edge of map, measure along the straight-edge the declination and see what star corresponds to them, and if the star is not marked, write in the Nautical Almanac name. This Avill make the chart more valuable to the navigator. We advise this to l)e done with all the stars on the maps before mounting thcMu on tlu' hoards for practical use. And, by the way, the method of finding the stars in the southern hemisphere is the same as that for the northern, with Double Altitudes. 109 the exception that the observer must face to the South instead of the North, locating first the Southern Cross, and from it striking lines and angles to locate other constellations. We hope that these instructions will be of assistance to the navigator, for many, we feel assured, would use star-observations to locate the ship's posi- tion if they could only learn the stars. Following this article are given the simultaneous observations of stars previously mentioned in the explanations of Summer's and Johnson's methods, and the navigator is advised to try them, but he must not imagine he will be successful at first, as it takes con- siderable practice to measure the altitude correctly. But practice makes perfect. If at any time the observer sees what he considers to be a star in or near a constellation, but which is not found on the star-map, this will be found to be a planet, and not a star. To find out what planet it is, enter the Nautical Almanac under a planet's name, and abreast of the date take out its right ascen- sion and declination and plot them on the star-map; if this gives the same position as that of the one observed, you have the planet's name ; if not, try another one. It is a very good plan for the navigator to have pins with the names of the planets attached, and from day to day, as the planets change their positions, he should place the pins according to their right ascension and declination. The navigator can then always tell a planet at sight, with the assistance of the constellations in its vicinity. LATITUDE AND LONGITUDE BY DOUBLE ALTITUDE OF STARS. 1894, June 14th, about midnight, when ship was in lat. 26° 51' S. and long. 44° 20' W. by D.R., the following nearly simultane- ous observations were taken : T. alt of fd Aquarii 36° 39', bearing E.; chron. 3»' 23"^ 10^ G.M.T. T. alt. of Spica 22° AiV, bearing W.; chron. 3" 24"" 00^ G.M.T. Required ship's position at tinae of observation. i:o Taylor's Modern Navigation. /3 Aquarii. June W 15*^ 23" 10^ M.T.G. Decl. 6° 02' 15" S. R.A. 21'^ 25'" 59» 90 00 00 P.D. 83° 57' 45" T. alt. 36° 39' 00" Spica. June 14'' 15'^ 24°^ 00« G.M.T. Decl. 10° 36' 29" S. R.A. 13'^ 19™ 36* 90 00 00 P.D. 79° 23' 31" T. alt. 22° 46' 00" Sid. T. mean noon, 5'^ 31™ 05^ 2 32 T. alt. 36° 39' Lat. 26 51 P.D. 83 58 Red. sid. time, sec .04954 cosec .00241 cos 9.44733 sine 9.78030 5'^ T. a Lat. P.D, 33™ It. 2) 37« 22° 46' 26 51 79 24 sec .04954 cosec .00748 2)147 28 129 01 73 44 36 39 64 30 22 46 cos 9.63398 37° 05' 41° 44' sine 9.82326 2)19.27958 sine 9.63979 2)19.51426 sine 9.75713 20^ 33™ 03« + 21 25 59 R.A. 17 59 02 R.A. of Mer. - 5 33 37 red. sid. T. 14 12 25 25 M.T.S, 14 15 23 10 M.T.G 2 57 45 15 30 14 15 11 15 Long. 44° 26' 15" W. 04"^ 38™ 56« + 13 19 36 R.A. 17 58 32 R.A. of Mer. - 5 33 37 red. sid. T. 14 12 24 55 M.T.S. 14 15 24 00 M.T.G. 2 59 05 15 30 14 45 1 15 Long. 44° 46' 15" W. Double Altitudes. 171 Lat. 26° 51' S. (1) 44° 26' W. T . az. N. 77° E. = a 0'.25 1 27 N. (2) 44 46 W. 0T23720.00(: 87 T, . az. S. 88° W. = 6 0.02 Lat. 25° 24' S. 0'.23 184 160 161 (1) 44° 26' W. 87. (2) 44° 46' W. 87. 22 W. 0.25 2 W. 0.02 . — Long. 44° 48' AV. 435 44° 48' W. 1.74 N. E. 174 S. ,W. S. W. 2T.75 N. E. Answer.— Lat 25° 24' S. ; lonoj. 44° 48' W. Examples for Practice. 1894, January 2;th, at 1^ 30°^ a.^l, when ship was in lat. 36° 26' S. and long. 50° 07' W., by D.R., the following nearly simultaneous observations were taken : Arcturus T. alt. 9° 21', bearing E.; chron. 0^ 0'" 0^ G. M. T. a Orionis T. alt. 14° 44' bearing W'; chron. 5'^ 1'" 30^ G. M. T. Required the ship's position at time of observation, by 'Johnson's Method, and prove same by chart. Ansivers.^Long. by Arcturus 51° 7' 15" W.; T. az. N. 57° E. Long, by a Orionis 49° 56' W.; T. az. N. 69° W. Correction for lat. 56' S.; ship's position lat. 37° 22' S.; long. 50° 22' W. 1894, May 20tli, p.m., when ship was in lat. 25° 15' i!^. and long. 152° W by D.E., the following nearly simultaneous observations were taken : Arcturus T. alt. 51° 10', bearing E.; chron. 5" 35"" 10s. Procyon T. alt. 31° 17', bearing W., chron. 5" 35'" 40^ 172 Taylor's Modekx Xavigation. Kequired the ship's position at time of sight, by Johnson's Method, and prove same by chart. Armoers.—Long, by Arcturus 151° 42' 30" W.; T. az. N. 89° E. Long, by Procyon 151° 25' 45" W.; T. az. S. 81°W. Correction for lat. 106' N.; Ship's position lat. 27° 01' N.; long. 151° 44' W. Illustration of Double ^tar. 0b3ER,vation5 LOOKING 50UTH 4yw AA"^ AS^W 46V 'i'^ot 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 27 -i- ^ Aquarii :^ ^ 4 A r \ 3 \ - L _rA^5P'^* - ?fi'^ - 7^°i - V 5hip> R}st( \ - 1 1 I 1 1 1 1 1 1 1 1 1 1 1 1 27*^ LINE5 OF POSITION- FOUND BY STR.IKING A R^IGHT angle: to JTAR'3 AZIMUTH 26* 25* DIVISION YIII. DEVIATION OF THE COMPASS. An Amplitude is the bearing of the sun when it is just rising above the horizon, or as it touches the horizon when setting. To Take the Observation. — As the sun's lower limb touches the horizon, take a bearing of it by the ship's compass, and note the ap- parent time at ship; also, note the direction of the ship's head at the time when the bearing was taken, because the deviation found will be for that point only. EULE. If the time at ship is a.m., add 12 to the hours and put the ship's date one day back; if the time is p.m., put the ship's date, hours, minutes, and seconds down as they stand; convert the longitude into time, and add it to the ship's time if the longitude is West, but subtract if East; the result will be the Greenwich apparent time (G.A.T.); now take out of the Xautical Almanac the sun's- de- clination and difference for one hour, abreast of the Greenwich date, and correct it the same as it is done in the meridian altitude, problem; mark down the latitude, and under it put the correct de- clination to the nearest minute; take out of Table 44 the secant of the latitude and the sine of the corrected declination; add these logs. ; the sum, rejecting the tens in the index, -will be the sine of the true amplitude (T. amp.). Table 44. If you read sine from the top, you must read the degrees at the top and the minutes on the left ; if you read sine from the bottom, read the degrees at the bottom and the minutes on the right. To Name the True Amplitude. — If the time is a.m., name it East; if p.m., name it West; and towards the North or South ac- cording as the declination is North or South. Under the T. amp. put the obs, amp., adding if of different names, subtracting if same name. The result will be the error of the compass. To Name the Error. — Let the student imagine himself standing in the center of the compass-card and looking towards the bearings ; then if the T. amp. is to the right of the obs. amp., the error is East; if to the left, the error is West. Under the error put the variation, adding if of different names, subtracting if same name. The result will be the deviation. 174 Taylor's Modern Navigation. To Name the Deviatimi. — Stand in the center of the compass and look towards the North point ; then if the error is to the right of the variation, the deviation is East; if to the left, the deviation is West. Example.— I'i'd^, January 14th, at 1^ 43'" a.m., A.T.S., in lat. 49° 50' N. and long. 127° 31' W. ; sun's obs. amp. was E.XS.; variation 22° 10' E. Kequired the deviation of the compass for the position of the ship's head at time of observation. Jan] [14'' 07^ 43" 12 00« 18 19 43 8 30 00 04 G.A.T. 14'^ 04^ 13"^^ 04« Long. 127° 31' W 4 60 ) 5 10 04 8^ 30'" 04* Decl. 21° 15' 25" S. 1 53 Cor. Decl. 21° 13' 32" S. 26".93 4 . 2 53 86 1077 2 60 ) 113.1 06 1' 53" Sec. of lat. 49° 50' N. 10.19043 Sine cor. Decl. 21° 14' S. 9.55891 Sine 9.74934 T. amp. E. 34° 10' S. Obs. amp. E. 11 15 S. Error Var. Dev. 00° 45' E. 22 55 E. 22 10 E. Deviation. 175 Example.— lS9i, May 1st at 6'^ 36'" p. m., A.T.S. in lat. 31° 20' N. and long. 42° 17' W.; sun's obs. amp. was W.1/4S.; variation 27° 51' E. Reqiiired the deviation of the compass for the position of the ship's head at time of observation. May G.A.T 1'^ 06" 3()' 2 49 00« 08 1*^ 09" 25'" 08^^ Long. 42^ 17' 4 W. 60) 169 08 2" 49m 08^ 45".24 Decl. 15° 09' 29" N. 9. 4 7 05 18096 Cor. decl. 15° 16' 34' N. 40716 60)425.256 W 7' 05' o^*- Sec. of lat 31° 20' 10.06846 Sine cor. decl. 15° 17' 9.42093 Sine 9.48939 T. amp. W. 17° 58' N Obs. amp. W. 2 49 S. Error 20 47 E Var. 27 41 E. Dev. 70 4'w A SHORT, PRACTICAL, AND CORRECT METHOD OF FINDING THE DEVIATION BY AN AMPLITUDE, USING TABLE 39, BOWDITCH EPITOME. In actual practice it is not necessary to work the problem of amplitudes by so lengthy a method as that given in the preceding rule, for the reason that it is impossible to observe the bearing nearer than a half-degree with the instruments used for the purpose on board ships. The method here given requires only the latitude to the nearest degree, and the declination to tlie nearest half -degree, taken at sight from the Nautical Almanac abreast of the date. 176 Taylor's Modern Navigation. With these elements enter Table 39 of Bowditch, and under the declinations, and abreast of the latitude, will be found the sun's true amplitude, in degrees and tenths; convert the tenths into minutes by multiplying by 6 ; name the true amplitude East if a.m. at ship, but West if p.m., and towards the North or South according as the declination is North or South. The remainder of the problem may be worked the same as in the longer method, but we advise the following rule for practice, as it entirely does away with the misleading term, error of compass . Rule for Practice at Sea. — Take from the chart the variation and apply it to the true amplitude, allowing East to the left and West to the right. The result will be the magnetic amplitude, or what the compass would indicate provided there were no deviation on it. To the magnetic amplitude apply the bearing by compass. The difference will be the deviation, which must be named East if the magnetic hearing is to the right of the compass, and West if to the left. Sa7ne Two Examples Worked with Table 39 of the Bowditch ' Epitome. Lat. nearest degree 50° N. Decl. 21° S. T. amp. Var. 33^ E. 33 54 S. 22 10 E. Mag. amp. E. 11 44 S. Comp. amp. E. 11 15 S. Dev. 00°29'E. Lat. nearest degree 31° N. Decl. 15° N. 17' W. 17 36 N. 27 51 E. T. amp. Var. Mag. amp. W. 10 15 S. Comp. amp. W. 2 49 8. Dev. T° 26' W. Deviation. 17? The very flight discrepancy existing between the two methods has no practical significance, as the observer is likely to make an error in the observed bearing larger than the difference between the two methods, and it is also almost impossible to steer a course inside of a degree, even on board the finest steamer with its modern steering- gear and excellent conipasses. SHORT METHOD OF WORKING AMPLITUDE BY THE AMERICAN AZIMUTH TABLES. Enter the table with the nearest degree of latitude and declina- tion, being careful to note if they are of the same name or of con- trary names ; look at the bottom of the page, under the nearest de- gree of declination, and the time of the object's rising or setting, with its true bearing at the time, will be found; mark down this true bearing and name it according to the rules printed at the bot- tom of the page, which are: In South latitude, and time a.m., read the bearing from S. to E. In South latitude, and time p.m., read the bearing from S. to W. In North latitude, and time a.m., read the bearing from N. to E. In North latitude, and time p.m., read the bearing from N. to W. When the true bearing or azimuth has been properly named, apply the variation, allowing East to the left and West to the right. The result will be the magnetic hearing. Then take the difference be- tween the magnetic and compass bearings, and the result will be the deviation, to be named East if the magnetic hearing is to the right of the compass-bearing, but West if to the left. Same Two Amplitudes Worked with the American Azimuth Tables. Lat. 50° N. j ^. 1230 53, E. t, ^,_ Decl.21°S. i 180 qq S. 56 07 E. T. az. 22 10 E. var. S. 78 17 E. mag. az. S. 78 45 E. comp. az. 00° 28' E. dev. Taylor's Mod. Nav. 12. 178 Taylor's Moderx Xavigation. Lat. 31° N. ) j^ ^2° 26' W. T. Decl. 15° N J '27 51 e az. var. N. 100 17 W. mag. az. 180 00 S. 79 43 W. mag. az. S. 87 11 W. comp. az. r 28' W. dev. The three methods, it will be noticed, practically coincide ; there- fore the navigator may use either one of them with the greatest confidence when at sea. Examples for Prarticc. — May he Worl-ed by Either of the Three Methods Given. 1894, March 4th, at e"" 20^^ a.m., A.T.S. in lat. 39° 51' N. and long. 132° 50' W.; sun's obs. amp. E.14S.; var. 18° 10' E. Re- quired the deviation for the direction of ship's head at time of ob- servation. Anstcer.—G.A.T. March 4*^ 3^^ 11°^ 20^; cor. decl. 6° 16' 25"S.; T. amp. E. 8° 10' S. ; error 5° 21' E. ; dev. 12° 49' W. 1894, December 2d, at 8'' 50°^ p.m., A.T.S., in lat 59° 40' S. and long. 168° E.; sun's obs. amp. S. 2° E. ; var. 23° 00' E. Required the deviation for the direction of ship's head at time of observation. Answer.— G.A.T. December 1'' 21'^ 38"^ 00^ cor. decl. 22° 00' 6" S.; T. amp. W. 47° 53' S.; error 44° 7' E. ; dev. 21° 7' E. 1894, August 1st, at 10" 20'" p. m., A.T.S., in lat. 69° 59' N. and long 18° 3' E.; sun's obs. amp. N.XW.; var. 16° 17' W. Required the deviation for the direction of ship's head at time of observation. Answer.— G.A.T. August 1^ 9" 7°^ 48^; cor. decl. 17° 52' 37" N.; T. amp. W. 63° 47' N.; error 14° 58' W.; dev. 1° 19' E. 1894, December 1st, at 9" 0" p. m., A.T.S., in lat. 60° S. and long. 16° E.; sun's obs. amp. S.W'.14W. ; var. 23° 10' E. Required the deviation for direction of ship's head at time of observation. Answer.— Cor. decl. 21° 51' 11" S. ; T. amp. W. 48° 6' S.; error 5° 55' W.; dev. 29° 05' W. 1894, June 3d, at 3" 38"" p.m., A.T.S., in lat. 52° 30' N. and Deviation. 179 long. 92° 10' W.; sun's obs. amp. N.W.XW.; var. 26° 00' E. Re- quired the deviation for direetion of sliip's head at time of observa- tion. Answer.— Cot. decl. 22° 24' 13" N.; T. amp. W. 38° 45' N. ; error 5° 0' E.; dev. 21° 0' W. 1894, November 1st, at 6^ 30'" a.m., A.T.S. in lat. 18° 59' N. and long. 157° 10' W. ; sun's obs. amp. E.XS.i/aS. ; var. 10° 20' W. Re- quired the deviation for direction of ship's head at time of observa- tion. Ansiver.—Cov. decl. 14° 35' 38" S.; T. amp. E. 15° 28' S. ; error 1° 2o' W.; dev. 8° 55' E. 1894, March 20th, at 6^ lO'" p.m., A.T.S., in lat. 54° 58' X. and long. 148° W.; sun's obs. amp. W. 2° S.; var. 17° 10' E. Required the deviation for direction of ship's head at time of observation. Answer.— Cot. decl. 0° 12' 58" N.; T. amp. W. 0° 23' N.; dev. U ° 47' W. 1894, September 2d, at 6^ 40°^ p.m., A.T.S., in lat. 44° 29' N. and long. 36° 12' E. ; sun's obs. amp. W.X^.; var. 5° 40' 0" W. Required the deviation for direction of ship's head at time of ob- servation. Answer.— Dew. 5° 20' E. 1894, October 26th, at 7'> 14"^ a.m. A.T.S., in lat. 53° 5' X. and long. 90° 40' E.; sun's obs. amp. E.S.E.; var. 7° 40' E. Required the deviation for direction of ship's head at time of observation. Answer.— Dew 9° 15' W. 1894, 'July 31st, at 6^^ 40°^ p.m., A.T.S., in lat. 26° 55' X. and long. 179° 29' E.; sun's obs. amp. X. 89° W.; var. 12° 57' E. Re- quired the deviation for the direction of ship's head at time of observation. Answer.— T)c\. 6° 39' E. 1894, May 1st, at 5'* 2°^ a.m., A.T.S., in lat. 47° 8' N. ; long. 160° 40' E.; sun's obs. amp. N.E.X^^.; var. 5° 30' E. Required the de- vit^tion for direction of ship's head at time of observation. Answer.— Dew 28° 29' E. 1894, October 31st, at 7^ 20"^ a.m., A.T.S., in lat. 53° 50' N. and long. 170° E.; sun's obs. amp. was E. 11° 15' S.; var. 30° 40' E. Required the deviation for direetion of ship's head at time of observation. A7iswer.—J)e\. 17° 45' ^Y. 180 Taylor's Modern Xavigation. 1894, June 26th, at 6^ 10"" p. m., A.T.S., in lat. 0° 10' S. and long. 15° 10' W.; sun's obs. amp. W.S.W.i^S.; var. 22° 10' E. Required the deviation for direction of ship's head at time of observation. Answer.— Bev. 26° 30' E. 1894, May 17th, at 4:^ 40'" a. m., A.T.S., in lat. 45° 52' X. and long. 136° 51' E.; sun's obs. amp. E.X.E. ; var. 5° 40' W. Ee- quired the deviation for direction of ship's head at time of obser- vation. Answer. — Dev. 0° 4' W. THE ALTITUDE AZIMUTH. The azimuth and amplitude problems are both used to ascertain the deviation, but the observations differ in one respect; viz., the amplitude is observed when the object is rising or setting, whereas the azimuth is taken at any time when the sun is above the horizon, provided its altitude is not greater than 60°. The Observation. — Take a bearing by the ship's compass, meas- ure the altitude with the sextant and note the mean time at ship or the chronometer time, being careful to note also the course the ship was on at the time, as the deviation found will be for that course only. Rule. First Case. — If mean time at ship was taken. If it is A.M. at ship, add 12 to the hours and put the date one day back. If it is P.M. at ship, mark down the date and time as they stand. The result in both cases will be the astronomical mean time at ship, to which must be applied the longitude in time, adding if West, subtracting if East. The result will then be the astronomical mean time at Greenwich. Second Case. — If time by chronometer is noted, apply its error, if any. The result will be G.M.T. Take out of the Nautical Almanac the sun's declination and cor- rect it for the G.M.T. and find the P.D.; correct the altitude as usual; mark down the P.D., latitude, and true altitude under one another, add them, and divide the sum by 2; this is the half-sum; subtract the half-sum from the P.D. or P.D. from half sum as the case iiiav be and call wliat is left the remainder. Deviation. 181 Take out of Table 44 the secant of the hititude, secant of the true altitude, cosine half-sum, cosine remainder (throwing away the lO's from the index) ; add these logs, and divide the sum by 2 ; the remainder will be the sine of half the azimuth; look for this half-sum of logs, in the sine column, and when found note the de- grees at the top and minutes to the left if you read sine from the top, but if you read sine from the bottom read degrees at the bot- tom and minutes to the right ; multiply these degrees and minutes by 2 ; the result will be the true azimuth. To Name the True Azimuth. — Xame the true azimuth opposite to the latitude, and towards the East if a.m., and towards the West if P.M. Under the true azimuth put the observed azimuth, adding if they are of different names and subtracting if same names; the result will be the error. To Name the Error. — Stand in the center of the compass and look towards the. true azimuth ; then if the true azimuth is to the right of the observed azimuth, the error is East ; if to the left, the error is West. Under the error put the variation; add them if different names and subtract them if the same name; the result will be the devia- tion. To Name the Deviation. — Stand in the center of the compass and look at the North point; then if the error is to the right of the variation, the deviation will be East; if to the left, the devia- tion will be West. Note. — By the rules given in Bowditch the half-sum of logs i? called cosine, and in this ease the true azimuth must be named the same as the latitude. Example.— 18di, March 3d, at 4" 36"^ 10« p.m., M.T.S., in lat. 31° 14' IST. and long. 174° 00' W.; sun's bearing by compass (obs. az.) S. 80° W.; obs. alt. of sun's L.L. 16° 49' 00" ; eye 16 feet; var. 14° 20' E. ; ship's head N.E. Required the deviation of the com- pass for the position of the ship's head at time of taking the ob- servation. March 3'' 04*^ 36"^ 10" M.T.S. Long. 174° 00' W. + 11 36 00 4 3 16 12 10 M.T.G. 60)69 6 00 24 00 00 11^ 36- 00" -j-h 4j^m from nearest noon. IS-:- Taylor's Modern Xavigatiox. Decl. 6° 19' 41" S. Diff. 1 hour. 7 31 57".81 Cor. decl. 6 27 12 S. 7 .8 90 00 00 46248 P.D. 96° 27' 12" 40467 60)450.918 "31' Obs. alt. 16° 49' 00" + 9 13 T. alt. 16° 58' 13" Parlx. 0' 08" S.D. 16 10 + 16 18 - 7 05 + 9^3' Dip 3' 55' Ref. 3 10 -7^' P.D. 96° 27' 12" Lat. 31 14 00 sec .06800 T. alt. 16 58 13 sec .01933 2)144 39 25 Half-sum 72 19 42 cos 9.48213 P.D. 96 27 12 Rem. 24° 07' 30" cos 9.96034 2)19.52980 sine 9.76490 35° 35' 2 T. az. S. 71 10 W. Obs. az. S. 80 00 W. Error 8 50 W. Var. 14 20 E. Dev. 23° 10' W. \v- E N V The deviation for ship's head N.E. is therefore 23° 10' W. Example.— lSd4:, February 5th. 8^ 18*" 58* a.m., M.T.S., in lat. 14° 32' N. and long. 148° E. ; sun's bearing by compass (obs.az.) Deviation. 183 S. 80° 42' E.; obs. alt L.L. 25° 59' 00"; eye 30 feet; var. 6° 10' E. ; ship's head N.N.W. Eequired the deviation of the compass for the position of the ship's head at the time of observation. Feb. 5<' 8" 18"^ 58-^ A.M. 12 M.T.S. 4 20 18 58 9 52 00 E. M.T.G. 4" 10^^ 26'" 58« Long. 148° E. 4 60)592 52™ 00« 2)146 40 30 Half-sum 73 20 15 cos 9.45758 P.D. 106 00 28 Rem. 32° 40' 13" cos 9.92522 2)19.44375 Decl. 16° 08' 17" 7 49 S. S. 106 14 26 ir. in 1 hour. 45" .12 10 .4 Obs. alt Dip, Refr. S.D. Parlx. T. alt. .01412 .04683 25° 59' 00" - 5 22 Cor. decl. 16 00 28 00 00 00' 28" P.D. Lat. T. alt 25 53 38 90 18048 45120 - 1 59 P.D. 106° 25 51 39 60)469.248 7' 49" => 00' 28" 32 00 sec 08 02 sec + 16 15 + 8 26° 08' 02" sine 9.72187 31° 48' S 2 T. az. 63 36 E. Obs.az .S 80 42 E. Error 17 06 E. Var. 6 10 E. Dev. 10° 56' E. The deviation for ship's head N.N.W. is therefore 10° 56' E. ISi Taylor's Modern Xavigatiox. Example. — ^^January Tth, p.m., at ship, in lat. 5° 21' N". and long. 163° E.; sun's bearing by compass (obs. az.) S. 87° W.; time by chronometer G** 17'^ 48°^ 39% which was 30^ fast of G.M.T.; obs. alt. of sun's L.L. 17° 20' 00"; I.E.— 20"; eye 16 feet; var. 25° 40' W. Eequired the deviation of the compass lor the position of the ship's head at the time of observation. Jan. 6-^ 17*^ 48'" 39« Decl. 22° 20' 37" S. Diff. 1 hour 30 2 01" 19".5 6.2 gd i7h 4gm gs G.M.T Cor. D. 22° 22' 38" S. 90 00 00 39 1170 60)120.90 P. D. 112° 22' 38" Obs. alt. 17° 20' 00" I. E. 20 Dip Refr. S. D. Par. 17 19 40 3 55 17 15 45 3 5 17 12 40 4- 16 18 + 8 T. Alt. 17° 29' 6" P. D. 112° 22' 38" Lat. 5 21 00 sec .00190 T. alt. 17 29 06 sec .02054 2)135 12 44 Half-sum 67 36~22 cos 9.58101 P. D. 112 22 38 Rem. 44° 46' 16" cos 9.85125 2)1^45470 Sine 9.72735 2'1' Deviation. 32^ 16' 2 T. az. S. 64 32 W. Obs.az. S. 87 00 W. W Error 22 28 W. Var. 25 40 W . Dev. 3° 12' E. iS 185 Examples for Practice. 1894, June 13th, a.m., at ship, in lat. 34° 20' S. and long. 49° 00' E.; sun's obs. az. E.XS.i^S.; sun's obs. alt. L.L. 12° 50' 00"; chron. showed June 12^ 17^ 12'° 4% which was fast of G.M.T. 3°^ 12«; eye 18 ft.; I.E.+l' 10"; var. 22° 50' W. Find the deviation of the compass for direction of ship's head at time of observation. Answer.— GM.T. 12"' 1?'' 8"" 52«; cor. decl. 23° 13' 19" N".; T. alt. 12° 58' 46"; half-sum of logs. 9.62314; T. az. N. 49° 40' E. ; error 54° 24' W.; deviation 31° 34' W. 1894, June 14th, 7'' 12™ 50« p.m., M.T.S., in lat. 54° 50' N. and long. 69° 50' W.; sun's obs. az. N.N.W.; obs. alt. L.L. 9° 10' 10"; I.E.— 1' 10"; eye 18 ft.; var. 50° 40' W. Find deviation of com- pass for direction of ship's head at time of observation. Ariswer.— G.M.T. W^ IP 52'" 10^; cor. decl. 23° 18' 45" N.; T. alt. 9° 15' 0"; half-sum of logs. 9.93242; T. az. S. 117° 43' W.; dev. 10° 52' E. 1894, November 1st, a.m. at ship, in lat. 49° 52' X. and long. 28° 3' W.; sun's obs. az. S.XE.; alt. of sun's L.L. 12° 2'; I.E. —2' 15" ; eye 18 ft. ; time by chron. October 31'» 22'' 16°" 58% which was 1°^ 18« slow of G.M.T. var. 22° 20' W. Find the deviation for direction of ship's head at time of observation. Answer.— G.M.T. October 31'^ 22'' 18°' 16«; cor. decl. 14° 30' 30" S.; T. alt. 12° 7' 28"; half-sum of logs. 9.62003; T. az. S. 49° 16' E.; dev. 15° 41' W. 1894, September 26th, 8" 40'° a.^^l, M.T.S.. in lat. 13° 58' N. and long. 174° 53' W. ; sun's obs. az. E.^S. ; obs. alt. sun's L.L. 38° 45' 15"; I.E. +2' 10"; eye 20 ft.; var. 13° 10' E. Find de- viation for direction of ship's head at time of observation. 186 Taylor's Modern Xavigation. Answer.— Cov. decl. 1° 28' 28" S.; T. alt. 38° 58' 00"; half-sum of logs. 9.79129; T. az. S. 76° 24' E. ; error 5° 10' E. ; dev. 8° 00' W. 1894, April 2d, p. m. at ship, in lat. 50° 3' N. and long. 153° 10' E.; sun's obs. az. W. 2° S.; obs. alt. sun's L.L. 12° 1' 40"; eye 20 ft. ; time by chron. April 1^ 18*^ 56"" 49^ which was 2-" 10« slow of G.M.T.; var. 10° 10' E. Find deviation for direction of ship's head at time of observation. A7iswer.—CoT. decl. 4° 57' 5" N. ; T. alt. 12° 9' 1" ; half-sum of logs. 9:82194; T. az. S. 83° 10' W.; dev. 15° 00' W. 1894, June 15th, a.^i. at ship, in lat. 33° 49' S. and long. 50° 10' E.; sun's obs. az. E.XS.; obs. alt. of sun's L.L. 12° 46' 10"; LE. —2' 40" ; eye 27 ft. ; time by chron. June U^ 16'^ 59°^ 50« G.M.T. ; var. 1° 30' E. Find deviation for direction of ship's head at time of observation. Answer.— Cot. decl. 23° 19' 16" N. ; T. alt. 12° 50' 08" ; half-sum of logs. 9.62690; T. az. X. 50° 8' E.; dev. 52° 37' W. TIME AZIMUTHS. A Bide to Find the Deviation of the Compass, Using the American Azimuth Tables. The altitude azimuth problem is used mostly when passing ma- rine board examinations, or when the azimuth tables are not to be obtained, but the tables are so cheap, that you will rarely find a vessel without one or more copies on board. They are useful not only in finding the deviation, but also in working observations, as explained in another part of this work. There are several good azimuth tables in use, but as this is an American work we will explain only the one published by the Hydrographic Oflfico. Explanation of How to Open the Book.—li the latitude and dec- lination have same name, open the first part of book, but if differ- ent names, the last part. At the top of the page is given the declination, from 0° to 23°. On the loft-hand side, the apparent time. a.m. On the right-hand side, the apparent time. p.m. At till' bottom is given the time of sun"> rising and sun's setting, with thr sun's true azimuth at those time-, and under these are Deviatiox. 18' printed the rules to name the azimuth, making it unnecessary for the navigator to memorize a rule. It will be noticed that the time at the sides is given for every ten minntes, therefore the sun's true azimuth may be found by simple inspection for every ten minutes of time. We think, how- ever, that the tables would be of much more value to the navigator if the azimuths were given for every five minutes, for, as they are at present arranged, it is necessary to interpolate if the A.T.S. is not on the even ten minutes. The first and most important element required when using these tables is the A.T.S., a knowledge of which must be within one min- ute of the actual time. The other elements are, the latitude to the nearest degree and the declination to the nearest degree, but if greater accuracy is re- quired, work to half-degrees and interpolate. As most seamen have very little knowledge in regard to ascertaining the correct A.T.S., for use in this question we will here give several rules to obtain the same, meeting, we think, any case that is likely to occur on either an ocean liner or a coasting-schooner. First Method. — To Set a Watch or Wheelhoii.se Clock to Apparent Time Sufficiently Near to Work the Time Azimuth. Take a watch and compare it with a chronometer, marking both times down ; to the time shown on the chronometer apply its error ; this will give the G.M.T. ; take from the Nautical Almanac, page 2 of the month, the equation of time and apply it to the G.M.T. as stated at the top of the column ; this will give the G. A.T. ; next take the longitude of the ship, convert it into time, and apply it to the G.A.T. by adding when in East longitude, and by subtracting when in West longitude. This will give the ship's apparent time at the instant of comparing the watch with the chronometer; note the difference between this correct ship's apparent time and what the watch showed, and then put the watch ahead or back, according to the difference found; you will now have ship's apparent time on the watch, and will be ready to takv any number of time azimuths, provided tlie ship does not change her longitude more than 15'. E.vamples in Correcting a Watch. 1894, January ITth. a.m. at ship, in long. 120° W. ; time by watch 3^ 10™, and at same instant a chronometer showed ll'^ lO'" 15« G.M.T. Find error of watch on A.T.S. 188 Taylor's Modern Xavigation. Chron. 11'^ 10'" 15« G.M.T. Long. 120° \V. Equa. - 10 24 4 io~59 51 G.A.T. 60)480 -_^^0_00 W. ^,— 2 59 51 S.A.T. 3 10 00 watch time Chron. P Equa. — 50'" 13 51« G.M.T. 57 1 + 11 1 1 36 31 ~08~ 20 54 G.A.T. 20 E. "U S.A.T. 00 watch time Watch is IP^ 46« fast of A.T.! Watch is 10-" 9« fast of A.T.S. 1894, February 2d, p.m. at ship, in long. 172° 50' E. ; time by watch I'' 20™, and at same instant a chronometer showed 1"^ 50"° 51« G.M.T. Find the error of watch on A.T.S. Long. 172° 50' E. 4 60)691 20 11*^ 31'" 20^ Examples for Practice. March 18th, a.m. at ship; time by watch 7^ 12"^, and at same instant a chronometer showed O'' 40'" 10« G.M.T.; long. 75° 27' W. Find error of watch on A.T.S. Answer. — 18"" 14® slow. May 27th, p.m. at ship; time by watch 9'' 46"", and at same in- stant a chronometer showed ll*^ 53'" 10® G.M.T.; long. 147° 25' E. Find error of watch on A.T.S. Answer. — O** 0™ 5® fast. June 30th, a.m. at ship; time by watch 9*^ 40'"; a chronometer showed 8"^ 46™ G.M.T.; long. 17° 15' E. Find error of watch on A.T.S. Answer. — ll""- 3G® slow. July 20th, a.m. at ship; time by watcl\ 2" 12'"; a chronometer showed 7^ 47"" 17® G.M.T.; long. 79° 41' W. Find error of watch on A.T.S. Aiisircr. — 10'" 2r)'' sh)w. Deviation. 189 Second Method. — To Find the Apparent Time at Ship When There is no Chronometer on Board. First Case. — It is presumed that the navigator is in possession of a good watch that will not alter more than one minute in a week. Set this watch, before leaving port, to Pacific Standard Time, which is calculated for 120° West longitude, and is therefore 8 hours slow of Greenwich M.T. ; for every degree that you are to the West of 120° put the watch back 4 minutes of time, and for every degree that you are to the East of 120° put the watch ahead 4 minutes of time; this will give the M.T.S.; take from the Nauti- cal Almanac, on page 2 of the month, the equation of time and ap- ply it to the M.T.S. as stated on the top of the column ; this will give the A.T.S. sufficiently near to work the time azimuth. Second Case. — If the vessel is on the Atlantic coast, where the time is calculated for 75° West longitude, then you would be 5 hours slow of G.M.T. ; then for every degree that you are to the West of 75° put the watch back 4 minutes of time, and for every degree that you are to the East of 75° put the watch ahead 4 min- utes of time; this will give the M.T.S. ; take from the Nautical Al- manac, on page 2 of the month, the equation of time and apply it to the M.T.S. as stated at the top of the column; this will give the A.T.S. sufficiently near to work the time azimuth. The preceding method.&' of determining the A.T.S. being thor- oughly understood, and the navigator having set his watch, we will now proceed to give the time azimuth worked out in full. The Observation. — Take a bearing of the sun by the ship's com- pass or Pelorus — this will be the compass-bearing, or observed azi- muth — and at the same instant note the time by a watch which has been previously set to A.T.S,, and also note the direction of the ship's head at time of taking the bearing; turn up the azimuth tables being very careful in regard to the latitude and declination having same name or contrary names, and find the required degree of latitude; when found, look at top of page for the declination, and under it, abreast of the A.T.S., will be found the sun's true azimuth, which must be named according to the rule printed at the bottom of each page; then if the degrees are more than 90, sub- tract them from 180° and change the North to South, or the South to North, but keep the name of East or West; under the true azi- muth place the variation, allowing East to the loft and West to the 190 Taylor's Moderx Navigatiox. right; the result will be the magnetic azimuth; under the magnetic azimuth mark the observed azimuth, and find the difference by adding them when contrary names and subtracting when same name; the result will be the deviation, to be named East if the magnetic bearing is to the right of the compass-bearing, but West if to the left. The following examples illustrate the practical application of this method, and the navigator is advised to study them thoroughly, as they are very important in modern navigation. Example in Finding the Error of a Watch and the Deviation by a Time Azimuth. 1894, February 12th, a.m. at ship, in lat. 43° S. and long. 74° 18' W. ; time by watch 6^ 54™, and at same instant a chronometer showed 11^" 59™ 3P G.M.T.; the supposed obs. az. S. 82° E.; var. 22° 14' W. Eind the deviation for the direction of the ship's head at time of observation. Chron. 11'^ 59'" 3P G.M.T. Long. 74° 18' W. 4 11*^ 59™ 14 3P 26 G.M.T. 11 4 45 57 05 12 G.A.T. W. 6 6 47 54 53 00 A.T.S. 60)297 12 Watch time Watch 6"^ 07^ fast of A. T. S. A.T.S. 6^' 48'" A.M. ) Lat. 42° S. [ T. az. S. 87° 42' E. Decl. 13^° S. ) Var. 22 14 W. allowed right. S. 65 28 E. mag. az. S. 82 00 E. comp. az. Dev. 16° 32' E. It will be noticed, when entering the tables, that the A.T.S. does not fall exactly on the ten minutes; therefore we must interpolate after the following manner : Take the two azimuths on each side of the time and find the change of bearing in ten minutes by sub- tracting the lesser from the greater ; divide this change by 10 and we have the change in one minute, which must be multiplied by Deviation. 191 the odd number of niinutes in the A.T.S. \\1ien a half-degree of declination is used, take the mean of the two azimuths on either side of the declination given. The student is recommended to work the examples given of the altitude azimuth jjroblems by the Time Azimuth Tables, which may be done by simply finding the A.T.S. from the time given, ignoring entirely the altitude and its correction. Example. — August 18th. p.m. at ship; time by chron. 0** 51"° 18' G.M.T.; obs. az. S. 77° 30' W. ; var. 10° 15' W.; lat. 40° N. ; long. 124° 50' W. Find the deviation by time azimuth. Chron. 0'> 51'" 18^^ G.M.T. Lonij. 124"50' W. - 3 40 4 47 38 G.A.T. 60)499 20 -8_^J0 W. ----2„, 4h 28"! 18" A.T.S. A.T.S. 41^ 28'" P.M. ) Lat. 40° N. \ T. az. N. 94° 37' W. Decl. 13 N. ) Var. 10 15 W. Mag. az. N. 84 22 W. Comp. az. S. 77 30 W. 161 52 180 00 Dev. 18° 8' E. TIME AZIMUTHS BY STARS OR PLANETS. The most important part of this problem is the finding of the star's hour-angle. Rule. Take a bearing of the star by ship's compass and note the time by a chronometer. Apply the error, if any, and get the G.M.T. 192 Taylor's ]\Iodekn Navigation. To the G.M.T. apply the longitude in time, adding when East and subtracting when West; the result will be the M.T.S. Take from the Nautical Almanac, page 2 of the month, abreast of the Greenwich date, the sidereal time, and correct it for the G.M.T. by using Table 3, Nautical Almanac. Add this corrected sidereal time to the M.T.S. and subtract from the sum the star's right ascension ; the result will be the hour-angle of the star West of the meridian. If the result is greater than 12 hours, subtract it from 24 hours, and the remainder will be the hour-angle of the star East of the meridian. If greater than 24 hours, reject 24 hours, and the hour- angle will be West of the meridian. If it is less than 12 hours, the result is the hour-angle West of the meridian. The star's declination and right ascension must be taken from the star-list given in the Nautical Almanac. To Use the Azimuth Tables. — If the star's declination is not greater than 23°, the azimuth tables given for the sun must be used in the following manner : Always read the H.A. from the p.m. side of the page, no matter if it is East or West of Meridian; but if the declination is greater than 23°, it will be found in a table published for the purpose by the United States government. In this table will be found declina- tions ranging from 24° to 70°, inclusive, and latitude from 0° to 70°, either North or South. In the latter table the hour-angles may be taken from either the right or the left hand side of the page. Care should be taken, however, to read the rules for naming thfl azimuths given at bottom of each page. If there is any doubt about naming the true azimuth of the star, take the sextant and measure the altitude; then, if it is rising, name it East, but if falling, name it West. Example.— l^U, May 21st, a.m. at ship, a chron. showed 10"^ lO'" 35* G.M.T., when the obs. az. of Altair was S. 80° E. and var 10° 40' E., the ship being in lat. 27° N. and long. 146° W. Required the deviation of the compass for the direction of ship's head at time of observation. I) KV [AT I OK. 193 Ast. G.M.T. May M.T.S. Sid. T.G.M. noon Red. from Table 3, 20t, nibasiire np the 196 Taylor's Modern Xavigatiox. jiim of the other, according to which is the greater, and divide the difference by 8; the resnh will be the magnetic bearing, to be named the same as the greater sum. The magnetic bearing being found, we next proceed to deter- mine the deviation for every fourth point of ship's head, thus: Take the difference between the first compass bearing of the distant object and the magnetic bearing; the result will be the deviation, to be named East if the magnetic bearing is to the right of the compass bearing, and West if to the left; mark this deviation down abreast of ISTorth; repeat this for each bearing taken, and we have the deviation of the compass for every four points. To Draw the Curve. With a pair of dividers measure on the center line of the diagram the number of degrees of deviation for ship's head North by com- pass, then place one leg of the dividers on Xorth and measure out along the dotted line to the right if the deviation is East, but to tbe left if West, and make a mark. Xext measure on center line the amount of deviation on X.E. by compass, and with one foot of the dividers on X.E. measure out on the dotted line again and make another mark; repeat this for every four points, with the deviation on Xorth marked at the bot- tom of diagram as well as at the top. Through all of the positions marked on diagram draw a flowing curve, always from the center line, not towards it; the result is termed a curve of deviation. From it a table of deviations may be made for each and every point and quarter-point, if desired, not only for deviation ship's head by compass, but also deviation for ship's head magnetic. To make a table of deviations for ship's head by compass for every point, place one leg of the dividers on X.XE. and measure out along the dotted line to the curve, then lay the dividers on center line and note the numlHT of degrees contained between the legs of the dividers; this will l)e the deviation on X.XE.. to be named East if the curve is to the right and West if to tlie left of the center line, according to the printed insti'iu-tions at top of diagram. * ' Xext place one leg of tlie dividers on X.X.P'. and nicasiire out on the dotted line to the curve again, and find tlie deviation as be- fore, then repeat for every point, and mark the same on a card. To find the deviation of the compass for every ])nint of ship's jorc (ind tlic .li )f tl for cxcrv Deviation. 191 head magnetic, measure out on tlie plain line instead of dotted lin-. The curve being drawn neatly, we will now explain how to find a course to steer by compass, and also how to correct a course actually steered. First Case. — Suppose a magnetic course is taken from a chart, and the compass-course is required. On the center line find the magnetic course and place one leg of the dividers on it, then measure out to the curve on or parallel to a plain line, keep the leg on the center line stationary and sweep with the other back to the center line in the same direction as the dotted line runs, and where it touches the center line will be the course to steer by compass to make the magnetic course taken from the chart. A little rhyme to assist the memory in regard to the above: "If you seek to steer a course allotted. Go out by the plain and come back by the dotted." Second Case. — Suppose a course is being steered by a compass and the magnetic course the ship is making is required ; proceed as follows : On the center line find the compass course, place one leg of the dividers on it and measure out to the curve on or parallel to a dotted line, keep the leg on the center line stationary and with the other sweep back to the center line in the same direction as the plain line runs, and where it touches will be the magnetic course the ship is making good. There is a rhyme for this, also: "From a compass course a magnetic course to gain, Go out by the dotted and come back by the plain." To correct bearings taken by tlie compass before laying the same on a magnetic chart, note the direction of ship's head at time of taking the bearing and find it on the center line; measure out to the curve on or parallel to a dotted line; this will give the deviation for whatever the ship was heading at the time. With this space in the dividers place one leg on that part of the center line representing the bearing, and if the devia- tion is East, measure down the line, but if We>t, measure up the 198 Taylor's ]\Iodekx Xavigatiox. Hue, and where the second leg touches the center line will be the magnetic bearing to la}- on a chart. For downright handiness this ]nethod is hard to beat, but, be it remembered, it is of use only to coasting-vessels having a compara- tively short run from port to port. If the vessel is navigating be- tween ports widely separated as to geographical position, recourse must be had to the taking of azimuths continually. Although the diagram is especially intended to be used when the sun is not visible, it may not be amiss to state, before concluding this article, that it may be used at other times, thus: Supposing the ship to be at sea and the weather clear, steady the ship's head on every four points of the compass and determine the deviation on them by azimuths, plot the results on the diagram as before and draw a curve. This is really a much better method than taking a bearing of the land, because of its being possible to steady the ship longer on a course, whereas when taking a bearing of the land it is of the utmost importance for the ship to make as small a circle as possible. The following problem is illustrated by the thicl: hlack curve on ihe diagram : Ship's? Head, bv Standard Compass. Bearing; of Dis- tant Object. Deviation. Sliip's Head, by Sta- dard Compass. Bearing of Dis- tant Objeot. Deviati .n. N. N.E. E. S.E. s. 50° ^y. S. 54° W. S. 59° W. S. 68° W. 20° E. 16° E. 11° E. 2° E. s. s.w. w. N.W. S. 79° W. S. 87° W. 8. 90° W. s. 7r w. 9° W. 17° W. 20° W. 1° W. S. 231° W. S.327 W. 8. 827° \V. 8)558 S. 69° 6' Call tliis S. 70° W., liecause it is nearer to 70° than 69° Correct magnetic bearing S. 70° W. S,59°W. S. 68°W. S. 70° W. S. 70° W. 20°E.forN.; 1()° E.forN.E.; 11°E. for E.; 2° E. for S.E. Devivtiox. 199 Comp.- j j^_^yo^y_ S.87°W. S.90°W bearings ) S.71° W, ^^^''^- j S.70° W. S. 70° W. S. 70° W. S.70° W bearing 9° \V. for S.; 17° W for S.W.; 20° Wfor W.; 1° W. for N.W. To Construct the Dcciatioii Curve on tlie Diagram. — The devia- tion for ship's head on North is 20° E. Measure 20° on the cen- ter line, and place one leg of the dividers on North and the other on the dotted line, passing through North to the right, and make a mark. Then take the deviation for N.E., which is 16° E. Measure 16° on the center line, and place one leg of the dividers on N.E. and the other on the dotted line, passing through N.E. to the right, and make a mark. Then measure the deviation for East and S.E. in the same man- ner, but when laying off the deviation for South and S.W., West and N.W., measure to the left of the center line because the devia- tions on those points are westerly. Eight deviations being then laid on the diagram, the curve can now be drawn. Take your pencil and draw a flowing curve very carefully through all of these marks. In drawing the curve by hand you must be very careful, as not one man in a dozen can do it at first with any degree of accuracy. The best way is to use a wooden parabolic curve, or a piece of flexible whalebone, and with the assistance of either of these the curve may be drawn more accurately than by hand. To Find a Compass Course to Steer from a Magnetic Course. — Look for the magnetic course on the center line, then go out from the center line to the curve on or parallel to a plain line, and re- turn to the center line on or parallel to a dotted line. The point returned to on the center line will be the course to steer by standard compass. Example. — W.XN^N. magnetic, to find compass course to steer. Look on the center line for W.XN.i/^N.; lay the parallel rulers along the nearest plain line; move the rulers until the edge is ex- 200 Taylor's ^Modekx Xavigatiox. iictly over W.X^-V2^; and draw a line from it to the curve; now lay the rulers over the nearest dotted line and move them over to that part of the curve cut by the first line; then draw a line back to the center line, and where the last line cuts the center line will be the compass course to steer. Ansiver.—'N. 62 ^^r W. It is not necessary to draw lines; the magnetic course may be found by sweeping with the dividers, as explained in a previous rule. Examples for Practice. — Magnetic courses, to find the compass courses. 1: S.W.XS. 2: N.XW. 3: S. 15° E. 4: N.N.E. 5: N.E.XE. 6: N. 72" E. Afisivers. 1: S. 52° W. 2: N. 24° W. 3: S. 8° E. 4: N. 3° E. 5: N. 40° E. 6: N. 57° E. To Find the Magnetic Course from a Compass Course Steered. — Look for the cojnpass' course on the center line, and go out from this center line to the curve on or parallel to a dotted line, and return to the center line on or parallel to a plain line. The point arrived at on the center line will be the magnetic course. ^xam/j/f.— Suppose you had steered S. 52° W. by compass, and you wish to find the magnetic course made good. Look on the center line for S. 52° W.; lay the rulers along the nearest dotted line, and move them over to S. 52° W., and draw a line towards the curve; then lay the rulers along a plain line and move them until they are over that part of the curve cut by the first line, and draw a line back to the center line. The point arrived at on the center line will be tlie magnetic course made good. Ansivcr.—S.W.X^- Examples for rrarlice. — CNnnpass com •sfs. to find the magnetic courses. 1: W.XS. 2: S.S.W. 3: S.E.XS. 4: East 5: E.N.E. Answers. 6: N.E.XN. 1: S. 59° W. 2: S. 9° W. 3: S.E.XS. 4: S. 79° E. 5: N. 82° E. 6: N. 51° E. J)i;\ lAiioN. 201 To Correct Conipass licdriiigs to Find Magnetic Bearings. — Xote the direction of the sliip's head at the time of taking the bearing. Look for the direction of the ship's head on the center line and measure from it to the curve along a dotted line with the dividers; then lay the dividers on the center line, and you will have the degrees of deviation, East if the curve is to the right, and West if it is to left. Apply this deviation to the bearings taken, allowing East to the right and West to the left; the result will be the magnetic bearing. The same result is atlained by a previous rule. Exnwple. — Ship's head N. E. by compass, bearing S. W. Re- quired the correct magnetic bearing. Measure from X.E. along the dotted line to the curve ; then lay the dividers on the center line, and you will find that you have 17° E. deviation, because the curve is to the right; apply this 17° E. deviation to the right of the bearing and you will get S. 61° W. magnetic. Examples for Practice. Magnetic Ship's Head. Bearings. Bearings. S.E.XE. N.N.E. N. 28° E. N.N.W. S.W\XS. S. 47° W. S.XE. W.4S. S. 78° \V. W.N.W. N.4E. N. 8° W. The folhiwing problem is illustrated by the red curve on the diagram. Ship's Head by Standard Compass. Bearing of Dis- tant Object. Deviation. Ship's Head by Standard Compass. Bearing of Dis- tant Object Deviation. N. N.E. E. S.E. S. 85° E. N. 85° E. S. 80° E. S. 69° E. 164° E. 264° E. ll|° E. 0^° E. s. s.w. w. N.W. S. 52° E. S. 41° E. S. 57° E. S. 69° E. 164° W. 274° W. 114° W. 04° E. Com Mag. S. 329° E. S.219°E. mag. bearing. . 85° E. S. 95° E. . 684° E. S. 684° E. 8)548 S. 68i° E X -bearings S bearings S 164° E. for N. 26^° E. for N. E. 202 Taylor's Modern Xavigatiox. Comp.-bearings S. 80° E. S. 69° E. Mag. bearings S. 68^° E. S. 68^° E. ni° E. for E. 0^° E. for S. E. Comp.-bearings S. 52° E. S. 41° E. Mag. bearings S. 68^° E. S. 68^° E. 16"^° W. for S. 27i° W. for S. \V. Comp.-bearings S. 57° E. S. 69° E. Mag. bearings S. 68^ E. S. 68^° E. lli° W. for W. 00^^° E. for N. W. In this case the bearings have not all the same names, but we make them of the same name by reckoning them all from the South. Note that N. 85° E. is S.' 95° E. Examples. — Given correct magnetic courses, to find compass courses. 1: N.N.E. 2: S.XW. 3: W.^ S. Answers. 1: N. 4° E. 2: S. 37° W. 3: N. 85° W. Examples. — Given compass courses, to find correct magnetic courses. 1: N.E.XE. 2: West 3: W.XN. Answers. 1: N. 81° E. 2: S. 78° W. 3: N. 88° W. Examples. — Ship's head E.X.E. ; bearings of two distant objects by compass X.W.XW. and E.XX. Find the correct magnetic bearings. N.W.XW. = N. e56° W. E.XN. = N. 79° E. Dev. 21 E. Dev. 21 E. Cor. mag. N. 35° W. N. 100° E. 180 Cor. mag. S.^0° E. The following probknu is illustrated by the ihin hlacJc curve on the diagram. Dkviat[ox. 203 Ship's Head, by StandarC. Compass. N. N.E. E. S.E. Huarmgs o taut Objc Ship's Head, Deviation, by Standard Compass. S. 22° W. S. 48° W. S. 56° W. S. 45° W. 3° E. 23° W. 31° W. 20° W. S. s.w. w. N.W Bearings^ of Dis- Deviation, tant Object. S. 29° W S. 2° E. S. 6° E. S. 8° W. 17° E 4° W. 27° E. 31° E. The sum of the S.W. bearings is 8. 208° W. The sum of the S.E. bearings is S. 8° E. 8)200 Cor. mag. bearing, S. 25° W. Comp.-bearings S. 22° W. Mag. bearings S. 25° \V. Dev. 3° E. on N. Comp.-bearings S. 56° W. Mag. bearings S. 25° W. Dev. 31° W. E. Comp.-bearings S. 29° W. Mag. bearings S. 25° W. Dev. 4° W. on S. Comp.-bearings S. 6° E. Mag. bearings S. 25° W. Dev. 31° E. on W. s. s. 48° 25° W. w. 23° w. on N.E. s. s. 45° 25° w. w. 20° w. on S.E. s 2° 25° E. W 27° E. on S.W. s s 8° 25° T7^ W W E. on N.W In this case some of the bearings are westerly and some easterly, so we add all the westerly together and all the easterly together and subtract the lesser sum from the greater and divide the re- mainder by 8. The result is the correct magnetic bearing of the distant object, to be named the same as the greater. Examples. — Given magnetic courses, to find compass-courses. 1: N.E.XN. 2: E.S.E. 3: W. 2° S. Answers. 1: N. 61° E. 2: S. 47° E. 3: S. 58° W. 204 Taylor's !Moderx Xavigatiox. Examples. — Given compass courses, to find magnetic courses. 1: N.XE. 2: W.XN. 3: S.W.i W. Ansicers. 1: N. 7° E. 2: N. 51° W. 3: S. 79° W. Example. — Ship's head S.W.XW.; compass bearings of two distant objects W.VoS. and X.i/^E. Find correct magnetic bearings, Ansivers. N. 65° E. N. 36^° E. Deviation hy Napier s Dingram. Example. — In the following table give the correct magnetic bear- ing of the distant object and thence the deviation. Ship's Head by Standard Compass. Bearing of Dis- tant Object by standard Compass. Deviation Required. Ship's Head by Standard Compass. Bearing of Dis- tant Object by Standard Compass. Deviation Required. North . . . N. E . . . . East .... S. E N. 80° E . . . South . . . S. W.... West.... N. W. . . N. 63° E N. 87° E. .. N. 43° E N. 85° E. . N. 55° E N. 82° E. . . N. 70° E From the above table construct a Xapier's curve, and give the courses you would steer b}' standard compass to make the following courses correct magnetic : Correct magnetic courses, X.E.X^""-, E.S.E., S.XW., S.W. Compass courses, Suppose you steer the following courses by standard compass, find the correct magnetic courses from the curve drawn : Compass courses, X.XE.. S. 54° E.. S.W.XW- W.X.W. Correct magnetic courses, You have taken the following hearings of a distant oljject by your standard compass as above. With the ship":^ liead S.W.. find the correct magnetic bearings. Compass bearings. East and S. '10° \V. An^ivcfs. Correct magnetic bearing, N". 70 E. Deviations, 10° W., 17° W., 15° W., 12° W.. 7° E., 27° E., 15° E. Compass courses. X. 51° E., S. 54° E., S. 2° W.. S. 24° W. Deviation. 20o Magnetic courses, X. 1° W.. S. (iG° E., 8. «1° W., X. (iO' W. Magnetic bearings, S. G3° E., N. 84° W. Deviatlun by A^apier's Dmgrani. Example. — In the following table give the correct magnetic bearing of the distant object and thence the deviation. Ship's Head, by Standard Compass. North. . N.E. .. East .... S.E Bearing of Dis- tant Object by standard Com- pass. Deviation Required. Ship's Head, by Standard Compass. Bearing of Dis- tant Object by Standard Com- pass. Deviation Required. N. 88° W. South . . . S.W West. . . . N.W S. 87° W. N. 67°W... N. 60° W. S. 66° W. . . S. 54° W. N. 66° W. . . S. 70° W. . . From the above table construct a Xapier's curve, and give the courses you would steer by standard compass to make the following courses correct magnetic : Correct magnetic courses, X.E.XE., S.E., W.S.W. Compass courses. Suppose you steer the following courses by standard compass, find the correct magnetic courses from the curve drawn : Compass courses, East, S.S.E., W.XS. Correct magnetic courses, You have taken the following bearings of a distant object by 3^our standard compass as above. With the ship's head S.W.XW. ^/-oW., find the correct magnetic bearings. Compass bearings, E.XS. and Xorth. A II steers. Magnetic bearing, X. 90° W. or West. Deviations, 2° W., 23° W.. 30° W.. 24° W., 3° E.. 24° E., 20° E. Compass courses, X. 86° E., S. 29° E., S. 43° W. Magnetic courses, X. 60° E., S. 35° E.. X. 66° W. Magnetic bearings, S. 47° E.. X. 31° E. 16° E. Deviation hi/ Napier's Diagram. Example. — In the following tahk- give the correct bearing of the distant object and thence the deviation. masrnetie 206 Taylor's Mooekx Xavigatiox. Ship's Head by Standard "Compass. North N. E. East . S. E.. Bearing of Dif tant Object by Standard Compass, N. 10° W N. 6°W N. 12° E, N. 20° E . Ship's Head Deviation 'by Standard Required. Compass. South iS. w. I West. N.W. Bearing of Dif tantObjcLt by Standard "Compass. N. 3° E. N. 20° W N. 18° W N. 12° W Deviation Required. From the above table construct a Xapier's curve, and give the courses you would steer by standard compass to make the following courses correct magnetic : Correct magnetic courses, E.XN.y2N., S.S.E., West. Compass courses, Suppose you steer the following courses by standard compass,, find the correct magnetic courses from the curve drawn : Compass courses, S.E.>4E., W.S.W., N.W. Correct magnetic courses. You have taken the following bearings of a distant object by your standard compass as above. With the ship's head E.XS., find the correct magnetic bearings. Compass bearings, S.E. and S.W. Answers. Correct magnetic bearing, N. 4° W. Deviations, 6° E., 2° E., 16° W., 24° W., ?° W., 16° E., 14° E.,. 8° E. Compass courses, N. 88° E., S. 10° E., S. '13° W. Magnetic courses, S. 74° E., S. 85° W., N. 36° W. Magnetic bearings, S. 64° E., S. 26° W. Deviation by Napier s Dlagrafn. Example. — In the following table give the correct bearing of the distant object and thence the deviation. magnetic Ship's Head by Standard Compass. Bearing; of |ii>- laiil ()l.jr,.| ■(Join pass. Ko.iuiivd. Shii.'s Head by Standard Compass. Bearing of Dis- tant Object by Standard Comprtss. Deviation Required. North . . . N. E . . . East S. E N. 13° E... N 9° E South . . . S. W N. 8° W.. '. N. 8° E N. 16° W. . West .... N, W. N. 23° E N. 24° W N. 20° E . . 1 Deviatiox. 20r From the above table construct a Xapier's curve, and give the courses you would steer by standard compass to make the following courses correct magnetic. Correct magnetic courses, ]N'. 10° E., S. 60° E., S. 80° W. Compass courses, Suppose you steer the following courses by standard compass, iind the correct magnetic courses from the curve drawn : Compass courses, S. 50° E., S. 15° E., X. 55° W. Correct magnetic courses, You have taken the following bearings of a distant object by your standard compass as above. With the ship's head S. 40° E., find the correct magnetic bearings. Compass bearings, S. 15° E. and X. 75° W. Answers. Correct magnetic bearing, X. 3° E. Deviations, 10° W., G° W., 19° E., 21° E., 11° E.. 5° W., 20° W., 17° W. Compass courses, X. 21° E., S. 82° E., X. 80° W. Magnetic courses, S. 24° E., S. 4° W., X. 73° W. Magnetic bearings, S. 10° W., X. 50° W. Eemarks ox t]ie Fixdixg of the Deviatiox. The methods given in this section to determine the deviation are only what every navigator deserving the name ought to be thoroughly conversant with ; for of what value is it to know where the ship is if the correct course to another place cannot be found? There are, no doubt, many watch-officers and shipmasters who think that the star and planet azimuths have no practical value, and are something so far above the ordinary that it requires a university education to enable one to master them ; but if the navi- gator will only take the trouble to investigate, he will find that they arc as easy and as useful as azimuths of the sun, and at the present time, owing to the use of so much iron and steel in the construc- tion of modern vessels, and to the installation of electric-light plants, star azimuths are an indispensable adjunct of modern navi- gation, as the following extract from the Army and Navy Register will prove : 208 Taylok's Modekx Navioatiox. . NAVY DEPARTMENT, Special Order No. !). Washington, July 19, 1901. The Department publishes for the information and guidanc-e of the service the following correspondence in regard to the effect on the standard compass of a ground in the bridge electric circuit: BUREAU OF EQUIPMENT, NAVY DEPARTMENT, Washington, D. C, June 15. 1901. Sir: 1. The Bureau calls attention to the inclosed copy of a letter re- ceived from the commanding officer of the U. S. S. Oregon on the disturb- ing effect on the standard compass caused by a "ground" in the bridge electric circuit. 2. The incident is of interest to the Bureau and of importance to the naval service, as it points out a possible danger to navigation that may occur on any ship equipped with an electric plant. 3. The Bureau requests that copies of the letter may be printed as a De- partment special circular and issued for the information of the officers of the service as a precautionary measure against a possible and unexpected danger to the safe navigation of a ship, the only remedy for which lies in increased vigilance when the electric circuits are in operation. Very respectfully, R. B. Bradford, Chief of Bureau. The Secretary of the Navy. UNITED STATES STEAMSHIP OREGON, Off Woosung, China, May 1. 1901. Sir: I have the honor to submit the following report concerning the effect on the standard compass of a "ground" in the bridge electric circuit : 2. Just before sunset, 5:20 P. jr. April 16, while steaming up the China coast on course NE. by N., it suddenly became necessary to change the course about a point to the eastward by bridge and steering compasses to make the allotted course by standard. An investigation mado it appear that the trouble was with the standard conipass. A Time Azimutli taken at once showed this to be the ease, as the deviation of standard compass was 10 degrees 04 minutes E., the tal)ulated deviation being 1 degi'ee 04 minutes E. 3. Tlic tioublc was at once attril)ulc(l (o a ••ground" in llic clcclric cir- cuit, and upon inquiry it was found that tlie bridge circuit liad just been turned on. This was turned off at once, when the standard compass re- sumed its normal condition, a second Time Azimuth sluiwing a deviation of 1 degree 09 minutes E. 4. The bridge circuit was onh'rcd luiiicd on again for experiment, when the cou'pass-card of standard was dliseivcd to ukivc rapidly Ihrougli an Dkviatiox. 209 arc of alxmt 10 degrees. The circuit was again turned nlV and oil-lanijis were used tliroughout the night. 5. A search for the "ground" was begun tlie next day and it was finally located in the starboard after searcli-light control, '{"his being cut out, tlie remainder of tlie bridge circuit was turiied on wilhonl exerting any inllu- enee on the compass. 6. The standard compass is mounted on a raised platform on the after part of the bridge deck. Tliis platform is 4 feet 2 inches wide and 8 feet 8 inches long. It stands about 9 feet above the bridge deck; is mounted on four brass stanchions, and has a perpendicular brass ladder at the after side. A brass hand-rail runs around the platform, the upper rail being about the height of the compass-card. This rail passes 2 feet from the cen- ter of tlie compass-card on the starboard and port sides, and 2 feet 9 inches from the center of the compass-card on the forward side. The search-light control is 3 feet below the after end of the bridge deck, making it 17 feet below and 17 feet abaft the compass-card of standard, and about 1 foot to starboard of amidship line. The nearest wires to the compass pass on the underside of the bridge deck in the midship line, 14 feet below the compass. Very respectfully, F. M. Bostwick, Lieutenant Coiniuinidcr V. 8. A^, Navif/ator. The Commanding Officer. A good result will always be had. providing the sun or star has not an altitude greater than 40°. This will be easily understood, for the reason that the greater the altitude, the more difficult it will be to get a good observed bearing ; theoretically speaking, it is always possible to determine the deviation at any time when the sun or a star is visible, but it is not possible from a practical point of view, as before remarked. It should always be borne in mind by the navigator that the de- viation found is only for the direction of the ship's head at the time of taking the bearing, and only for that particular part of the world where the observer happened to be at the time, and for no other. The ship should also be steadied on a course at least seven minutes before a bearing is taken, to overcome as nnu'h as possible the retentive magnetism, whieh is always a doulitful quantity. amounting to as much as one and a half points under certain con- ditions, and this assertion is made from the personal experience- of the author. When swinging a ship to find tlie deviation alone, at least two hours should be taken, and the writer here wishes to caution the student in regard to a tendency among a certain class of seamen to perform hurry-u]i jobs and to In-ag afterwards how short a time they could do it in. I have frequently heard old navigators bragging, and recall one particular case — that of a master of a large Taylor's Mod. Nav. 14. 210 T.vYLOii'y MoDEitx Xavigatiox. passenger-steamer, who simply slowed the engines, then put the helm hard over, and took the hearings as the ship flew around, without once steadying the helm. When asked how the result came out in such cases, he said, "Well, it may not be quite correct ; but, then, I always have a good lookout kept." And he is only one of many others where a good lookout is the only thing that keeps them off the rocks. On board vessels plying on the United States coasts, it is a very rare occurrence to swing a ship and take azimuths; the master simply notes the course between points on a clear day, and if she "fetches" a little inshore, he keeps her out a little next trip, or the contrary, and if asked any questions in regard to the amount of deviation on his navigating-compass, he cannot give the slightest information about it. As a case in point, the following incident came under the writ- er's notice: Some years ago a certain vessel touched bottom, but managed to reach port. At the inquiry the master was asked to produce a deviation-card. He informed his inquisitors that he did not have it with him; so he was ordered to produce it next day. In the interval, not having a card, he enlisted the services of a friend to help him make one to fit the courses given in his testimony. It was done, and the master was exonerated. This is a very bad case, but it will go to show the criminal carelessness and ignorance of some coasting-navigators, if you can call them such; but we are very glad to state that the above is an extremely rare case. The excuse most masters give for not swinging ship is that the owners will not give them time ; but this is a very lame excuse, for no owner with any business sense will prevent the master from doing what he considers necessary for the safety of the vessel ; and supposing the owner does object to the delay and expense, the master has plenty of time when the owner cannot see him, provid- ed he knows how; and it is the province of this book to tell him. if ho is not already in possession of the requisite knowledge. Should the master not be able to take azimuths, there are several other methods of determining tbe deviation. The first is by using Napier's Diagram, as already described, and l)y I\((>tg('-I)<'ariiigs. There are minu'rous ranges on our coasts and in our luirbors, if the navigator will only use them. The United States government prints and j)ublishes charts of ranges for tlu' benefit of seamen. Dkviatiox. 211 which may 1)0 procured from the local Hydrograjjlnc officials by simply asking for them. These ranges may be utilized after the following manner : Place the ship's head on a certain course upon which the devia- tion is desired ; bring ship in line with the range and take a bearing by the compass, and the difference between the compass bearing and the magnetic bearing taken from the chart will be the devia- tion, to be named East if the magnetic bearing is to the right of the compass bearing, and ^Yest if to the left. Some of the published ranges are of very little practical value, because they are at right angles, or nearly so, to the set of the tides ; therefore only those ranges running in the same or in the opposite direction to the set of the tides should be used, so that the vessel can be steadied on the course a sufficient length of time. If the range runs athwart the tide, the ship is swept out of range so quickly that it is hard either to get a good bearing or to steady her head. There is yet another good way of getting the deviation, but it has one bad point, and that is, it requires two men to do it — one on shore and the other on board — and the element of doubt is, whether the man on shore is attending to business. This method is called Reciprocal Bearings, and is popular in European countries, but is not much used in America. It is carried out after the following manner : Place a compass on shore in such a position that it will not be affected by iron; in other words, so that it will show magnetic and be visible from the ship. The man on shore must be instructed to take a bearing of the ship when a prearranged signal is made, and to number the bearings. The man on board must always keep within sight of the man on shore, and after steadying the ship's head on a certain course he must make a signal and take a bearing of the man on shore, and the man on shore must take a bearing of the ship. When a sufficient number of bearings have been taken and the shore observer is brought on board, all the shore-bearings must be reversed. As they wall be magnetic, the difference be- tween the reversed shore-bearings and the bearings from the ship will be the deviation, to be named as before explained. As a final word of caution, l)c it remembered that the results iti all the dif- ferent methods will dei)end upon the care exercised by the observer. 213 Taylor's Modern Navigation. and he must not at any time be careless, as on the care exercised the safety of the ship will depend. INSTEUMENTS USED ON BOARD SHIPS FOR TAKING BEARINGS. There are numerous instruments in use for this purpose. Some of them are called compass-correctors, which is a misnomer. They should be named deviation-detectors. Others are so-called labor- saving devices, their greatest value consisting in the fact, from the inventor's point of view, that no azimuth tables are required; but in the author's opinion these devices are simply toys, correct in theory, but in actual practice not to be relied upon, owing to the in- tricate nature of their construction and liability to get out of order by rough usage. This matter of entirely dispensing with azimuth tables is wrong, and no owner or shipmaster should waste money on useless instru- ments for a more accurate result will be had by using the tables than by the use of these catchpenny instruments, the principal claim of the so-called inventors being that the tables are entirely unnecessary. Azimuth tables are the most useful publications issued by the United States government, for not only can the deviation be found with great accuracy and few figures, but, as already explained in the modern method of determining ship's position, they are absolutely necessary in the modern practice of navigation. If it were not so, the United States Hydrographic Otfice would not bother about printing and selling them for so ridiculously small a sum as that for which they are sold to the navigator. Wc speak in the above forcible manner because navigators are likely to be misled l)y the desire of storekeepers to sell an instru- ment of which they have not the slightest knowledge; their only ob- ject in selling being the liberal commission allowed by the maker. The most serviceable and useful instrument is called the Felorus, a cut of which is printed in this article. It is simply a dumb-card whereon is engraved the points and degrees of the compass, balanced so as to swing free in the gimbals. It is an instrument to measure the angle between the ship's head and the object observed. Sight- vanes are attached to enable the observer to get a line of sight. A milled-head clamp-screw is ])rovided, situated in llu' center, to clamp the siffht-vanes whenever it is necessarv to do so. Another small Deviation. 213 screw will be found on the outer cdg-e of the plate, which is used to clamp the inner plate to the ring. This instrument is generally of such solid construction that if it happened to take a journey into the lee scuppers little or no damage would be done to it, except that the sight-vanes might be bent, but this would be easily detected and as easily repaired, whereas the labor-saving devices, so called, if they went on the same trip, would be irretrievably ruined. Before using the Pelorus, it is of the utmost importance that it be placed correctly, namely, so that a fore-and-aft line, or a line which is parallel to it, will pass through the center of the card and the lubber-point on the outer ring. If this is not correctly done, all observations taken by it will be in error; therefore great care should be taken, and if the navigator has not the requisite knowl- edge, some experienced person should be employed. In regard to the placing of the Pelorus it is not always advisable to enlist the services of an employee of a ship-yard, for the writer has seen, many times, such men finding the line by the seams on the deck or by measuring simply from the side of a house and taking the middle of the house for a center line. It is hardly neces- sary to state that such work is liable to be in error. The proper way is to work from stem of ship to stern-post, and if there are any obstructions in line of sight, measure to one side or the other a certain number of feet until a clear view can he had fore and aft, and refer this line to the center, or to any place where it is re- quired to place the Pelorus-stands. There' should be at least two 214 Taylor's Moderx ?s' avigatiox. of these stands, one on each side of the bridge, so that if the smoke- stack, sails, or a boat obstructs the line of sight, the Pelorus may be shipped on the other side. The Pelorus being accurately placed in its proper stand, we will now explain the different methods of using it. First Method. — To find the observed bearing of a distant object, either of the sun, a star, or land. Place the same course that you are steering on the lubber-point of the Pelorus ; keep the vessel steady on her course ; move the sight- vanes until the object is seen directly through them, and cut by the thread, then clamp them; read what is on the Pelorus, and this reading will give the observed bearing of the object. If taking an azimuth amplitude or bearing of the land, this would be the com- pass-bearing. Second Method. — To set the ship's head correct magnetic. Enter the time azimuth tables and take therefrom the sun's true azimuth corresponding to the apparent time at ship, the latitude, and declination, being careful to note if the latitude and declination are of same name or of contrary names ; to this true bearing taken from the azimuth tables apply the variation of the place, allowing easterly to the left and westerly to the right; the result will be the magnetic azimuth; place the sight-vanes to this magnetic azimuth and clamp them; place the magnetic course that you wish to steer on the lubber-point and clamp it also, then port or starboard the helm until the object is seen directly through the sight-vanes ; the ship will then be on the magnetic course, which is clamped on the lubber-point. If the deviation is required, it will l)e found in this manner. The course set on the Pelorus is the correct magnetic course, and the difference between it and the one shown by the compass will be the deviation for whatever the ship was heading at the time, to be named easterly if the correct magnetic course is to the right, and westerly if to the left of the compass course. Third 7l/e^//.0f/.— Slacken all the screws in the Pelorus, clamp the sight-vanes to the magnetic bearing of the sun, keeping the ship steady on her course ; move the sight-vanes, which are clamped to the plate, until the object is seen through them ; when this is done nicely and the ship is still steady on her course, clamp the plate; the course indicated on tlu' liil)bcr-poiiit of the PcU)rus will be the Deviation. 215 correct magnetic course the ship is steering at the time, and the difference between this magnetic course and the one shown by the compass will be the deviation, to be named easterly if the Pelorus is to the right of the compass course and westerly if to the left. KuLE TO Use Field's Pelorus. It will be noticed, when using this Pelorus, that there are two circles, the outer one being given in degrees, starting from 0° and reaching to 180°, and the inner one being a representation of a compass, but with the East point placed where the West ought to be. This method of turning the compass around is a very handy one when it is understood. For instance, place the box on the correct fore-and-aft line, or a line which is parallel to it, the same as in the previous methods; bring 0° of the outer circle so that it will come in a direct line with ship's head; then bring South of the inner plate so that it will be in a direct line also ; move the South point of the inner plate to the right or left, according to the name and amount of the variation; then clamp the inner and outer plates together. (The above method is to be used for north lat- itude only, but if in South latitude, simply bring the North to the 0° instead of the South.) Now enter the azimuth tables and take therefrom the true bear- ings; watch where the shadow of the center-pin falls, and on the inner plate will be indicated the magnetic course the ship is steer- ing; the difference between this and what the ship is heading at the time will be the deviation, to be named the same as in the preced- ing rule. If the shadow of the pin does not fall on the course that you wish to make, then port or starboard the helm until it does; the ship will then be steering the correct course that you wish to make. THE SHADOW-PIN. Some compasses have attachments fitted to the compass-bowl whereby the observed azimuth may be read directly from the card. This is the best and most reliable way ; for by it any error that might occur in the incorrect placing of the Pelorus or in the waj-ping of the stand by excessive heat would be entirely eliminated. The commonest and most easily understood method is that of the shadow-pin, but it has several drawbacks, as will be seen. The pin must be accurately centered in the bowl that is at a point 216 Taylor's Modeen Navigation. indicated by the intersection of two diameters, and must be at right angles to the plane of the compass-card. The pin must always be straight ; if not, an incorrect reading of the card will be taken. To test the pin, proceed in the following manner: Place it in position, keep ship's head steady, and note where the shadow falls, then turn the pin half round and see if the shadow falls on the same place. If so, it is straight; if not, it is bent. The pin being straight, and it is required to take a bearing of the sun, note where the shadow^ falls, and read opposite; but it will be found that if the sun has a very low altitude there will be no shadow thrown on the card, and if it has a high altitude, the shadow will not reach as far as the edge of the card. Still, with these drawbacks, it is a very useful thing to use, pro- vided the observer is careful to see that the pin is straight. Last, but not least important, is Thompson's Azimuth Mirror, supplied with Thompson's Compensating Binnacle, the most ac- curate instrument for determining azimuths in existence, and so easy to handle that inside of five minutes from the time of first taking hold of it the navigator can be an expert observer. Printed instructions are supplied with each, so that it is unnecessary to give them here. This is not an advertisement, for the compass and mirror do not reed my indorsement, as they are now, and have been for a number of years, in use on board of our largest steamers. There are several other instruments in use, but lack of space com- pels us to mention only those most frequently found on board ships. o o o a o '73 C a a o U o z o o > « 1 o i 1 1 D ■till g 1 p: c 1 5. il DIVISION IX. CHART-WOEK. Before proceeding with chart-work itself, we will endeavor to give a description of the instruments used for this class of work, and also a description of the different kinds of charts. The Parallel Ruler. This instrument, if such a name may properly be applied to it, consists of two pieces of w^ell-seasoned ebony with brass joints, and is used for referring a line to one of the compasses printed on a chart so that the course may be found, or when taking bearings of the land to refer the same from the compass to the point observed. The navigator should test it after the following manner: Exam- ine the bearings and see if they work easily, but they should not be too slack, for if they are, it is possible for the edges to get out of parallel; then see if the two outer edges also are parallel; this may be done by drawing a straight line on a piece of paper with the assistance of one edge of the rulers; then advance the rulers, say, about a foot, and draw another line; then place the other edge of the rulers to the lower line and advance towards the upper one again and see if the second edge lies exactly along it; if so, the two edges are parallel, if not, reject the rulers. It should be borne in mind that although these rulers are made of well-seasoned ebon}'-, still they are likely to warp in the course of time, there- fore the navigator ought to test them frequently, or he is lial)le to lay the course off maybe a quarter of a point in error. The above description is of the regular ruler, so common in every-day use that mention seems unnecessary; still, the writer has seen many men using rulers that had as much as a quarter of an inch play. Field's Parallel Uider. This is an instrument that makes compasses printed on a chart unnecessary; for if the navigator will only take the trouble to ex- amine one of these, he will find one edge of it graduated to degrees. Jt will also be noticed that on chart? of large localities, like ocean or track charts, the compasses printed on them are at widely differ- ent places, making it necessary for the navigator to "scull'' from one side of the chart to the oth^i', l)er()rc he can get the course; and if there is any error in lh(^ parallelism of the rnlcrs. it is in- creased everv time he moves them: and if there is no error, they CllAKT-WORK. ^r.) iire still liahlc In slip, if he is not vci'v earcl'iil. By the use of Field's ruler it would l)e luucli easier to p't tlu' course, for liv simply moving the rulers until the mark in the center of the blank side is on a true meridian, then bringing both parts together, and reading the degrees on the other edge which cut with the same meridian, the true course will be found. Some of these rulers — the very latest — have brass arms arranged so that they will tum- ble over, making it unnecessary to slide them. This is a very good plan, for by the use of these rulers the chart is not soiled, as it is when sliding rulers are used. Tlic Transparent Protractor. The handiest of all instruments is the Transparent Protractor, as will be seen. Bute — Place the hole in the center of the Protractor over the position of the ship on the chart; then set the edge of the Pro- tractor true by the parallel lines around its edge, cutting or run- ning parallel to a true meridian on the chart ; then, if the true course is required, stretch the thread to any point, and the reading on the compass where the thread passes over will be the true course. If the compass course is required. With the thread draw a true Xorth line and keep it taut; hold the Protractor with its center ever ship's position, with the other hand turn the Protractor to the East or to the West the amount of variation and deviation; hold protractor steady and shift the thread to the place you wish to steer for. and where it cuts the compass will be the compass course to steer. THE THREE-ARM PROTRACTOR. OR STATIOX- POINTER. This instrument, until very recently, was very little known, and at the present time, although quite a number talk wisely about it. very few seamen have ever seen it, unless they have at some time paid a flying visit to a United States man-of-war or a surveying- ^■essel. Thq reason of this, however, is its cost, as owing to the limited salary enjoyed ( ?) by licensed officers, they cannot be ex- pected to purchase one for themselves; but as one instrument is sufiieient for a vessel, I think that the owners ought to supply it, as it is especially to their interest for the ship to make as quick a passage as possible. Tn fact, all navigating ap]ilianees should be supplied to ships by the owners, for they lose many a dollar by 220 Taylor's ]\Iodekx Xavigatiox. the master and officers attemi^ting to navigate the vessel with obso- lete charts and worn-out, old-fashioned instruments. An illustration of this useful instrument ma}' be seen in the American Bowditch E23itome, with a more or less lucid explanation; still, there may be some that cannot understand what is there given, therefore I will endeavor to explain further here. The principle upon which the instrument is constructed is as follows : Through any three points, not in a straight line, a circle can be drawn. Try it thus: Make three marks, not in a straight line, within the scope of the dividers. Take anything more than one half the distance between two of the marks, and with one foot of the dividers on one of them de- scribe a circle; with the same space in dividers place one leg on the other mark and draw another circle; then through the two points of intersection of the circles draw a line of indefinite length ; then do the same with the other marks and draw another line, and at the point where this last line cuts the first, place a leg of the dividers and measure out to either of the three marks and describe a circle. It will then be seen that the circle passes through all of them. For further instruction in regard to the above, the student is referred to any good book on elementary geometry. The usefulness of this instrument, we hope, will be thoroughly appreciated by the simple fact that bearings of tlie land l)y com- pass are unnecessary. This is a very great recommendation, when we take into consideration how doubtful the compass errors are, owing to the extensive use of iron nowadays. It should be borne in mind, however, that a correct result de- pends very much on the accuracy of the chart and on the fact that three distant objects must be visible at same time. To Observe. Station two officers with tlu'ir st'xtaiits. one to iiu'a>inv from the center object to the right and the other to measure to the left; these two angles must then be set on the instrument ; the one to the right must be clamped to the right of tlie fixed arm in center, and the other must be clamped to the left of it ; then when all three arms are fixed lay the Protractor on the chart so tliat the three arms will point to each of the three objects observed ; when this is done, make a mark on the chart directly under tlie center CiiAin-WuKK. 221 of tho circle. This will be ship's position. With the assistance of a piece of tracing-paper, as describetl in liowilitcli. tlio operation is still more graphic. There may be some awkwardness at first when mcasiiring hori- zontal angles, but practice will make perfect; and if the master of a ship will only insist that his oflficers shall be experts in such matters, they will undoubtedly learn. DIVIDERS. This simple little instrument, which is so very necessary in navigation, needs no description here, yet care should be taken in its selection. Dividers should work smoothly on the joints, but should not be slack. Keep them so that when opened a certain space they will retain their position. The best makes have an appliance so that they may be tightened with a key. This is much better than con- tinually clinching them witli a hammer, as must he. done with the cheap variety. The points should be even and well tempered, so that they will not bend. It is not desirable that they should be very sharp, as they are likely to penetrate the chart if the navigator has a heavy hand. CHARTS. We have in the United States three ditferent kinds of charts. They are called : 1. The Gnomonic Projection, which is used exclusively for deter- mining the Great Circle Track. 2. The Polyconic Projection, until very recently was the method used for United States coasting-charts, but at the present time is used only for charts of large localities and for harbor-charts. 3. Mercator's Projection, wliich is the method used at the pres- ent time to chart our coasts, is much more convenient than the Polyconic. It is also the method used in Great Britain. This fact is important, because when an American chart cannot be pro- cured, the navigator may be able to obtain a l^ritish one. To distinguish one projection from another, read tlie following: Place the chart so that you look Xorth ; tlien notice if the merid- ians are always the same distance apart, and also if the parallels 222 Taylor's ]\Iodekx Xavigatiox. running to the East and West are at right angles to them; if so. then it is a Mercator's chart; but if the meridians converge as you go towards the pole, either North or South, then it is a Polyconie chart. If the navigator is still in doubt, ho will find the neces- sary information printed among the remarks. It is very important that this should be understood before using a chart, on account of the necessity of plotting the ship's position and of measuring the distance, which is different on a Mercator from what it is on a Polyconie chart. The method of doing so will be explained further on. To know if the chart is for Xorth or South latitude, and for either East or West longitude, read the following: Face the North as before, and see if the degrees of latitude in- crease or decrease towards the North or South. If they increase towards the North, it is a North-latitude chart, Imt if they de- crease, it is a South-latitude chart. If the degrees of longitude increase towards the West, it is a West-longitude chart, but if they increase towards the East, it is an East-longitude chart. To know if it is a true or magnetic chart, read the following; In regard to this subject it will be found, by inspecting a few United States coasting-charts, that both the true and magnetic compasses are given on some of them, while on the others either true or magnetic only is given, and if the words "True Compass" or "Magnetic Compass" are not printed on the chart, which chart it is may be found after the following manner : Place the North part of chart in front of you and examine the compasses thereon, and if the North and South are printed right on or parallel to a true meridian, then it is a true chart, but if they are slewed out of the Meridian, either one way or the other, then it is a magnetic chart. Most coast charts are magnetic, while oci'an track eliavts are true; tlierofore. wlicn using tlie true chart, both variation and de- viation, if any, must be used to obtain a compass course to steer; but when a magnetic chart is used, deviation only is to be applied to obtain a compass course, allowing East to tlio left and West to the right, which is the opposite rule to that used in the day's work. Variatio7i.— On the United States coasting-charts, the amount of variation for the localities is printed on the chart, in or near the compasses, with the amonnt o\' animal cliange. aiul in regard to (iiAiri-WoKK. 253 this change the navigator cannot be too careful, for in some parts of the world it is considerable, whereas in others it is so small that in a man's lifetime it will not change to any practical amount. If the change is considerable, the navigator should examine the date of publication, and if it is an old chart, and a later one cannot be procured, he should allow for the change, being careful to note if it is increasing or decreasing. But charts are published by the United States government at so small a cost to the navigator that any one too mean to provide himself with the latest edition is not fir to have charge of a ship; and here again we wish to whisper in tlie ear of the owner, that many men are trying to navigate ships with obsolete charts, who, with a knowledge of the worthlessness of these charts, arc so careful, that long passages are the result. Ship-owners should be compelled to supply to ship-masters all the charts that may be required. The ship would then be navigated with greater safety, and quicker passages would be made. Ocean track charts have wavy lines running across them, called lines of ecpial variation; therefore, to get the proper variation from such a chart, the navigator must select that line which is closest to the ship's position and search along it until the amount of varia- tion is found. But the United States government pul)lishes, every year, what is called a Variation and Dip Chart, whereby the varia- tion may be found with considerable accuracy by simply plotting the ship's position on same and taking the line of equal variation closest to the position. All ocean-going vessels should have a copy on board, for they are cheap enough, costing only about fifty cents. The figures on charts represent the depth of water either in fath- oms or in feet at the mean of lower low water. Reference should be made to the printed instructions to determine the matter of fathoms or feet. The letters printed close to the figures represent the nature of the bottom, and may be interpreted by referring to the table of signs and abbreviations printed for the purpose among the remarks. Scale of Charts. — A large scale is used for charts of small locali- ties, such as harbor charts; but charts of large localities, such as ocean charts, are necessarily on a small scale. PILOT-CHARTS. These exceedingly useful charts on j\[ercat()i''s projection may be procured free of cost from the local ITydrographic Office. They are not intended for navigational purpn-es. in tlie strict sense of 224 Taylor's Moderx Navigation. the word, JDut to assist the navigator by means of the valuable infor- mation contained thereon, and are to be used in conjunction with other charts and instruments, such as barometers and thermome- ters. On them will also be found the principal Great Circle Tracks, with lines of equal variation. These charts are issued monthly, and the real object of their publication is to provide the navigator with information in advance, regarding the weather to be expected and the probable direction of the wind, the latter being illustrated by an ingenious system of symbols, which is fully explained. Valuahle information in regard to currents is given, with their probable direction and rate, with explanations as to whether per- manent or surface, or if influenced by winds during certain sea- sons. The position of derelicts and drifting logs is stated, with their probable position calculated for the future, — a very valuable bit of information for navigators, putting them on guard so that a good lookout may be kept. Tracks of Circular Storms are charted, with information re- lating to the probable place of formation, curvature, and break-up, and seasons when most prevalent, with rules for handling the ship. A sub-chart of Isobars and Isotherms is given, cautioning the navigator in regard to the behavior of the barometer and ther- mometer. Much other information is contained on the charts, extremely valuable to the modern navigator. As a final word, we wish to direct the attention of the navigator to the fact that most of the information contained on <:he charts is compiled from data collected by the Hydrographic Office from ship-masters and officers; therefore, whenever it is possible, records should be made in a systematic manner of all changes in weather, passing of derelicts, and especially of the behavior of the barometer and the direction and force of tlie wind whenever a cireuUir storm IS encountered. This information should be forwardrd to the Office immediately upon ship's arrival, which will be courteously acknowledged by the officer in charge. The master should insist upon liis ollicers ket'ping the meteorolo- gical log on the blanks furnished for the ])ur])ose, for l)y so doing they are assisting one another to navigat<' their vesst'ls with a greater degree of safety. CIIART-WOUK. 225 To Find the Course between Two Places on a Chart. Lay tlu' flat edge of the parallel rulers over the two places and move theni until the flat edge is exactly over the center of the com- pass, then read the course from the side of the printed compass that is towards the place it is desired to go to; this will be the true course if a true chart is used, but the magnetic course if a magnetic chart is used. To Find the Cotnijuss Course to Steer to Make Good the Course Taken from the Chart. If the true course was found, apply to it the variation for the locality the ship is in, allowing East to the left and West to the right : the result will be the magnetic course. To the magnetic course apply the deviation, allowing East to the left and West to the right; the result will be the compass course to steer. If a magnetic chart is used, no attention need be paid to the variation further than what has been previously mentioned in re- gard to date of chart; the only correction, therefore, in this case i? the deviation, to be applied as before stated. The above rules will be the same for both Mercator and Poly- conic charts. To Find the Distance on a Mercator's Chart. Take the space between the two places in the dividers, and lay the dividers on the middle latitude abreast; the number of miles contained between them will be the distance, provided the scope of the dividers enables the taking of the whole distance at once; if not, take one half or one third of the space, proceed as before, and multiply accordingly. To find the distance on a Polyconic chart reference must be made to the scale of nautical miles provided for the purpose, and the distance must not. under any eii'eiiiustances'. be measured on the latitude side oF the chart. To Plot Latitude and Longitude on a Mercator Chart. Select from the latitude side of chart the number of degrees, and with the dividers measure the required number of minutes; with this space in dividers, move across the chart abreast of the proper degree until the nearest degree of longitude is found, and on the Taylor's Mod. Nav. 15. Taylou's Modern Xavioatiox. meridian measure the odd minutes and make a distinct mark; now lay the rulers exactly along a parallel and move them until the flat edge is over this mark and draw a line ; the ship will be somewhere on this line. Now from the top or l)otto)n of the chart measure the longitude, and with this space in the dividers lay them on the line drawn, being careful in regard to the direction in which the Chart Illustrating Cross Bearings, and two Bearings of one Object, with Course and Distance Run Between. longitude is increasing, and make nnotlicr mark; tliis will be the desired position. When drawing lines and making tcitiporary marks on a chart do so vci-y liglitly, so that llicy may easily be rubbed ofl'. T(i Flinl llic Ldlihnlr iiitil Loinjllinlr of a I'Jdce. Measure from ibe nearest parallel to the plaee and then lay the dividers on the hititmle abreast and read the degn'es and minutes; ClIAUT-WoKK. 22' this will be the latitude. A'ext measure from the nearest meridian to the same place, transfer the dividers to either top or bottom of chart, read the degrees and minutes, and the longitude is found. If using a Polyconic chart, reference must be made to the interme- djate scale nearest to the position, and the latitude must not, on any account, be measured from the side, nor the longitude from top or bottom. The reason for this will be very obvious to the stu- dent if a Polyconic chart is examined. Find Ship's Fosition hy Cross-Bearings. It in the vicinity of the land, and two objects be distinctly visi- ble at one and the same time, the ship's position can be determined with great accuracy if care is exercised in taking the bearings, cor- recting the same for deviation for direction of ship's head and plot- ting same on chart. Thus: Take the two bearings as close together as possible, apply to them the deviation for Avhatever the ship was heading at the time, allowing East to the right and West to the left; the result will be the Magnetic Bearings. Lay the rulers on the magnetic compass so that the flat edge is directly over the center and also over the part indicating one of the bearings; advance the rulers until over the point whereof the bearing was taken and draw a line •. then do the same with the second bearing, and where the lines intersect will be ship's position. To Find Ship's Position hy Two Bearings of One Point with the Assitstance of the Course and Distance Run Between. Take a bearing of the point and note the time and what is on the patent log if you have one out; keep going on the same course until the bearing has altered one or two points, and then take an- other bearing of the same object; correct the bearings for the de- viation for the ship's head as before and lay them on the chart; next lay the ruler over the magnetic course the ship is steering, and with the distance the ship has sailed in the interval between bearings in the dividers, move the rulers until the legs of the di- viders touch the bearings, and where the foot of the dividers touches the second bearing will be the ship's position at the time of taking the second or last bearing. (This method requires the use of both hands, the left moving the rulers and the right holding the dividers.) There is, still another method, as follows: Lav the l)earino-> down on the chart as before, and with the 328 Taylor's Modern Xavigation. rulers bring the course over to any part of the bearings and draw a line; then with the distance traveled in the interval in the di- viders, place one foot on the first bearing where the course-line crosses it and measure along the course and make a mark ; now lay the rulers on first bearing and advance until the flat edge is over this mark, and draw a line so that it will cut the second bearing. This method will also give the ship's position at time of taking the second bearing. To Find Ship's Position by Four-Point Bearing^ or Double the Bearing. This very handy little problem is of the greatest practical value Chart Illustrating the Four Point Problem or Double the Angle to the navigator when coasting, for by it the distance off a point may be found without recourse to a chart. Take a bearing of a point when it is four points from ship's iiead, namely, four ])()ints off the bow; note wliat is on the patent C]iai;t-\\()KK. 229 log and also the time; proceed on course without changing it until the object is directly abeam. The distance traveled in the interval will be the distance off wIumi it was nhcam. It will bo noticed that the above four-point bearing was doubled to eight points when the object was brought abeam, therefore the problem may be applied to two, three, or three and a half points from the bow, the ship steaming on her course until the angle is doubled, the distance traveled being the distance off the point. There are in Bowditch two tables for the above purpose. By reference to these tables and by paying strict attention to the rules given they will be found to be of considerable benefit when coast- ing. It is not necessary to explain these tables here, as we con- sider the Bowditch explanation sufficiently explicit. Current Sailing. The preceding rules given to find the course to steer, it should be thoroughly understood, are only for finding the course in locali- ties where there is no current, and as there are very few places where there is no current, it stands to reason that some method must be used to counteract the current when one exists. The following explanation, we hope, will be sufficiently plain to the ordinary, every-day navigator, so that this dangerous item in navigation may be overcome, provided, however, that the direction and rate of cur- rent is known. Authentic information in regard to the set and drift of ocean currents may be found on the pilot-charts or in books of sailing directions, or maybe from the navigator's previous experience; but, no matter from what source the information is obtained, due re- gard must be paid to previous w^eather conditions, as quite a num- ber of ocean currents are influenced by wind, and depend a great deal on the season, temperature, etc. The navigator should not confuse ocean currents with tidal cur- rents, as the causes of the two are quite different, but the method to find a course to steer in order to counteract either one or the other is the same. 1. If the current is setting in the same direction as the vessel is traveling, the speed over the ground will be the sum of the rate of the current and the speed of the ship. 2. If the current is setting in an opposite direction to the 230 Taylor's Modkrx iSTAviGATiON. course of the shiiD, the rate of progression will be the speed of ship minus rate of current. 3. If the set of tlie current is at right angles to course of ship, the vessel's speed will neither be accelerated nor retarded, but she will be driven off her course. To counteract the effect of the cur- rent, find out how many hours it will take the vessel to make a cer- tain distance, by dividing the distance by the speed of the ship per hour, and multiplying the result by the rate of the current per hour; this will give the total amount of set. jSText lay the rulers over the direction of the set and advance them over to the point the ship is steering for, and draw a line in the opposite direction to what it is setting; along tliis line measure with the divich'rs tlie total amount of set and make a mark; now, with the rulers over ill is mark and the point of departure, move them until the flat edge is over the center of the compass and read the course. 4. As a rule, however, the current is not always so obliging as to set in the preceding manner; for it may set in an ()l)lique direc- tion, as follows: If the current is setting so as to catch tlie ship abaft the beam, ii will increase the vessel's speed, and at the same time will drive her off her course. If it catches her anywlu>re forward of tlie l)eam, it will retard her speed, and at ibe same time set her off her course. Under these conditions the navigator should find the current course after the following manner. ])aying strict attention to the dia- gram accompanying tlie article. Draw a line on the chart from the ])lace of ship to the place ClJAKT-WOKK. -^31 tile ship is bound to, and mark the point of departure A and tlio point to which the ship is bound B. From A draw a line representing the set of the current and mark it C ; on this line AC lay off the amount of set per hour, say for about three or six hours ; then with the distance the ship would sail in the above length of time in the dividers, place one foot at C and describe an arc,, cutting the first line drawn at D; now lay the rulers over D and C, move them over to the compass, and the current course is found. The distance the ship will make good in the interval will be from A to D. To Find the Compass Course to Steer to Malcc a Magnetic Course Taken fro)n a Chart. It will, no doubt, be remembered that the rules for applying the variation and deviation to the true and magnetic courses have already been explained in a previous part of this section, yet, al- though this has been done, there still remains a very important item, relating to the selection of the proper deviation to apply to a magnetic course before the compass course is found. It should be borne in mind, as we progress, that there are three kinds of courses, namely, the True, Magnetic, and Compass. Some writers, whose authority is not to be questioned, use the term ''Magnetic" for the Compass Course, and "Correct Magnetic" for what the compass would indicate when not influenced by iron in the vicinity. We do not say they are incorrect, but it is our opinion that the terms "Compass Course" and "Compass Bearing" are the best terms to apply to anything indicated by a compass, and the simple term "Magnetic" the best term for what the compass would indicate provided it had no deviation. This little digression, we hope, will be pardoned, as we consider it necessary to explain the ambiguity of the terms as used in different books on the subject. To resume, it is generally considered advisable to det.'rmine tlu^ deviation for ship's head by compass as frequently as possible, the same to be entered in a book kept for the purpose, or if the vessel is simply a coaster, it may be noted on a card and hung up in some convenient place, like the chart-house, for easy reference. Sometimes these cards have the magnetic courses marked abreast of the direction of the ship's head. This is all very well when coast- ing between ports not very widely separated, but it will not do for a vessel that makes long voyages. 282 Taylor's Modern' Xayigatiox. Again, sometimes, but very rarely, a deviation-card is found giving the deviation for ship's head magnetic, but as this would be of nse only on vessels running practically on the same courses and in the same locality, day in and day out, it is hardly necessary to give it more than passing mention. If the student will turn back to Napier's Diagram and examine the curves drawn thereon and reread the rules, it will be noticed that if the space is measured between the center line and the curve on or parallel to a dotted line, the deviation is found for ship's head by compass, but if measured on or parallel to a plain line the deviation is found for ship's head magnetic. The difEerence between the two amounts of deviation will be considerable, under certain conditions, especially when the compass has large errors, and on those courses where the deviation changes very rapidly. It is therefore of the utmost importance that the terms "Devia- tion for ship's head by compass" and "Deviation for ship's head magnetic" be thoroughly understood, for ignorance in regard to them may be the means of placing the ship on the rocks. As an illustration, let us suppose the ship to be heading North by com- pass, and that on this course there are two points of easterly devia- tion. In this case the ship would be heading N.X.E. magnetic ; and if it were required to steer North magnetic, it would be neces- .sary to steer by compass N.N.W. Now. as the deviation is governed by the angle the compass- needle makes with the mass of iron near it. or in other words, as it depends on the direction of the ship's head, it will, no doubt, he easily understood that the deviation for North by compass could not be the deviation for North magnetic, for the reason that it is necessary to place the ship's head by compass in a direction to counteract tlie effect of the deviation. Again, take the case of a vessel sent to sea on a clear day, the master having no knowledge of the deviation of his standard com- pass. As soon as the vessel is outsidt" he can place the ship's head on the magnetic course, take an azitmith and determine the devia- tion, then apply this deviation to the magnetic course. East to the left and West to- the right, and the result will be an approximate course. Now he will place the ship's head on this last course, take an azimuth and again find the deviation, applying this last devia- tion to the magnetic course again, and get another approximate Chart-Work. 'i'-V-^ course, repeating tliis until, no matter how nuui\' azimuths are taken, each deviation found is the same. This will prove that the ?]iip is now heading on the desired magnetic course. The foregoing is .simply an illustration, for we hardly expect that any master would be so foolhardy as to proceed to sea with- out some knowledge of the deviation of one, at least, of the vessel's compasses. If he does so, the sooner he is relieved of his command, the better for all concerned. The proper mode of procedure to determine the correct amount of deviation to apply to the magnetic course to obtain the compasi; course to steer is as follows: From a table of deviation, (or, better still, from the regular book containing the compass records), take the deviation for the magnetic course and apply East to the left and West to the right; the result will be the approximate course. Enter table again with this approximate course, take the corresponding deviation, apply this to the magnetic course and obtain another approximate course ; enter table again with this last approximate course, repeating the operation until the deviations and the course are always found to be the same, no matter how often the table is entered. The result will be the proper deviation, and the correct course to steer by the compass. If it is required to correct a course by compass to find the mag- netic course, it would only be necessary to enter the table and take therefrom the deviation at sight, as the table is given for sliip's head by compass. The following questions are worked on Chart Xo. 1000, from Cape Sable to Cape Hatteras : Examples for I'mctice in Finding the True Course, Magnetic Course, and Distance between Two Places. From Sandy Hook light- vessel to Barnegat? AnsAver.— T. co. S. 16° W.; mag. co. S. 26° W.; dist. 44 miles. From Barnegat to Shinnecock? Answer.— T. co. X. 49° E.; mag. co. X. 59° E.; dist. 99 miles. From Shinnecock to Xantucket Shoal light-ship? Answer.— T. co. S. 84° E. ; mag. co.S. 71° E.; dist. 133 miles. 234 Taylor's ]\Ioderx Xavigatiox. From Xantucket Shoal light-ship to Tucker Beach light? Answer.— T. co. S. 73° W. ; mag. co. S. 83° W.; dist. 227 miles. From Cape Ann to Cape St. j\[ary ? Answer.— T. co. X. 65°yoE.: mag. co. X. 811/:.° E. ; dist. 200 miles. From Cape Cod to Seguin Island? Answer.— T. co. N. 8° E. ; mag. co. N. 24° E. ; dist. 101 miles. From Cape Elizaheth to Seal Island, Nova Scotia? Answer.— T. co. S. 86° E. ; mag. co. S. 71° E.; dist. 182>{. miles. Example. What is the magnetic course and distance from Brier Island to Boon Island? Answer.— Mag. co. S. 851/0° W.; dist. 190 miles. Ship's head on the magnetic course found, Mount Desert Eock bore magnetic !N".E.XE.i/2E. and Matinicus Rock bore magnetic N'.W.^W. What was the ship's position by cross-bearings ''' Answer.— Lat. 43° 41' N".; long. 68° 32' W. Ship still heading on the magnetic course found, Monhegan Island bore magnetic JST.N.W., and after continuing on same course 12 miles it bore magnetic X.E. What was the ship's position at the time of taking the second bearing, and her distance off Mon- hegan Island ? Answer.— Lat. 43° 34' N.; long. 69° 27' W.; dist. off, 13 miles. And suppose there was a current setting the ship to the S.E. magnetic at the rate of one mile an hour, ship steaming 12 miles an hour, what magnetic course would you steer from Brier Island to Boon Island, and what distance would the ship make good in four hours ? Answer. — Cur. co. S. 89° W. Distance made good in four hours. 45 miles. Find the magnetic coui'se and distance from Cannet Rock in order to pass three miles off Seal Island, Nova Scotia. Answer. — Magnetic co. S. 9° E. ; dist. 74 miles. Slii])'s liead on the niai^iietic course found. Brier Island bore Chaht Work. 235 iiuigiu'tie E.Xi^-V2N-, find Cape St. Mary bore magnetic S.E.X E.i^E. What was the ship's position by eross-bcarings? Answer.— Lat. 44° 8' 30" N. ; hmg. (K^ 3(i' W. Ship still heading on magnetic course found,. Cape St. Mary bore magnetic E.l^S., and after continuing on same course 10 miles it bore magnetic N.E.i/oN. What was the ship's position at the time of taking the second bearing, and her distance off Cape St. Mary? Answer.— Lat. 43° 54' N.; long. (i()° 19' 30" W. Dist. off, 12 miles. DEYIATION-CARD. (To be used in all of the chart-questions given in this book.) Ship's Head by Compass. Deviation. Ship's Head by Compass. Deviation. North 5° W. South 4° W. N.XE. 8° W. S.XW. 2- E. N.N.E. 9° W. s.s.w. 9° E. N.E.XN. 10° W. s.w.xs. 15° E. NE. 11° W. s.w. 22° E. N.E.XE. 12° W. s.w.xw. 21° E. E.N.E. 14° W. w.s.w. 20° E. E.XN. 1B° W. w.xs. 19° E. East 17° W. West 18° E. E.XS. lf)° W. W.XN. 15° E. E.S.E. 1B° W. W.N.W. 11° E. S.E.XE. 14° W. N.W.XW. 8° E. S.E. 13° W. N.W. 4-^ E. S.E.XS. 11° W. N.W.XN. 1° E. S.S.E. 1)° W. N.N.W. 2° W. S.XE. 7° W. N.XW. 3° W. Examples in Fuidiinj the I' ropey Deviation to Apply to a Magnetic Course to Obtain a Correet Compass Course. Mag. CO. S.W.XW'. gives from table of deviations 2U° E. Mag. CO. S. 51° W. Dev. 21i° E. S. 29^° W. 1st approx. CO. S.W. XS.^S. gives dev. 13^° E. Mag. CO. S. 51° W. Dev. 13^° E. S. 37^° W. 2d approx. co. S.W.|S. gives dev. 16° 45' E. 236 Taylor's Modern Navigation. Mag. CO. S. 51° W. Dev. 16° 45' E. S. 34° 15' W. 3d approx. co. S.W.XS. gives dev. 15° E. Mag. CO. S. 51° W. Dev. 15 E. S. 36° W. 4th approx. co. S.W.|S. It will be noticed that the amounts of deviation alternate ; there- fore take the mean of the two last amounts as the proper deviation to apply to the magnetic course to obtain the correct compass course to steer, and if it is required to prove it, simply enter the devia- tion table again and it will be found to repeat itself. Thus : — Dev. 16° 45 E. Dev. 15 00 E. 2)31 45 15° 52' E. Mag. CO. S. 51° 00' W. Dev. 15 52 E. S. 35° 08' W. compass course to steer. In actual practice, and with a compass with a small error, the operation will not be so long. Mag. CO. S.W.XS.^S. gives dev. 12° E. Mag. CO. S. 28° W. Dev. 12 E. S. 16° W. 1st approx. co. S. X \V.4 W. gives 5.^° E. dev. Mag. CO. S. 28° W. Dev. 5^° E. S. 224° W. 2d approx. co. S.S.W. gives 9° E. dev. Mag. CO. S. 28° W. Dev. 9° E. S. 19° W. 3d approx. co. S.XW.f W. gives 7° E. dev. Mag. CO. S. 28° W. Dev. 7° E. S. 21° \V. 4th approx. co. S.XW.^W. Chart Work. 237 After this, no matter how many times the deviation table is en- tered, ?° E. deviation will be found; therefore it must be the proper deviation to use. Mag. CO. E.XS. gives dev. 16° W. Mag. Co. S. 79° E. Dev. 16 W. S. 63° E. 1st approx. co. S.E.XE.^ E. gives dev. 15° W. Mag. CO. S. 79° E. Dev. 15 W. S. 64° E. 2d approx. co. S.E.XE.^ E. gives dev. 15^° W. Mag. CO. S. 79° E. Dev. 15^ W. S. 63^ °E. the correct compass course to steer, the de- viation being 15^° W. When working the following chart questions, all bearings must be corrected for the deviation of ship's head. Find the compass course and distance from Nantucket Shoal light-vessel to Navesink. T. co. S. 87° W. Mag. CO. N. 83° \V. W.^S. Dev. 184 E. N. lOli W. 180 S. 78^° W. 1st approx. co. W.XS. Mag. CO. N. 83° W. Dev. 19 E. N. 102 W. 180 Comp. CO. S. 78° W. Dist. 201 miles; dev. 19° E. Ship heading on the compass course found, Shinnccock bore by compass N.E.^N., and Fire Island light bore by compass W.X X.14X. What was the ship's position by cross-bearings? Shinnecock. Fire Island. N.E.I N. = N. 36° 34' E. W.XN.iN. = N. 75° 56' W. Dev. 19 00 E. Dev. 19 00 E. N.E.XE. = N. 55° 34' E. N.W.XW = N.56° 56' W. Answer.— Lat. 40° 32' N. ; long. 72° 56' W. 238 Taylor's Modern Xavigatiox. Ship still heading on the compass course found, Fire Island bore by compass X.XW.%W., and after continuing on the same course 18 miles it bore by compass N.E.X-N^-%^'- What was the ship's position at the time of taking the second bearing, and her distance off Fire Island? 1st Bearing. 2d Bearing. N.XW.|W. = N. 19° 41' W. N.E.XN.|N. = N. 25° 19' E, 19 00 E. N. 44° 19' E 3° 23' W. Dist. off, 121/2 And sujDposing there was a current setting the ship to the Xorth magnetic at the rate of i/o mile an hour, ship steaming 10 miles an hour, what compass course would you steer from Xantucket light-vessel to Navesink? The distance of 201 miles divided by 10 miles will give 20 hours, the length of time the vessel will take to travel the distance. This. 20 hours multiplied by the rate of current will give 10 miles as the total amount of set; therefore the magnetic course to counter- act the effect will be: Dev. .^N = 19 00 E. w. Dev. N. W N. 38° 41' N.E, Answer. — -Lat . 40° : 27' ^^; long. 73° miles. Mag. CO. N. 87° W. = W.iN. Dev. 17° 15' E. N. 104° 15' W. 180 OC S. 75° 45' W. lst>pprox. co. W.XS.i S. Mag. CO. N. 87° W. Dev. 19 15' E. N. 106^5' W. 180 S. 73° 45' W. 2d approx. co. W.XS.^ S. Mag. CO. N. 87° W. Dev. 19 E. N. 10fi° W. 180 S. 74° W. Current co. to steer by compas! Chart-Work. 230 It will be noticed here that all bearings are by compass; there- fore they must be corrected for the deviation of ship's head namely, 19° E., allowing East to the right and West to the left, before they are placed on the chart. If the chart had been true, the variation also would have had to be applied in the same manner, but as it io a magnetic chart it is necessary to apply only the deviation to the compass-bearings to obtain magnetic bearings. Example. Find the compass course and distance from ^linot's Ledge to Seguin Island. Answer.— Mag. eo. X. ^3° E. ; dev. 12° W. : eonip. co. X. 00° E. ; dist. 97 miles. Ship's head on the compass course found, Isles of Shoals light bore by compass X.14W. and Boon Island bore by compass X.X.E. What was the ship's position by cross-bearings ? Answer.— Lat 42° 43' 30" X.; long. 70° 26' W. Ship still heading on the compass course found, Cape Elizabeth bore by compass X.XE.%E., and after continuing on same course 11 miles it bore by compass Xorth. What was the ship's position at the time of taking the second bearing, and her distance off Cape Elizabeth ? Answer.— Lat. 43° 18' X.; long. 69° 59' W. Dist. off, 181/2 miles. And supposing there was a current setting the ship to the X.X. W. magnetic at the rate of li/o miles an hour, ship sailing 12 miles an hour, what compass course would you steer, and wliat distance would the ship make good in five hours? Answer.— Mag. co. X. 49° E. ; dev. 13° W.; comp. co. X. 62° E. Dist. made good, 63 miles. J'J.raiii pie. Find the compass course and distance from Barnegat to Gay Head. Answer.— Comp. co. X. 85° E.; dev. 17° W. Dist. 178 miles. Ship's head on the comi)ass course found. Shinnecoek bore l»y compass W.X.W. and Montauk bore by eom])ass X.E.XE.14E. What was the ship's position by cross-bearings? Answer.— Lat. 40° 53' X. : long. 72° 01' W. 240 Taylor's Modern Navigation. ShiiD still heading on the compass course found, Block Island bore by compass ISr.E.i4N"., and after continuing on same course G miles it bore by compass N.i^W. What was the ship's position at the time of taking the second bearing, and her distance off Block Island? Answer.— Lat. 41° 4' 30" N.; long. 71° 29' W. Dist. off, 6I/2 miles. And suppose there was a current setting the ship to the North magnetic at the rate of I14 miles an hour, ship steaming 12 miles an hour, what compass course would you steer, and what distance would the ship make good in six hours ? Answer.— Mag. co. N. 73° E. ; dev. 17° W. ; comp. co. East, Dist. made good. 73 miles. Example. Find the compass course and distance from Shinnecock to Fen- wick Island Shoal light-vessel. Answer.— Mag. co. S. 48° W. ; dev. 14° E. ; comp. co. S. 34° W. Dist. 182 miles. Ship's head on the compass course found, Absecon light bore by compass N.W.%N., and N.E. end of Five-fathom Bank light- vessel bore by compass S.W.i/oW. What was the ship's position by cross-bearings ? Answer.— Lat. 39° 6' N.; long. 74° 14' W. Ship still heading on the compass course found. Cape May bore by compass W.XN.1/4N., and after continuing on same course 19 miles it bore by compass N.W.X^. What was the ship's position at the time of taking the second bearing, and her dis- tance off Cape May? Answer.- Lat. 38° 32' N.; long. 74° 43' W. Dist. off, 26 miles. And suppose there was a current setting the ship to the N.N.W. magnetic at the rate of % of a mile in one hour, ship sailing 9 miles an hour, what compass course would you steer from Shinne- cock to Fenwick Island Shoal light-vessel? Answer.- Mag. co. S. 43° W. ; dev. 13° E.; comp. co. S. 30° W. ('hart-Questions Worl-ed on Chart No. 5002, Pacific Coast. Example. Find the compass course and distance from Point Reyes to Point Sur. Chart- Work. 2il Answer.— Cornp. co. S. 34° E.: dev. 11° W. Dist. 115 miles. Ship's head on the compass course found, Farallone? light bore by compass W.^N., and Point Bonita bore by compass X.E.X^"- What was the ship's position by cross-bearings ? Answer.— Lat. 37° 38' N.: long. 122° 43' W. Ship still heading on the compass course found, Monterey light bore by compass E.XS., and after continuing on same course 8 miles it bore by compass X.E. What was the ship's position at the time of taking the second bearing, and her distance off Monterey light ? Answer.— Lat. 3(i° 33' 30" X.; long. 122° 2' W. Dist. off, 7 )niles. And supposing thore was a current setting the ship to the E.S.E. magnetic at the rate of IV2 miles an hour, ship sailing 10 miles an hour, what compass course would you steer from Point Keyes to Point Sur, and what distance would the ship make good in 9 hours ? Answer.— Comp. eo. S. 30° 30' E. ; dev. 10° 30' W. Dist. made good. 103 miles. Example. Find the com])ass course and distance from 2 miles off Point Fermin to Point Conception. Answer.— Comp. co. S. 80° W.: dev. 19° E. Dist. 118 miles. Ship's head on the compass course found. Point Hueneme bore by compass N.E.XN., and Anacapa Island bore by compass South, what was the ship's position by cross-bearings? Answer.— Lat. 34° 6' X.; long. 119° 21' W. Ship still heading on the compass course found, Santa Barbara light bore by compass X.W.14X., and after continuing on the same course 9 miles it Ix^rc l)y compass X.XE.V4E. What was tlie ship's position at the time of taking the second bearing, and her distance off Santa Barbara light? Answer.- Lat. 34° 17' X.; long. 119° 52' W. Dist. off. 10 miles. And suppose there was a current setting the ship to the E.X.E. magnetic at the rate of one mile an hour, ship steaming 10 miles an hour, what compass course would you steer, from 2 miles off Point Fermin to Point Conception, and what distance would the ship make good in seven hours? Answer.— Comp. co. S. 77° W. ; dev. 19° E. Dist. made good, 64 miles. Taylor's Mod. Nav. 16. 242 Taylor's Modern Xavkutiox. Example. Find the compass course and distance from 3 miles ofE Point Arena to Point Eeyes. Answer.— Comp. co. S. 38° E.; dev. 12° W. Dist. 6G1/0 miles. Ship's head on the compass course found, Table Mountain bore by compass N.XE.i^E., and Ross Mountain bore by C(unpass N.E.i^E. What was the ship's position by cross-bearings? Answer.— Lat. 38° 24' N.; long. 123° 19' W. Ship still heading on the compass course found. Bodega Head bore by compass E.I/2N., and after continuing on same course 11 miles it bore by compass X.E.XN.3/4X. What was the ship's position at the time of taking the second bearing ? Answer.— Lat. 38° 9' N.; long. 123° 10' W. And suppose there was a current setting the ship to the X.PLXX- magnetic at the rate of two miles an hour, ship steaming 8 miles an hour, what compass course would yon steer, from 3 miles off Point Arena to Point Reyes, and what distance would the ship make good in 8 hours? Answer.— Comp. co. S. 26° E. ; dev. 10° W. Dist. made good. 601/0 miles. Excuiiple. Find the compass course and distance from Point Arguello to Piedras Blancas. Answer.— Comp. co. N. 45° W.; dev. 4° E. Dist. 72 miles. Ship's head on the compass course found, Port Harford bore by compass X.ysE., and Point Sal bore by compass E.XS. What was the ship's position by cross-bearings? Answer.— Lat. 34° 59' N.; long. 120° 50' \V. Ship still heading on the compass course found, Port Harford l)ore by compass E.XN.14N., and after continuing on sann^ course 7 miles it bore by compass E.34S. What was the ship's position at the time of taking the second bearing, and her distance off Port Harford ? Answer.— Lat. 35° 16' N. ; long. 121° 2' W. Dist. olT, 16 miles. And supposing there was a current setting the shi]) to the East magnetic at the rate of IVo miles an hour, ship steaming 12 miles Chart-Work. 243 - sel may be close in and still not hear a signal, although it is in operation. This therefore exonerates the lighthouse people from the imputation of carelessness among their employees. The best plan, when listening for a signal, would therefore be to have a man as high up on the mast as possible to listen, for the masthead may enter the zone of sound quite a long time before the signal is heard on deck. This may not always be the case, but we advise the navi- gator to try the plan suggested, for the old-fashioned method of placing the ear to the deck is out of date. It may be used to hear a train approaching, but there are no iron rails on the ocean. The preceding was inspired by reading the reports of investiga- tions made by the United States government, and by my own and other navigators' experience, and it is plainly the duty of the navi- gator to exercise caution, and never to neglect the lead, for it is better to find the bottom of the sea with the lead than with the ship's keel. The navigator will not then have to make all kinds of explanations before a l)oard of inquiry as to how it happened. DIVISION \. TlIK TIDKS. The tides are regulated l)y the joint attraction or combined action of the snn and moon. The moon, being the closer to the earth, exerts the more attractive force, while the sun, although much largei-. doe^^■ not exei't so nuicli Unw as tlic ninon, being so far distant from the earth. That particular part of the earth's surface over which the moon is vertical has the largest tides, that part of the earth's surface directly opposite having the smallest tides. Large tides are called "spring tides" and the small tides aie called "neap tides." The sun raises a smaller tidal wave than tlie moon, hut both, if jointly acting on one particular part of the earth's surface, will raise higher tides than the moon does by itself. We have several methods of finding the time of high water at any place, one being the Epitome method of using the establish- ment of the port, or the moon's meridian passage, but the latter, although theoretically correct, is lial)le to be very much in error, owing to local causes. All the great nations of the earth have a regular system of tide-oljservations at numerous stations scattered along their coasts, where instruments register the tides. The in- strument so nsed is called a "tide-gauge." By means of these automatic observations local tide conditions are found and pre- dicted for future use. These predictions are then tabulated for the use and guidance of the mariner. But even these tide-tables, although prepared with extreme care, and by men of high scientific attainments, give the time of high and low water under normal conditions, but the time of actual occurrence may be somewhat different, for the following reasons : The pressure of the wind, when blowing directly into a harbor, forces the Avater in, in the case of a flood-tide making it run much faster than it would under ordinary conditions, thus hanking the water up in the harbor^ and in the case of an ebb-tide retarding it and holding it back, so tliat ine eblj-tide will i-un nnu-h longer t!:'an it really ought, making the time of liigh water gi\-en in tlie tables somewhat in error, the amount depending iipon the force and direction of the wind. Again, supposing there have been very heavy rains in tlie vicinity or a melting of snow in tlie mountains. Tn s\ich cases, the waters would naturally drain into the valleys and rivers, and in their en- deavor to reach the sea. ri'tard tlie tlood-tide with tlu'ir weiudit. and 248 Taylor's Moderx Xavigatiox. accelerate the ebb-tide, and at the same time cause the ebb-tide to run longer than the time tabulated. Navigators, understanding these points, must use the tide-tables with caution, for the amount of rain or the direction of the wind cannot be predicted years in advance. If they could, then the tables might be so computed as to take into consideration these conditions. A knowledge of the tides, with the time of their occurrence, to- gether with the strength of currents, is very necessary to the navi- gator, especially where he has to cross shallow bars at the entrance to ports. Bule to Find the Time of High Water hy Means of the American Tide-Tahles. Turn up Table 3, which contains the tidal difference, tidal con- stants, and the standard ports for reference, etc.; look down the left hand column until you find the name of the port for which you wish to find the time of high and low water, and when found, take the name of the standard port for reference directly abreast of it, also the number of the page and the local time of the tidal differ- ence for high and low water, being careful to note the signs of plus or minus which are prefixed to them; next turn up the standard port in the body of the book, and under the month and abreast of ihe date take out the figures which stand abreast ; it will be noticed here that there are two lines for each date, the top line giving the times of the tides as they occur, and the figures which stand under these times giving the heights ; mark them all down : next see which is the high and which the low water by noticing the figures of the heights which stand under the times; if high water, the height will be large, and if low water, the height will be small; having now distinguished which is high and which is low water, take the tidal differences which are found in Table 3, and apply them according to the sign of plus or minus; this will give the times of high water and of low water for that date ; if the hours are less than 12, it is jnorning time, if more, it is afternoon, and when reduced by 12, will give time in the afternoon. The navigator should be very careful to read the explanation at the foot of each page in regard to the time, as the time at ship may differ considerably from the time given by the tables. Example. — March 16, 189G. Acquired the times of high and of low water at Cape Clear, Ireland. The Tides. -4'.) Look in the index at vud of tables for Ii-eland and take the num- ber of the page, which is 410. turn up page 410 and search for Cape Clear, under Irehmd. and when found note the standard port for reference, whicli is Queenstown. page 288. Differences for time H.W. — 0'' 43™; L.W. — 0" 56'". Differences for heights, H.W.— 3^5; L.W.— 0M5. Next open the tables at page 288, and under March, abreast of the 16th day, will be found: Times 0:0B 6:07 12:22 18:25 (hours and minutes). Heights 0.7 10.6 1.8 10.5 (feet and tenths). By examining the heights under the different times, it will >? seen that the figures under 6:07 and 18:25 are greater than the others, therefore these two times must be for high water and the others for low water. L.^^^ Times 0:06 Differences 0:56 23:10 11:10 p.m. of previous day. The first time given by table being :06, and the low water dif- ference being subtractive, it is necessary to borrow 24 hours, giving a result of 11'* 10"* p.m. of preceding day, leaving only three times of tidal occurrences for March IGth. In such a case it is necessary to take the first time of tide for the next day, viz., March 17th, which is 0:38, and subtract the low- water difference and if the difference is greater than the tabu- lated time, the result will be the time of the last tidal occurrence on March Ifith, but if less, there will be no other for that day. h. m. First tide on March 17th. 0:38 Height. 0.1) ft. L.W. difference H.W. L.W. H.W. 6:07 12:22 18:25 0:43 0:56 0:43 5:24 A.M. s day. 11:26 A.M. 17:42 5:42 P.M. h. m. 0:38 - 0:56 23:42 16th 11:42 V Time of 2d L.W. on Marcli 16th 11:42 p. m. Example.— Jaimarj 16. 1896. Find the times of high and of low water at Boston, Massachusetts. By searching in Table 3 of the Tide-tables it will be found that Boston is a standard port for reference, therefore it will be neces- sarv to take only the numlier of the page, viz., ry2. and on that 250 Taylor's :\[odern Xavigation'. page, under Jaiuiary, abreast of the IGtli day, take the time and heights and mark tliem down, thns : Times 0:12 6:10 12:18 18:42 (hours and minutes). Heights 8.7 0.6 10.1 -.4 (feet and tenths). The heights under t]ie first and second times being the greater, tlie times above them must therefore be the high water and the others the low water. Exdmplc. — Find the times of higli and of low water on February 1, 189(3, for Guaymas harbor. Gulf of California. By reference to the index it will be found that the Gulf of Cali- fornia must be looked for on page 362, and on referring to this page it will be found that San Diego is the standard port, page 120. Time difference, H.W. +2i> 'OS'^^ ; L.W. +2^^ lO'". Height difEerence, H.W. +0^5; L.W. O'.!). Next open the tables at page 120 and find San Diego. Then under February, and abreast of the 1st day, take the times and lieights, and mark them doAvn, thus: Times 4:24 10:27 17:00 23:24 (hours and minutes). Heights 1.3 6.0 -0.7 5.2 (feet and tenths). It Avill now be seen that 10 :27 and 23 :24 have the greatest heights under them, therefore they are the times of high water and the others low water. L.W. H.W. L.W. H.W. Times 4:24 10:27 17:00 23:24 Difference + 2:10 + 2:02 + 2:10 + 2:02 6:34 a.m. 12:29 19:10 25:26 0:29 P.M. 7:10 p.m. 1:26 a.m. of next date. The times of high aiul of low water at Guaymas wdll therefore l)e, L.W. &" 34'" A.M. ; H.W. 0" 29'" p.m. ; L.W. 1^ 10'" p.m. But the fourth gives the time of high water at 1** 26"^ a.m. of next day. In such case, and having a -f- difference, take the time of last tide from the preceding day and add the difference to it, and if the i'csult is greater than 24 hours, reject 24. The result will be the time of the lirst tidal occurrence on tlie required day — in this case the hist tide for the preceding day, viz.: h. m. Last tide .lanuary 31st 22:50 Height, 5.1 H.W. difference + 2:02 24^2 Time of the first H.W. on Feb. 1st at Guaymas 00:52 a.m. TiiK Tides. 251 HrLl' TO FiXl) TIIK ITkIOIIT ok TiDK at a SlUOKDINATE PORT. I^ntcr 'I'alilc -"! willi the name of lliu port, and take out the name of the standard port and the height ditl'en'nee for l.oth hi-'h and J()\v water, noting tht' sign of -|- or — . as in the previous r.xainplcs; luvxt enter Tal)le 1 with the name of the staiuhird port and the in this regard from variation. Variation is a constant amount in a certain position, whereas deviation is n different amount on caeli and every course. Definitions. 281 Q. 42 — What is the hour-angle of a celestial body? It is the angle at the pole between the celestial meridian passing through the body and observer's meridian. See Fig. 9. Q. 43 — What is the observed altitude? It is the altitude observed with the sextant and corrected for the index error, if any, Q. 44 — What is the apparent altitude? The angular height of an object's center above the sensible hori- zon. The observed altitude corrected for dip and semidiameter gives the apparent altitude. See Fig. 6. Q. 45— What is the true altitude ? The angular height of an object's center above the rational hori- zon, or it is the observation reduced to the center of the object ob- served from the center of the earth. The corrections used in this case are refraction and parallax. See Fig. 6. Q. 46 — What is zenith distance? It is the distance a celestial body is from the zenith, which is 90° from any part of the horizon. See Fig. 9. Z, zenith dis- tance. Q. 47 — What is an azimuth? It is an arc of the horizon between the meridian which passes tlirough the observer and the vertical circle passing through the center of the body. It is reckoned from the N. or S. point of the horizon. See Fig. 9. See angle at Z. Q, 48 — What is meant by an artificial horizon ? The artificial horizon is a bowl of liquid in a state of perfect rest, such as a tray of mercury, and is used in the following manner: Place the artificial horizon on a table or box directly between you and the body to be observed. Place yourself in a position so that you can sec the reflected body in the artificial horizon. Then take the sextant and bring the body observed down to touch the one which is seen in the bowl. This will give just twice the amount of angle required; therefore, divide the angle and you will get the observed altitude of the body. See Fig. 7. Q. 49 — What are parallels of latitude ? Parallels of latitude are small circles parallel to the equator. Any place on any one of these parallels will have the same latitude. Fig. 1. T T and t t. 282 Taylor's Modern Navigation. Q. 50_ — What is dift'erenro of Intitude? Difference of latitude is an arc of a meridian between the lati- tude of any two places, or the difference of latitude is the distance a ship sails to the true North or South. See Fig. 1. D 1 and L d. Q. 51 — What are meridional parts? Meridional parts are found in fable 3 of most epitomes. They are the increase in the size of a degree of latitude, corresponding to the separation of the meridians. The reason of this is that it is used in the problem of Mercator's Sailing, which is based on the supposition that the world is fiat instead of round. The proper ex- planation of this problem will be found under the head of Mer- cator's Sailing. (See problem of Mercator's Sailing for Fig. Bow- ditch.) Q. 52— What is leeway ? It is the angle between the ship's wake and the line of her keel. To ascertain the amount, stand on the fore part of the compass and look directly astern. Take a bearing of the ship's wake and note the angle between the fore-and-aft line and the trend of the wake., and you will have the amount of leeway the vessel is making. Q. 53 — What is civil time, or civil day? The day begins at midnight and ends on the following midnight. It is used for measuring time on shore. The first half of the day is called a.m.^ or ante-meridian, the other half being called p.m., or post-meridian. Q. 54 — What is astronomical time? The day that begins at noon and ends on the following noon, reckoned through 24 hours. In the practice of navigation as- tronomical time is used, as all the elements in the Nautical Alma- nacs are computed for the astronomical date, or noon time. There is no A.M. or p.m. astronomical time. Q. 55 — What is meant by sidereal time? The westerly hour-angle of the first point of Aries ; or, in other words, it is the time shown by the stars. Q. 56 — What is meant by mean time? It is the westerly hour-angle of the mean sun. The mean sun is any imaginary sun which keeps uniform time, which the true sun does not. Q. 57 — What is apparent time? It is the westerly hour-angle of the true sun; or, in other words, the time shown by the sun which we see. Definitions. 283 Q. 58 — What is meant by equation of time? It is the diiference in time between the place of the true sun and that of the mean sun, and is used to convert mean time into ap- parent time, or apparent time into mean. The value of this equa- tion of time is found on pages 1 and 2 of the Nautical Almanacs, and the sign whether to add or to subtract is given on the top of the columns. Note — Four times a year it is at its greatest amount, namely, on February 11th, May 14th, July 26th and November 3d; and four times a year it is nothing, namely, on April loth, June 15th, August 31st and December 24th. Q. 59 — Is the Pole-Star situated exactly at the Pole? No; it is about 1 1-3° from it. Q. 60 — What is the best time for taking an observation to find the longitude? When the body is on or near the prime vertical ; in other words, when it bears true East or true West. Q. 61 — What is a chronometer? A very fine watch or clock compensated with a temperature- balance, and protected as far as possible from sudden jars or shocks, and from sudden changes of temperature. It regis-ters the Greenwich Mean Time w^hen correct. Q. 62 — What is the length of a nautical mile? Six thousand and eighty feet. DIVISION XII. KEEPING THE CHIEF OFFICER'S LOG-BOOK, OR SHIP'S JOURNAL. A sample page of which will be found on page , at the end of this article. The keeping of this book and the writing of the proper entries is one of the important duties of the Chief OfEicer. It is, however, a lamentable fact that few officers take a suffi- cient amount of pride in keeping the book neatly or accu- rately, and when one considers the amount of importance of the log-book in relation to law-suits for insurance, protests, and exten- sions, it is surprising that ship-masters and ship-owners do not more vigorously insist that the book be properly kept and written in a legible manner. Many indolent officers do not attempt to write up the log until the passage is nearly ended. It will thus, no doubt, be easily understood that many matters of importance are likely to be omitted unless the officer has an excellent memory. On board of the large and well-disciplined ocean liners, the log- book is made up immediately after the position of the ship has been determined at noon, each officer signing abreast of liis "watch," in a column provided for the purpose. After this has been done the log-book is taken to the master, who, after examining it to see that the proper entries are made, signs it himself on the bottom of each page. This is an excellent rule, the chief officer having, in it, a check against mistakes. Should he, however, discover a wrong entry, he m.ust not endeavor to erase it, but should draw a line in red ink through the mistake and mark his initials near it. Tinder no circumstances should a page be torn from the log-book, for if a log-book should be so mutilated and afterwards offered as evidence in a lawsuit, it would be valueless, if detected by the op- posing counsel. Log-slates, so much in use formerly, have now given place to the rough log-book. This book is generally kept in the wheelhouse for the making of entries as the incidents occur, after which the entries are copied into the chief officer's log-book. This is certainly much better than using a slate, not only for tlK health of those concerned — for slates are filthy thing? to use — but whenever a slate was used and tlie weather at all damp it was neces- Chief Officeu's Log-Book. 28") sary to place the slate in the galley oven to dry before the writing became legible. There are quite a number of different arrangements for log- books, some of them having only every two hours printed, making it necessary to write between the lines very frequently, but this kind of a log-book is used only on lumber-schooners, whose owners prac- tice a great amount of false economy. All log-books, for no matter what class of vessel, should devote the entire left-hand page to the civil date, arranged so that the noon hour comes in the middle of the page, with the necessary spaces for entering ship's position by either dead-reckoning or observations, the upper half for a.m. and the lower half for p.m. If so arranged, the whole page will repre- sent a civil date, and from i:he middle of one page to the middle of the next, an astronomical day. This arrangement will do away with confusing the civil with the astronomical day, a very common occurrence when an ancient style of book is used. The opposite page to the right should be devoted entirely to remarks concerning observations, passing points of land, making or taking in of sail, state of weather, and all other items relating to the navigation of the ship. Some officers even place among the remarks that they have used a fathom or so of spun yarn, and such foolish items. Such remarks are very unnecessary, yet if a new brace were rove off, or sails w'ere shifted or blown away, these remarks would be necessary. By examining the sample page of a log-book on page , it will be noticed that a column is devoted to the giving of the state of thi' weather by using symbols. This is an excellent plan. It saves trouble and space, and contributes to neatness. The system is called Beaufort's Scale, a copy of wliich is here given. Wind is also indicated by nunibors in tlic column marked ^•Force." WINDS. (Numerals to be used to indicate the force of the winds as ap- plied to a sailing-vessel closehnulod l)y tlic wind.) 0— Calm. 1 — Light airs (or suflicient to give steerage-way). 2 — Light breezes (all sail may be carried and make from 1 to 2 knots per hour). 3 — Grentle breezes (all sail may be carried and make from 3 to 4 knots per hour). 286 Taylor's Modern Navigation. 4 — Moderate breezes (all sails may be carried and make from 5 to 6 knots per hour). 5 — Stiff or fresh topgallant breezes (courses, jib, spanker, whole- topsails and topgallantsails may be carried). — Fresh breezes (topgallantsails over single-reefed topsails, courses, jib, and spanker may be carried). 7 — Fresh breezes (double-reefed topsails, whole courses, jib and spanker may be carried). 8 — Moderate gales (three-reefed fore and main, close-reefed miz- zentopsail with single-reefed courses and foratopmast-staysail may be carried). 9 — Strong gales (three-reefed fore-and-main topsail with close- reefed courses and fore-storm staysail may be carried ) . 10 — Gale (close-reefed maintopsail and close-reefed foresail with forestorm staysail may be carried). 11 — Heavy gale (storm-sails only can be carried or close-reefed main topsail and forestorm staysail or staysails only). 12 — Hurricane (no sails can be carried, lying to or scudding un- der bare poles). Symbols to Be Used in Recording the State of the Weather. b — Clear blue sky. e — Cloudy weather. d — Drizzling or light rain. f — Fog or foggy weather. g — Gloomy, or dark, stormy-looking weather. h— Hail. 1 — Lightning. m — Misty or liazy weather. — Overcast. p — Passing showers of rain. q — Squally weather. r — Rainy weather or continuous rain. s — Snow, snowy weather, or snow falling. t— Thunder. u — Ugly appearance or threatening weather. V — Variable weather. w — Wet or heavy dew. I />g of S. S. From Towartls . "Date y,ar Voya^ Mo. _^^ 1 1 1 g's;^^^.^s^s;i" 0„.r„.. WIND. 1 1 1 B.»>,«T... T,.r„UT,». thirstier. 1 I N.-.o.L»e.o.. VT Helgbt Thot. M % 1 A.M. n _____ 1 ,, _____ 10 n ^oon. I Laliluda bv o . .. Latitude by observation " Longitude by observation " Latitude by D.R o . .. Longitude by D.R. " ■ " Ikchei of Wateb in Weuj Course made good sine* preceding noon : Coi. Ccp. Co*. Distance made good since preceding noon : miles. Distance by Log since preceding noon ; miles. Current per hour: miles. Bet trui- j (Longitude by Frou Variation ol Compass: To Error o( compass observed at KEVOLUTIONS rOR li HOUM DeviaUon of Compass on - P. M 1 2 3 4 ' 6 6 ~^ ' 7 ' 8 9 ■ 10 11 ' ^ Mid '~~~~~ Signatur, of Chitf Offle*r Signatur* of Mtuttr ~ " ■"■» In Commanded by V-.- RECORD OF THE MISCELLANEOUS EVENTS OF THE DAY ___"" __,^_ . _^ H;^ — ^jsino ,hm,h ,\:l. 1 .Frr -.alo ■ 1 ■ "^ - ~ - — ' ^ -^ Chief Officer's Log-Book. 287 Symbols to Be Used in Uecording the State of the Sea. B — Broken or irregular seas. C — Chopping, short or cross sea. G — Ground-swell. H — Heavy sea. L — Long, rolling sea. M — Moderate sea or swell. E — Rough sea. S — Smooth sea. T— Tide-rips. In the columns for barometer and thermometer should be en- tered their respective readings, for by them future weather condi- tions may be anticipated bv the experienced mariner, and in the case of the thermometer the approach of ice may be detected by a sudden falling in temperature. All entries in course and distance columns, with the variation of the locality and deviation on the course steered, should be very care- fully entered in a plain hand, and whenever the course is changed the exact time should be noted, with the reading of the patent log, if one is in use. If foggy weather, the exact time of the fog shutting down, with any alteration in speed of ship, soundings, and the time of weather clearing, should be noted. A special entry should always be made if the weather is boister- ous, after the following manner: "Ship laboring heavily, and shipping quantities of heavy water." This entry is necessary, for the reason, that if the master is forced by circumstances to note a protest and afterwards to extend it, before being able to collect the insurance, the log-book would be offered as evidence of bad weather to exonerate the ship from blame in regard to unseaworthiness, etc. Side-lights exhibited from sundown to sunrise, pumps strictly attended to, man on lookout, with the temperature and amount of water in the holds, are also very important entries. In conclusion, we wish to emphasize the fact that carelessness or untidiness, or downright wilfullness, in regard to false entries will render the officers keeping the book liable to severe censure, and perhaps be the means of the revocation of his certificate as an officer. DIVISION XIIL THE OFFICIAL LOG-BOOK. By certain acts of Congress, every vessel making voyages from a port in the United States to any foreign port (except ports in the British North American possessions), or, being of the burden of seventy-five tons and upwards, from a port on the Atlantic, to a port on the Pacific, or vice versa, shall have an official log-book, and every Master of such vessel shall make or cause to be made therein, entries of the following matters, that is to say : First. Every legal conviction of any member of his crew, and the punishment inflicted. Second. Every ofEense committed by any member of his crew for which it is intended to prosecute or to enforce a forfeiture, together with such statement concerning the reading over such entry, and concerning the reply, if any, made to the charge, as is required by the provisions of Section 4597, Third. Every offense for which punishment is inflicted on board, and the punishment inflicted. Fourth. A statement of the conduct, character and qualifica- tions of each of his crew; or a statement that he declines to give an opinion of such particulars. Fifth. Every case of death happening on board, with the nature thereof and the medical treatment. Sixth. Every case of death happening on board, with the cause thereof. Seventh. Every birth happening on board, with the sex of the infant and the names of the parents. Eighth. Every marriage taking place on board, with the names y.nd ages of the parties. Ninth. The name of every seaman or apprentice who ceases ta be a member of the crew otherwise than by death, with the place, time, manner, and cause thereof. Tcntli. The wages due to any seaman or apprentice who dies during the voyage, and the gross amount of all deductions to be made therefrom. Eleventh. The sale of the effects of any seaman or apprentice who dies during the voyage, including a statement of each article sold, the sum received for it. Metkorological Log. 289 2\celftli. In every case of collision in which it is practicable so to do, the master shall, immediately alter the occurrence, cause a statement thereof, and of the circumstances under which the same occurred, to be entered in the official log-book. Such entry shall be made in the manner prescribed in Section 4291, and failure to make such entry shall subject the offender to the penalties pre- scribed by Section 4292. Instructions in regard to all entries are printed in the first part of the book, with the most recent laws governing merchant seamen, payment of wages, food, signing on and discharging the crew, etc. The book is supplied to masters by the United States Shipping Commissioners when signing the crew, and delivered to them again at the expiration of the voyage. Masters should be careful, however, to have all entries, no mat- ter of what nature, properly witnessed and signed by at least two members of the crew, to prevent argument at tlTe time of paying off. and to save the ship from expenses. THE METEOROLOGICAL LOG. OR WEATHER REPORT. The proper keeping of this record is of the utmost importance, and one that should be more frequently and accurately kept than it is at the present time, for by it future weather conditions are pre- dicted or foretold, and conditions peculiar to certain localities may be recorded and charted for the future use and benefit of the mari- ner. It is a deplorable fact, when one considers the importance of weatherology, that the log is rarely kept on xlmerican vessels out- side of ocean liners, the licensed ( ?) officers of, particularly, sailing- vessels and cargo-steamers, entirely ignore the earnest request of the United States Hydrographic Office, for the reason that they think the keeping of the record is "fancy navigation," and so diffi- cult that it requires an exceedingly high degree of intelligence and a college education, entailing a considerable waste of time, and consequent loss of sleep, if the form? have to be filled out during the watch below. This is not so, for the forms supplied to record the required in- cidents and conditions of weather are arranged in so simple a man- ner that even a half-witted person could almost understand how to fill them out, and the length of time required to do the same would not occupy more than five minutes even for a poor penman. Taylor's Mod. Nav. 19. 290 Taylor's Modern Navigation. If it is the wish of the master that a log of this kind should be kept on board of his vessel, he should first procure the necessary forms from the nearest branch Hydrographic Office and designate one of the junior officers for the purpose, with instructions that the entries must be made with regularity, neatness, and precision, and that the same be submitted to him for approval, as regularly as the chief officer's log-book. All instruments used for the purpose, such as barometers, ther- mometers, etc., should be compared and adjusted as frequently as possible, especially whenever the vessel is in a port where there is a branch Hydrographic Office, as the officers in charge have stand- ard instruments on hand for the purpose of comparison, the same Ijeing free of cost to the navigator. If there is any error, it should be noted, and if it reads too high or too low, all readings must be reduced to the standard l)efore the\ can be utilized. All the necessary information for intending observers, with the blank forms for recording events, wind, current, and pilot-charts, may be procured from the officers in charge of the local office, free of cost, they being only too anxious to supply any information that they possess, and will courteously acknowledge, by letter, the re- ceipt of the same from any contributor. The blank forms are made up in about the size of an ordinary receipt-book. On the first page, inside of the cover, will be found instructions to recorders, relating to the time of observation. This is important, as the Office wishes observations to be taken when it is mean noon at (ireenwich, so that they will all be simultaneous. Synil)ols are used to indicate the weather, strength of wind and sea, the same as already explained under the heading of Chief Of- ficer's Log-Book, but, in addition to this, cloud-classifications must also be used, the following being the official description. The United States government has, however, on this subject, published colored plates illnstrating the different cloud-formations. The following cloud-rornis are arranged according to a general descending scale of altitude, observation having shown that there are live main eloud-levels, viz.. cirrus (highest), cirro-cumulus, alto-cnmnlus. cnmnliis, and strains (lowest). 1. Cirrus (Ci.) — Detached clouds, delicate nnd fibrous-looking, taking the form of feathers, generally of a white color, sometimes arranged in belts which cross a ))ortiun Lot;. 291 and, by an effect of periipective, converge toward one or two oppo- site points of the horizon. (The Ci.-S. and the Ci.-Cu. often con- tribute to the formation of these belt.--.) 2. Cirro-;Stratus {Ci.-S.) — A thin, wliitish slieet. at times completely covering the «ky, and only giving it a wliitish appear- ance (it is then sometimes called cirronel)ula), or at others present- ing, more or less distinctly, a formation like a tangled web. This sheet often jirodnces halos around the sun and moon. 3. ('irro-Cuiiiuliis (Ci.-Cu.) — Small globular masses, or white flakes without shadows, or having very slight shadows, arranged in groups and often in lines. 4. Alto-Cumulus (A.-Cu.) — liather large globular masses, white or grayish, partially shaded, arranged in groups or lines, and often so closely packed that their edges appear confused. The de- tached masses are generally larger and more compact (changing to S.-Cu.) at the center of the group; at the margin they form into finer flakes (changing to Ci.-Cu.). They often spread themselves out in lines in one or two directions. 5. Alto-Stratus {A.-S.) — A thick sheet of a gray or bluish eolor, showing a brilliant patch in the neighborhood of the sun or moon, and which, without causing halos, may give rise to coronae. This form goes through all the changes like the Cirro-Stratus. but by measurements made at Upsala, its altitude is one-half less. 6. Strato-Cumulus (S.-Cu.) — Large globular masses or rolls of dark cloud, frequently covering the whole sky, especially in winter, and occasionally giving it a wavy appearance. The laj'er of Strato- Cumulus is not, as a rule, very thick, and patches of blue sky are often visible through the intervening spaces. All sorts of transi- tions between this form and the Alto-Cumulus are noticeable. It may be distinguished from Ximbus by its globular or rolled ap- pearance, and also because it does not bring rain. 7. Nimhiis (N.), Faiti-Clouds — A thick layer of dark clouds, without shape and with ragged edges, from which continued rain or snow generally falls. Througli the openings of these clouds an upper layer of Cirro-Stratus or Alto-Stratus may almost invariably be seen. If the layer of Nimbus separates into shreds, or if small loose clouds are visible floating at a low level, underneath a large Nimbus, they may be described as Fracto-Nimbus (Fr.-N.), "scud" of sailors. 292 Taylor's Modern Navigation. 8. Cumulus (Cu.), ^Yoolpacl^ C/owt^s— Thick clouds of which the upper surface is dome-shaped and exhibits protuberances, while the base is horizontal. These clouds appear to be fornied by a diurnal ascensional movement Avhich is almost always observable. When the cloud is opposite the sun, the surfaces usually presented to the observer have a greater brilliance than the margins of the protuberances. When the light falls aslant, these clouds give deep shadows; when, on the contrary, the clouds are on the same side as the sun, they appear dark, with bright edges. The true Cumulus has clear superior and inferior limits. It is often broken up by strong winds, and the detached portions un- dergo continual changes. These may be distinguished by the name of Fracto-Cumulus (Fr.-Cu.). Cumulus sometimes presents a mammillated lower surface. It is then called Mammato-Cumulus (M.-Cu.) 9. Cumulo-Nimhus (Cu.-N.), the Thunder-cloud , Shower- Cloud — Heavy masses of clouds rising in the form of mountains, turrets, or anvils, generally having a sheet or screen of fibrous ap- pearance above ("false Cirrus"), and underneath, a mass of cloud similar to "Nimbus." From the base there usually fall local showers of rain or of snow (occasionally hail or soft hail). Same- times the upper edges have the compact form of Cumulus, forming into massive peaks, round which the delicate "false Cirrus" floats, and sometimes the edges themselves separate into a fringe of fila- ments similar to that of the Cirrus cloud. This last form is par- ticularly common in spring showers. The front of thunder-clouds of wide extent frequently presents the form of a large bow spread over a portion of the sky, which is uniformly brighter in color. 10. Stratus (S.) — A horizontal sheet of lifted fog. When this sheet is broken up into irregular shreds by the wind, or by the sum- mits of mountains, it may be distinguished by the name of Fracto- Stratus (Fr.-S.). ]\TQte — The attention of mariners is esi)ecially called to the value of observations of cirrus, as this form of cloud is often closely con- nected with barometric depressions. If the cirrus occur in radiat- ing bands crossing the sky, the point of convergence of these bands should be noted ; if in the form of a cloud-bank, or sheet, upon the horizon, the center, or point of greatest density of this bank, as Meteorological Log. 293 this point will sometimes serve to indicate in a general manner the direction of the center of an}' cyclonic disturbance. Great care should be taken when recording the cloud-forms with the direction from which it is moving and its approximate altitude, as it will often be of great value to the mariner regarding a shift of wind, and assist him to interpret the strange behavior of the barometer; this would be especially useful if in a locality where circular storms were prevalent, as it would serve to indicate the probable direction from which the wind would be first experienced. [Xotc — For theory of cireuhir storms see Bowditch, as it is not the intention to give an exhaustive account of them in this book.) The accompanying forms, numbered here for the sake of easy reference, are duplicates of those supplied by the U. S. Hydro- graphic Office to observers. Form Xo. 1 is a sample page showing the space for entries under ordinary conditions, with cloud diagrams, to illustrate the motion and altitude of clouds. 294 Taylor's Modern Navigation. oc UJ z li 2 5«E s £ ^ iij ^5- I ^<5>^ p^ 3 ^ 7 < < £«2 N , / Q K UJ <^m H < / 0. 5 5 / U 1 si'S S H < 5 » z Z 3 o 5 (C S J. . w ^ i \ o • pi \ £ ^1 \ o i £ o o 2 m o < < X % w H 2 u . 0$ H o p i ^ ^ w2 2 ^1 W Q H tt iJ p h'^ QtU [1- z 50 ^1 DC o E JO i o Q. OC fe s Du [d o K >■ § PC PC [I] i p t? " « -«! - X 3 y K^ h if- b. < "8 3 j? S^' c^ u<. ° ".^' ''■ o Hg 0" s 111 1 K 1^1 '', .. , u< "^ ^ Form Xo. 2 is for rccordino^ ordinary storms. SHIFTS OF WIND. Give compass points to sliow shifts of wind about time of lowest barometer. M i M M Q z. S i : : : : I j : < s J3 2 * 1 %» < 111 5g« 1 6 z o 1 Form Xo. 3 is especially fox recording circular storms, called in the West Indies Hurricanes, China Typhoons, and Bay of Bengal and Indian Ocean Cyclones. P3 • ; Q 05 o Pi 4 o a o Q i < tiJ < 1^ w p \ N si is? - t u WJ3 Ed o CH O it ^2. o -§.= ?l II .-21 HI li go I 1 = •1 1 < p£&5 i i 5 03 Q O c ? IS a: Q p. ^ 3 o i g >• Meteorological Log. 29'/ Special care should be taken, when uue of tliese storms is en- counted, to record each change in tlie direction of the wind, sea, force, weather, clouds, and especially the behavior of the barometer with the change of ship's course, remembering that all these ob- servations, with the data collected from other sources, a storm theory may be evolved for the benefit of seamen who may subse- quently be navigating in the same vicinity, and should any inci- dents or phenomena occur which are of note, it is the duty of the mariner to forward a written account of the same to the nearest Branch Hydrographic Office. Form No. 4 is for recording the appearance of ice, and is very important, for the reason of the necessity of cautioning other vessels that ice may be found in a certain vicinity at certain times of the year. By examining a great number of reports of this kind a very good idea can be arrived at in regard to what time of the year to be on the lookout. The passing of wrecks, driftwood, etc., should also be entered on the form, with a short description of the same, latitude, longitude, etc., for by these means ocean currents may be determined, and in the case of derelict vessels the position may be published from time to time, so thnt the navigator may be placed on his guard. 298 Taylor's Modern Navigation, H O w w u 1 o 1 1 1 1 ^ 1 s H ft CO 1 i i u H PJ H 5 a C/D' o D o u w 0:^ CO H U w w a U w Si go a o 1 i * E i ! i ! CllKONOilETEU. 299 When one considers the immense expense and the amount of or- ganized intelligence required to provide the navigator with impor- tant information, so that he may navigate his vessel with a greater degree of safety, it is surprising that they do not, as a body, take more interest and work with more enthusiasm to supply the Hydro- graphic Office with data, so that the same may be arranged and tabulated in a scientific numner, eventually to be returned to them for their guidance. There is no country in the world outside of the United States where so valuable a mass of information is supplied free of cost to the mariner; therefore it is plainly their moral duty to assist those who assist them to their utmost. THE CHKOXOMETEE. Handling — Too much care cannot be taken in handling this very necessary and important instrument of navigation, as the follow- ing article will make apparent, for there is no doubt that many vagaries or erratic errors are caused, through ignorance, from care- less handling. Inexperienced persons, not having a sufficient amount of knowl- edge regarding the importance of careful handling, will not even take the trouble to secure the gimbals with the stay provided in every chronometer for that purpose, when carrying it to or from the ship. This is wrong; for by suddenly or sharply turning a corner, it may be so jarred that the delicate interior may be so dis- arranged or interfered with, that it may even stop for a while, and afterwards by giving it another sharp twist it may start again. If this is done, and the careless carrier should deliver it to the un- suspecting master with the error and rate it had when leaving the shop (which has been totally changed by the rough handling), the master with all confidence would receive it and attempt to navigate his vessel, thereby the result being that a most unaccountable error would be detected eventually and perhaps the loss of the vessel might occur. The chronometer makers or repairers should therefore see to it tliat the person to whom the chronometer is intrusted to take 'from or deliver the chronometer to a vessel, is one having full knowledge of his responsibility; for no matter how careful the people are in the shop, or what their reputation for care and skillful ness may be, it is liable to be entirely ruined by carelessness in delivering. Care on Board — The chronometer should be placed in an outside 300 Taylor's Modern Xavigatiox. box having its interior cushioned with hair, to diminish the risk of alteration of the rate from sudden jars by a heavy sea striking the ship, or from bumping violently against a dock. The box will also be of considerable benefit in protecting the chronometer from moist- ure and vapor arising from cargoes. When selecting a position to keep the chronometer for easy access when taking observations, it should at the same time be so placed where it will not be exposed to sudden changes of temperature, such as near a door or companionway, whereby, if opened, the salt sea breeze or spray may dash in upon it, for by this the air in the in- terior may become condensed, causing perhaps a minute particle of rust to form on the works, seriously affecting the rate. This has frequently occurred, causing the navigator considerable uneasiness. It should also be placed as far as possible from magnetic sub- stances, such as iron, a compass, or adjusting magnets, as the fol- lowing will illustrate: A certain young man, whose name is witliheld for obvious rea- sons, having been appointed master of a coasting lumber vessel, was extremely particular in regard to the vessel's equipments, such as ropes, blocks, sails, etc., but neglected entirely those instruments, namely, the chronometer and compass, whereon the safe navigation of his vessel entirely depended. This man came to the writer on his arrival after completing his first voyage, and complained that the chronometer (he had only one on board) had acted very strangely, in fact, the ship's position was found to be about 36 miles in error when making port. Not having time to visit his vessel, I advised him to send the chronometer to a reputable person for repairs and cleaning, as it was of doubtful age, and there was no record of the last time it was cleaned. He took my advice, leaving it on shore and taking another one in its place, yet on his return from his second voyage he reported the same occurrence. I therefore made a special visit to the vessel and found that the compass used for steering was situated in a little "cubby hole" cut into the after part of the deck-house, the cap- tain's cabin being situated in the same part of tlie house: he had fixed the chronometer on a shelf to the after wall of his cabin, with- in two feet of the compass. We immediately changed the position of the chronometer to the fore part of the cabin and afterwards there was no complaint, for the obvious reason that it was at a reasonable distance from a mag- netic substance. CliKOXOMETER. 301 This incident, it is to be iioped, will caution the intelligent reader. • More Than One Ckrunonieter Xecessary. Vessels making long voyages should have not less than three chronometers on board and in the case of a large ocean steamer there ought to be another one for the exclusive use of the officers, situated in the officers' mess room or some other convenient place of easy access. If only one is on board and any accident, such as running down, breaking or clogging of the works, or if it suddenly changes its rate, the navigator is placed in a very awkward position, endangering the lives and property under his charge, especially if navigating in the vicinity of a group of islands or shoals, such as those found in the Pacific Ocean. If there are two chronometers on board it is certainly better than one, especially if one should run down, etc., still the navigator would not be very much better off, for if one of them should change its daily rate it would be very difficult, in fact absolutely impossible, to tell which of the two was wrong. But if three are on board and one goes wrong, there are two others for a check to tell which one it is, providing, however, that the navigator is careful to compare the three, and note the errors every day and enter the same in a book kept especially for the pur- pose, a sample of which is attached to this article. We cannot, however, expect a coasting schooner to carry three chronometers, in fact it is not really necessary, as the masters of such vessels have plenty of opportunity to verify ship's position by bearings of the land. They should, however, carry one if the owner is a particularly liberal person, yet if he is not, the master ^l■ould carry one himself at his own expense, to keep his hand in and not get rusty. It is the opinion of the author tliat marine insurance com- panies should insist, before writing a policy, that vessels be prop- erly supplied with a sufficient number of chronometers, according to the prospective voyage, the risk would be sensilily diminished. Wimding. On the under side of the bowl will be found a hole in a movable plate, which covers the keyhole in the bowl when not winding, to prevent the dust or moist atmosphere from entering the bowl itself. 303 Tavlok"s Modern Navigation. If it is the intention to wind, open the box gently — do not shim the lid — take the bowl in left hand and turn it upside down, slew the plate around until the keyhole is seen, then insert the key. Turn the key easily, do not jerk it, until the winding is stopped short ; then remove the key, see that the plate covers the keyhole, and let the bowl gently resume its proper position — do not let go with a jerk — then close the box. If the key slips when winding, it is proof that you are turning the wrong way, and to prove that it is wound, examine the little dial on the face of the chronometer. If the hand points to tviniL it is not wound; if it points to up, it is wound. If it is between wind and down, it is past the time for winding. This should never occur, as it may cause an alteration in the daily rate. Wind at the same time each day. Do it yourself, or one of the officers. Do not appoint the cook or steward for this important dut}", for they are likely to l)e in too much of a hurry, and l)ang things around, if they smell something burning on the stove. The Best Kind of Chronometers Are those commonly called two-day, but wdiich in reality run 56 hours; those called eight-day are not so reliable, as the tension on the works diminishes the nearer it approaches down, unless bal- anced to counteract. If either a two- or eight-day chronometer is used, it should be wound regularly each day, especially if the eight- day is not properly balanced. One of the great objections to the eight-day chronometer is the liability of a person to forget to wind on the proper day and perhaps let it run down altogether. Should, however, the chronometer run down, and. after winding it up, it refuses to start, give it a quick eiicular horizontal motion until it does. Rating. Under the heading of "Longitude by Chronometer," the methods of finding the daily and accumulated rate have been thoroughly ex- plained, therefore we will only discuss the different methods and facililies for finding the total error on a certain date. First Method — At all important seaports of the world there are time signals for finding the error of the chronometer. Sometimes it is the firing of a gnu, collapsing of a cone or the dropping of a ball, either nno of ilu' signals being made at iMean Xoon at place ClIKONO-MKTEH. . 303 for a standard ]\Ieri(lian. By watching the signal and noting the instant of time by the chronometer, the error for the particidar day of observation will be determined, but as sometimes the mechanism of the signal may get out of order, and thereby not made at the proper instant, the othcer in charge always notifies the daily papers, so that the navigator, by reference to the same, may know if the signal was made at the proper instant. Second Metliod — The error of the chronometer may be deter- mined with tolerable accuracy wlien in the vicinity of land well sur- veyed and charted, by the following rule, providing a number of observations are taken, worked out separately and the true place of the horizon well defined, but as the last item is as a rule so doubt- ful, any error found by observing above the sea horizon must be used with caution; still, if a vessel has made a long voyage, it will certainly be a very useful check. Rule — Locate the ship's position, latitude and longitude, very carefully by taking bearings of the land, and at same instant take one or more sights, the same as when taking an observation to as- certain the longitude, apply the assumed error of chronometer, work out and find the longitude. If this longitude coincides with the one found by bearings of the land, the error assumed will \ye correct ; if not, the assumed error will be incorrect to the amount of the difference of longitude in time between the correct and incor- rect longitude. Or, to the Mean Time at ship found by working the sight, apply the longitude of the place in time. If East subtract, if West add. The result will be the correct Greenwich Mean Time. Take the difference between it and the time shown by chronometer. The re- sult will be the total error for that date. Slow if the chronometer time is less than G.M.T. Fast if the chronometer time is more than G.M.T. As previously remarked, a correct result will depend on the true place of the horizon and also the amount of care taken when ob- serving. If practicable and tlie ship is provided with an artificial horizon, it would be much better to land and make the observation, taking two stars, one to the East and other to the West, in preference to the sun. working each sight separately. The result in tliis case would be entirely reliable. There are several other methods of finding tbe error, principally the problem of erpial altitude and the transit of a lieaveiily l)ody. and 304 Taylor's Modern Xavigatiox. although they are theoretically correct, in actual practice, for the ordinary navigator, they are entirely unreliable. To obtain the daily rate of a chronometer it would be necessary to determine the error on two dates about six or seven days apart by either of the methods here given, or by comparison with a standard chronometer such as may be found in the Branch Hydro- graphic Offices in the United States, the difference of the error divided by the number of days giving the daily rate. Rates of Chronometer. Shop rates given by "shopticians" are as a rule unreliable for use at sea, owing to the difference of location and the liability to change by carrying from shop to ship, and change of temperature. Shop rates as given to the navigator on printed slips rarely mention any- thing regarding that a change of rate may occur owing to a change of temperature. They are not to be blamed for this, for the rea- son that if many seamen were to receive a slip mentioning such a thing they would be likely to ask the chronometer man why he could not give a rate good for all climates. Still if they would, when rating, subject the chrenometer to an even temperature for every 10° above normal up to about 90°, by placing it in an oven or incubator for a few days, for each 10°, and then note on the slip the changes in the rate, the master could, if he watched the temperature, get a much better result from his chronometers. It must be understood, however, that the tempera- ture meant is for the interior of the case, not for what it is on deck, for there may be quite a difference between it and the deck temperature. Sending Clironometers Ashore. If a vessel is in port and taking on board a cargo where the ship would be subjected to severe shocks by dropping heavy weights on the deck, or if the multifarious duties of the master may make him forget to wind as regularly as at sea, or if a steam winch is situated directly over the usual place for keeping the chronometer, it is cer- tainly advisable that it should be sent ashore to be taken care of by skillful persons. It should never bo intrusted to the tender mer- cies of an office boy if left in the owners' or agents' office. As a final word of caution, do not trust the chronometer to any person calling himself a chronometer maker or repairer, unless you have first satisfied vourself that lie is a reliable man. for there are Chroxometer. 305 / manv watchmakers, claiming to be chronometer makers also, who are totally unfit to perform the important dut}' of rating, cleaning and even of takinsi" care of a chronometer. What to Do if the Chroiiuiiietcr Should Break Down. Kun the ship to the latitude of your destination and steer to the true East or West, as the case may be, keeping a good lookout, as the ship will be running on dead reckoning longitude, but latitude by observation. In the case of a vessel bound to a United States port, it is cer- tainly not possible to miss the continent of North America, but if bound to an island port great care should be taken to discover the position of the snip before running down the longitude, as she may be running away from it instead of towards it. This could be done by Lunars, but as a rule vessels whose owners are too mean to provide more than one chronometer have rarely a master who is in possession of the requisite knowledge and a sex- tant fit for taking such observations, and as Lunars are obsolete, owing to the extreme difficulty in obtaining even a favorable result, the same has been entirelv omitted from this work. Taylor's Mod. Nav. 20. 30G Taylor's ^Ioderx Xavigation. J. a; < CO u (O Z c/o < U >^ d < -1 - 11 s s ^ - - - 'P < < « Ed •< 1 ■i CO - Q Ml S -^ S c 'H 'S w X s ' « I s - - - - " PS s td 3 c 1 -^ 1 ti - .Jig (5 i » s - ^1 - < J EC H i s s 5 i I 1 ■5 ■^ w •< < £ 1 s - 1 i i 1 ?. 1 \_^ I_ DIVISION XIV. THE MARINER'S COMPASS. This instrument, so essential in tlie practice of navigation, is of such ancient lineage, that its origin is forever buried in oblivion; still, some of the earlier writers, notably the 'Jesuit missionaries to China, have proven witliout a doubt that, in a crude form, it was in use in that country centuries before it was ever lieard of in Europe. The first mention of its use in Europe was by a merchant travel- ing across the Mediterranean Sea, and Mdien writing of his travels he mentioned the fact that the mariners stuck a needle in a eorn- husk, then, after passing over it a lodestone, placed it in a howl of water; it was then found to indicate the North, whereby they were enal)led to steer their craft to port. The credit of attaching the needle or needles to a card has been claimed l)y both the Italians and the French; but it is safe to say that the modern method of doing it is. no doubt, considerably dif- ferent from the first attempt. It is not the intention of this work to delve too deeply into the history of this most valuable instrument; so we will here leave that part to tlie professional historian and proceed with the essen- tials of a good com]iass and other matters not generally known to seamen. The marking of the card is of the first and primary importance. This should be done to degrees and very accurately, the degrees commencing at for North and South, and ending at 90° for East and West. As all modern navigators always calculate to degrees, it would be a verv good plan if the old-fashioned idea of "boxing the compass" in points were done away with entirely; for there have been many mistakes made on stormy nights when giving the course, from not hearing correctlv, courses having been steered as many as four points in eri'or. in mistaking E.N.E. for E.S.E.. and so on. In fact, there was one particular case that came under the author's notice some years ago, where a large steamer was run ashore in the vicinity of Rio de 'Janeiro for this reason. At a very recent date the United States Hydrograpliic Office printed a form of compass-card entirely doing away with ]ioints, and at the time asked for the opinion of navigators in regard to it. It is to be regretted that it received very little of the attention it deserved, and although not entirclv approving, as the change 308 Taylor's Modern Xavigation. Avould be too radical, still if all the points were dispensed with, excepting X.S.E. and W., it would be very beneficial to the naviga- tor. The next essential is to have a properly tempered needle, — or needles, I should say, for it is rarely that a compass is seen now- adays having only one. The shape should be round, never flat. In the best makes of compasses there are as many as eight at- tached to the card. This gives more directive power and causes the compass to be more sensitive. When attaching the needles to the card, great care should be taken that the line of force is exactly parallel to the North-and- South line of the card. Any error in this respect would be very dangerous, as observations by Amplitudes or Azimuths to deter- mine the deviation would not reveal it. The point of suspension comes next in order, as the pivot upon which the compass-card rests and revolves must be accurately centered in both the card and the bowl. It should be understood that on the under side of the card is a cup containing an agate, on this cup the card rests when on the pivot. The point of this pivot is, or should be, highly polished, so that when the card is resting upon it there will be the least possible friction. Should there be a flaw in the agate, it will eventually dull the point of the pivot, the result being that the card will become sluggish or appear to stick, requiring to be frequently shaken up to make it move. If such a thing happens, the compass should be sent on shore as soon as possible to some reputable shop for repairs. Care should be taken to prevent the edge of the card from touching the inside of the bowl. This is very likely to occur if the pivot has not been properly centered, and may be discovered by turning the bowl slowly around in a circle and watching to see if at any time the card follow the motion. Although the card should move freely, still there should not be too much space, for if there is, the helmsman may steer as much as one quarter of a point in error, if he is steering with a large wheel and the compass is not situated directly in front of him. The Luhher-Line should be very accurately draM-n in tlie bowl, and should be placed exactly on the fore ])art, for any error in these respects will give a constant amount of deviation, dangerous because hard to detect. Tliis will be more elaborately treated as we progress. C'oMi'Ass Adjustment. 309 I'urckimnij a Compass. Tn purchasing a compass, seamen should not always take the word of the maker or the agent, for they arc not always competent judges, as the following incident will illustrate: It was the writer's fortune once to he employed by a large steam- ship company for the purpose of compensating compasi.'es on a cer- tain vessel recently turned over to them by the builders. On going on board it was found that she had been supplied with a very fine lot of binnacles, — fine from the brass-finishers' point of view, — which proved to be absolutely valueless in directive power of the compass-needles. The lubber-points, also, were painted on the in- side of the bowl in such thick lines that in steering it was possible to steer by them almost half a point in error. The compasses were rejected, and eventually the writer had a visit from a very indig- nant maker ( ?). In course of conversation I asked him if he guaranteed his com- passes. He answered very emphatically, "Yes." "For how long?" was my next query, and his answer was, "for always." This answer alone proved that the man did not have the slightest knowledge of the first principle about the instrument he was sup- posed to manufacture; for it is common knowledge among even the uninitiated, that any piece of steel or iron, when magnetized, will eventually lose a considerable amount of its power, never re- taining the full amount of its original strength, the tenacity de- pending on the temper: the excess of what it can hold will leave it, eventually reaching at what is generally understood as a state of saturation, and even afterwards it will gradually diminish in strength unless it is kept in close contact with another body of equal power, with opposing poles together. Take for instance the horseshoe magnet : if the keeper is left off, it will gradually lose its power. The best magnets in the world to-day are made under the super- vision of Lord Kelvin, the greatest authority on such matters now living. They are guaranteed for five years at the most. While we are discussing the so-called compass makers and re- pairers it may not be amiss to give another instance: A few years ago, a shipmaster, an old friend, telephoned to me to come down to his ship and examine the compasses, as there was something radically wrong. Before going down I placed in my pocket a small but powerful magnet, which I generally use whrn 310 Taylor's Moderx Xavigatiox. testing a compass by deflecting the needie. Arriving on board, I attempted to deflect and found that the compass barely moved, al- though the magnet was held so as to touch tlie bowl. I informed the master that there was something very much the matter with the card, but I could not tell without opening the bowl. The mas- ter was very much surprised, as it had been in the hands of a "compass-repairer" ( ?) only one month previously. I insisted, however, in opening the bowl (it was a liquid com- pass), but was not prepared for what I found, viz.: The compass was so old, and the tubes containing the needles having leaked, there was not one piece of needle one-half inch long, they were so eaten with rust. The repairer (God save the mark!) had simply emptied out the liquid, gave the interior a clean coat of paint, re- filled the bowl, and returned it to the master. Such incidents as these will serve to show that the master cannot be too careful to whom he intrusts the vessel's navigating appli- ances when needing repairs. Parsimonious Owners. It is not an uncommon occurrence for masters or "cheese-par- ing" owners to perambulate among pawnshops and Junk-stores and "pick up" an ancient compass and expect the vessel to be navigated therewith. To this kind of people we have nothing to say, for we do not expect for one minute they would even think of consulting a book of this kind, so let them go; still, to the honest and ambi- tious navigator, we certainly hope that the remarks and authentic incidents here related will be of some benefit, remembering that some compass-makers may Ije excellent mechanics in their own particular line of business, but. as a rule, they have not the slight- est knowledge of the practical use of the compass at sea, and, there- fore, they are not competent judges, any more than a tool-maker, for he can only m'ake tools, and, with rare exceptions, cannot use them. Tlie liquid compasses iirc very much in favor in the United States, whereas in Europe dry compasses are mostly used. It is hard to determine which is the better, for excellent results have been had with both, and as steadiness of the card at se;! is the greatest recommendation for the liquid, yet if the card is con- structed on the Thompson ])hui of extreme liglitness. and corre- spondingly less friction witli the inininiutn \vu\)- pose that through it the vessel loses ten miles each day. lu a run of thirty da}'? she would lose three hundred miles. Call this one good day's run. Calculate the cost of fuel for one day and add to it the daily expenses, such as wages, food, and insurance, and per- haps the loss of a tide, and it will be seen that parsimony in regard to compasses and other navigating appliances is a bad business proposition. The engineer of a steamship needing anything for his depart- ment simply makes the assertion that certain supplies or repair- are necessary, and they are immediately supplied to him ; but if the master needs anything to assist him in the safe navigation of his vessel, he is frowned upon, and informed that Captain So-and-so does not consider it a necessity — why should he? The master is supposed to supply himself, at his -^wn expense, with certain instruments to enable him to navigate his vessel ; but it has never been required of the engineer that he should provide tools for work in the engine-room. Why make the difference ? When building a new vessel, the master or compass-adjuster should be consulted in regard to the arrangement of the bridge and the fittings in the vicinity of the compasses. This is. however, rarely done, the engineer or constructor having full control of such matters. It is quite correct that the engineer should he regarded as the most competent person to superintend the construction of the vessel's hull and machinery, but he is certainly not a competent per- son so far as the bridge is concerned. As before remarked, most contracts for building expressly state that the vessel shall be supplied with compasses ready for sea, the same being selected by a person connected with the ship-l)uiUling firm, called a buyer, who, as a rule, has not the slightest knowledge about the essentials of a good compass. It is actually criniinal ti> intrust so important a matter to such a notoriously incompetent person. In the author's opinion, such matters should be left entirely to the discretion of the master, for if the builder supplies the com- passes, there is just as much reason that he should supply charts, sextants, barometers, thermometers, and chronometers, for they are all necessary implements required in navigating a ship. Kemember, gentlemen, that there is an old saying, 'i']vi ry man to his trade. — the shoemaker to his last, and the cook to the fore- Compass Adjist.mkxt. 315 sheet." Willi ti'i< paitiiiii- j-liot we will now itrocccd witli magnetism in iron ^Ili})s. :\IA(;XKTISM. Webster deiines magnetism as "tlu' I'orei' in nature wliieh gives rise to the plx'nomena of attraction, polarity, etc.," exhibited by the lodestone and otluM- magnetic bodies, and which also Jiad l)een de- scribed as "that l)ranch of physical science which treats of the na- ture and properties of magnets and of their action on each other.'' The lodestone, which means, in English, "to lead," was called by Pliny, "ferriim viviim," or quick iron. They are black in color, and are found mostly in Asia Minor. They were considered by the ancients to have magnetic properties I)ecause of their pow'cr in at- tracting minute particles of iron. Bars or elongated masses of steel or iron, when charged with magnetism by contact or friction with another magnetic body, be- come what are known as artificial magnets. The earth itself is a large natural magnet, the ctfect being termed ''terrestrial magnetism," or in other words, the magnetism con- tained in the earth. Local attraction is magnetism contained in some mass other than the ship's hull, etc., but which is sufficiently near to the ship to disturb the compass-needle, and which disappears as soon as the ship moves a sufficient distance from the disturbing mass. Permanent magnetism is that which is contained in a ste(d bar, having in itself an independent power. Transient magnetism is a power induced into a mass of soft iron by having an independent magnet in its vicinity, or whicli is in- duced by the magnetism of the earth. It is not stable, liut depends upon the position of the disturbing mass, or the geographical posi- tion. Subpcrmanent magnetism is an independent force acquired by soft iron, but which is subject to a loss of power in tlie lajise of time. :\rAGXETl.SM OF THE EARTH. If the reader will kindly turn to tlie defmitions and examine the figure representing the terrestrial s]ihere, it will be noticed that the 316 Taylor's Modern Navigation. magnetic poles are not at the same place as the true poles, bu!, in- stead, are situated at some distance from them. Now, as there are magnetic poles, so also must there be magnetic meridians and a magnetic equator. This will go to show that there are two ways of looking at the world, viz., one in its true character and the other iu its magnetic character ; and let it be remembered that it is the lat- ter which will be referred to throughout this section. The magnetic pole is that pole towards which the compass-needle points when not affected by iron in its vicinity. Magnetic meridians are great circles passing from the magnetic North Pole to the magnetic" South. Pole. The compass-needle will always lie along one of these when it is free from deviation. If the needle deviates from it, the resulting angle will l)e the devia- tion. The magnetic equator is a circle passing around the earth, about half-way between the magnetic Poles, and really means that if a magnetic needle is freely suspended so that it will move vertically, it will hang perfectly horizontal as long as it is on the magnetic equator, but should the needle be taken to any other part of the world, it wall leave its horizontal position and one end will dip. Dip or inclination of the magnetic needle is tlie angle between the position of the needle and a horizontal plane. A line drawn through the needle itself would represent a line of force. This dipping of the needle is caused by its pointing towards the magnetic pole through earth, instead of towards the North point of the horizon. It is of the utmost importance that this definition be thoroughly understood, as the dip of the locality where the ship was built has a considerable influence on the magnetic character of the ship. The dip on the magnetic equator is zero, as the needle hangs hor- izontally. At either the magnetic North or the magnetic South Poles the needle would be vertical, or would have a dip of 90°. It must not be assumed that it jumps to this dip all of a sudden, for such is not the case, as it gradually changes from the horizontal and assumes the vertical as the ship leaves t\\o iiiagiietic ciiiiator and approaches the magnetic poles. Charts of the di]) I'oi' the whole world are published each year by the Tnited States government, tlie magnetic dip for any place may 1h' determined by simj)ly re- ferrini,'- to these charts. CoiiPASs Adjustment. 317 Chance for Argument. It is popularly supposed that the North end of the compass-needle points towards the North. This supposition is incorrect ; therefore, it is necessary that the student should be disabused of this idea be- fore he advances much further, or he is likely to become very much entangled. To prove this we will give the First Law of Magnetism, Wliicli is. Opposite properties attract; Similar properties repel. If this is so, then the North end of a compass-needle could not point North, — in fact, it must point South. This is very confusing, because by this law a North will repel a North, and a South will repel a South, but a North will attract a South, and vice versa. The only safe way is to speak of that end of the compass-needle that points towards the North as the North-seeking end, and al- though many modern writers have given various names to the poles according to their own ideas, in this work Airy's method of color will be used, as it quickly catches the eye, and serves the purpose of illustration better than any other method. Eed will therefore always be understood as meaning the North- seeking end, and Blue as meaning the South-seeking end of a mag- net. The student will then see at a glance the "first law of mag- netism," as same colors placed together will repel, but contrary colors will attract. MAGNETISM IN AN IRON' SHIP. Before taking up the all-important study of conn)ass-a(ljustment it will be necessary for the student to thoroughly understand the distribution of the magnetism in the hull, beams, masts, and fun- nels of an iron ship, to analyze the causes and sort them out. so to speak, so that when compensating the errors of the compass pro- duced thereby, it may l)e done in an intelligent and practical nnui- ner, for without a thorough knowledge of the causes, no one can expect to be a successful compass-adjuster. A ship built of iron should be considered in the light of a very large magnet. She is so in fact, for she acquired magnetism while underffoinof construction, bv tlu- hammerino- and rivetinsc of the ribs 318 Taylor's MoDEitx Navigation. and plates when fitted together until they became a more or less elongated mass capable of receiving and retaining a certain amount of polarity. This magnetism, so induced into the hull, is termed Subperma- nent, the position of the poles in the ship depending on the direction of the ship's head while on the stocks and on the magnetic dip of the locality wliere the ship was built. It should not be understood that the ship will retain all the magnetism so acquired, for such is not the case; in fact, there will be a very rapid change in the amount after the ship leaves the stocks until the iron in the ship's hull reaches the saturation-point, when it will remain practically con- slant for all time and places, unless the construction of the hull is altered. If the ship's head was placed, after the launching, in an opposite direction from that pointed to when she was being built, a large amount of the magnetism induced by the hamuiering, etc.. would be hammered out of her again ; therefore, it would be a good plan if the owners of the vessel insisted on this being done, when specifi- cations are submitted to them for approval. The reason is obvious, for as the Subpernianent magnetism changes so rapidly after the launching, any compass adjusted before the hull reaches the satura- tion-point will not remain in the same for even one day ; and al- though the matter of completing the ship with her head in an op- posite direction may not entirely do away with the excess of the Subpermanent magnetism, it certainly will assist in materially de- cj-easing it, with the result that the compass will not &how such an ex- tremely variable error. It may not be possil)le always to do as above advised, owing, perhaps, to the peculiar location of the ship-yard or its wharves; still, the master, before taking the ship to sea, should insist, as far as practicable, that the ship be anchored for a few days in such a position that the direction of her head will be sub- jected to alternation by the change of the tides. If these instructions are not carried out. any adjustment made or deviation ascertained will not be worth the scratch of a pencil. Vessels built of hard iron or of steel receive nmgnclisui slowly. and are correspondingly more retentive, and will take a much k.nger time to get rid of the excess of the Subpermanent magnet- ism; therefore, with a vessel built of steel, it is more imperative to alter the direction of her head than with a vessel built of com- paratively soft iron. Subpermanent uiagnetisni ])roduc<'s semicircular deviation, which means that Easterlv dcvialion will be found on one-half of CojLPAss Adjustment. 319 the compass, and Westerly deviation will be i'ound on the other half, with the point of no deviation diametricalk ojjposed ; that i<, if thcM'c is ni> deviation on Xorth there will he none on South. There will also be two points diametrically o])pose(l where it is greatest; but the names of the deviation will be opposite; that is, if 20° E. is found on West, then 20° W. will be found on l^ast. The student should bear in mind that he will not always find tlii.- actually shown by a compass unless he eom])utes the coetheient, which will be explained further on. Transient magnetism in a ship is contained in all iron that is vertical, such as iron masts, funnels, ventilators, davits, stanchions, etc. All vertical iron, no matter whether it is on board of a ship or on shore, becomes magnetized by induction of the earth's magnetic force; the disturbing effect it has on a compass-needle depending on the dip of the locality. The lower end of a bar of vertical iron always takes on the char- acter of the pole that is nearest to it, and the upper end the opposite character. Therefore, in North magnetic latitude the lower end will always be North, or red, and will, therefore, push the North or red end of a compass-needle away. Consequently, the upper end will be South, or blue, and will attract the Xorth or red end of a compass-needle. The reverse will be the effect for a South latitude. A bar of iron held vertically over the magnetic equator would not have the slightest effect on any compass in its vicinity, for the reason that the induction of or by the magnetic poles is neutralized by the iron being equidistant from both; but if the bar is taken from the magnetic equator towards either one of the magnetic polos, it immediately becomes magnetized. If the bar is held vertically over the North magnetic pole it will then receive, by induction, the full effect of the earth's magnetic force, the lower being red of great intensity, and the upper blue. This changing of the magnetic intensity found in vertical iron is one of the principal causes of the great alternation in the deviation of the compass as the ship shifts her position on the surface of the earth, and. as no doubt will l)e seen by this time, the disturbing power depends on the magnetic dip of the locality where the ship happens to be. 320 Taylor's Modern Xavigatiox. Transient magnetism foimd in vertical iron produces, als'O, semi- circular deviation, as previously described; but as the causes are totally different, and as the one is practically constant for all lat- itudes, while the other is constantly changing, the method of com- pensation cannot be the same. This will eventually be explained. Magnetism Contained in Iron Lying Horizontal, Such as the Beams and BuR-heads of an Iron Ship. As already explained, the magnetism in the ship's hull (Subper- manent) and vertical iron (Transient) both produce semicircular deviation and from different causes; but the deviation caused by horizontal iron is produced by a totally different law, viz., horizontal induction, the result being termed Quadrantal Deviation, which is so named because it is greatest at the quadrantal points, X.E., S.E., S.W., and X.W., but is zero at the cardinal points, X., S., E., and W. To demonstrate the effect of horizontal iron, the student is ad- vised to test by experiment with any compass what is here asserted. If a bar of soft iron is held so that it is in a direct line wffch a compass-needle, but with one end near the Xorth. it will be found tbat it will have no disturbing effect on the compass-needle; but if it is moved so that it will make an angle of not greater than 90°, the bar pointing directly to the center, it will immediately attract the Xorth, having the greatest disturbing effect when the angle is 45°. If the bar is held at right angles to the compass-needle, with the end pointing towards the center, it will have no effect. If it is held in a direct line with the needle, but with the end near the South, there will be no disturbance; but if held at any other angle except 90°, the South will be attracted to it, the great- est effect being when the bar is pointing towards the center of the compass at an angle of 45° with the compass-needle. Tlierei'ore, the law of disturbance, as illustrated, is. that a T)ar of horizontal soft iron will attract that end of the coni])ass-nee(lle that is nearest to it; the result being, (hat luu'izontal iron has the least effect when it is lying in the sanu' line of force as the needle, parallel to it or at right angles with it, hul has its greatest "effect when I he mass is at an angle of 45° with the compass-needle. It FIG. 5 ^\^^ flips Head NORTH e/ 3TARB0/1RD side X N FIG. 4 (Sljips Head SOUTH ur PORT SIDE E N FIG. 5 Compass Adjustment. 321 will, therefore, be seen, that as the direction of the ship's head al- ters, so also must the angle between the needle and the horizontal iron, causing a change in the deviation. EXPLANATIOX OF COLORED DIAGEAMS. Fig. 3, Ship's Head North in North Latitude. This illustration shows the Subpermanent magnetism contained in an iron vessel owing to her head being North while building. The arrow S.jST., represents the dip of the locality, and the line EE, at right angles to it, represents the equator of the dip. A vessel built under such conditions will have red or Xorth mag- netism in her fore foot, and blue or South magnetism in the upper part of her stern, with the greatest intensity in those places, but which gradually diminish towards the equatorial line, as illustrated by the intensity of coloring. That part of the deck which the line EE passes through is neutral, and a compass placed in such a position would not be affected by Subpermanent magnetism, as it would practically be equidistant from the poles of the ship, but if it were placed on any other part of the deck, it would be immediately affected. The line of force in the ship being fore and aft, and the compass- needle lying in the same direction, namely, fore and aft, also, or in other words, if the ship is heading North or South by compass, there will be no deflection of the needle, but if the North or red end of the needle should point to the North or red end of ship, and the South or blue end of the needle should point to the South end of ship, the compass will be sluggish, but if the blue end of the needle points to the red end of the ship, then the needle will be sensitive. If the needle leaves the ship's line of force, it will be immediate- ly disturbed, especially by the stern, as there is more blue on deck aft than there is red forward, the North end of the needle being at- tracted towards the stern will cause the maximum amount of dis- turbance when the ship is heading East or West, or when the needle is at right angles to the line of force in the ship. Fig. 2, Ship's Head West. This illustration shows the stern of the ship and the Subperma- Jient magnetism, owing to her being built with her head "West. 322 Taylor's Modern Navigation. In this case the lower part of the starboard side will be red, viz., that part below EE, and the upper part of the port side will be blue, with great intensity, the port side of the ship having greater effect than the starboard side, owing to the blue pole of the ship being nearer to a compass situated on the deck. The result will be that if the ship is heading on an East or a West course the neeedle will lie athwartships, and in the ship's line of force. In such a case there will be no deflection of the needle, and therefore no deviation ; but if the ship is heading so as to bring the North or red end of the compass-needle to the blue side of the ship, then it will be sensitive, but if the blue end of the needle is directed to the blue side of the ship, it will be sluggish. The greatest effect on the compass-needle will be found when the needle is fore and aft, as it would be at right angles to the line of force in the ship, the needle being attracted strongest to the port side. Fig. 1, Ship's Head East, Bow View. This illustration shows the Subpermanent magnetism in a §'hip with her head east while building. The port bilge having been nearest to the North, is therefore red, and the upper part of the starboard side is blue, owing to its having been farthest from the North while building. The effect on a com- pass will be that the red end of the needle will be attracted to the starboard side. Fig. Jf, Ship's Head South, Showing Port Side. This illustration shows the effect on a ship with her head South while building. In this case the most power is in the upper part of the bow, and is blue, because it was the part of the ship farthest from the North while building. The greatest intensity of red magnetism will be in the lower part of the stern. This is the contrary case to that of ship's head north while building. Fig. 5, Ship's Head North and Vertical Iron. The hull of ship in this case will have the same coloring of Sub- permanent magnetism as that in Figure 3, but with the port side towards the reader, so it needs no further explanation, but the 322 Taylor's Modern Navigation. In this case the lower part of the starboard side will be red, viz., that part below EE, and the upper part of the port side will be blue, with great intensity, the port side of the ship having greater effect than t'he starboard side, owing to the blue pole of the ship being nearer to a compass situated on the deck. The result will be that if the ship is heading on an East or a West course the neeedle will lie athwartships, and in the ship's line of force. In such a case there will be no deflection of the needle, and therefore no deviation ; but if the ship is heading so as to bring the North or red end of the compass-needle to the blue side of the ship, then it will be sensitive, but if the blue end of the needle is directed to the blue side of the ship, it will be sluggish. The greatest effect on the compass-needle will be found when the needle is fore and aft, as it would be at right angles to the line of force in the ship, the needle being attracted strongest to the port side. Fig. 1, Ship's Head East, Bow View. This illustration shows the Subpermanent magnetism in a ship with her head east while building. The port bilge having been nearest to the North, is therefore red, and the upper part of the starboard side is blue, owing to its having been farthest from the North while building. The effect on a com- pass will be that the red end of the needle will be attracted to the starboard side. Fig. Jf, Ship's Head South, Showing Port Side. This illustration shows the effect on a ship with her head South while building. In this case the most power is in the upper part of the bow, and is blue, because it was the part of the ship farthest from the North while building. The greatest intensity of red magnetism will be in the lower part of the stern. This is the contrary case to that of ship's head north while building. Fig. 5, Ship's Head North and Vertical Iron. The hull of ship in this case will have the same coloring of Sub- permanent magnetism as that in Figure 3, but with the port side towards the reader, so it needs no further explanation, but the < m Compass Adjustment. 323 smoke-stack is to represent the transient magnetism found in vertical iron. This case is for North magnetic latitude, therefore the lower part of the stack being nearest to the North magnetic pole, it must take on the character of that pole, so it is colored red, while the upper part, being farthest away, must take on the contrary charac- ter, and is therefore blue. The effect on a compass would be that of attracting more strongly the North end of the needle towards the stern, that is if the compass is placed on the fore part of the funnel and elevated above the deck, as both the top part of funnel and stern of ship have blue magnetism. Should, however, the compass be placed on the deck near the lower end of smoke-stack, then the North end of the needle would be repelled thereby, the amount of the re- pelling force depending on the mass. This idea of placing the verti- cal iron, or smoke-stack, with the hull, is to serve the purpose of illustration, but be it remembered that the magnetism in the hull, called Subpermanent, is practically the same for all latitudes, where- as the magnetism in the vertical iron depends upon the magnetic latitude of the ship or dip of locality. Fig. 6, Ship's Head N.E., Dech Plan. This illustration shows the deck plan of a ship with her head N.E. while building. It will be seen, in this case, that the port bow was nearest to the' North while building, and is therefore red, and the starboard quar- ter farthest from North, and is therefore blue. The effect on a compass will be, if the ship is heading in a direc- tion the same as or opposite to that of her head when being built, there will be no deviation, because the needle would be lying in the ship's line of force. This is a combination of that of a ship's head built North or East, as the red is found partly in the bow and partly in the port side, and the blue is partly in the stern and partly in the starboard quarter. The maximum effect on the compass-needle will be when the ship is heading N.W. or S.E., because at those times the needle will be at right angles to the ship's line of force, the North or red end of the needle being attracted towards the stern and the star- board quarter. Fig. 7, Shifs Head S.W., Deck Plan. This illustration shows the deck plan of a vessel built with her head S.W. It is the contrary case to that of a ship built with her 32-i Taylor's Mouerx Xavigatiox. head X.E. Here the South or blue magnetism is found in the port bow and the red in the starboard quarter. The efEect here will be no deviation when ship is heading S.W. or X.E., but the greatest efEect will be when the ship is heading on X.W. or S.E., as at such times the needle will be at right angles to the ship's line of force. the North end of the needle being attracted to the bow and the port side of the ship. Fig. 8, Ship's Head East, Deck Plan. This illustration shows the magnetic character of a ship built with her head East. In this case the subpermanent magnetism will lie in the sides of the ship, and none in the ends of the ship. The preponderance of power will be in favor of the blue, as its intensity is in the upper part of the starboard side, and correspondingly nearer to a compass situated on the deck, whereas the red will be in the lower part of the port side or bilges. The effect on a compass will be that of attract- ing the Xorth end of the needle to the starboard side, with no fore- and-aft attraction whatever. Fig. 11, Ship's Head S.E., Deck Plan. This is a contrary case to that of a ship built with her head X.W.. with the points of no deviation the same and the points of maxi- mum deviation also the same, but with blue magnetism in the star- board bow and red in the, port quarter. In this case the needle will be attracted towards the fore part of the ship and the starboard side. Fig. 9, Sliip's Head N.W.. Deck Plan. This illustration shows the magnetic condition of a ship built with her head X.W. In this case the starboard bow will have red magnetism and the port quarter blue, the effect here being that on X.W. and S.E. courses the needle will lie in the ship's line of force, and therefore will have no deviation, whereas on N.E. or S.W. courses the maxi- mum effect will be felt, a,& the needle would be at right angles to the ship's line of force. Here the North end of the needle is attracted partly to the port quarter and partly towards the stern. > 2 So Compass Adjustment, • ' i' 325 Fig. 10, Ship's Head West, Deck Plan. This illustration is a contrary case to that of a ship built with her head East. There is no fore-and-aft attraction, but all athwartship attraction, the needle being attracted to the port side. The points of no deviation would be East and West and maxi- mum at Xorth and South. Innumerable diagrams could be given, showing the subperma- nent magnetism for other directions of ship's head while building, but the author feels assured that those that have been given will be sufficient to illustrate the subpermanent character of ship. From these diagrams it will be seen that the North end of the compass- needle is drawn to or repelled from different parts of the ship, and the reason why. The student will also see, by this time, that the compa&'s-needle may be disturbed by different parts of the ship, not only by the hull, but also by vertical iron, both of these pro- ducing semicircular deviation, but, as before remarked, the effect of the subpermanent is practically constant, whereas the effect of the transient magnetism is vertical iron continually varies, accord- ing to the dip of the locality. There is also another disturbing power to be taken into consideration, namely, that contained in horizontal iron. The effect is totally distinct from the others. This we will treat of when we finish wdth the semicircular deviation. SORTING OUT THE DEVIATIOX. This is done by giving a name to each disturbing power, accord- ing to which part of the ship the N^orth end of needle is at- tracted. These forces are designated by the letters A, B, C, D, and E, and are called coefficients. Coefficient A represents an effect on the compass that is constant for all directions of the ship's head. It may be caused by a poorly constructed card, the needle not being parallel to the jSTorth and South line, unequal distribution of iron in the vicinity of the com- pass or a lubber-line wrongly placed. A, as a rule, is very small, or, at least, it should be ; if not, the card and lubber-line should be examined. The coefficients B and C represent the semicircular deviation, or, in other words, the amount of deviation produced by both the subpermanent magnetism in vessel's hull and the transient mag- netism in vertical iron. 326 Taylor's Modern Navigation. Coefficient B represents a force acting fore and aft, such as would occur in a vessel built with her head North or South. — (minus) B when the Xorth end of the needle is drawn to- ward the stern, and + (pl^^s) B when drawn towards the bow. Coefficient C represents a force acting athwartship,-[-C when North end of needle is drawn towards the starboard side, and — C when, drawn to port side. The value of the coefficients depending to a great extent on the direction of the ship's head while building. Take, for instance, the colored figure of a ship built with her head North. Here the attraction would be all fore-and-aft, and none athwartship. In such a case the North end of the needle would be attracted towards the stern ; therefore the coefficient would be all — B and no C whatever. In the case of ship's head South while building, the attraction is also fore and aft, and none athwartship ; therefore the needle is drawn towards the bow, giving all -{-B and no C. In the case of ship's head East while building, there is no fore- and-aft attraction, but all athwartship, and as the North end of the needle is drawn to the starboard side, there is all -\-C and no B. In the case of ship's head West while building, there is all athwartship attraction, and none fore-and-aft. Here the needle IS drawn to the port side, therefore there is all — C and no B. In the case of ship's head N.E. while building, the North end of the compass-needle is drawn equally towards the stern and the starboard side. The result is therefore — B and -f C in equal amounts. In the case of a ship's head N.W. while building, the North end of the needle is drawn towards the stern and the port side equally. This would be — B and — C in equal amounts. In the case of a ship's head S.E. while building, the North end of the needle is attracted towards the bow and the starboard side. This would give -)-B and -|-C in equal amounts. In the case of a ship's head S.W. while building, the North end of the needle is drawn to the bow and the port side. This would give -|-B and — C in equal amounts. The student Avill, no doubt, understand that if the ship was built with her head in any other direction than those given the value of the coefficient would be different; that is, if her head was N.N.E. FIG. 6 (§})ips Head N.E. FIG. 7 FIG.8 'v '5'l'P5 Head „s Compass Adjustment. 327 when building, the value of B would be greater than C, but if built with her head E.N.E., the value of C would be greater than B. From what has already been said, the following is deducted: Ship's Head The North end of Compass Needle while Building. on Bridge will be Drawn. N. Toward the stern. N.E. Toward the starboard quarter. E. Toward the starboard side. S.E. Toward the starboard bow. S. Toward the bow. S.W. Toward the port bow. W. Toward the port side. N.W. Toward the port quarter. The reader must understand that all remarks regarding the hull relate exclusively to the subpermanent character of the ship. To further illustrate the subject the following table is given, showing the approximate deviation : Ship's Head while Building. Approximate Maximum Easterly Deviation Occurs. Approximate Maximum Westerly Deviation Occurs. N. w. E. N.E. N.W. S.E. E. N. S. S.E. N.E. S.W. S. E. w. S.W. S.E. N.W. w. S. N. N.W. S.W. N.E. It will be noticed, in this table, that on one-half the compass there is Easterly deviation and on the other half Westerly deviation, hence the name, "semicircular deviation." QUADRANTAL DEVIATION. This error is caused by the induction of horizontal iron, such as iron beams, either extending fore and aft or athwartships. It is so named because it produces the maximum amount of deviation when ship is heading on the intercardinal points, namely, N.E., S.E., S.W., and N.W., and is practically harmless when ship is heading on the cardinal points, namely. North, South, East and West. 328 Taylor's Modern Navigation. The effect on a compass of horizontal soft iron extending fore- and-aft or athwartship is illustrated or named coefficient D. +0 represents the effect of continuous athwartship iron, such as the ordinary iron beams in a ship. It produces -\- or Easterly devia- tion in both N.E. and S.W. quadrants and — or Westerly deviation in the N.W. and S.E. quadrants, completely disappearing on the cardinal points, North, South, East, and West. — D represents the effect of fore-and-aft iron, and is exactly opposite to -^-D, as it produces + or Easterly deviation in the N.W. and S.E quadrants, and — or Westerly deviation in the X.E. and S.W. quadrants. — D will rarely be found in actual practice, owing to the pre- ponderance of athwartship iron over the smaller amount of fore- and-aft iron used in the construction of modern vessels, therefore a -j-D will almost invariably be found. It may not be amiss to state, before finishing with D, that if a compass be placed between divided iron, such as in a hatchway or a skylight, the contrary effect to what has been said will be pro- duced, -j-D becoming — D, and so on ; but this, also, is a rare case, as no one would be so foolish as to place a compass in such posi- tions, for the reason that the iron, being divided, would act as two separate magnets. CoetHcient E represents the effect of horizontal iron when lying at an angle of forty-five degrees to the fore-and-aft line, or in other words, it is caused by the horizontal iron in the vicinity of the compass not being symmetrically distributed. +E is produced by iron extending from the starboard quarter to the port bow, and — E when the direction of the iron is from the port quarter to the starboard bow. If the compass were placed between divided iron, the sign of the coefficient would be changed as in the case of D. Coefficient E causes quadrantal deviation, and is greatest when the ship is heading North, South, East, and West, and is therefore contrary to D. -f E represents -f or Easterly deviation in the North and South quadrants, between N.E. and N.W. and S.E. and S.W., and — or Westerly deviation in the East or West quadrants; a — E coefficient is exactly opposite, as — or Westerly deviation, is found in the North and South quadrants, and -f- or Easterly in the E. or W. quadrants. Coefficient E is, as a rule, very small, and is closely allied to a real A coefficient. Compass Adjustment. 329 COMPUTATIOX OF THE COEFFICIENTS, OR ANALYZ- ING THE NATURAL DEVIATION OF A COMPASS. First swing the ship, steadying her head on every four points, and determining the natural deviations of the compass, by either Azimuths or Napier's diagram. Rule to find the value of coefficient A : Add together algebraically the deviations found when ship was heading on North, South, East, and West. This is done by first naming the Easterly deviations +, and Westerly deviations — ; then take the sum of the -|- signs and the sum of the — signs, subtract the smaller from the greater and di- vide by 4; the result will be the value of coefficient A, which must be named according to the name of the greater sum. Exatnple. [orth + 2° 40' South - 3° 20' l^est + 20° 50' + 23° 30' East -18° 10' -21° 30' -21° 30' 4)2° 00' Coefficient A + 0° 30' Coefficient B, reverse the sign of the deviation found when ship was heading West and add to it the deviation for ship's head East, divide the sum by 2. and the result will be the value of B, with the common sign prefixed to it. Example. West (with sign changed) +19° 20' East (sign not changed) +18 40 2)38~00 Coefficient B +19° 00' Coefficient C — This coefficient is found by adding together the deviations found when ship was heading North and South by com- pass, changing the sign of the deviation for South, and dividing the sum bv 2 : the result will be the value of C. 330 Taylor's Modern Navigation. Example. South (Avith name of deviation changed) +10° 10' North (with name not changed) +14 20 2)24~~30 Coefficient C +12° 15' Coefficient D— Note the deviations on N.E., S.W., S.E., and N.W. by compass, marking it + if Easterly and — if Westerly; change the signs of deviation on N.W. and S.E. and place + de- viations under each other and — deviations under each other; take the sum of the + signs and the sum of the — signs and subtract the sum of the one from the sum of the other, according to which is the greater sum, and divide the difference by 4; the result will be the value of D, to which must be given the sign of the greatest sum Example. N.W. (sign changed) +19° 30' S.E. (sign changed) -13° 20' N.E. +15 20 S.W. - 8 10 + 34 50 -21° 30' -21 30 4)13 20 Coefficient D + 3° 20' Coefficient E, note the deviations on North, South, East, and West by compass; change the sign of the last two, namely. East and West, and place the + signs under each other and the — signs under each other ; take the sum of the + and — signs separately, subtract the lesser sum from the greater and divide the difference by 4 ; the result will be the value of E, to which must be given the sign of the greater sum. Example. North - 5° 10' South +10° 30' West (sign changed) -12° 50' East (sign changed) +12°^0' -18°" 00' +22° 50' -18° 00' 4) 4° 50' Coefficient E+ 1° 12' Compass Adjustment. 331 COMPUTING THE VALUE OF EACH COEFFICIENT FOR EVERY POINT OF THE COMPASS. The first step is to draw a table in the same manner as that of the one attached to this article, making a column for each coeffi- cient and placing its value at the head of the column. A being a constant quantity for each point, its value and sign must be placed abreast of every point of the compass. B, having its greatest effect on East or West, must be entered at its full value in the table, abreast of those points, retaining its sign for East, but changing it for West. The value of this co- efficient is therefore greatest at East and West, but is zero at North and South. Rule to Compute B for Each Point. Convert the value of B into degrees and decimals by simply di- viding the minutes by 6. Example.— 20° 2^= 20.4. Enter Table 1 of Bowditch with the number of points from North or South by compass as a course, and the degrees and tenths as a distance ; the departure abreast will be the value of B, in tenths of a degree for the given number of points from North or South, and must be given the same sign as the coefficient in the Eastern semicircle, but a contrary sign for the Western semicircle. Example. — Given B-|-19° 50', required its value for S.S.W. B + 19° 50'-19.8 } J. -t;e -A, +u i S.S.W. = 2 points \ ^^P- '^■^='^ ^^"^^'' '"'^'^y- This 76 equals 7°. 6, or— 7° 36'. the value of B for S.S.W. C has its largest value at North and South, and zero at East and West; therefore place the full value of C with its proper sign abreast of North, and the same value abreast of South, but with the sign reversed. Rule to Compute C for Each I'oint. Enter Traverse Table with the number of points from either North or South as a course, and with the degrees and tenths of degrees of the value of C as a distance, and take therefrom the difference of latitude corresponding thereto. This difference of latitude will be the value of C, in tenths of degrees for the given number of points from North or South. 332 Taylor's Modern Navigation. Example. — Given +C 8° 45', required its value for N.X^. + C 8° 45' =8. D. lat. 85.3 = 85 tenths N.XE. =1 point 85 tenths equals 8.5, or +8" 30', the value of C for N.XE. D is the greatest on the quadrantal points, so place the entire amount on N.E., S.E., S.W., and N.W., marking them + in the X.E. and S.W. quadrant.-; and — in the S.E. and N.W. quadrants, and its value on the other points is computed by the following rule : Bvle. Eeduce coefficient D to tenths of degrees as before, and enter the Traverse Table with TWICE the number of points from either North or South as a course, and with degrees and tenths as dis- tance, take out the departure; the result will be the number of tenths of degrees for the given angle. Example. — Given +D 7° 6', required the value for N.N.W. N.N.W. = 2t)SnCx2 = rpoints | ^^^P' ^^-^^SO tenths 50 tenths equals--5° 0', the value of D for N.N.W. E is greatest on North, South, East, and West; therefore place the full amount abreast of those points. Its value on the others IS calculated by the following rule : Bule. Enter Traverse Table with TWICE the number of points, as in D, but take the difference of latitude as the value of E for the given angle. Example. — Given — E 1° 10', required the value for S.S.E. ^-i-H<:DcqCi^_cOi— iCii>.cD^co-^Oo:)COi>-coic i-HCJQOt^i>^cocdicicidid':^^'-^^'-^-rj<'-T^'cococococo .55 C<10CiC01>-I>'CDCDCDiC'>OiOiO»0'^"^-^-^-^-^"^ cOi— iOOiGor^t^t^i:D':o<:oiciC^id^io-^-^-^-^'-^'"^ c^^Or^oo^cooc.cooii>;'^_c-(:D^CNi--HOcci:^cq |:DOvo-^as(^^cc>C5oo(M^cot^-^co■rt^cDOicoolLOc^^o cn^ioc^coo^cor-^c^jooiOfNGicyD^c^jOcocoiococq-rHO idc6TH'ooioicoGOt-^i>^i>^cDcd<:c>cDi:Did»dididid>did 1— I T-H T— ( 1— I OCDT-iT-iO0iai00iO<:0(MC-t^t^t>-C0C£)C0<:DCDC0iCiO ^ OicO'^COfNi-iOOOlCnjCOOOGOC^t^t^t-CDCDcDCDCDCD cqcC!CDTt<-<+icococDcot^t^T-icooOT-i<:DCO(MT— ico^coco lOCOC005QOa5(M^DT-l;^COi-HO:5l>;»0^ o^-^ldc6(^^^-^T-^oooioicoodo6GO^^I>^t--•*^-^cD<:ccDcD (Mi-tTHTHrHTHT-lrHi-l OOcOOOOOCMC^J^OCOOO-^OOfMCDCNOOOC^"^ 00C0O"^(MC0i0G0C^t--'*05iCC^0^i:DC0THail-;iOC0rH c<^ai^>^ld-^c6c• (M,-t,-l-rHT-(,-l-r-(l-lTH-r-lT-l W" Compass Adjustment. 341 If the preceding instructions in regard to adjusting are strictly carried out, the navigator will make a successful adjuster; but if there is an attempt on his part to appear smart, by swinging the ship and adjusting in a very short space of time, he will eventually find that the adjustment made, or remaining errors determined so hurriedly, will be far from l)eing correct, owing to what is termed Retentive Magnetism. RETENTIVE MAGNETISM is caused by the inductive force of tlie earth acting on the hull of the ship, when she has been on one course for any length of time. Its amount depends on t"he length of time an iron vessel has been on a course and the force of the waves striking the ship. It is a very variable quantity, and its value is impossible to determine, no matter how much scientific knowledge the adjuster may possess. The effect on a compass is always a tendency towards the last course the ship was steering. To illustrate retentive magnetism I will give a case: The author was adjusting the compasses of a very large iron steamer. She was the modem type of tramp, having iron decks and houses, the bridge-deck being the only part of the vessel built of wood. After making the adjustment on North correctly, it was neces- sary to turn the ship's head South. On this being done, an ap- parent error of nearly one point was detected, which caused the ofiicers to east smiling glances in the direction of the adjuster. Noticing this, the master was requested to place one of his best officers at the Pelorus to take Azimuths, but at the same time to keep the vessel heading South by the compass. This was done, and twenty minutes afterwards the compass was found to indicate South magnetic, without touching the magnet that had been placed to adjust on North, much to the surprise of the officers. This was an extreme case of retentive magnetism, and is an ex- cellent illustration of the bad policy of performing the hurry-up jobs one sees so frequently. The lesson to be learned by the foregoing is, that a vessel should be steadied on a course for at least fifteen minutes before an obser- vation is taken to determine the deviation, and twenty minutes when adjusting. 342 Tayloe's Modern Navigation. FURTHER INFORMATION IN REGARD TO THE FLINDERS BAR. A Flinders Bar is a bar of iron from two and a half to four inches in diameter and about two feet long. This bar is first cut in two pieces, then one of the pieces is again cut in two, and yet again one of these pieces is cut in two ; this is done until the small- est piece is about one inch in length. These pieces are placed in the vertical bra^'s tube attached to the outside of a modern binnacle when adjusting the semicircular deviation caused by vertical iron. As before remarked, the magnetism contained in vertical iron depends for its strength on the dip of the locality. Now, if the ship is on the magnetic equator there will be no dip, and consequently no magnetism in vertical iron. This is very important, as any deviation found on an East or West course when ship is on the magnetic equator must be caused solely by the subpermanent mag- netism in the vessel's hull. Knowing this, and supposing the com- pass to be adjusted on East or West by a permanent magnet while the ship is on the magnetic equator, it stands to reason that any deviation subsequently found on East or West after leaving the magnetic equator must be due solely to vertical iron. Therefore, after changing the magnetic latitude about twenty or tliirty de- grees, place ship's head on East or West magnetic and compensate all the error found, by means of the Flinders bar, on the principle that "like cures like." If this is carefully done, the compass will have but a very small error in any latitude. Fig. 12 is to illustrate the effect of vertical iron. The compass being placed between the two smoke-stacks and equi-distant from both, the effect of one on the compass will be counterbalanced by the other, and as the intensity of the magnetism in one smoke-stack changes, so it does in the other, the result being that neither of them has any effect on the compass. Again, supposing the ship to be in a South magnetic latitude. Here the lower ends of both smoke-stacks would be blue and the upper ends red, the balance of power always being maintained, no m.atter what latitude the ship may be in. This is the principle of the Flinders Bar adjustment, and with- out this method of compensation tlie deviation will continually change as the ship alters her magnetic latitude. Compass Adjustment. 343 RULE TO FIND THE DIRECTION OF THE SHIP'S HEAD WHEN BUILT. This rule is of value only when ship is on the magnetic equator, as at that time vertical iron has no effect. The value of the Subpermanent B and C must be known. Rule. Enter the Traverse Table with the value of B as difference of latitude and C as departure (in the same manner as finding the course by inspection in the Day's Work) and take out the course corresponding thereto; the result will be the approximate direc- tion of the ship's head when building, to be named Xorth if B is — , but South if -|-, and towards the East if C is -|- and towards the West if — . THE HEELING ERROR. The preceding part anent the compensation of the compass er- rors relates exclusively to conditions when ship is perfectly upright, but as the ship heels (by the pressure of the wind or trimming of cargo, etc.), another disturbance of the compass-needle occurs, but from two separate causes. In the compensations previously described, horizontal force only was taken into consideration, whereas in the case of the heeling error vertical force must be considered. This vertical force arises from the change in the action of the subpermanent magnetism acquired when building, and the change in the character of horizontal iron, owing to the horizontal iron assuming a more or lesy vertical position by the vessel heeling. The effect on the compass-needle produced by the heeling of the vessel depends upon the position of the subpermanent poles in the vessel's hull and the amount of heel. The amount of heeling error caused by this subpermanent mag- netism will depend upon the degree of heel and the angle the com- pass-needle makes with the ship's line of force. The effect on a compass-needle produced by the horizontal iron assuming a more or less vertical position, through the vessel heel- ing, will depend upon the magnetic latitude, or dip, in much the same manner as the effect of vertical iron, already explained. The amount of heeling error produced by the horizontal iron, such as beams, now assuming a vertical position, will depend : 1. On 344 Taylor's Modern Navigation. the degree of heel. 2. On the angle the compass-needle makes with the athwartship iron; and 3. On the magnetic latitude of the ship. The combined effect of these forces acts somewhat different, a> the disturbing power of the vessel's beams varies, whereas the sub- permanent is practically constant. The most common effect, for a vessel built and navigated in jSJorth latitude, is to attract the North end of the needle towards the highest side of ship ; but this is not always the case, as some- times the subpermanent may be stronger than the transient power in the beams, and may cause a deflection of the needles to the low side of ship. By referring to the colored diagram it will be seen that with the ship's head North the whole of the upper part of the stern is blue, and that the vertical force is acting downwards, the contrary effect for Sonth, and by referring to some of the others it will be seen that blue magnetism is nearer to the compass, while in others the red is nearest. Vertical iron also has an effect, but it is generally very small, and in practice may be considered a part of the others. Fig. 13 — ^Tliis illustration represents a vessel in an upright posi- tion, with red polarity in the bottom and blue towards the deck; therefore, as ship is upright, there cannot be any heeling error. It will be noticed in this diagram that the spheres at the sides of ihe compass are colored blue on the top and red below; this is the same coloring as for vertical iron in North magnetic latitude. This may be determined by experiment if the student is curious, for by holding a sphere with its top part near the North end of a compass- needle, it will be found to attract the North, but if held so that its lower part be near the North end of a compass-needle, it will be found to repel a North, but if these spheres are held so that their centers lie in the same horizontal plane as the compass-needle, they have no effect on the compass when ship is heading on North, South, East, or West. The student must bear this in mind as he pro- -gresses. Fig. 14 — This illustration represents a vessel heeling to star- board with the blue magnetism brought (through ship's heeling) in to the same horizontal plane as the compass-needle. The error produced by the heeling in this case should be compensated by a vertical magnet placed directly under the center of the compass- card. Compass Adjustment. 345 Fig. 15 — This figure illustrates the effect of the iron beams when ship is heeling in North magnetic latitude. P, port side; S, starboard side; F, looking forward; C B, com- pass-bowl; M, magnet; V F, vertical force. Here the vessel is heeling to port, therefore red magnetism is found in the port ends of the beams, because it is nearest to the North magnetic pole, and blue in the starboard ends because it is highest and therefore farthest from the North magnetic pole. V F, being blue, would have the effect of attracting a North end of a compass-needle downwards, and the blue end of beams being on the starboard side, their effect would be to attract the North end of a needle to that side. Now, by looking carefully at the coloring of the two balls it will be noticed that the top part of the compass- bowl is in line with both the lower or red part of the starboard ball, and upper or blue part of the port ball. It will, therefore, be seen that the blue part of the port ball will attract, and the red part of the starboard ball will repel, the North end of a compass-needle, thereby overcoming to a great extent the attraction of the starboard ends of the beams. The magnet M with the red end up will also tend to reduce the heeling error. This magnet is generally placed in a small brass tube situated in the binnacle, directly under the center of the card, and which may be raised or lowered at pleasure by the adjuster. Fig. 16 shows the vessel upright, therefore no heeling error, but the magnet M would be used to counteract V F. Fig. 17 shows a vessel heeling to starboard. The effect of the beams is to draw the North end of needle to port side. This is, however, partially compensated by the two balls at the sides of the compass, and remainder being compensated by the vertical magnet M. It will, therefore, be noticed that the quadrantal correctors are not only used to compensate the quadrantal deviation but materially as'sist in reducing the heeling error. The Heeling Adjustment. The old-fashioned idea was to heel the vessel about ten degrees to port or starboard and then make the adjustment. This method is obsolete, owing to the great expense entailed in listing a vessel, by shifting cargo, etc. The modern method of doing it is much more convenient and less expensive to the owners. 346 Taylor's Modern Xavigatiox. EULE. Procure a small dipping-needle or meridian-finder with a spirit- level attachment. Take this needle on shore to some place where it will be free from local attraction, bed it up level, and carefully note the readings; now take this needle on board of the ship, remove the compass-bowl to a good distance, and place the dipping-needle in the binnacle- stand, bedding it up until its stand is level and the center of the dipping-needle is in the same plane that the compass-needle oc- cupies when it is in its proper place. Next place the proper magnet in the vertical tube and raise or lower it until the dipping-needle gives the same reading as it had on shore ; then remove the dipping-needle and replace the compass- bowl; the adjustment is then finished. In the matter of placing the magnet, it may not be too much to state that it is impossible to place the magnet with the wrong end up, for by so doing it would be impossible to make the dipping- needle read the same as on shore. Value of Heeling Adjustment. It will be noticed by referring to diagrams 15 and 17 that the North end of a needle will be attracted sometimes to the port and sometimes to the starboard side. Now, suppose that a vessel is steering on a North course, so that the needle would be at right angles to the beams, and that she is rolling in a seaway, the effect would be to alternately attract the needle to the port and star- board sides ; this would set up a swinging motion of the card, mak- ing it very difficult for the helmsman to steer a good course, but if the heeling error is compensated by the iron spheres and vertical magnet, the rolling of the ship will be partially counteracted, the result being a comparatively steady card in all kinds of weather. From what has been said the value of the heeling compensation will be understood, but the navigator should bear in mind tliat the adjustment is good only for the latitude wherein it was made, and that, no matter how accurately the compass has been compensated, the deviation is liable to alteration at any time ; therefore, he should test the compass by amplitudes and azimuths whenever possible, re- membering always that eternal vigilance is the price of safety. . Compass Adjustment. [ "' - ^, 347 Fig. 18 — The object of this illustration is to show^a good arrange- ment for a steamer's bridge. It will be noticed by thKeolorifag of the vertical iron that the sliip is in North magnetic latitude. The Flinders Bar is shown on the fore part of the binnacle, to counteract the effect of the vertical iron abaft the compass. The shafts leading from the steering-wheels to the steering-engine are made of brass as far down as the under side of the main deck, after which the shafting is of steel. It will be noticed that the wheel-house compass is considerably forward of the upper or standard compass; this is as it should be, for the reason that the needle of one compass will be influenced by the needle of another if the compasses are placed too close together. The ventilator placed on the fore part of the bridge, with its upper part colored blue, is supposed to be iron; this is bad, because the turning of the cowl will produce a variable compass error. This iron ventilator should be removed and a brass or copper one should replace it. The iron travelers and bands on the fore boom are also very bad, as they produce a very variable compass error ; the amount of devia- tion caused thereby will depend upon the position of the boom and the direction of the ship's head. The traveler will not always be blue, for the reasons explained in the description of horizontal iron, when held end on to the compass. Brass travelers and bands should be substituted for iron ones in this case. With the two exceptions given, namely, the iron travelers and ventilator, the arrangement of the bridge is the best possible for a modern steamer. Table for Working Johnson's Method. LATITUDE. 10 12 14 o 1 8 10 12 14 16 18 20 22 24 26 28 30 32 a I -00 roi I -02 I -02 I -03 4-85 4-12 I -04 1-05 I -06 i-o8 1-09 i-ii I-I3 115 i-i8 I s'67 471 4-OI 570 47Z 4 -02 573 475 4-04 576 478 406 5-79 4-8i 4-09 ill 4- 16 5-97 495 4-20 6-03 S-oi 4-26 6-12 S-o8 4-32 6-'2I 5-,6 4-38 6-30 5-28 4-46 6-^2 5-34 4-54 6-5S 5-43 4-63 6-69 5-55 473 6 5 4 16 18 20 3 '49 3 -08 2-75 3-50 3-09 276 3-52 1)1 3-54 313 279 3-56 315 2-8i 359 318 2-83 3-62 3-20 2-86 3-66 3-24 2-89 3-70 3-28 2-92 376 3-32 2-96 3-82 3-37 3-01 3-88 3-43 3-06 3-94 3-49 3-12 4-02 3-55 3-17 4-11 3-63 3-24 4 3 3 22 24 26 2-47 2-25 2-05 2-47 2-26 2-05 2-48 2-27 2-07 2-SO 2-28 2-o8 2-52 2-30 ^•10 2-54 2-32 2- 1 1 2-57 2-34 2-13 2-6o 2-37 2-15 2-63 2-39 2-18 2-66 2-43 2*21 2-70 2-46 2-24 2-75 2-50 2-28 2-80 2-55 2-32 2-86 2-59 2-37 2-92 2-65 2-42 2 2 2 28 30 32 1-88 173 I -60 1-83 173 I -60 1-90 1-91 176 163 1-92 177 1-64 1-94 1-78 1-65 1-96 1-80 1-66 1-68 2-00 1-84 1-70 2-03 1-87 1-73 2-06 1-89 175 2-09 1-92 1-78 2-13 1-96 I-8I 2-17 2-00 1-85 2*22 2-04 .-89 2 ■ 34 36 38 1-48 .•38 1-28 1-48 1-38 1-28 1-49 1-50 1-40 1-29 1-51 1-41 1-30 1-53 1-42 1-31 '•54 1-44 1-32 1-56 '•45 1-34 1-57 I "47 1-35 I -60 1-49 1-37 I-$2 1-5* 1-39 1-65 1-53 141 1-68 155 1-44 171 1-59 h-48 1-51 40 42 44 1-19 rii 1-04 1-19 I'll I -04 1-20 1"I2 I -04 1-21 113 1-05 1-22 114 1-06 1-23 I-I4 1-07 1-24 1-15 1-08 1-25 1-17 1-09 1-27 1-18 i-io 1-28 I-20 I-I2 1-30 1-22 113 1-32 1-24 VIS 1-35 1-26 117 1-28 I-20 1-41 .1-31 1-22 46 48 50 0-97 0*90 0-84 o-^7 0-90 0-84 0-98 085 098 0-91 085 0-99 0-92 0-86 i-oc 0-93 0-87 I 01 0-94 087 1-02 0-95 0-88 1-03 0-96 0-89 1-04 0-97 0-91 1-06 0-99 0-92 1-07 i-oo 0-93 1-09 I -02 0-95 I-Il 1-04 0--97 I-I4 I -06 0-99 52 54 56 078 073 o'bj 0-78 073 o'bj 079 073 0-68 079 074 068 0-80 C-74 0-69 0-80 075 0-69 0-81 0-75 6-70 0-82 0-76 0-71 0-83 0-77 0-71 0-84 C-78 0-72 o-8s 0-79 073 0-87 0-81 0-75 0-88 0-82 0-77 0-90 0-84 0-78 0-92 0-86 0-79 58 60 62 0-63 0-58 0-53 o'63 0-58 o'53 0^63 0-59 0-54 063 059 .0-54 0*64 0-59 0-54 0-64 o-6o 0-55 0-65 0-60 0-55 0-66 0-61 0-56 0-66 0-62 0-56 0-67 0-62 0-57 0-68 0-63 0-58 0-69 0-65 0-59- 0-71 0-66 0-60 0-72 0-67 0-61 0-74 0-68 0-63 c 64 66 68 0-49 0-45 0-40 049 0-45 0-40 0-50 0-45 0-40 0-50 0-4S 0-41 0-50 0-46 0-41 0-51 0-46 0-41 0-51 0-46 0-42 0-52 0-47 0-42 0-52 0-47 0-43 0-53 048 0-43 0-S4 0-49 0-44 o-ss 0-50 0-45 0-56 0-50 0-45 0-56 0-51 0-47 0-57 0-52 0-47 70 72 74 0-36 0-33 0'29 0-36 0-33 0*29 0*36 0-33 0-29 0-37 0-33 029 0-37 0-34 0-30 0-37 0-34 0*30 0-37 0-34 0-30 0-38 0-34 0-31 0-38 0-3S 0-31 0-39 0-35 0-31 0-39 0-36 0-32 0-40 0-36 0-32 0-41 0-37 0-33 0-42 0-37 0-33 0-43 038 0-34 76 78 80 0-25 0-2I o-i8 0-25 0-21 o-i8 0-25 0-2I o-i8 0-2 5 0-2I o-i8 0-25 0-21 018 0-26 0-22 o-i8 0-27 0-22 o-i8 0-27 0-22 0-18 0-27 0-22 019 0-27 0-23 0-19 0-27 0-23 019 0-28 0-23 0-20 0-28 0-23 0-20 0-29 0-24 0-20 0-29 0-25 0-21 82 84 86 0-14 o-io 0*07 0-I4 o-io o"07 0-14 o-io 0-07 0-14 o-io 0-07 0-I4 O-IO 0-07 0-14 O-IO 0-07 0-I4 o-ii 0-07 o-is o-ii 0-07 o-is o-ii 0-07 0-15 O-II 0-08 0-15 O-II 0-08 0-15 0*11 o-o8 O-IS o-ii 0-08 0-16 0-12 0-08 0-17 0-12 0-08 88 89 0*03 o-oi 0-03 o-oi 0-03 O-OI 0-04 O-OI 0-04 001 0-04 O-OI 004 O-OI 0-04 0-01 0-04 O'OI 0-04 O-OI 0-04 001 0-04 O-OI 0-04 O-OI 0-04 O-OI 0-04 001 90 O'OO 0*00 O'OO 0-00 000 o-co o-oo o-oo 0-00 000 0-00 0-00 0-00 O'OO OOD o-oo 0-07 0'I4 18 0-2I 0-25 0-29 0-33 0-36 0-40 0-45 0*49 0-53 0-58 0-63 This table is taken from Johnson's Latitude and Longitude in Cloudy Weather, published by J. D. P^ 145 Mlnorles, London, E., and is printed here by the express permission of the author, Mr. A. C. Johnso Table for WouKiNf; Johnson's Method LATITUDE. ■i « "^ 12 14 34 36 38 40 42 44 46 48 50 52 54 56 58 60 a ye? 471 4-01 121 6-84 567 4-84 I -24 7-01 S-8i 4-95 1-^7 1-31 1-35 6-33 5-40 1-39 7-88 6-S4 5-S« 1-44 8 -'16 677 577 1-49 7-03 5-99 1-56 8-82 7-32 6-24 1 62 1-70 179 i-i>9 2 00 7-20 5-97 5 09 7-40 6-14 5-23 9-21 7 '64 6-5. 9-65 8-00 6-82 / 10-14 8-41 7-17 / 10-70 8-88 7-57 / 11-33 9-41 8 02 16 18 20 3'49 3-o8 275 4-2 1 371 3-31 4-31 3-8o 3-39 4-43 3-90 3 '49 4"55 4-02 3*59 4-69 414 370 4-85 4-28 382 5-02 4-43 3 95 5-21 4-6o 411 5-42 479 4-27 5-66 5-00 4-46 5'93 4-67 6-24 5' 50 4-91 6-58 5-8i 5-19 6-97 6-15 5-49 22 24 26 2'-47 2-25 2 '05 2-98 171 2:47 3-o6 277 ^'53 2-6o 3-23 I'll 333 302 2-76 3 "44 3-12 2-85. 3-56 3-23 295 3 -70 3-36 3-06 3-85 3-49 3-19 4-02 3-6S- 3'33 4-21 3-82 3-49 4-43 4-02 3-66 4-67 4-24 3-87 495 4-49 4-10 28 30 32 1-88 173 I -60 2-27 209 1-93 2-32 214 1-98 2-39 2 -20 2-03 2-09 2-53 2-33 2-15 261 2-41 2-22 2-71 2-49 2-30 2-8i 260 2-39 2-92 2-69 2-49 3 -OS 2-8i 2-6o 3-20 295 2-72 3-36 3-10 2-86 3'55 3-27 3-02 376 346 3-20 34 36 38 1-48 138 1-28 179 1-66 '•54 1-83 170 1*58 1-88 174 I 62 I'll 167 1-99 1-85 1-72 2-06 1-91 178 2-13 ,•98 1-84 2:22 2-06 I-9I 2-31 2-14 1-99 2-41 2-24 2 -08 2-52 2'34 2-.8 2-46 2-29 2-80 2-6o 2-41 2-96 275 2-56 40 42 44 i-ig III I -04 1-44 1-34 1-25 I '47 1-37 1-28 1-51 1. 41 1-31 1-55 1-45 >-35 I 60 I 49 139 >-66 '•54 1-44 1-72 I -60 1-49 178 1-66 '■55 1-85 1-94 1-80 1-68 2-03 2-13 2-25 2-09 '•95 2-38 2-22 2-07 46 48 50 0-97 0-90 0-84 ri6 1-09 roi 1-19 III 1-04 1-23 1-14 I -06 1-26 I-I7 1-09 1-30 I -21 i"i3 1-34 '•39 1-30 1-21 1-44 '■35 1-25 1-50 1-40 1-31 1-56 1-46 .•36 1-64 ■•53 I 43 1-50 1-82 1-70 1-58 III 1-68 52 54 56 078 073 0-67 0-94 0-88 o-8i 0-96 0-99 0-92 0-85 I -01 0-95 0-88 I -OS 0-98 0-91 1-09 l-oi 0-94 I '12 I -04 0-97 I-I7 1-09 i-oi 1-22 I-I3 ro5 1-27 ri8 IIO '•33 123 I-I5 1-40 1-30 I-2I '•47 1-37 1-27 1-56 '•45 '•35 58 60 62 0-63 0-58 0-53 075 070 0-64 077 071 0-66 079 073 0-67 081 075 0-69 0-84 0-78 0-72 0-87 o-8o 074 0-90 0-83 0-70 0-93 0-86 079 0-97 0-90 0-83 I-OI 0-94 0-86 I -06 0-98 0-90 1*12 1-03 0-95 i-i8 1-09 I 00 1-25 1-15 1-06 64 66 68 0-49 045 0-40 0-59 0-54 0-49 o-6o o'55 0-50 0'62 0-56 0-51 0-64 0-58 0-53 0-66 o-6o 0-54 0-68 0-62 0-56 0-70 0-64 0-58 073 0-66 0-60 0-76 0-69 0-63 0-79 0-72 0-65 0-83 076 0-69 0-87 0-79 0-72 0-92 0-84 0-76 0-97 0-89 081 70 72 74 0-36 0-33 0-29 0-44 o"39 0-34 0-45 0-40 0-36 0-46 0-41 0*36 0*47 0-42 0-37 0-49 0-44 0-38 0-51 0-45 0-40 0-52 0-47 0-41 0-S4 c-49 0-43 0-57 0-51 0-44 0-59 0-53 0-46 0-62 o*55 0-49 0-65 0-58 0-52 0-68 0-61 0-54 0-73 0-65 0-5: 76 78 80 0-25 0-21 o-i"8 0*30 0-25 C-2I 0-31 0'26 0"22 0-31 0-27 0-22 0-32 0-28 0-23 0-33 0-29 0-24 0-34 0-29 0-24 0-36 0-30 0-25 0-37 0-32 0-26 0-39 0-33 0-27 0*40 0-34 0-29 0-42 0-36 0-30 0-45 0-38 0-31 0-47 0-40 0-33 0-50 0-42 0-35 82 84 86 0-14 10 0-07 0-17 0*13 o'o8 0-I7 0-I3 o-o8 o-i8 0-I3 0-09 o-i8 0-14 0*09 c-19 0-14 0-09 0-19 0-14 o-io 0-20 o'i5 o-jo 0-2I o-i6 o-io 0-22 o-j6 o-ii 0-23 C-17 o-ii 0-24 0-18 0-12 0-25 0-19 012 0*26 0-20 0-13 0-28 0'2I 014 88 89 0-03 O'OI 0*04 O'OI 0-04 o-oi 0-04 O-OI 0^04 O'OI 0-05 O'OI 0-05 O-OI 0-05 0-0 I 0-C5 0-02 0-05 0-02 0-06 0-C2 c-06 0-02 006 002 0-07 0-02 0-07 0-02 90 00 O'OO o-oo o-oo O'OO o-oo 0-oc 0-97 o-oo 1-04 o-oo o-oo O-OO 0-00 0-00 o-oo 0-00 o-oo 067 073 0-78 0-84 0-90 ril I-I9 1-28 — 1-48 1 60 173 This table is taken from Johnsons Latitude and Longitude tn Cloudy Weather, published by J. D. Potter, 145 Minories, London, E., and is printed here by the express permission of the author, Mr. A. C. Johnson. Table to Correct the Observed Altitude of the Sun' (For Practice at Sea.) Lower Limb. 1 Obs. Alt. UEIOUT OF THE EYE ABOVE THE BEA IH FEET. 6 H 10 12 1 14 16 18 ; 20 22 ( 24 26 1 28 30 1 32 34 36 5 3.8 3.5 / 3.1 ' i ' 2.8 2.5 2.3 2.1 1.8 1.6 1.4 1.2 1.0 0.8' 0.6 0.5 0.3 6 20 4.3 4.0 3.6 3.3! 3.1 2.8 2.6 2.3 2.1 1.9 1.7 1.6 1.3 1.1 l.O 0.8 5 40 4.8 4.5 4.1 3.8 3.5 3.3 3.1 2.8 2.6 2.4 2.2 2.0 1.8 l.b 1.5 1.3 6 5.3 4.9 4.6 4.3 4.0 3.7 3.5 3.3 3.0 2.8 2.6 2.4 2.2 2.1 1.9 1.7 6 20 5.7 5.4 5.0 4.7 4.4 4. 1 3.9' 3.7 3.3 3.2 3.0 2.8 2.6 2.5 2.3 2.0 C 40 6.0 5.7 5.3 5.0 4.7 4.6 4.3 4.0 3.8 3.6 3.4 3.2 3.0 2.8 2.7 2.3 7 6.4 6.0 5.7 6.4! 5.1 4.8 4.6 4.4 4.1 3.9 3.7 3.5 3.3 3.2 3.0 2.7 • 7 20 6.7 6.31 6.0 5.7 5.4 6.1 4.9 4.7 4.4 4.2 4.0 3.8 3.6 3.5 3.3 3.1 7 40 6.9 6.6, 6.2 5.9 5.7 5.4 6.2 4.9 4.7 4.5 4.31 4.1 3.9 3.8 3.6 3.4 8 7.2 6.8j 6.5 6.2 6.9 6.7 6.4 5.3 5.0 4.8 4.6 4.4 4.2 4.0 3.9 3.7 8 20 7.5 7.11 6.7 6.5 6.2 5.9 6.7 5.5 6.2 5 4.81 4.6 4.4 4.3 4.1 3.9 8 40 7.7 7-3! 7.0 6.7 6.4 6.1 5.9 5.7 5.5 5.2 5.01 *-8 4.7 4.5 4.3 4.1 9 7.9 7.5 7.2 6.9 6.6 6.4 6.1 6.9 5.7 5.5 6.31 5.1 4.9 4.7 4.5 4.4 9 20 8.1 7.7 7-4 7.1 6.8 6.6 6.3 6.1 5.9 5.7 5.5 5.3 5.1 4.9 4.7 4.6 9 401 8.3 7.9 7.6 7.3: 7.0 6.7 6.6 6.3 6.1 5.8 5.6 5.4 5.3 5.1 4.9 4.7 10 8.5 8.1 7.8 7.5| 7.2 6.9 C.7 6.5 6.2 6.0 6.8 5.6 5.4 5.3 6.1 4.9 10 30| 8.7 11 0, 8.9 8.3 8.0 7.71 7.4 7.2 6.9 6.7 6.5 6.3 6.1 6.9 5.7 5.5 5.4 6.2 8.6 8.2 7.9 7.6 7.4 7.2 6.9 6.7 6.5 6.3i G.l 5.9 5.7 5.6 5.4 11 30, 9.1 8.8 8.4 8.1 7.8 7.6 7.4 7.1 6.9 6-7 6.5 6.3 6.1 5.9 5.8 6.6 12 9.3 9.0 8.7 o.a 8.0 7.8 7.6 7.3 7.1 6.9 6.7 6.5 6.3 6.2 6.0 5.8 13 9.6 9.3 9.0 8.7 8.4 8.1 7.9 7.7 7.4 7.2 7.0 6.8 6.6 6.5 6.3 6.1 14 O! 9.9 9:6 9.2 8.9 8.7 8.4 8.2 7.9 7.7 7.5 7.31 7.1 6.0 6.3 6.6 6.4 15 10.2 9.8 9.5 9.2 &9 C.7 8.4 8.2 8.0 7-8 7.6 7.4 7.2 7.0 6.9 6.7 IG 10.4 10.1 9.7 9.4 9.1 8.9 8.7 8.4 8.2 8.0 7.8 7.6 7.4 7.2 7.1 6.9 17 oio.cib.s 9.9 9.6 9.3 9.1 8.9 8.6 8.3 8.2 8.0 7.8 7.6 7.4 7.3 7.1 18 O!l0.810.4 10.1 9.8 9.5 9.3 9.0 8.8 8.6 8.4 8.2 8.0 7.8 7.6 7.6 7.3 19 0,11.010.6,10.3 10.0 9.7 9.4 9.2 9.0 8.8 8.5 8.3 8.1 8.0 7.8 7.6 7.4 20 Oill. 110.710.4 10.1 9.8 9.6 9.3 9.1 8.9 8.7 8.5 8.2 8.1 7.9 7.7 7.6 21 0'U.'2!l0.9:i0.510.2l0.O 9.7 9.5 9.2 9.0 8.8 8.6 8.4 8.2 8.1 7.9 7.7 22 0;11.4;il.0|10.7|10.4,10.1 9.8 9.6 9.4 9.1 8.9 8.7 8.5 8.3 8.2 8.0 7.8 23 11.511.110.810.510.2 9.9 9.7 9.6 9.2 9.0 8.8 8.6 8.4 8.3 8.1 7.9 24 11.611.210.910.6:10.3 10.0 9.8 9.6 9.3 9.1 8.9 8.7 8.5 8.4 8.2 8.0 25 11.711.3:11.010. 7|10.4 10.1 9.9 9.7 9.4 9.2 9.0 8.8 8.6 8.5 8.3 8.1 26 11. 7[11. 411. 010.710.5 10.2,10.0 9.7 9.5 9.3 9.1 8.9 8.7 8.6 8.4 8.2 27 11.8 1'.. Sin. l!l0.8il0.5 10.3110.1 9.8 9.6 9.4 9.2 9.0 8.8 8.6 8.6 8.3 28 11. 911. 6111. 2110.910.6 10.4!l0.2 9.9 9.7 9.5 9.3 9.1 8.9 8.7 8.6 8.4 30 12. 11.7111.311.0 10. 8|10. 510. 3il0. 9.8 9.6 9.4 9.2 9.0 8.9 8.7 8.5 32 12. 2 11.8111.5:11.2 10. 9110.6:10.4110. 2 9.9 9.7 9.5 9.3 9.1 9.0 8.8 8.6 34 12.3111.911.6111.311.0 10.710.510.3 IO.8IO.61IO.4 10.1 9.9 9.6 9.4 9.2 9.1 8.9 8.7 36 12.4;i2.0lll.7 11.4 11.1 10.2 9.9 9.7 9.6 9.3 9.2 9.0 8.8 38 I2.5I12.I 11.8 11.511.2 10.910.710.5 10.2 10.0 9.8 9.6 9.4 9.3 9.1 8.9 40 12.5 12.2 11.8 11.6111.3 11.010.8|l0.5 10:8 10.1 9.9 9.7 9.5 9.4 9.2 9.0 42 12.612.2 11.9 11.611.3 11.1 10.810.6 10.4 10.2 10.0 9.8 9.6 9.4 9.3 9.1 44 12.7,12.3 12.0 11.7 11.4 U.l 10.910.7 10.5 10.2 10.1 9»8 9.7 9.5 9.3 9.1 46 12.7112.4 12.0 11.7 11.6 11.2 11.0 10.7 10.5 10.3 10.2 9.9 9.7 9.6 9.4 9.2 48 12.8:12.4 12.1 11.8 11.5 11.3 11.0 10.8 10.6 10.4 10.2 10. 9.9 9.6 9.5 9.3 50 12 8I2.5I12.2 11.9 11.6 11.3 11.1 10.9 10.6 10.4 10.3 10.0 9.8 9.7 9.5 9.3 52 12.9 12.5 12.2 11.9 11.6 11.4 11.1 10.9 10.7 10.6 10.3 10.1 9.9 9.7 9.6 9.4 64 13.0 12.6 12.3 12.0 11.7 11.4 11.2:11.0 10-7 10.5 10.3 10.1 10.0 9.8 9.6 9.4 56 13.0,12.6 12.3 12.0 11.7 11.5 11.2,11.0 10.8 10.6 10.4 10.2 10.0 9.8 9.7 9.6 58 I3.0I12.7 12.3 12.0 11.7 11.5 II.3I1I.O lO.R 10.6 10.4 IO.21IO.O 9.9 9.7 9.5 60 13.lll2.7!l2.4 12.1 11.8 11.611.311.1 10.9 10.6 10.4 10. 2' 10.1 9.9 9.7 9.5 62 OJl.S. 1 12.8,12.4 12.1:11. 8:11. will. 411. 1110.910.7 10.610.3110.1 9.9 9.8 9.6 64 ©13.2 12. 8112. 5 12.211.911.611.411.2,10.910.7 16.6 10.3 10.1 10.0 9.8 9.6 C6 o|ia.2 12.8 12.5 12.2'll. 911. 7!ll. 411.2111. 010.8 10.6 10.4fl0.2 10.0 9.8 9.7 70 13.3 12.912.6 12.312.0 11. H 11. 5;ll. 311. 0,10.8 10.6 IO.4IIO.2 10.1 9.9 9.7 80 13.4 13.1 12.7 12.4|12. 1I1I.9 11.7111.411.2111.0 10.8 10.61 10. 4 10.2 10.1 9.9 90 13.G 13.2!l2.9 12.612.3112.0 11.811.6,11.3111.1 10.9M0.7110.6 10.4 10.2|10.0| Month j Jan. 1 Feb. 1 .Mar. |April,| JVlayJ June, July, 1 j Correction! +0'.3|-|-0'.2J+0'.l| O'.O |-0'.2|-0'.2 -0.31- \\xg. Sept. 1 Oit. Nov. Dec. -0'.2 -O'll+O'.l +0.2 ^O-J NAUTICAL ALMANAC ELEMENTS FOR THE WORKING OF PROBLEMS CONTAINED IN THIS BOOK. JANUARY, 1894. AT GREENWICH APPARENT NOON. THE SUN'S 5 Sidereal Equation s. Semi- to be 5 diameter Added to o Apparent Diff. for Apparent Diff. for Semi- Passing Apparent Diff. for 1 Right Ascension. 1 Hour. Declination. 1 Hour. diameter. Meridian. Time. IHour. h m s s g m s s 1 18 48 22.70 11.040 S.22 59 21.9 12.76 16 18.36 71.05 3 52.72 1.180 6 19 10 22.88 10.957 22 28 10.2 18.41 16 18.28 70.77 6 9.73 1.097 7 19 14 45.60 10.936 22 20 35.2 19.51 16 18.25 70.70 6 35.82 1.076 13 19 40 50.20 10.788 21 25 59.3 25.91 16 18.00 70.24 9 0.68 0.928 14 19 45 8.77 10.759 21 15 24.9 26.93 16 17.94 70.15 9 22.63 0.900 15 19 49 26.65 10.731 21 4 26.2 27.94 16 17.88 70.05 9 43.89 0.871 16 19 53 43.82 10.701 20 53 3.4 28.95 16 17.81 69.96 10 4.45 0.842 17 19 58 0.28 10.671 20 41 16.8 29.94 16 17.74 69.87 10 24.29 0.812 22 20 19 11.32 10.512 19 36 38.7 34.65 16 17.29 69.35 11 52.30 0.654 26 20 35 54.22 10.381 18 38 22.8 38.14 16 16.82 68.92 12 48.83 0.523 27 20 40 2.98 10.348 18 22 57.1 38.98 16 16.69 68.80 13 0.98 0.490 28 20 44 10.92 10.315 18 7 11.5 39.81 16 16.55 68.69 1312.35 0.457 FEBBUAEY. 2 21 4 38.64 10.147 16 43 37.5 43.68 16 15.81 68.12 13 57.15 0.290 4 21 12 44.05 10.079 16 8 6.0 45.12 16 15.49 67.89 14 9.42 0.222 5 21 16 45.54 10.045 15 49 55.0 45,80 16 15.32 67.78 14 14.34 0.188 6 21 20 46.22 10.011 15 31 27.6 46.47 16 15.15 67.66 14 18.46 0.154 11 21 40 37.47 9.844 13 55 22.2 49.54 16 14.28 67.10 14 26.90 0.012 12 21 44 33.34 9.811 13 35 26.5 50.10 16 14.09 66.99 14 26.21 0.045 21 22 19 22.71 9.544 10 26 59.6 54.37 16 12.26 66.09 13 46.70 0.312 22 22 23 11.44 9.518 10 5 10.0 54.76 16 12.03 66.00 13 38.90 0.338 28 22 45 51.57 9.378 7 51 11.9 56.78 16 10.60 65.50 12 39.86 0.477 JANUARY, 1894. AT GREENWICH MEAN NOON. THE SUN'S J3 1 Equation of Time, Sidereal Time, ^ to be or 5 Subtracted Right Ascension o Apparent Diff. for Apparent Diff. for from Diff. for of 1 Right Ascension. 1 Hour. Declination. 1 Hour. Mean Time. 1 Hour. Mean Sun. h m s ' s m s s h m s 1 18 48 21.98 11.036 S. 22^59' 22.7 12'.'74 3 52.64 1.180 18 44 29.34 6 19 10 21.75 10.954 22 28 12.2 18.40 6 9.61 1.097 19 4 12.14 ^ / 19 14 44.39 10.933 22 20 37.4 19.50 6 35.70 1.076 19 8 8.69 18 19 40 48.58 10.786 21 26 3.2 25.90 9 0.54 0.928 19 31 48.04 14 19 45 7.09 10.757 21 15 29.2 26.92 9 22.49 0.900 19 35 44.60 15 19 49 24.91 10.728 21 4 30.8 27.93 9 43.75 0.871 19 39 41.16 IB 19 53 42.03 10.698 20 53 8.3 28.93 10 4.31 0.842 19 43 37.72 17 19 57 58.43 10.668 20 41 22.0 29.92 10 24.15 0.812 19 47 34.28 22 20 19 9.24 10.510 19 36 45.6 34.63 11 52.17 0.654 20 7 17.07 26 20 35 52.01 10.380 18 38 31.0 38.13 12 48.71 0.523 20 23 3.29 27 20 40 0.73 10.347 18 23 5.7 38.97 13 0.88 0.490 20 26 59.85 28 20 44 8.65 10.314 18 7 20.4 39.79 13 12.24 0.457 20 30 56.41 FEBEUARY. 2 21 4 36.28 10.147 16 43 47.7 43.67 13 57.09 0.290 20 50 39.19 4 21 12 41.68 10.079 16 8 16.7 45.11 14 9.37 0.223 20 58 32.31 5 21 16 43.16 10.045 15 50 5.9 45.79 14 14.30 0.189 21 2 28.86 6 21 20 43.84 10.011 15 31 38.8 46.46 14 18.42 0.155 21 6 25.42 11 21 40 35.10 9.844 13 55 34.2 49.53 14 26.91 0.012 21 26 8.20 12 21 44 30.98 9.811 13 35 38.6 50.09 14 26.23 0.045 21 30 4.75 21 22 19 20.52 9.545 10 27 12.1 54.37 13 46.77 0.312 22 5 33.75 22 22 23 9.28 9.519 10 5 22.5 54.76 13 38.98 0.338 22 9 30.30 28 22 45 49.59 9.379 7 51 24.0 56.79 12 39.96 0.477 22 33 9.63 MARCH, 1894. AT GREENWICH APPARENT NOON. ^ THE SUN'S o Sidereal Equation S Time of of Time, n Semi- to be diameter Added to o Apparent D iff. for Apparent jDiff.for Semi- Passing Apparent Diff.for O Right Ascension. 1 Hour. Declination. 1 Hour. diameter. Meridian. Time. 1 Hour. 3 h m s 22 57 4.55 9.318 S. 6°42'34.'l 57'.57 16 9.85 65!28 m s 12 3.28 0.537 4 23 47.94 9.299 6 19 29.6 57.80 16 9.60 65.22 11 50.16 0.556 5 23 4 30.90 9.281 5 56 19.6 58.02 16 9.34 65.15 11 36.59 0.574 10 23 22 59.62 9.201 3 59 24.9 58.82 16 8.06 64.87 10 22.75 0.654 11 23 26 40.28 9.187 3 35 51.8 58.93 16 7.81 64.83 10 6.89 0.668 16 23 44 59.04 9.129 1 37 37.4 59.24 16 6.51 64.64 8 43.12 0.725 17 23 48 38.03 9.121 1 13 55.5 59.25 16 6.24 64.61 8 25.61 0.734 18 23 52 16.83 9.113 50 13.2 59.26 16 5.98 64.59 8 7.90 0.742 19 23 55 55.45 9.106 26 31.2 59.24 16 5.71 64.56 7 50.01 0.749 20 23 59 33.91 9.099 S. 2 49.6 59.22 16 5.44 64.54 7 31.97 0.755 21 3 12.24 9.095 N. 2051.2 59.18 16 5.17 64.53 7 13.80 0.759 22 6 50.46 9.091 44 30.8 59.12 16 4.89 64.51 6 55.52 0.763 24 14 6.70 9.086 1 31 45.4 58.97 16 4.34 64.49 6 18.74 0.768 25 17 44.74 9.085 1 55 19.7 58.88 16 4.06 64.49 6 0.28 0.769 29 32 17.03 9.090 3 29 8.9 58.35 16 2.93 64.49 4 46.56 0.764 30 35 55.23 9 094 3 52 27.6 158.181 16 2.65 64.50 4 28.26 0.761 Equation of Time, to be APRIL. Added to Subtracted Apparent Time. 1 43 11.92 9.103 N. 4 38 52.0 57.81 16 2.08 64.53 3 51.94 0.752 2 46 50.45 9.108 5 1 57.1 57.60 16 1.80 64.55 3 33.96 0.746 7 1 5 5.56 9.146 6 55 56.1 56.30 16 0.42 64. (i8 2 6.54 0.708 8 1 8 45.18 9.156 7 18 24.0 56.00 16 0.15 64.71 1 49.65 0.699 14 1 30 48.30 1 34 29.88 9.225 9.239 9 30 21.9 9 51 50.1 53.87 53.47 15 15 58.56 58.30 64.97 65.03 13.71 0.630 15 1.23 0.616 25 2 11 47.24 9.417 13 16 38.2 48.71 15 55.72 65.65 2 9.06 0.438 27 2 19 20.28 9 460 13 55 10.4 47.61 15 55.22 65.79 2 29.08 0.395 28 2 23 7.58 9.482 14 14 6.2 47.04 15 54.97 65.86 2 38.31 0.373 30 2 30 43.81 9.528 14 51 15.9 45.86 15 54.47 66.01 2 55.15 0.328 MARCH, 1894. AT GREENWICH MEAN NOON. , THE SUN'S r Equation Sidereal ^ of Time, Time, ^ to be or z. Subtracted Right Ascension ~ Apparent Diff. for Apparent Diff. for from Diff. for of c Right Ascension. 1 Hour. Declination. 1 Hour. Mean Time. 1 Hour. Mean Sun. h m s s 1 m s s h m .s 3 22 57 2.68 9.319 S. 6 42 45;8 ' 57.58 12 3.39 0.537 22 44 59.29 4 23 46.11 9.300 6 19 41.0 57.81 11 50.27 0.556 22 48 55.84 5 23 4 29.11 9.282 5 56 30.9 58.02 11 36.71 0.574 22 52 52.40 10 23 22 58.04 9.203 3 59 35.1 58.83 10 22.87 0.654 23 12 35.17 11 23 26 38.73 9.189 3 36 1.8 58.94 10 7.01 0.668 23 16 31.72 16 23 44 57.71 9.131 1 37 46.1 ! 59.25 8 43.22 0.725 23 36 14.49 17 23 48 36.75 9.123 1 14 3.8! 59.27 8 25.71 0.734 23 40 11.04 18 23 52 15.60 9.115 50 21.3 59.27 8 8.00 0.742 23 44 7.60 19 23 55 54.26 9.108 26 39.0 59.26 7 50.11 0.749 23 48 4.15 20 23 59 32.77 9.101 S. 2 57.1 1 59.23 7 32.06 0.755 23 52 0.70 21 3 11.15 9.096 N. 20 44.0 i 59.19 7 13.89 0.760 23 55 57.26 22 6 49.41 9.093 44 24.0 59.14 6 55.60 0.764 23 59 53.81 24 14 5.74 9.088 1 31 39.2 58.99 6 18.82 \ 0.768 7 46.92 25 17 43.84 9.087 1 55 13.8 58.89 6 0.36 [ 0.769 11 43.47 29 32 16.31 9.092 3 29 4.3 58.37 4 46.62 0.764 27 29.69 30 35 54.56 9.096 3 52 23.2 58.20 4 28.31 0.761 31 26.24 Equation of Time, to be APRIL. Subtracted from Ad 9 5 43.62 9.582 16 38 56.1 41.48 5 41.51 1 0.275 9 2.11 7 9 9 33.27 9.556 16 22 12.6 42.14 5 34.61 1 0.300 9 3 58.66 8 9 13 22.32 9.531 16 5 13.4 42.79 5 27.10; 0.325 9 7 55 22 9 9 17 10.76 9.506 15 47 58.8 43.43 5 18.99 0.350 9 1151.78 10 9 20 58.61 9.481 15 30 29.0 44.05 5 10.28 0.375 9 15 48.33 12 9 28 32.56 9.433 14 54 45.4 45.26 4 51.11 0.423 9 23 41.44 13 9 32 18.67 9.410 14 36 32.2 45.84 4 40.67 0.447 9 27 38.00 14 9 36 4.23 9.387 14 18 5.0 46.41 4 29.67 0.470 9 31 34.56 15 9 39 49.25 9.364 13 59 24.3 46.97 4 18.14 0.492 9 35 31.11 18 9 51 1.16 9 301 13 2 3.4 48.59 3 40.38 ! 0.556 9 47 20.78 19 9 54 44.13 9.280 12 42 31.2 49.10 3 26.80 576 9 51 17.33 20 9 58 26.63 9.2(il 12 22 46.8 49.(i0 3 12.74 0.595 9 55 13.89 21 10 2 8.67 9.243 12 2 50.6 50.09 2 58.23 0.614 9 59 10.44 22 10 5 50.27 9.225 11 42 42.8 50.5ti 2 43.27 0.632 10 3 7.00 27 10 24 12.10 9.142 9 59 21.3 52.74 1 22.32 0.714 10 22 49.77 SEPTEMBER, 1894. AT GREENWICH APPARENT NOON. THE SUN'S j: Equation c Sidereal of Time c Time of to be "^ Semi- Subtracted ,s diameter from Diff. "o Apparent Diff. for Apparent Diff. for Semi- Passing Apparent for Right Ascension. 1 Hour. Declination. 1 Hour. diameter. Meridian. Time. 1 Hour. h m s s s m s s 1 10 42 24.83 9.071 N. 8 11 59.1 54.'56 15 53'. 67 64.41 7.70 0.783 2 10 46 2.39 9.059 7 50 5.8 54.89 15 53.90 64.37 26.64 0.795 3 10 49 39.66 9.047 7 28 4.9155.19 15 54.14 64.33 45.87 0.807 15 11 32 50.86 8.968 2 56 9.1 1 57.79 15 57.17 64.08 4 52.64 0.886 16 11 36 26.07 8.967 2 33 0.4 57.93 15 57.43 64.07 5 13.92 0.887 22 11 57 57.98 8.982 N. 13 14.9 : 58.46 15 58.99 64 11 7 20.99 0.872 23 12 1 33.62 8.988 S. 10 8.6 58.50 15 59.26 64.13 7 41.84 0.866 24 12 5 9.41 8.995 33 32.8 58.52 15 59.52 64.15 8 2.56 0.859 25 12 8 45.36 9.002 56 57.6 1 58 53 15 59.79 64.17 8 23.10 0.852 26 12 12 21.50 9.010 1 20 22.3 I 58.53 16 0.05 64.20 8 43.46 0.844 27 12 15 57.84 9.019 1 43 46.8 58.51 16 0.32 64.23 9 3.62 0.835 30 12 26 48.26 9.050 2 53 54.6 58.34 16 1.15 64.34 10 2.70 0.805 OCTOBER. 12 30 12 41 12 44 13 44 13 48 13 59 14 3 14 18 14 22 25.58 9.062 19.36 9.101 57.94 9.116 18.12 9.465 5.61 9.493 32.34 9.583 22.71 r,.614 51.76 9.742 45.96 9.775 3 17 14.0 4 26 57.6 4 50 6.0 10 47 51.1 11 9 7.6 12 11 56.1 12 32 30.5 13 52 48.0 14 12 20.1 58.26 57.91 57.77 53.39 53.00 51.67 51 .20 49.12 48.55 1.42 2.26 2.55 6.95 7.21 7.98 8.24 9.26 9.52 64.38 64.52 64.58 65.81 65.90 (i6.20 66.31 (',6.74 66.85 10 21.88 11 17.61 11 35.53 15 19.61 15 28.65 15 51 52 15 57.69 1() 14.80 0.114 16 17.16 0.082 0.793 0.754 0.739 0.390 0.362 0.272 0.241 SEPTEMBER, 18U4. AT GREENWICH MEAN NOON. THE SUN'S c Sidereal _£ Equation of Time, Time, or to be Right Ascension o Apparent Diff . for Apparent Diff. for Added to Diff. for of >> Right Ascension. 1 Hour. Declination. 1 Hour. Mean Time. 1 Hour. Mean Sun. h m s s m s s h m s 1 10 42 24.85 9.073 N. 8 li 58.9 54.57 7.70 0.783 10 42 32.55 2 10 46 2.45 9.061 7 50 5.3 54.90 26.65 0.795 10 46 29.10 3 10 49 39.77 9.049 7 28 4.1 55.20 45.88 0.807 10 50 25.66 15 11 32 51.59 8.970 2 56 4.3 57.81 4 52.71 0.887 11 37 44.30 16 11 36 26.86 8.969 2 32 55.2 57.94 5 14.00 0.887 11 41 40.86 22 11 57 59.08 8.984 N. 13 7.7 58.47 7 21.10 0.872 12 5 20.18 23 12 1 34.78 8.990 S. 10 16.2 58.51 7 41.96 0.866 12 9 16.73 24 12 5 10.61 8.997 33 40.7 58.53 8 2.67 0.859 12 13 13.29 25 12 8 46.62 9.004 57 5.8 58.54 8 23.22 0.852 12 17 9.84 26 12 12 22.81 9.012 1 20 30.8 58.54 8 43.58 0.844 12 21 6.39 27 12 15 59.20 9.021 1 43 55.6 58.52 9 3.75 0.835 12 25 2.95 30 12 26 49.77 9.052 2 54 4.4 58.35 10 2.84 0.805 12 36 52.61 OCTOBER. 1 12 30 27.15 9.063 S. 3 17 24.1 58.28 10 22.01 0.793 12 40 49.16 4 12 41 21.07 9.102 4 27 8.6 57.93 11 17.75 0.754 12 52 38.82 5 12 44 59.70 9.117 4 50 17.2 57.78 11 35.67 0.739 12 56 35.38 21 13 44 20.54 9.46('. 10 48 4.7 53.39 15 19.71 0.390 13 59 40.24 22 13 48 8.06 9.494 11 9 21.3 52.99 15 28.74 0.362 14 3 36.80 25 13 59 34.87 9.584 12 12 9.7 51.66 15 51.59 0.272 14 15 26.46 26 14 3 25.27 9.615 12 32 44.1 51.19 15 57.75 0.241 14 19 23.02 30 14 18 54.40 9.743 13 53 1.3 49.11 16 14.84 0.114 14 35 9.24 31 14 22 48.62 9.775 14 12 33.3 48.55 16 17.18 0.081 14 39 5.80 NOVEMBER, 1894. AT GREENWICH APPARENT NOON, o THE SUN'S Sidereal Equation of Time, IS Time of to be ^ Semi- Subtracted ■*^ diameter from c Apparent Diff. for Apparent Diff. for Semi- Passing Apparent Diff. for 1 Right Ascension. 1 Hour. Declination. 1 Hour. diameter. Meridian. Time. 1 Hour. 1 h m s 14 26 40.95 9.808 S.14°3138!6 47.97 16 9!77 66.97 m s 16 18.74 0.049 2 14 30 36.72 9.841 14 50 42.8 47.37 16 10.02 67.08 16 19.50 0.016 4 14 38 30.681 9.907 15 28 7.2 46.12 16 10.52 67.31 16 18.66 0.051 5 14 42 28.87 9.941 15 46 26.5 45.48 16 10.77 67.43 16 17.04 0.085 6 14 46 27.87 9.975 16 4 30.0 44.81 16 11.02 67.55 16 14.59 0.119 10 15 2 32.13 10.114 17 13 58.1 41.98 16 11.96 68.03 15 56.61 0.257 11 15 6 35.29 10.149 17 30 36.7 41.23 16 12.19 68.15 15 50 02 0.292 12 15 10 39.29 10.184 17 46 57.2 40.47 16 12.41 68.27 15 42.60 0.327 20 15 43 41.92 10.467 19 46 4.1 33.80 16 14.04 69.19 14 12.67 0.609 21 15 47 53.56 10.502 19 59 24.6 32.90 16 14.23 69.30 13 57.64 0.643 22 15 52 6.01 10.536 20 12 23.4 31.98 16 14.41 69.41 13 41.79 0.677 Equation of Time, to be Subtracted DECEMBEE. from Added to 70.29 Apparent Time. 1 16 30 32.50 10.809 S. 21 51 47.6 23.05 16 15.92 10 44.80 0.949 2 16 34 52.22 10.834 22 48.1 21.99 16 16.07 70.38 10 21.70 0.974 5 16 47 54.88 10.904 22 25 15.7 18.75 16 16.51 70.61 9 8.92 1.045 6 16 52 16.84 10.925 22 32 32.6 17.65 16 16.65 70.68 8 43.58 1.066 13 17 23 3.08 11.044 23 10 59.7 9.75 16 17.46 71.08 5 33.77 1.184 14 17 27 28.30 11.056 23 14 39.9 8.60 16 17.55 71.12 5 5.19 1.196 20 17 54 4.59 11.106 23 26 53.9 1.58 16 17.96 71.26 2 8.74 1.246 21 17 58 31.19 11.109 23 27 17.6 0.40 16 18.03 71.26 1 38.78 1.249 22 18 2 57.84 11.111 23 27 13.0 0.78 16 18.0S 71.27 1 8.78 1.251 23 18 7 24.52 11.111 23 26 40.0 1.96 16 18.13 71.27 38.74 1.251 24 18 n 51.18 18 16 17.79 11.110 11.107 23 25 38.7 23 24 9.1 3.14 4.32 16 18.17 16 18.20 71.26 71.25 8.72 1.250 25 21.26 1.247 NOVEMBEE, 18!U. AT GREENWICH MEAN MOON. J3 THE ^UN'S o Sidereal Equation of Time, Time, J3 or z to be Right Ascension ? Apparent Diff. for Apparent Diff. for Added to Diff. for of S Right Ascension. 1 Hour. Declination. 1 Hour. Mean Time. 1 Hour. Mean Sun. h m s 8 m s s h m s 1 14 26 43.61 9.808 S.14 3l'5i'.6 47.97 16 18.74 0.048 14 43 2.35 2 14 30 39.40 9.841 14 50 55.7 47.37 16 19.51 0.015 14 46 58.91 4 14 38 33.38 9.907 15 28 19.8 46.12 16 18.64 0.051 14 54 52.02 5 14 42 31.57 i 9.941 15 46 38.8 45.47 16 17.01 0.085 14 58 48.58 6 14 46 30.57 1 9.975 16 4 42.1 44.80 16 14.56 0.119 15 2 45.13 10 15 2 34.82 10.114 17 14 9.2 41.97 15 56.54 0.257 15 18 31.36 11 15 6 37.97 10.149 17 30 47.5 41.22 15 49.94 0.292 15 22 27.91 12 15 10 41.96 10.184 17 47 7.8 40.46 15 42.51 0.327 15 26 24.47 20 15 43 44.40 10.466 19 46 12.0 33.79 14 12.53 0.609 15 57 56.93 21 15 47 56.00 10.500 19 59 32.3 32.89 13 57.49 1 0.644 16 1 53.49 22 15 52 8.41 10.534 20 12 30.6 31.97 13 41.63 0.678 16 5 50.04 Equation of Time, to be Added to DECEMI S.21 51 51.7 3EE. 23.04 Sul)tracted from Mean Time. 1 16 30 34.44 10.806 10 44. ('.3 0.949 16 41 19.06 2 16 34 54.09 10.831 22 51.9 21.98 10 21.53 0.974 16 45 15.62 5 16 47 56.54 10.901 22 25 18.5 18.74 9 8.76 1.045 16 57 5.30 6 16 52 18.43 10.922 22 32 35.2 17.64 8 43.43 1.066 17 1 1.86 13 17 23 4.11 11.040 23 11 0.6 9.74 5 33.66 1.184 17 28 37.77 14 17 27 29.24 11.052 23 14 40.6 8.59 5 5.09 1.196 17 32 34.33 20 17 54 5.00 11.102 23 26 53.9 1.58 2 8.69 1.245 17 56 13.68 21 17 58 31.49 11.105 23 27 17.6 0.40 1 38.75 1.249 18 10.24 22 18 2 58.05 11.107 23 27 13.0 0.78 1 8.75 1.251 18 4 6.80 23 18 7 24.63 11.107 23 26 40.0 1.96 38.73 1.251 18 8 3.36 24 18 11 51.20 18 16 17.73 11.106 11.103 23 25 38.7 23 24 9.1 3.14 4.32 8.72 1.250 1.247 18 11 59.92 25 21.25 18 15 56.48 VENUS, 1894. GREENWICH MEAN TIME. JANUARY. MAY. .a c o o 1 Apparent Right Ascension. Var. of R. A. for 1 Hour. Apparent Declination. Var. of Decl. for IHour. Meridian Passage. p Apparent Right Ascension. Var. of R. A. for 1 Hour. Apparent Declination. Var. of Decl. for 1 Hour. Meridian Passage. Noon. Noon. Noon. Noon. Noon. Noon. Noon. Noon. 25 26 27 28 h m s 22 23 39.23 22 23 23.60 22 22 58.71 22 22 24.53 —0.461 0.844 1.230 1.617 — 5°2d46'.8 5 7 14.1 4 54 31.5 4 42 41.5 +34 87 32.83 30.69 28.45 h m 2 42 2 0.0 155.6 151.1 21 22 23 24 h m s 1 1 17.91 1 5 22.29 1 9 27.48 1 13 33.50 + 10.165 10.199 10.233 10.268 +4° 28 47.9 4 51 31.6 5 14 18.8 5 37 8.7 +56.74 56.89 57.02 57.12 h m 21 5.0 21 5.1 21 5.2 21 5.4 Day of the Month..., 1st 6th 11th 16th 21st 26th 31st Day of the Month 1st 6th nth 16th 21st 26th 31st Semidiameter Hor. Parallax 17:7 18.4 19:1 19.8 2d!7 21.4 22:4 23.2 24'2 25.1 26! 1 27.1 28 !0 29.0 Semidiameter Hor. Parallax ll!8 H".2 12.211.6 l6'.7 11.0 id!2 10.5 9'.7 10.0 9.3 9.6 8:9 9.2 MARS, 1894. GREENWICH MEAN TIME. JANUARY. MARCH. 5 Apparent Right Ascension. Var. of R. A. for IHour. Apparent Declination. Var. of Decl. for 1 Hour. Meridian Passage. c c 1 Apparent Right Ascension. Var. of R. A. for 1 Hour. Apparent Declination. Var. of Decl. for 1 Hour, Meridian Passage. 1 Noon. Noon. Noon. Noon. Noon. N'on. Noon. Noon. 14 15 16 17 h m s 16 29 56.16 16 32 .50.64 16 35 45.48 16 38 40.69 +7^262 7.278 7.293 7.308 — 21°41 34.9 21 48 25.9 2155 5 8 22 134.6 — 17'.35 16.89 16.43 15.97 h m 20 53.3 20 52.3 20 51.2 20 50.2 1 h m s 28,20 9 47.12 29 20 12 45.54 30 20 15 43.68 31 20 18 41.53 +7.440 7.429 7.417 7.405 -21 5 25.4 20 57 23 20 49 9.8 20 40 45.9 + 19.87 20 32 20 77 21.21 h ni 19 45.4 19 44.5 19 43.5 19 42.5 1st 6th nth 16th 21st 26th 31st Day of the Mon th 2d 7th 12th 17th 22d 27th Semidiameter Hor. Parallax 2:a 4.0 2:3 4.1 2:4 4.2 2:4 4.2 2:5 4.3 2:5 4.4 2:6 4.5 Semidiameter Hor. Parallax 5.1 3:0 5.2 3.'l 5.4 3.'l 5.5 3!2 5.6 3:3 5.8 Note.— The sign + indicates north declinations; the sign — indicates south declinations JUPITEK, iai)4. GREENWICH MEAN TIME. NOVEMBER. Apparent Right Ascension. Noon. h m s 6 26 17.67 6 26 5.94 6 23 43.34 6 23 23.52 Var. of R. A. fori Hour. -0.471 0.50H 0.810 0.842 Apparent Declination. +23 11.8 23 24.0 23 2 36.0 23 2 52.8 Var. of Dec), fori Hour. Meridian Passage. +0.50 15 20.9 0.52 0.69 0.71 15 16.8 14 39.0 14 34.7 SATURN, mn. GREENWICH MEAN TIME. MARCH. "^K^t"' I^r'a^^I Apparent Asc'l'ifsfon. ^lll^ I Declfnation. h m s 13 33 27.87 13 33 15.58 13 33 3.02 13 32 50.18 —0.506 0.518 0.529 0.540 Var. of Decl. fori Hour. Meridian Passage. -6 50 20.2 +3.46 14 22.3 6 48 56.4 3.52 14 18.2 6 47 31.3 3.58|14 14.0 6 46 4.9 3.63 14 9.9 Day of tlie Month Polar Semidiameter., Horizontal Parallax.. 20.8 2.0 21.3 2.0 21.7 2.0 22.1 2.1 Day of the Month 6th. Polar Semidiameter. Horizontal Parallax. 8.8 1.0 1.0 8.9 1.0 9.0 1.0 FIXED STARS, 1894. MEAN PLACES FOR THE BEGINNING OF 1894. Name of Star. Magni tude. Right Ascension, Annual Variation. Annual Variation. a Tsiuri {Aldeha ran) ... /3 Orionis (Bigel) a Orionis (var.) a Canis Majoris [Sirius) a Canis Min. (Procyon) a Leonis (Regnlus) a^ Crucis a Virginis (Spica) a Bootis (Arcturus) /8' Scorpii a Lyrae ( Vega) a Aquilae (Altair) /8 Aquarii a Pis. Aus. {Fomalhai(t). . Note— The sign + indicates north declinations; the sign — indicates south declinations h m 4 29 5 9 5 49 6 40 7 33 10 2 12 20 13 19 14 10 15 59 18 33 19 45 21 25 22 51 50.26 26.60 25.97 28.63 45.20 43.63 42.21 36.48 49.59 16.40 20.99 36.70 58.75 47.58 + 3.438 + 2.882 + 3.247 + 2.644 + 3.143 + 3.200 + 3.298 + 3.154 + 2.735 + 3.481 + 2.031 + 2.928 + 3.161 + 3.324 + 16 17 45.0 - 8 19 28.0 + 7 23 12.9 -16 34 15.6 + 5 29 46.7 + 12 29 6.4 -62 30 41.7 -10 36 28.9 + 19 44 3.6 -19 30 54.4 + 38 41 6.1 + 8 35 18.5 -62 14.8 -30 11 2.3 + 7.60 + 4.38 + 0.93 - 4.73 - 9.01 -17.48 -20.01 -18.89 -18.87 -10.12 + 3.18 + 9.29 + 15.68 + 19.00 THIS BOOK IS DUE ON THE LAST DATE STAMPED BELOW AN INITIAL FINE OF 25 CENTS OVERDUE. LD 21-100?n-8,'34 YD n:^?4H