El ''■'■■- ■. ■ -.-■■ H £ -.•■..-• -•■■■■■ -■•:-■ •'■•■•.. ,; " ' : ' ■"•■ '■■■ ■ .Jam >.■'..■;■ '.•..'■'.'■•■ ■'•■'.;■:■.-'■;■■:•■' "•'■'■■-■.:'.■■ ■■••••■■:■■■ ■i: :■■■ •'■:"■■■■-' ■ .-'■'••' SSssSssfc ■••-.•■. •-.■■/-■' ■■■■■■■■.:•;■■•■:. ' •:•' ; : :; : : ...'■• . ■•,.'-■•/■• ■'••'■..■■" ;•::;■'■■.■•■-'■■.• .■■•••.■•••'■•/:•'■:.■.• .■/■!'■•:,.. '■■■•■ H : ^B : '■"'■" 'V ■•'"'■ HWiBWHHfg ;. ; ."-. .■:■■■■■■ :• .-•;.■■•■'• ■■•••■■.■..•-■ ■■-'■-''■■■■'. k£ •.'•'•■■ ' ' M. 21918/14. [Crown Copyright Reserved. ADMIRALTY MANUAL OF NAVIGATION 1914. I . O \ I ' < » \ : PUBLISHED I'.Y Ills MAJESTY'S STATIONERY OFFICE i M i»i- purchased through in. Booksellei or directly from II. M. STATION!. i:Y OFFICE at the following addresses • Imperial Hocse, Kikosway, Lob don, Vf.0.2, and 28, A) don - w I'll KK STKKKT, M \N< III Ml I. - I. VNDR1 ■ CUKSC'ENl L'ARDIl I III ROD : i. POH 8i >K BY, I.'i i'.. M'.'.' STREET, Dl mi v. L919. Prict 6s Net, The Lords Commissioners of the Admiralty have decided that a Standard Work on Navigation is required for the information and guidance of the Officers of His Majesty's Fleet; for this purpose the " Admiralty Manual of Navigation " has been compiled by Commander Henry E. F. Aylmer and Naval Instructor John White, M.A., under the supervision of the Director of Navigation. The Manual is designed to supply the needs of Junior Officers and also of Officers qualifying for the duties of Navi- gating Officer, and is to be regarded as the Standard Work on Navigational questions in His Majesty's Fleet. By the publication of this Manual the following books are superseded and may be destroyed : — Notes bearing on the Navigation of H.M. Ships. Handbook of Pilotage. By Command of Their Lordships, Admiralty, S.W. December 101 I. 10 610$ \\ i I I iIn 13 7000 l 10 11 PREFACE. The Admiralty Manual of Navigation consists of four parts : — Part I. deals with the rhumb line and the position line, as well as with finding the error of the chronometer and the times of rising and setting of heavenly bodies ; Part II. deals with pilotage; Part III. deals with the movements of the atmosphere and ocean ; Part IV. gives descriptions of the various navigational instruments, and explains how their errors are eliminated or allowed for. Thanks are due to — The Astronomer Royal, The Director of the Meteorological Office, for their valuable assistance, and to W. G. Perrin, Esq., for reading the proofs of the book. The method of keeping the reckoning during manoeuvres is the work of Lieutenant - Commander L. H. Shore, R.N. Figs. 262 and 263 have been reproduced from ' Les Nouvelles Methodes de Navigation " by A. Ledieu, and the permission which has been granted by — Mr. Elliot Stock to reproduce Fig. 153, Messrs. Elliott Bros, to reproduce Figs. 240, 251, 252, 253, The Sperry Gyroscope Co. to reproduce Figs. 247, 248, Messrs. Cary, Porter & Co. ,, ,, Fig. 256, is gratefully acknowledged. The following books have been consulted : — American Practical Navi- Nathaniel Bowditch, LL.D. gator. Cours de Navigation - - E. du Bois. Descriptive Meteorology - W. L. Moore, LL.D., Sc.D. Deviations of the Compass Captain E. W. Creak, C.B., F.R.S., in Iron Ships. R.N. Elementary Meteorology - R. H. Scott, M.A., F.R.S. Encyclopaedia Britannica. Etude sur les Courbes de G. Hilleret. hauteur. Ganot's Physics - - E. Atkinson, Ph.D., F.C.S. A. W. Reinold, M.A., F.R.S. Ill Geodesv .... Colonel A. R. Clarke, C.B., F.R.S., R.E. Glossary of Navigation - Chaplain and Naval Instructor J. B. Harbord, M.A., R.N. I Ivdrographical Surveying - Rear-Admiral Sir W. J. Wharton, K.C.B., F.R.S., R.N. Rear-Admiral Mostyn Field, C.B., F.R.S., R.N. Lehrbuch der Navigation (Reichs-Marine-Anit. ) Magnetism, General and Humphrey Lloyd, D.D., D.C.L. Terrestrial. Mathematical Instruments - J. F. Heather, M.A. A. T. Walmisley, M.I.C.E. Maximum and Minimum Staff Captain Charles Brent, R.X. Altitude and other Pro- Naval Instructor A. F. Walter, blems. R.N. Naval Instructor George Williams, R.N. Meteorology, Practical and Sir John Moore, M.A., M.D., Applied. D.P.H., D.Sc, F.R.C.P. Modern Navigation - - Chaplain and Naval Instructor William Hall, B.A., R.N. Navigation and Compass Commander W. C. P. Muir, U.S. Deviations. Navy. Navigation and Nautical Staff Commander W. R. Martin, Astronomy. R.N. Navigation and Nautical Chaplain and Naval Instructor Astronomy. F. C. Stebbing, M.A., R.N. Papers in the Philosophical Archibald Smith, F.R.S. Transactions of the Royal Captain F. J. Evans, F.R.S. , R.N. Society, 1860, 1861. Popular Lectures and Ad- Sir William Thomson, LL.D., dresses. F.R.S., F.R.S.E. Practical Manual of Tides W. H. Wheeler, M.I.C.E. and Waves. Practice of Navigation - Lieutenant Henry Raper,F.R.A.S., F.R.G.S., R.N. Principal Winds and Cur- Captain 11. Jackson, R.N. rents of the Globe. Spherical and Practical William Chauvenet. Astronomy. Star At l,i- - - - H. A. Proctor. Tides and Kindred Pheno Sir G. H. Darwin, K.C.B., F.R.S. mena. Watch Make] Handbook - P. .J. Britten. Weather - - Hon. Ralph Aben-nmiby. Wrinkles in Practical Navi- Captain S. T. S. Lecky, F R.A.S.. gation. F.R.G.S., R.N.R. And numerous Government publications. IV CONTENTS. PART I.— NAVIGATION AND NAUTICAL ASTRONOMY. CHAPTER I. Positions on the earth's surface. Article page 1. Figure of the earth ------ 1 2. Angular latitude and longitude 1 3. Circle of curvature of a meridian - - - - 2 4. The nautical mile ------ 2 5. Length of a nautical mile - - - - - 3 6. The geographical mile - - - - 3 7. Length of the geographical mile - - - - 3 8. Linear latitude and longitude - - - 3 9. The knot ------- 4 10. The earth approximately a sphere - - - - 5 11. Difference of latitude and difference of longitude - - 5 CHAPTER II. Direction on the earth's surface. 12. True bearing ------- 6 13. The magnetic compass - - - - - 6 14. Magnetic variation ------ 7 15. Deviation of the compass - - - - , - 8 16. Methods of applying deviation and variation - - 9 17. The gyro-compass - - - - - - 10 CHAPTER III. The course and distance by the Mercator's chart. 18. The rhumb Line. Course and distance - - - 11 19. Relation between the arc of a parallel of latitude and the corresponding arc of the equator - - - - 12 20. The Mercator's chart - - - - - 12 21. Construction of a Mercator's chart - - - - 15 22. Plotting positions on a Mercator's chart - - - 16 23. To find the compass course from one position to another - 17 24. To find the distance from one position to another - - 19 25. To allow for a current when finding the course - - 19 CHAPTER IV. The covrse and distance by calculation. Article page 26. Fundamental formulae for the rhumb line - - - 21 27. Formula for the depart ure - - - - 22 28. Formulae for course and distance - - - -2 29. Approximate formula for the departure - - - 23 30. Approximate method of finding the course and distance by the traverse table - - - - - - 24 CHAPTER V. The great circle track. 31. The gnomonic chart - - - - - 27 32. Special cases of the gnomonic chart - - - - 30 33. Construction of a gnomonic chart - - - - 30 34. To draw the great circle track on the Mercator's chart - 33 35. Great circle track by calculation - - - - 36 36. Great circle track by Towson's tables - - - 37 37. The composite track - - - - - - 39 CHAPTER VI. The dead reckoning and estimated positions. 38. The dead reckoning position - - - - 41 39. The estimated position - - - - - 41 40. Working the reckoning by chart - - - - 42 41. Working the reckoning by calculation - - - 43 42. Current by difference between dead reckoning and observed positions - - - - - - - 46 43. Keeping the reckoning in a tideway - - - 46 44. Track of a ship while turning - - - - 46 45. Keeping the reckoning during manoeuvres - - - 49 46. Examples of keeping the reckoning during manoeuvres - 55 CHAPTER VII. Position line by observation of terrestrial objects. 47. Inn liability of the estimated position. Position line - 59 48. l'< >s i lion line by compass bearing .... 59 49. Position line by horizontal sextant angle - - 61 50. Position line by distance from an object - - - 61 51. 'I • ial rrfracl ion - - - - - 61 52. Abnormal n fraction - - - - - - 62 68. Altitude of a terrestrial objeol .... 62 54. Depression of a terrestrial objeol - - - - 62 5. r ). 'I'll'- i.l. -• i -\ ■•! ■'.- .-'H ami shore horizons - - - <'»- 56. Formula for the dip of the sea horizon - - - 68 57. I »i tana of the sea horizon ■ 58. Formula for the dip of tic- shore horizon 69. Distance bj vertical sextant angle - M i bore Di tanoe Tables - - - -70 VI CHAPTER VIII. Position by observation of terrestrial objects. Article page 61. To fix the position of a ship - - - - 71 62. Position by cross bearings - - - - - 71 63. Position by bearing and horizontal sextant angle - - 72 64. Position by bearing and distance - - - 73 65. Position by horizontal sextant angles - - - 73 66. Running fix - - - 77 67. Use of soundings in obtaining the position - - - 79 CHAPTER IX. The heavenly bodies and their true places. 68. Necessity for astronomical observations - - 80 69. The stars - - - - - - 80 70. The constellations - - - - - - 80 71. Designation of bright stars - - - - - 80 72. Magnitudes of stars - - - - - - 80 73. The solar system - - - - - - 81 74. The nebular theory - - - - - - 81 75. How to recognise the stars - - - - 82 76. The movement of the earth - - • - - 84 77. The celestial concave. The ecliptic and celestial equator - 84 78. Positions of heavenly bodies - - - - 85 79. Variation in right ascension and declination - - 87 CHAPTER X. The Greenwich date and correction of right ascension and declination. 80. The year and the month - - - - - 88 81. Celestial meridians of observer and heavenly body - - 88 82. The day ....... 88 83. The solar day - - - - - - 88 84. The mean solar day and mean solar time - - - 89 85. Change of time for change of longitude - - - 90 86. The Greenwich date - - - - - - 91 87. Correction of right ascension and declination - - 91 (a) The sun. (6) The moon. (c) The planets. (d) The stars. 88. Adjusting ship's clocks for change of longitude - - 93 89. Standard times - - - - - - 94 Vll CHAPTER XI. The zenith distance axd azimuth at the estimated position. Article page 90. Connection between a position on the earth and a heavenly body ....... 96 91. The azimuth - - - 96 92. The zenith distance - - - - - 90 93. The astronomical triangle - - - - - 90 94. The hour angle - - - - - - 97 95. The equation of tune - - - - - 97 90. The right ascension of a meridian (or sidereal time) - 98 97. Formula for the hour angle of a heavenly body - 98 98. Correction of the equation of time - - - 99 99. Change in the right ascension of the mean sun - - 100 100. Correction of the right ascension of the mean sun - - 100 101. Calculation of the zenith distance and azimuth at the estimated position - - - - 101 102 Azimuth tables and azimuth diagram - 103 CHAPTER XII. The true zenith distance and astronomical position line. L03. The true zenith distance - - - - - 104 104. Formula for astronomical refraction - - - 105 105. Semi-diameter ...... 100 106. Parallax - - - - - - - 107 1"7. Augmentation of the moon's semi-diameter - - - 108 108. Examples of the correction of altitudes - - - 109 L09. The geographical position of a heavenly bod y - - 111 1 10. The true bearing of the geographical position - - 112 111. The circle of position - - - - - 113 112. The astronomical position line - - - - 114 113. The most probable position from a single obsers al ion - 110 114. The value of a single position lino .... 117 CHAPTER XIII. PoernoK by astbonomioax position ua ii.".. Position from two or more ob ions - - - 119 llo. Examples of finding posrl ion by plotting and by calculation I 19 Example (1). Position from simultaneous observations bj plotting (hi on chart, (6) on squared paper - - 120 ExampU (2). Po itiOD from simultaneous olisi-rv ations bj calculation ------ 123 Example (3). Position from uoo Lve ob ervations (a) by calculation, (6) bj plotting on the chart - - 125 117. Error in a po ition due to error in the obsen ed altitudes - 127 Vlll CHAPTER XIII.— continued. Article page 118. Error in a position due to uncertainty of the error of the deck watch - - - - - - 129 119. Error in a position due to error in the observed altitudes and to uncertainty of the error of the deck watch - 131 120. Error in a position due to error hi the reckoning between the observations - - - - - -131 121. Error in a position due to error in the reckoning between the observations, and to the error in the observed altitudes 133 122. Error in a position due to error in the reckoning between the observations, to error in the observed altitudes, and to uncertainty of the error of the deck watch - - 133 123. Particular case of very large altitudes - - - 133 124. Position by astronomical and terrestrial position lines - 135 CHAPTER XIV Other methods of determining an astronomical position line. 125. Meridian passages of heavenly bodies - - - 138 (a) The sun - - - - - - 138 (b) The stars - - - - - - 138 (c) The moon - - - - - - 141 (d) The planets - - - - - - 141 126. Position line by meridian altitude - 142 127. Maximum and minimum altitudes - - - - 146 128. Position line by ex -meridian altitude - - - 146 129. Position line by altitude of Polaris - 150 130. Position line by " Longitude by chronometer " method - 152 131. Longitude by equal altitudes - - - - 154 132. Notes on observations for determining position lines - 160 CHAPTER XV. Rising and setting of heavenly bodies, twilight, &c. 133. Hour angles of heavenly bodies when on the rational horizon 163 134. S.M.T. of visible sun -rise and visible sun -set - - 164 135. Twilight - - - - - - - 166 136. S.M.T. of visible moon-rise and visible moon -set - - 168 137. Identification of stars - - - - - 169 138. Torrid, Frigid, and Temperate zones - - - 170 IX CHAPTER XVI. The error and rate of the chronometer. Article page 139. Meaning of the terms error, rate, and accumulated rate - 173 140. System of daily comparisons - - - - 173 141. How to take time accurately with a deck watch - - 174 142. Error of the chronometer by time signal - - 175 143. The mean comparison - - - - - 175 144. Error of the clironometer by astronomical observation - 176 145. The artificial horizon - - - - - 177 14G. Observations in the artificial horizon - - - 178 147. Error of the chronometer by absolute altitudes - - 180 148. Errors involved in absolute altitudes - - 184 149. Error of the chronometer by equal altitudes - 185 150. Formula for the equation of equal altitudes - - 186 151. Errors involved in equal altitudes - - - - 187 152. Example of error of chronometer by equal altitudes - 187 153. Summary of necessary comparisons - - - - 191 154. Notes on observations for error of chronometer - - 191 155. The rate of the chronometer - - - - 194 PART II.— PILOTAGE. CHAPTER XVII. The Admiralty chart and artificial aids to navigation. 156. Coasts - - - - - - - 196 157. Dangers • - - - - - 198 158. Depth of water - - - - - 199 1 59. Quality of the bottom - - - - - 199 160. Tides and tidal streams. Currents - 200 161. General abbreviations ..... 201 162. System of buoyage in tlio Uuitiil Kingdom- - - 202 163. System of lighting - - - - -205 164 Fog signals - - - - - - - 208 165. Reliability of f..- -i-nuls ..... 208 166. Submarine bell - - - - - 209 167. Printing <>f the chart - ... 210 ins. Chart correction - - - - - - I'll 169. Reliability of eh . . . - -211 170. Sailing Direction ...... 218 X CHAPTER XVIII. The track of the ship and the avoidance of danger in pilotage waters. Article page 171. The track - - - - - - - 214 172. Leading marks ...... 215 173. Lines of bearing ------ 216 174. Turning on to a predetermined line - - - - 216 175. Clearing marks ------ 219 176. Clearing bearings ------ 221 177. The vertical danger angle - - - - - 221 178. The horizontal danger angle - - - - - 221 179. Avoidance of danger in thick weather - - - 222 180. Preparing the chart ------ 222 181. Selection of a position in which to anchor - - - 224 182. To anchor a ship in a selected position - - - 224 183. To moor a ship in a selected position - - - 226 184. Example of the preparation of a chart with a view to anchoring ------- 228 185. Conning the ship - - - - - - 230 PART III.— THE ATMOSPHERE AND OCEAN. CHAPTER XIX. The weather. 186. The atmosphere ------ 232 187. The pressure of the atmosphere - - - - 232 188. Cause and direction of wind ----- 233 189. Permanent winds, Trades and Westerlies - - - 235 190. Periodic winds. Monsoons ----- 236 191. Land and sea breezes - 236 192. Diurnal variation of the barometer ... - 237 193. Local winds ------- 237 194. Causes of clouds, rain, &c. - - - - , - 238 195. Causes of fog - - - - - - 238 196. Atmospheric electricity - - - - - 239 CHAPTER XX. Forecasting the weather. 197. The synoptic system of weather analysis - - - 241 198. The seven fundamental forms of isobars - - 242 199. The cyclone - - - - - - - 242 200. The secondary cyclone ----- 243 201. The anti-cyclone - - - - - - 244 202. The wedge - - - - - - - 245 203. Straight isobars - - - - - - 245 204. The V depression - - - - - - 245 205. The col - - - - - - 246 206. Revolving storms ------ 247 207. The indications of the approach of a revolving storm - 249 208. Rules for determining the path of, and avoiding a revolving storm ------- 250 209. Weather in the British Islands and North Sea - - 251 210. Storm signals - - - - - - 252 211. Forecasting by a solitary observer - - - - 253 XI Article 212. 213. 214. 215. 216. 217. 218. 219. 220. 221. CHAPTER XXI. Ocean currents, waves. &c. Currents ...... Atlantic Ocean stream currents Pacific Ocean stream currents Indian Ocean stream currem - Ocean waves ..... To find the dimensions and period of a wave The specific gravity and colour of sea water Change of draught on passing from sea to river water Temperature of the sea Ice - - - - - TAGE 256 266 257 258 259 259 260 261 261 261 222 223 224 225 226 227 228 229 230 CHAPTER XXII. Theoretical tides. The tide generating forces The horizontal tide generating force The lunar and anti-lunar tides The effect of the earth's rotation The effect of declination The effect of parallax The solar and anti-solar tides The composition of the lunar and solar tides Priming and lagging of the tide 264 266 267 268 269 269 270 270 27 1 231. 232. 233. 234. 236. 236. 237. 238. 239. 240. 241. 242. 243. 244. 246. 246. 2 J 7. 248. 249. 260. 28 1 . CHAPTER XXIIL Observed tides and use of ttdts tables. Tidal streams. Disagreement between theory and observation Rise and range of a tide ..... The primary and derived tide waves The age of the tide ...... The amount of the priming and lagging The iiitun establishment of a port .... 'I 'o find the time of high water on any day from the mean tblishment ...... 'I'll- \ -uIlmi- establishment of a port-, or the 1 1 .U.K. and C. - T<> I iiK I the time of hiidi water on any da\ from the ELW.F, and C. ----- - of finding the time of high water I Kurnal inequality ...... Tide prediction. Standard porta .... To find the height o! the tide at any time, \,-. Examples of finding the height of the tide at any time iparison between the t Idea at i wo places. Tidal constant ■ I of meteorological condit i< The cause of t idal b1 reams Tii la] bream in a channel 'l err of turning of tii Levi I reams The I., i . of tidal breams The tidal streams round the British Island 273 273 276 276 276 270 277 27S 27S 280 280 281 281 2s 2 286 287 288 288 289 289 290 Xll PART IV.— NAVIGATIONAL INSTRUMENTS. CHAPTER XXIV. The magnetic compass. The magnetism of the earth and ship. Article page 252. Magnetism - - - - - - - 291 253. The effect of a magnet on an isolated pole - - - 293 254. The molecular theory of magnetism .... 295 255. Magnetic induction ------ 295 256. Artificial magnets ------ 296 257. Effects of temperature on magnets - 298 258. Terrestrial magnetism ..... 298 259. Changes in the variation ..... 299 260. Obtaining the variation by observation on shore - - 299 261. To find the true bearing of an object by observation - 300 262. Example of finding variation on shore - - - 301 263. Local attraction ---... 304 264. The compass ------- 304 265. To compare the earth's horizontal force at two places - 305 266. The permanent magnetism of a ship - - - 305 267. The induced magnetism of a ship - 306 268. The horizontal forces at the compass when the ship heels - 311 269. The sub-permanent magnetism of a ship - - - 312 CHAPTER XXV. The magnetic compass — (continued). The analysis and correction op the deviation. 270. The deviation of the compass - 314 271. The principle of compass correction - - - - 316 272. The exact expression for the deviation of the compass - 316 273. The meaning of A - - - - - 317 274. The approximate expression for the deviation - - 318 275. The component parts of the deviation - - - 318 276. Relations between the exact and approximate coefficients - 319 277. To find the approximate coefficients from observation - 320 278. To find the exact coefficients - 321 279. The correction of coefficient B' 322 280. The correction of coefficient C" - - - 324 281. The correction of coefficient D' - - - 324 282. The correction of coefficient E' 326 283. The correction of the total quadrantal deviation - - 326 284. The induction in the soft iron correctors due to the compass needles ----- - 329 285. The coefficient A' - 330 286. To obtain X by observation ----- 330 287. The effect of spheres on X and the formula for X 2 - - 331 288. The effect of sub -permanent magnetism - - - 332 289. The effect of lightning - - - - - 333 290. The expression for the deviation when the ship heels - 333 291. The meaning of n - - - - - 335 292. The correction of the heeling coefficient J - - * - 335 293. The heeling error instrument .... 335 294. The correction of heeling error in harbour - - - 337 295. The correction of heeling error at sea - - - 338 296. The change of the heeling error due to change of magnetic latitude ... - - - - • 338 Xlll CHAPTER XXVI. The magnetic compass — (continued). The description and practical correction of the compass. Article page 297. The bowl of the Chetwynd compass - - - 340 298. To remove a bubble from the com.pi - - - 341 299. The binnacle - - - - - - 34 1 300. The Thomson compase - - - 343 301. The azimuth mirror ------ 344 302. How to take bearing - - - 344 303. The bearing plate or Pelorus - 346 ::<»4. The compass m a conning to \\vr - - - 347 305. Precautions to be observed with regard to electrical instru- ments, &c. ------ 347 6. To obtain the deviation by observation - - - 351 307. To find the true bearing of an object by the Mercator's chart - 353 308. The adjustment of compasses - 354 309. To obtain the deviation of and to adjust a between-deck compass ------- 355 "10. Swinging ship for deviation - 356 311. Necessity for frequent observations for deviation - - 358 312. The criteria of a good deviation table - - - 358 313. Obtaining the variation by observation at sea 359 CHAPTER XXVIT. The gyro-compass. :"'. 14. Gyrostats and gyroscopes ----- 360 315. The effect of a couple on a gyrostat - - - -.360 3 ! 6. The effect of the earth's rotation on a gyroscope - - 361 317. The effect of the earth's rotation on a gyroscope suspended from a point above its centre of gravity - - - "62 318. The damping of the oscillations of a gyroscope - 363 319 The effect on a gyroscope when carried on board ship - 364 320. The effects of the rolling and pitching of the ship on a gyroscope 36 5 321. Description of the " Sperry " gyro-compass- - 366 322. Damping of the oscillations of and the automatic correction of the " Sperry " gyro-compass - - - - 367 323. The " Sperry " receivers ----- 368 324. Description of the " Anschutz " (three gyro) gyro -compass - 368 Damping of tho oscillations of and applying the corrections to tho "Anschiitz " (three gyro) gyro-compass - - 369 The " Anschutz " receivers - - - - - :;71 CHAPTER XXVITI. Tin: BEXTANT. 327. The principle of i in ■ Bextant - 328. I >• cripl ion of I be sextant - The vernier - 330. The Bextant tela cop 331. r i be i Ktant parallax The errors oi ti. ant :;:;:;. The error of perpendicularity 33 1 Side error i lollimal ion error 336, Index error - rror ut - 373 ! 1 7 ."> 375 .",76 377 :;77 378 :;7s 378 379 380 381 XIV CHAPTER XXIX. The chronometer. Article page 339. The principle and general description of the chronometer - 383 340. The driving mechanism ..... 384 341. The winding and maintaining mechanism - - - 384 342. The train - - - - - - - 385 343. The motion work ...... 385 344. The escapement - - - - - - 386 345. The balance - - - - - - - 387 346. Time of oscillation of the balance .... 387 347. The thermal compensation of the chronometer - - 388 348. Testing of chronometers at the Royal Observatory - - 390 349. The formula for the rate ..... 390 350. Variation of the rate due to age - - - - 391 351 Abnormal variations in the daily rate - - - 391 352. To wind and start a chronometer - - - 393 353. The stowage and care of chronometers on board ship - 394 CHAPTER XXX. Various instruments. 354. The patent log ----- - 396 355. The speed by steaming over a measured distance - - 397 356. The error of a patent log - - - - 398 357. The speed by the revolutions of the engines - - 399 358. The sounding machine ..... 399 359. The depth by chemical tube - - - - - 401 360. Change of depth by the number of fathoms of wire run out - 402 361. How to take soundings ..... 403 362. The station pointer ------ 404 363. The marine barometer ..... 405 364. The aneroid barometer ..... 408 365. The barograph - - - - - - 408 366. Thermometers ...... 409 367. The maximum thermometer ----- 409 368. The minimum thermometer ----- 410 Appendix A. — Extracts from the Abridged Nautical Almanac, 1 914 - 411 Appendix B. — Daily weather report of the Meteorological Office. Change of units of measurement - - 427 Appendix C. — Hydrographical Surveying - - - - 437 INDEX. Arts. 1, 2. PART I.— NAVIGATION AND NAUTICAL ASTRONOMY. CHAPTER I. POSITIONS ON THE EARTH'S SURFACE. Fig. 1. 1. Figure of the earth. As navigation is concerned with the successive positions of a ship as she passes from one place on the earth's surface to another, it necessarily involves a knowledge of that surface and a method of expressing positions on it. The earth is an oblate spheroid, whose greatest and least radii are approximately 3,963 and 3,950 statute miles respectively. The earth tarns about its >hortest diameter, which is called it- axis, the extremities of the axis being called the poles of the earth. An oblate spheroid is a figure traced out by the revolution of a semi-ellipse, such as PQP' in Fig. 1, about its minor axis PP'. The successive positions of PQP' are called meridians. That meridian which passes through the transit instrument at the Royal Observatory at Green- wich is called the prime meridian. The circle traced out by the point Q, which is the extremity of the semi-major axis of the ellipse, is p called the equator. The earth revolves about its 7 feet and 6 = 2-08549 x.10 7 feet and substituting these values, we find that the length of the sea or nautical mile in latitude L is given by n = [0070-8 — 31* 1 cos 2L] feet. It will be seen from this equation that the sea or nautical mile varies with the latitude, being shortest at the equator where its Length La 6045*7 feet and longest at the poles where its length i- 6107*9 feet. The lengths of the nautical mile, in various latitude-, are given in an's Tables. For convenience, when discussing small distances, the tenth part of a nautical mile is called a cable. 6. The geographical mile. — The geographical mile is the length of an arc of the equator which subtends an angle of 1' a1 the centre of the earth. The equator being a circle, the Length of the geographical mile i- the same al all parts of the equator. 7. Length of the geographical mile. !u Fig. 5 Lei ED be an arc of the equator which subtends an angle of I' ba centre C, then the length of ED i- the Length of the geographical mile. Now IJ> CE • m. of K('I> EC .n. ot l' ECsin r « in l'. The ■ if the geographical mile i- 6087' I feet. 8. Linear latitude and longitude. The ;.< .-it i<»n of a place on I he c.nt h- -ant may '!«■ expre sed by reference to t he equator and prime meridian. The Linear Latitude of a place La the Lengl h of t he arc of i he meridian of i he place intercepted between the equator i the place, h i- measured In nautical miles, and is named North oi South according as the place is North or South of ihc equator. Fig. 5. Art. 9. Fig. 6. In Fig. 6 let the meridian EP be divided into sea or nautical miles at the points G, H, &c. ; then, since EG is a nautical mile, and since a nautical mile is an arc of a meridian between two places whose latitudes differ by 1', the angular latitude of G must be 0° 1' N. Similarly, since GH is a nautical mile, the angular lati- tude of H must differ from that of G by 1', and must therefore be 0° 2' N., and so on. If the length of EB is 40 X 60 or 2,400 sea or nautical miles, the angular latitude of B must be 40° N. We may, therefore, say that, if a place is in latitude 10 D N., the length of the arc of the meridian, intercepted between the equator and the place, is 600 nautical miles. Conversely, if a place is situated 300 nautical miles North of the equator, its angular latitude is -^r- or 5° N. It is customary to write 1 nautical mile as i' and 60 nautical miles as 1°, because if a place is situated a particular number of nautical miles North or South of the equator, the angular latitude of the place contains the same number of minutes of arc. It should be remembered that linear latitude is a measurement of length and not angle, and if we refer to a linear latitude 10° N., we refer to a length along the meridian of 600 nautical miles measured in a Northerly direction from the equator. The linear longitude of a place is the smaller arc of the equator intercepted between the prime meridian and the meridian of the place ; it is expressed in geographical miles and is named East or West according as the place is East or West of the prime meridian. Let us suppose that the equator is divided into geographical miles, then, since the geographical miles is the length of an arc which subtends 1' at the centre, two geographical miles subtend 2' at the centre, three geographical miles subtend 3' and so on. For this reason, it is usual to write a geographical mile as 1', and to write 60 geographical miles as 1°; but it should be remembered that linear longitude is a measure- ment of length and not angle, and if we refer to a linear longitude 10° E., we refer to a length along the equator of 600 geographical miles measured in an Easterly direction from the prime meridian. 9. The knot. — In navigation the unit of speed is the speed of one nautical mile per hour, and this unit is called the knot. A ship, steaming 10 nautical miles per hour, is said to be steaming 10 knots, and this should never be expressed as " 10 knots per hour." As it is impracticable to construct speed recording instruments, such as patent logs, to register the length of a nautical mile as it varies in different latitudes, it becomes necessary to decide upon some suitable length for the nautical mile which these instruments may be constructed to indicate. The length decided on is 6,080 feet, and the British Admiralty knot is therefore a speed of 6,080 feet per hour. The reason for the adoption of this length is uncertain, but it is supposed to have 5 Arts. 10, 11- been taken because it is the nearest round number to 6082 '2 which is the length in feet of the nautical mile in the English Channel. 10. The earth approximately a sphere. — Although the earth is an ( 'I >late spheroid, for nearly all purposes of navigation it is sufficiently accurate to assume it to be a sphere whose radius is the mean of the earth's greatest and least radii, that is, 2-089055 x 10 7 feet. The errors involved in this assumption are very small and entirely lost in practice amongst the many other errors incidental to navigation. < >n the assumption that the earth is a sphere, the length of an arc <>f a meridian subtending an angle of 1' at the centre is 6,077 feci, and this length is tlie same as the mean length of a sea or nautical mile between the equator and the poles; therefore, this length to the nearest round number, that is 6,080 feet, has been taken as the length of the mean nautical mile which is the same as the length on which the Admiralty knot i^ based. This value of the mean nautical mile give^ a mean value for the cable of 202*7 yards. It is customary to regard a cable as 200 yards, which is the same as the length of eight shackles of chain cable, called a " cable's length," a shackle being 12.1 fathoms or 25 yards Jong. Another reason for regarding the earth as a sphere is that the linear latitude and linear longitude are then measured in the same units, namely, the length of a mean nautical mile, and there is no further need to consider the geographical mile, or to draw a distinction between pilar latitude and longitude and linear latitude and longitude in numerical calculations. Under the worst conditions arising from this assumption, the error in the linear latitude cannot exceed '31 per cent.. while that in the linear longitude cannot exceed half this value. It should be noticed that when we regard the earth as a sphere, the meridians Income semi-great circles, and the angular latitude of a place i- the angle at the centre between the plane of the equator and the radius of the earth which passes through the place. 11. Difference of latitude and difference of longitude. — One position on the earth's surface is related to another by the difference of latitude and difference of longitude. The difference of latitude between two places, usually written year, and care should therefore be taken that the correct variation is used ; the annual change in variation for all places is given on the variation chart. It will thus be seen that, if we know the variation and the direction of magnetic North, we know the direction of the true meridian: there- fore, at ■ i by aid of the magnetic compaa and the variation chart we I. mow the directions of two meridians which intersect at the observe r, namely, the magnetic and true meridians; consequently, the direction ol any point may be referred to either one of these meridians. The bearing of a point, when measured from the true meridian, is called the true bearing and, when measured from the magnetic meridian, it is called the magnet ic bearing. Art. 15. 8 For example, suppose that an observer is at a place where the variation is 20° W., and that the compass needle lies along the line OM (Fig. 9), which is the magnetic meri- dian. The line OT which is drawn so that the angle TOM is 20°, and M is to the West of T, is the true meridian. It will be seen that the direction of North (true) is N. 20° E. (mag.). Again, if OX is the great circle which passes through the observer and a point X, and if the angle MOX * is 60°, the magnetic bearing of X is N. 60° W. The angle TOX being 80°, * —__ the true bearing of X, is N. 80° W. (280°). 15. Deviation of the Compass. — On account of the magnetism in the iron and steel of which the ship is con- structed, the compass needle may not he exactly in the magnetic meridian but to one or other side of it. The angle between the compass needle and the magnetic meridian is called the Fig. 9. deviation, and is named East or West according as the North seeking end of the needle lies to the East or West of the magnetic meridian. In a ship there are generally several compasses, one of which is in a very carefully selected position in order that it may be affected as little as possible by the magnetism of the ship; this compass is called the standard compass. The other compasses are situated at the various steering positions, and observations taken with them must always be checked by comparison with the standard compass. Each compass is provided with a mark or pointer called the lubber's point, situated inside the bowl and close to the edge of the compass card and in such a position that the line joining it to the centre of the compass card is parallel to the fore-and-aft line of the ship ; therefore the gradua- tion of the compass card which is opposite to the lubber's point gives the direction of the ship's head as indicated by that particular compass card. As the compasses are differently situated with regard to the iron and steel of the ship, they are differently affected by the ship's magnetism and consequently two compasses, similar in every respect but situated in different parts of the ship, generally have entirely different deviations. In general the deviation of a compass is different for different directions of the ship's head, and is obtained for various directions of the ship's head by observation. A specimen deviation table, such as is made out and hung up in the vicinity of the compass to which it applies, is shown below : — Ship's Head. Deviation. Ship's Head. Deviation. / N. . 2 00 E N. by E. 2 25 E N.N.E. 2 45 E N.E. by N. 3 00 E o / N.E. 3 00 E N.E. by E. 2 40 E E.N.E. 2 00 E E. by N. 1 10 E s I Art. 16. Ship's Head. Deviation. Ships' Head Deviation, E. 00 s.W. o 00 E. E. by S. 1 10 w. s.W. by \Y. :} 45 E. E.S.E. 1 20 w. w.s.w. 4 10 E. S.E. by i: 3 1.-. \Y. W. bv S. 4 15 E. S.E 3 50 w. \v. 4 00 E. S.E. by s. 4 00 w. * W. by X. 3 30 E. S.S.E. 3 45 w. W.X.W. 2 55 E. S. by !•:. :: 00 w. X.W. by \\". •> 20 E. s. 2 no w. X.W. 1 50 E. s. by W. 45 w. N.W. bv X. 1 30 E. S.S.W. 40 E. N.N.W. 1 30 E. S.W. b\ s. 1 55 E. N. by YV. 1 40 E. This table will be referred to in working examples throughout the book. 16.— Methods of applying deviation and variation. — We have now to find the direction of the ship's head (magnetic) and the ship's head (true), when the direction of the ship's head by compass is known; for example, suppose that the ship's head by the compass, the deviation tabic for which is given above, is N. 50° W., and that it is required to find the direction of the ship's head (magnetic). On reference to the table we see that the deviations are given for every point (11° 15'), and as X. 50 \V. lies between N.W. and N.W. by W., we take the deviation as 2 imi' E. 1 1 1 Fig. 10 let OM represent the magnetic meridian, and OC the direction of the North point of the compass needle, so that the angle MOG is 2°, and G lies to T the East of M. Let the line OH represent the direction of the ship's head or lubber- point, the angle COR being 50°. Then it will be Been thai the angle MOB. is 48°, so that the direction of the ship's head is X. 4 s \V. (mag.). If the variation at the ship, from the variation chart, is found to be 20 \\\, let the line OT represent the true meridian, so that the angle TOM is 20° and .1/ lies to the West of T ; then it will be -••••II that the angle TOR is 68°, so that the direction of t hr ship's head is X. <>8° W. (true) C2'.r2°). In order to avoid mistakes, the student i recommended to draw figures when applying variation and deviation, but cir cumstancee may arise when this is impracti ca ble, and so we must have some rules i>\ which the operation can be carried out mentally; these rules are as follows ; _ (a) Given the compass direction to find the magnetic (or given the magnet lc to find t he I rue) : — [magine yourself to be standing at the centre of the compass card and looking in the given direction; apply Ki terly deviation (or variation) to the right, and apply Westerly deviation (or variation) to the left. Fig. 10. Art. 17. 10 (6) Given the true direction to find the magnetic (or given the magnetic to find the compass) : — Reverse the rule above, that is, apply Easterly variation (or deviation) to the left, and apply Westerly variation (or deviation) to the right. As some compass cards are now graduated from 0° to 360° (from North through East), it is convenient when using them to name Easterly deviations and variations +> and Westerly deviations and variations — . (a) and (b) now become : — (a) Apply deviation and variation according to their algebraical signs. (6) Apply deviation and variation contrary to their algebraical signs. The following examples illustrate the application of these rules : — (a) * Ship's head (compass) ----- Deviation from table ----- S. 50° 3 00' E. or 30 W. 130° 00' - 3 30 Ship's head (mag.) ----- Variation from chart ----- S. 53° 20 30' E. or 00 W. 120° 30' - 20 00 Ship's head (true) ----- S. 73° 30' E. or 106° 30' (b) Ship's head (true) Variation from chart - Ship's head (mag.) Deviation from table (for N. 20° AY Ship's head (compass) - N. 40° 00' W. or 320° 00' - - 20 00 w. - 20 00' _ _ N. 20° 00' W. or 340° 00' •) - - 1 30 E. or + 1 30' - N. 21° 30' W. 338° 30' 17. The gyro-compass. — The gyro-compass is an instrument sur- mounted by a card which is graduated in a similar manner to that of the magnetic compass, Fig. 8, except that the degrees are marked from 0° to 359° from North through East, and indicates true directions in obedi- ence to the mechanical laws on which it is based. There is a slight correction, due to the course and speed of the ship, which has to be applied to the bearings indicated by it ; this correction is explained in Part IV. The movements of the gyro-compass are communicated electrically to receivers, which are placed as convenient in different parts of the ship. 11 Art. 18. CHAPTER III. THE COURSE AND DISTANCE BY THE MERCATOR'S CHART. 18. The rhumb line. Course and distance.- -We are now led to the consideration of the problem of how to pass from one position on the earth's surface to another. As when about to set out for a place by land, so in setting out for a place by sea, the first question that arises is. Which is the way? Neglecting other considerations, it will obviously be of great advantage if the direction of the ship's head is the same at all points of the track, that is if the track cuts all the meridians at the same angle. Now a line on the earth's surface which cuts all the meridians at the same angle i- called a rhumb line. If, therefore, two places on the earth's surface are joined by a rhumb line and the ship steered along this line the direction of the ship's head will remain the same; this direction is called the course. The course is measured from North or South, ording as the d Lat. is N. or S., from 0° to 90° towards East or West, according as the d Long, is E. or W. (§ 11). The equator, parallels of latitude and the meridians are all rhumb line-. In Fig. 11 F is the place "From'' which the ship starts, T is the place " To " which she is bound. The curved line, FABCT, is the rhumb line joining the two places, and the angles PFA, PAB, PBC, PCT, &c, all being equal, any one of them may be regarded as the course. The length of the rhumb lira- between F and T, expressed in nautical miles. Is called the dis- y/ lance between F and '/'. Now the shortest distance I- etween tWO places is 1 lie arc of i he great circle which joins I hem. A '_ r rea< circle, however, cuts I he meridians at different angles, BO i hal to -t i am along a great circle would necessitate constant altera- tions in t he direction <>f I lie snip's head. We have therefore i<> choose between the rhumb line at every point of which the direction he same, but which is longer than the arc of the great circle, and the arc of ilic great circle ;it ivciv point of which ilie direction is different hut which i shorter than the rhumb line. The great convenience <>t keeping the hip- head in a constant direction, as well as tin- simplicity of tin- calculation involved in finding this direction, gives a preference to the rhumb line, except over very long di tanci / F/> their distances apart at the equator on the earth's surface. r~ / /b a < y c / / / / f a- c 1 oo Chart. Fig. i::. The parallels "I latitude are rhumb lines, and tiny cut tin- meridians .it right angles; therefore, from (l) and (2) the parallels < » i latitude are represented on the chart b\ i j bem of parallel straight lines at ri .i ngle i to 1 he meridians. We have now to find at what distance from eq the variou lines should be drawn which represent the parallels <>l latitude. To do this, let u- consider a rhumb line which does not run either North <>r South, i i meridian, or East "i West, a a parallel of latitude. Let FT be a rhumb line on the earth's iirface, joining the point F ■ ■ i t he equator t" ■> point T, t hen /•"/' bj (1) i n presented on the chart l-\ light line fl. Art. 20. H Let a large number of equidistant parallels of latitude be drawn between F and T, and let the length of a meridian intercepted between any consecutive two be dl. Let the rhumb line FT intersect any two consecutive parallels in A and B. Let the meridians of A and B intersect the equator in A' and C respectively, and let the parallel of latitude through A intersect the meridian of B in C. Let the corresponding points on the chart be denoted by small letters. If CB, that is dl, is so small that the triangle CBA may be considered a plane triangle right-angled at C, then, since by (2) angles on the earth's surface are equal to the corresponding angles on the chart, the two triangles ABC, abc, are similar, and therefore cb ca ca 1 CB = CA = CA' cosL = cosT where L is the angular latitude of A, and the spheroidal form of the earth is neglected. Therefore CB cb = T cos L or cb = dl sec L. Therefore, if two near parallels of latitude intercept a length dl of a meridian, the corresponding length on the chart is dl sec L, where L is the angular latitude of the lower parallel. Let the angular latitude of B be L + dL, so that CB. that is dl, , subtends an angle dL at the centre of the earth. Then if B is on the n ih parallel, L = (n — 1) dL, and cb = dl sec (n — 1) dL. Therefore the length of a' a on the chart is dl sec + dl sec dL -f- dl sec 2dL -f- . . ~f dl sec (n — 1) dL. Now dl = R X dL, where R is the earth's radius. Therefore a'a = R x dL [sec + sec dL + sec 2dL + . . . -f- sec (n — 1) dL]. The value of this series, when n is infinite, is pi * 90 ° + L R log e tan - — , or, reduced to ordinary logarithms, R X 2-302585 x log tan 9 °° , + L . When R is expressed in nautical miles, the value of this expression is called the meridional parts (m.p.) for latitude L and is tabulated in Inman's Tables for every minute of arc from 0° to 90°. Therefore the distance on the full sized chart, between the line which represents the parallel of latitude L and the line which represents the equator, is the meridional parts for latitude L. 15 Art. 21. It follows that the length on the chart, between the lines which represent the parallels of latitude L and L', is the difference between the meridional parts for latitude L and the meridional parts for latitude X', and this difference is generally written rf.m.p. When L = 90°, the meridional parts become infinite and therefore the chart of the earth's surface extends to infinity in either direction perpendicular to the equator. It will be seen that on the full sized Mercator's chart small lengths are sec /. times their length on the earth's surface, and that small areas are see 8 L times their areas on the earth's surface It should be noticed that ft ab AB n.AB FT ni.p. be ' BC a. BG rf.Lat. which is the relation between the distance ft on the full-sized Mercator's chart and the actual distance FT. 21. Construction of a Mercator's chart. — To construct a chart of con- venient size we should mentally construct a full-sized chart, which we have just considered, and then reduce this according to sonic particular scale. Let us construct a chart of the earth's surface on a scale of 10° •of longitude to the inch, the meridians and parallels to be drawn at every 20°. The length of the ecpiator is 360° or 360 X 60 nautical miles; therefore, since the chart is to be drawn on a scale of 10° or 600 nautical miles to the inch, the line representing the equator is 36 inches long. Draw a line of this length to represent the equator in the middle of the sheet. Since the meridians are to be drawn at every 20°, and the scale is !" of longitude to the inch, divide this line into 18 equal parts, each 2 inches long. Mark the left hand extremity of the line 180° W., and then, towards the right, mark the intermediate points of division I \V., 140° W., &i . down to , then 20° E„ 40° E.,&c.,as far a- the righl hand extremity which marks 180° E. Through these points erect perpendiculars to represent the meridians. We have now to draw the parallels of latitude at every 20 . On the full-sized chart the distance of the parallel .if latitude of 20° from i lie equator i- the meridional parts for 20°. Now the meridional parts for 20 i- 1225- i f nautical miles, and on a scale of 10° of longitude to the inch, which is the same as (ion nautical miles to the inch, this i^ represented by 2*04 inches. Draw two lines parallel to the equator on the chart al a distance ot -•«>! inches from if ; mail, the extremities of 'he upper line 20 X. and the extremities of the lower line 20 s. These hue- represent the parallels Of 20 North latitude and 20 South latitude pectively. In the same way all the other parallels may lie drawn. The configuration of the land, the positions of rock-, shoals, &c. now be placed on the chart by means of their respective latitudes and longitudi In order that charts may be on a lai • de, it is necessary t" construct them tor portions "I the earth's surface only. In such charts the equator may not be included, and the differences between successive kllel oi latitude on the chart are found l>y reducing to inches, i ording to icale, the difference! between the corresponding meridional Art. 22. 16 As an example, let us construct a chart from 142° E. to 146° E., and from 54° N. to 58° N., the scale of the chart being 1° of longitude to the inch. The meridians and parallels are to be drawn for every degree of longitude and latitude respectively. The difference of longitude of the extreme meridians of the chart is 4°, and, since the scale of the chart is 1° of longitude to the inch, we draw a line 4 inches long at the bottom of the page (Fig. 14), to represent the parallel of latitude of 54° N. Divide this line into four equal parts, and mark the left hand extremity 142° E., the right hand extremity 146° E., and the points of division as in the figure. Through the extremities of this line, and the three points of division, erect perpendiculars to represent the meridians. The distances between the various parallels of latitude are found] as shown in the following tabular form : — Latitude. Mer. Parts. f/.m.p. d.m.p. on chart Nautical Miles. Naiitical Miles. Inches. 58° 4294-30 111-68 1-86 57 4182-62 108-72 1-81 56 4073-90 105-93 1-76 55 3967-97 103-33 1-72 54 3864-64 We now draw the parallels of latitude. The parallel of 55° is drawn at a distance of 1-72 inches from the line at the bottom of the page. The parallel of 56° is drawn at a distance of 1-76 inches from the parallel of 55°, and so on. In order to be able to put down positions on the chart with accuracy, it is necessary to graduate the extreme parallels and meridians of the chart. The graduation of a parallel is the same as that of the equator, and simply consists of dividing the length representing degrees into a number of equal parts. The graduation of the meridian is effected by carrying still further the process of finding the positions on the chart of the parallels of latitude. In Eig. 14 the chart has been graduated for every 10' of latitude and longitude. 22. Plotting positions on a Mercator's chart. — Example. Plot on the chart Fig. 14 a position / whose latitude is 56° 50' N. and whose longitude is 142° 50' E. The position obviously falls within the rectangular area on the chart comprised between the parallels of 56° N. and 57° N. and between the meridians of 142° E. and 143° E., the nearest parallel being 57° N. and the nearest meridian 143° E., so that the position lies near to the N.E. corner of the rectangle. Place the edge of the parallel rulers against the parallel of 57° N., move it until its edge passes through the graduation of 56° 50' N. and then draw in a short line representing a portion of the parallel of 56° 50' N. in the neighbourhood of the N.E. corner. Again, place the edge of the parallel rulers against the meridian of 143° E., move it until its edge passes through the graduation of 142° 50' E. and then draw a short hue representing a portion of the meridian of 142° 50' E. in the neighbour- hood of the N.E. corner. The intersection of these two short lines is the position on the chart required. 17 Art. 23. 142*E. 14-3'F.. M l-'K. I 15TE 58°X. 57N 66 T* 64H 14-CK N 56*N. .:. N 5r>°N r >-J-*N 14:: I. 23. To find the compass course from one position to another. Lei /and i !><• ili<' two positions <>n the ohart. Join fi by a *traigh1 line, then \\«- notice that the direction "i t from /' is between South and East nine). If we measure the angle which the line fi makes with the x 6108 B Art. 23. 18 meridian, we find it to be 146° 30' and consequently the true course from F to T is 146° 30'. We have now to find the compass course. True course - - - - 146° 30' 180 00 Variation from variation chart - Magnetic course - Deviation from deviation table - Compass course - Therefore the compass course to steer is S. 21|° E. On the majority of the published charts a diagram of a compass card is printed which gives magnetic and true directions for every degree. Fig. 15 shows such a compass card, the variation being 7° 40' W. s. 33 30 E. 8 12 W. - s. 25 18 E. 3 45 W. - s. 21 33 E. 10' ■ '■ / vy ''.jo. o- 9~ V » 'v.. •ai •• .01 .o ,v A P" * -'■..,. •°«r .081 JO* Fig. 15. When such a compass is printed on the chart the magnetic course may be found by transferring the line ft, by means of the parallel rulers, to a position passing through the centre of the compass ; the magnetic course may then be immediately read off. When using this method we must bear in mind that the variation changes slightly from year to year; consequently the information given on the engraved compass card should be examined and, if necessary, a correction made to any 19 Arts. 24, 25. direction taken from it. For example, in Fig. 15, the variation is given as 7 D 40' W. (1916), decreasing about 8' annually. Coarse as taken from compass on chart - S. 2f)°45'E. I lhange in variation (1912 to 1910) - 32 W. Magnetic course (1912) - Deviation from deviation table - Compass course - S. 25 13 E. 3 45 \V. S. 21 28 E. 16 °N therefore the compass course to steer is S. 21°-J E. as before. 24. To find the distance from one position to another. — Let the two positions on the Mercator's chart be / and t (Fig. 16). Let the parallel of latitude through / inter- sect the meridian through t in m. Let F, T and M be the points on the earth's surface represented by /, t and m on the chart, then the length of FT is the distance be- tween the points represented by / and (. and TM is the difference of latitude between the same points and may be ascertained from fhe graduations at the side of the chart. 15°N Fig. 16. \<>\Y FT ft (§20); therefore /£ represents the distance on the TM ~ tin same scale as tm represents the known difference of latitude. Thus, it the latitudes of F and T are 15° N. and 16° N. respectively, and if the lengths of ft and tm on the chart are 3 and 1 • 5 inches respectively, the distance is 12o miles. The degree of accuracy thus obtained is seldom necessary, and it ifi customary to take, on the dividers, the largest convenient length, say. that corresponding to a difference of latitude of 10' {ab in Fig. 16) from the Bide of the chart, and from that part of the scale midway between the parallels of F and T, and to ascertain the number of miles represented by ft on the assumption that// represents the distance on the same scale as ab represents 10 miles. The latter method is sufficiently accurate for all practical purposes, provided the distance <\f lo miles, the error, provided thai the divider- have been accurately Bet, will n<>i exceed I per cent., when the distance is 600 miles and the mean latitude 60 . Where the rhumb line crosses the equator we maj till measure distances in tin manner, but in all ca i where 'jre.it accuracy is required the distance should be found by calculation, as explained in the following chapter. 25. To allow for a current when finding the course. When a ship's motion is influenced by currents or tidal streams, her direction of movement is not, in general, the &ame a that < >f tin- fore-and-aft line. i: 2 Art. 25. 20 The direction of the ship's track at any time is called the course made good, and the actual speed over the bottom of the sea in that direction is called the speed made good; the latter is often referred to as the speed over the ground, in distinction to the speed through the water. The direction in which a current is running is called the set of the current, and the speed in knots at which it is running is called the drift of the current. The set and drift of a current may be obtained from a chart called a current chart, and the direction and rate of a tidal stream from an atlas called an Atlas of Tidal Streams, as explained in Part III. To find what course should be steered in order that the course made good should be as desired, the triangle of velocities is employed. Example : — In § 23 the magnetic course has been found to be S. 25° \ E. From the current chart it has * been found that a current running S.S.W. (mag.) 2 knots will probably be ex- perienced. It is required to find the compass course. From/, Fig. 17, lay off fx to represent S.S.W. 2 knots (the set and drift of the current expected) on any convenient scale. With centre x and radius xy to represent 10 knots (the ship's speed through the water on the same scale) describe a circle cutting iin y ; then the direction of xy which is S. 34° E. (mag.) gives the course in order to make good S. 25°i E. (mag.) on the assumption that the set and drift of the current is S.S.W. 2 knots. Magnetic course - Deviation from deviation table Fig. 17. s. 34° 4 E. W. s. 30 E. Compass course - The speed made good along the line ft is given by the length fy which represents a speed of 11*2 knots. 21 Art. 26. CHAPTER IV. THE COURSE AND DISTANCE BY CALCULATION. 26. Fundamental formulae for the rhumb line. — When great accuracy is required, the course and distance arc found by calculation. In Pig. 18 let FT be the rhumb line joining two places F and T. Between F and T let a large number (n) of equi- distant parallels of latitude be drawn cutting the rhumb line in F, A, B, C, &c. Let the meridians through these points intersect the equa- tor in D, A', B', C, &c. and the parallels of latitude in X, Y , Z, &c, as in the Figure. In the small triangles FAX, ABT, BCZ, &c, the angles FXA, AYB, BZC, &c, are right angles ; the angles FAX, ABY, BCZ, &c, are all equal, each being equal to the course ; also the sides AX, BY, CZ, &c, are. all equal; Earth therefore the triangles are YiQ. 18. equal in all respects, and, as they are very small, may be considered plane right angled triangles. In the triangle FAX, AX = FA cos course .'. ii . AX = n . FA cos course .• . d Lat. — Distance cos course (1) Again n FX /'.I sin course FX = n . FA sin course. .\..u FX AY + BZ + &C is called the departure (Dep.) and is named East or Wesi according as the d Hong, is named ftast or West. Since FX A ) HZ = &<■.. the departure n . FX. .-. Departure distance sin course (2) Dividing equation (2) by ih<- corresponding sides of equation (I), we have depart are Tan '-"in se d Lat (3) Arts. 27, 38. 22 27. Formula for the departure.— In Fig. 18 let the latitudes of F and T be L and 27 respectively and let the difference between the latitudes of adjacent parallels be dL, then we have DA' - FX sec L = 5^-" sec L n A'B' = AY sec (Z, + dL) = --^ sec (£ + dL) B'C = BZ sec (L + 2tfL) - =^ sec (L + 2dL) n and so on. By addition we have, since 2X4' f A'B' + 2?'C' + &c. is the d Long., cZ Long = Dep - [sec L + sec (L + dL) + sec (L + 2dL) + . . + sec {U - dL) n \_ d°t) r — - '" sec + sec dL -f sec 2 Now n x R dL = d Lat. \ n = ^ - ■ ' ■ R dL , T Dep. x R dL d Long. = — d Lat. sec O + sec dL + sec 2 dL + . . + sec (L' — dL) — sec — sec dL — sec 2dL — . '. — sec (L — dL) the product of R dL and the difference of the two series within the brackets on the right is the difference of the meridiorial parts between F and T (§ 20). Therefore Dep. X rf.m.p. d Long . = . ^ Lat Or „ d Long, x d Lat. Dep. = f (4) d.m.p. 28. Formulae for course and distance. — From (3) and (4) we have m d Long, ian course — . a.m. p. From (1) we have Distance = d Lat. sec Course. (A) When the d Long, is 0°, the course is 0°, and the distance is equal to the d, Lat. From (2) we have Distance = Dep. cosec Course. (B) When the d Lat. is 0°, the course is 90° and the distance is equaJ to the departure. 23 Art. 29. On account of the different rates at which the secants and cosecants of angles which are mar and 90° vary, it is advisable to find the distance from formula (B) when the course is very large. Example: — Find the course and distance from Plymouth, Lat. 50 20' X., Long. -I 9' \\\. to Bermuda, Lat. 32* id' X., Long. 64 tit' \\\ Plymouth - Lat. 50° 20' N. m.p. 3505*70 Long. 4° 09' W. Bermuda ..-.., 32 19 \. .. 2050*83 ,, 64 49 W. 18 01 S. '/.m.p. U54-87 60 40 W. 60 60 d Lat. 1081' S. dLong. 3040' \V. ./ Long. 3640 '• m course , - = , ... „_ 9. Art. 30. 26 We will now show by an example how the course and distance may be found by means of the traverse table. Exam/pie : — Find the course and distance from F Lat. 56° 50' N., Long. 142° 50' E. to T Lat. 55° 00' N., Long. 145° 00' E. F Lat. 56° 50' N. T „ 55° 00' N. Mid. Lat. 56° 50' N. „ 55° 00' N. Long. 142° 50' E. „ 145° 00' E. 1 50 S. 60 • 2/111 50 Lat. 55 55 N. 2 10 E 60 d Lat. 110' S. d Long. 130' E. Dep. = d Long, cos Mid. Lat., = 130' cos 55° 55' = 72' -8 by traverse table. Dep. 72-8 Tan Co f/Lat. " 110 Searching the tables till we find 72-8 as Dep. corresponding to 110 as d Lat., the course and distance will be found to be S 33°| E., 132 miles. 27 Art. 31. CHAPTER V. THE (ii:i:.\T CIRCLE TRACK. 31. The gnomonic chart. In § IS it was remarked that the shortest distance between two places is along the arc of the great circle which joins them. When a saving of time is a prime consideration, it is necessary to find how a ship should be steered in order that her track may coincide as far as possible with the great circle arc. To do this it is necessary to lay down the great circle arc on the Mercator's chart, and this is easily done by the aid of charts constructed on the gnomonic projection. On these charts great circles are represented by straight lines, and therefore they show at a glance w hether the great circle track leads the ship into any danger. The gnomonic chart is constructed on the following principle — Every point of half the surface of the earth is projected from the centre on to a tangent plane at some selected point, called the point of contact. The plane of the equator contains the earth's centre, and, therefore, the equator, when projected from the centre on to a tangent plane, become^ a straight line. Similarly, the meridians become straight lines converging to that point which is the projection of the pole; and every _ peat circle of the earth becomes a straight line. The planes of the parallels of latitude do not contain the earth's centre; therefore parallels of latitude when projected on to the tangent plane become curves, which are sections of cones. In Fig. 20, let a tangent plane YZ touch the earth at the point of contact C whose latitude is L r , and let us consider the projection of meridians, parallels, &c, on this tangent plane. Lei "/ be the projection of an arc of the equator EQ, and j> be the projection of the pol< P : then pCq is the projection of the meridian of C, and Ls called the central meridian of the chart. Lei /..i and /,/,. be the latitudes of two points .! and B <>n the centra) meridian, and situated on either side of the point of contaci C. Let jectionsof the meridians in a series of points C, C", &c. ; then the pro- jections of the points of the parallel p of latitude L u are placed on the projections of the meridians De- reference to the points C, C, C", &c. To place the point C, C", ('< " and ('("/> are righl angles, we have <>< OC* CC* (Ojr ,,<'-) I (,,<'- P C'*). ... oo't otf* -pC'\ from u inch it follows that the angle OC'p i la right angle, and consequentri the angle <>i><" \< the latitude oi C" /.,'). Fig. 21 COq) (*) Arts. 32, 33. 30 Now in the triangle OC'd' we have C'd' = OC tan d'OC = OC tan (L D - L c '). Also in the triangle OpC* OC = Op sin OpC = Op sin L c ', and in the triangle pCO Op = OC cosec OpC = R cosec L c . Therefore OC — R cosecL c sin L c '. Therefore C'd = R cosec L c sin L c ' tan (L D — L c '). Now the side ox of the spherical triangle ocx (Fig. 20) is equal to the angle opx = L c '. Therefore cos G = tan L c cot L c ', or tan L c ' = tan L c sec (7. There- fore to find C'd' we have the formulae C'd' = i2 cosec L c sin X c ' tan (L D — L c ') ) where tan L c ' = tan L c sec C ) ' ' When L D is greater than L c ', C'd' should be laid off towards the pole, and, when less, towards the equator. At the point of contact, angles on the earth's surface are correctly represented on the chart ; when the angle, between a great circle through the point of contact and a great circle which does not pass through the point of contact, is a right angle, this angle is correctly represented; with these exceptions, angles on the earth's surface are not correctly represented, 32. Special cases of the gnomonic chart. — When the point of contact is at either pole, the meridians are projected as straight lines radiating from the point of contact, the angle between any two lines being equal to the d Long of the meridians of which they are the projections. The parallels of latitude are projected into a system of concentric circles, the centre being the pole. The radius of the parallel of latitude L D is R cot L D . When the point of contact is on the equator, the meridians are projected into a system of parallel straight lines ; the equator is pro- jected into a straight line perpendicular to the meridians ; the parallels of latitude are projected into hyperbolas. From formula (2), or by drawing a figure, we see that the distance of any meridian from the meridian through the point of contact is R tan G. From formula (5), or by drawing a figure, we find that the dist- ance from the equator of a point on the parallel of latitude L D , is R sec G tan L D . 33. Construction of a gnomonic chart. — The formulae (l), (2), (3), (4) and (5) all involve one linear measurement, namely the radius of the earth R, so that the size of the chart depends on the length which we assign to R. To determine this we must take into consideration the height of the sheet of paper at our disposal, which we will suppose to be h inches, so that the length ab on the chart is h inches. Referring to Fig. 22, draw ba down the middle of the page and divide it at the point C so that bC = R tan (L B — L c ), and ( 'a = R tan (L (; — L A ) . Through a and b draw two lines at right angles to ab. 31 Art. 33. From formula (1) wo have, since ab is represented by // inches on the chart, // inches tan {L c — L A ) + tan {L n — Jj C ) and this gives the value of R which is to be used in formulae (2), (3), (4) and (5). b'" b" b' b / / 1 /d'" / C / c ' a" a Fig. 22. From a, lay off aa' as calculated from (2), and from b lay off bb' as calculated from (3). Join a'b' ; then a'b' represents the meridian whose longitude differs from that of ab by 0. In the same way another meridian a"b" can be drawn whose longitude differs from that of ab by 2G, and so on. From C drop perpendiculars CC, CC", &c, on to the meridians. To draw the parallel of latitude L D lay off Cd as calculated from (4). From (" lay off Cd' as calculated from (5). From C" lay off C'V" calculated from (5), and so on. Through the points d, !)'• middle of 1 1 >< ■ page, as shown in Fig. :_>;{. Since (/, /; I.,) (/., /. , | the point of contact C is at ili<' middle point of i he line ab. Through a and b dnw lines at right angles to ab. From formulas (2) and (3) calculate aa', bb', aa", bb", &c giving G the values 10°, 20°, 30° and 10 oa to be able to draw in the meridian for '\ ei 3 i (| of longitude. = o *2 98 re o = O "5 iO b co to CO O iO 00 ** 1/3 O O 10 •3 CO to CO o M CO O 9 >o CD * '10 © = Or O^ O-o ► ' eo >■*- CN c M -O O* ~i 1-4 ft CO (-1 8*- rH i0 IT) in OH 33 Art. 34. The results are as follows : — £10° aa' 1-205 inches G 20° G30° #40 aa aa' aa' 2-610 4-140 0-018 W 730 inches bb" 1 .".07 bb"' 9 391 „ 66"" 3 47.") Having laid off the points a', b', &c, join «' 6', a" 6", &c, and so obtain the meridians. Mark these meridians, on the left, 130° W., 140 ? \V.. 150° W.. and WO W. : and on the right 110° W., 100° W„ 90° W.. and 80° \\ . From the point of contact C drop perpendiculars on the various meridian- and so rind the points C, C", &c. Calculate the latitudes of the points C, C", &e., by the second formula of (5), and these will be found to be as follows : — C Sir/' 49° 06' C"" 52° 32' We shall now draw in the parallels of latitude of 30° S., 35° S., 40° S., 45° S., 50° 8., and 55° S. First, rind the distances from the point of contact C of these parallels by formula 4. Next, find the distances of the parallels of latitude from C, C", &c\, by the first formula of (5), and we find the various values to be as follows : — Inches. C d. C d' C" d" C" d'" C"" d"" L„ 30° 2- 144 2-224 2-487 2-961 L D 35° 1-408 1-484 1-720 2-148 — L D 40° •704 •767 •981 1-370 — L D 45° — •061 •245 •613 1187 L D 50° •704 •625 •463 134 •397 L„ r,r, 1-408 1-358 1-191 •884 Plot the positions of d, d', d", &c, for the various parallels of latitude and draw curves through them, as shown in Fig. 23; mark the curves 30 S., 35° S., 40° S., 50° S.. and 55° S. The chart is bounded on the right and left by drawing lines parallel to the central meridian. 34. To draw the great circle track on the Mercator's chart. — To draw the great circle Hack Oct ween j wo places/ and t on t he .Mercator's chart, first draw it on the imomonic chart as shown in Fig. 23, and note the Latitudes of tin- point- where the track crosses various meridians. These point- should then 0.- plotted on the Mercator's chart by means of their latitudes and Longitudes, and a smooth curve drawn through them. In Pig. l' I t lie ciir\ <• in full line shoVi a 1 lie great circle 1 rack on I he .Mercator's chart, and the pecked line- in Pigs. 23 and 2 1 show the rhumb line. The rhumb line lies on the equatorial side of the great circle track, unless it. coincides with the equator or a meridian. A- it i- impossible to -t■ * : us Vi J3 err Art. 35. 36 ship and a new course determined on which to steer. If observations show that the ship has been set off the great circle, it is inadvisable to attempt to regain the original track. 35. Great circle track by calculation. — When a gnomonic chart is not available, the series of points with which to plot the great circle on the Mercator's chart may be found by calculation, but under these circum^ stances we cannot tell whether the great circle track will lead the ship into danger till the points have been plotted on the Mercator's chart. The method of calculation will be best shown by calculating the latitudes of the points in the foregoing example. In Fig. 25 let P be the pole of the earth, and F and T the two places. Then in the spherical triangle FPT, PF is the co-Lat. of F, = 90° - 50° = 40°. Similarly PT is the co-Lat. of T = 45°. The difference of longitude between F and T is 60° W. ; therefore the angle P is 60°. Having the two sides PF and PT and the included angle FPT the side FT is found by the formula hav FT = hav {PT - PF) + hav 0, where hav 6 = sin PF sin PT hav P. PF 4:0° L sin 9-80807 PT 45° L sin 9-84949 P 60° L hav 9-39794 Fig L hav B Nat hav 6 Nat hav (PT - PF) (5°) Nat hav FT 9*05550 •11363 •00190 •11553 FT =39° 44' -5, from which we see that the distance along the great circle arc from F to T is 2,384-5 miles. Having the three sides of the spherical triangle PFT, we now find the angle F by the formula hav F = cosec PF cosec PT -y/'hav (PT + TF — PF) hav ( PT -TF + PF) L cosec 10-19193 L cosec 10-19427 PF - FT - PF ■FT - 40° - 39 00' 44-5 PF -FT PT - - 45 15-5 00 PT +FT - PT +PF - - 44 - 45 44-5 15-5 \L hav \L hav 4-58047 4-58520 Lh&v F 9-55187 F = 73° 18'-2 37 Art. 36. We have now to find in what latitudes the great circle arc FT cuts the meridians of 100° W., 110° W., &c. Let PV be the meridian which cuts FT at 90°; it is rirst required bo find the angle VPF and the side PV. In the right-angled spherical triangle PVF tan P = cot F sec PF, and sin PV = sin P^ sin P. P - 73° 18'*2jLcot i)--477(>.-> L sin 9-98132 PF - 40° 00' A sec 10-11575 L sin 9-80807 L tan P 9-59280 L sin PF 9-78939 P = 21° 23' PF =38° 00', Lat V = 52 ° 00 '- Let the meridian of LOO \V. intersect the great circle arc FT in .4 then in the right-angled triangle PVA we have VPA = VPF - APF = 21 ° 23' - 10° 00' = 11° 23'. Also PV = 38° 00'. Now taniM = tan PV sec VPA. .-. cot Lat. of .4 = tan 39° sec 11° 23'. Similarly for the meridian of 110 c \Y. we have cot Lat. of .4' == tan 38° sec 1° 23' and for the meridian of 120° W. we have cot Lat. of A" = tan 38° sec 8° 37' and so on. The calculations are shown below : — Lon^-. VPA. 100° w. 11° 23'. 110° \Y. 1° 23'. 120° W. 8° 37'. 1 30° W. 18° 37'. 140° W. 28° 37'. '.••89281 10-00863 9-89281 1000013 9-89281 10-00493 9-89281 10- 02334 9-89281 10-05658 Lat-. 9-90144 51° 27' 9-89294 52 00' 9-89774 51° 41' 9-91615 50° 30' 9-94939 48° 20' Having obtained these Latitudes, the curve is plotted on the Mercator's chart : the course to steer and the total distance arc found in the manner explained irj the preceding article. 36. Great circle track by Towson's tables. The points on the great circle track which have to be transferred to the Mercator's chart may be easily found by aid of Towson's Great Circle Tables and Linear Index, which are supplied to all II. .M. ships with the ohaii set. The instructions for using them are bound up with the tables and should be carefully studied. When obtaining tli«- points i»\ these tables, it i- recommended to draw figures as shown in the tour following examples. Since any two great circle bi ect one another, the greal circle through /• and T is bisected by the equator .it two point-. Q and E. The figures -liou the whole of thi i circle FT and the whole of the equator. ExampU ( I ) : — /•' Lat. 50 ' s. Lou-. 150° <>')' \Y\. d. Long. 60 W. Art. 36. 38 From Index the Lat. of vertex is 52°. Long, from vertex, 21° 23' E "Meridian in." Fig. 26. Longs. Longs, from vertex Lats. from tables 90° 00' 21 23 50 00 100° 00' 110° 00' 11 23 1 23 51 27 52 00 120° 00' 8 37 51 41 130° 00' 18 37 50 30 140° 00' 28 37 48 20 150° 00* 38 27 45 00 Example (2) : — F Lat. 54° 00' N. T Lat. 30° 00' N. Long. 10° 00' W. Long. 60° 00' W., d. Long. 50° W. Lat. of vertex, 55° 00' N. Long, from vertex, 16° 00'. E " Both out." Fig. 27. Longs. 10° 00' 20° 00' 30° 00' 40° 00' 50° 00' 60° 00' Longs. from vertex 16 00 26' 00 36 00 . 46 00 56 00 66 00 Lats. .... 54 00 52 04 49 03 44 48 38 38 30 00 Example (3) : — .PLat, 15° 45' S. Long. 6° 00' W. Lat. of vertex, 44° 00'. T Lat, 32° 19' N. Long. 64° 00' W., d. Long. 58° W. Long, from vertex, 73° 00'. E "Equator in." Fig. 28. Longs. . . . 6° 00' 15° 00' 25° 00' 35° 00' 45° 00' 55° 00' 64° 00' Longs, from vertex 73 00 82 00 88 00 78 00 68 00 58 00 49 00 Lats. .... S. 15 45 S. 7 41 N. 1 56 N. 11 22 N. 19 53 N. 27 05 N. 32 19 39 Art. 37. Example (4) : — i^Lat. 8° 55' X. Long. 79° 00' W. Lat. of vertex. 37° 00'. rLat. 33 37' S. Long. 151° 00' E., d. Long. 130° 00' W. - ■ rroO Long, from vertex, 78° 00'. Longs. 79° 00' 80° 00' 90° 00' 100° 00' 110° 00' 120° 00' 130° 00' 40° 00' Longs. from 78 00 79 00 89 00 81 00 71 00 61 00 51 00 41 00 ex. N. N. X. S. s. S. S. s. Lat-. 8 55 8 13 46 6 40 13 46 20 04 25 21' 29 38 Both in. Fio. 29. Lon_ r -. Longs, from vertex Lat^. - l.-.0° 00' 160^00'; 170° 00' 1180° 00' 170°00' 31 00 21 00 11 00 1 00 9 00 s. s. s. s. 32 51 35 08 36 29 ' 36 59 S. 160° 00 19 00 S. 36 40 ' 35 28 151° 00' 28 00 S. 33 37 In Towson's tables, the column headed "course" gives the angle PFT of the spherical triangle shown in Fig. 25, and this must not be confused with the course to be steered. The column headed " distance," gives the distance in miles from the nearest vertex, measured along the great circle FT. 37. The composite track. — When the vertex lies between the two places /' and 7'. t he great circle track takes the ship into a higher latitude than that of F or T, and in many cases takes the ship into a higher latitude than is desirable on account of the ice and bad weather likely to be encountered. Under these circumstances we have to determine the shortesl traek which does not cross a particular- parallel of latitude. This problem will be easily understood by considering the following: — In Fig. 30, let A and V, be two points on a line which cuts the circle C\ it is required to find the shortesl route between A and B without going inside the circle, the pointe and the circle being in the Jam plane P From . I and l'> draw tangents t< i t he circle, touching it al I ' and E ; t hen the shortesl route will be along the tangent AD, then along the circular arc DE and I ben along t he tangent EB. Similarly, if it U de ired to steam from F to T by the shortest route without crossing a certain parallel of latitude, great circle arcs are drawn Fig. 30. Art. 37. 40 from F and T, Fig. 31, to touch the parallel of latitude at D and E. The track to be followed is the great circle arc FD, the arc of the parallel DE and the great circle arc ET. This track is called the composite track between F and T. It is easily determined, if a gnomonic chart is available, by drawing straight lines from F and T to touch the limiting parallel of latitude at points D and E. The points on the great circle arcs FD and ET are plotted on the Mercator's chart as shown above, the course to steer along the parallel DE is either East or West. We will now show, by an example, how the longitude of the two points D and E on the limiting parallel may be found by calculation. It is desired to steam by the shortest route from F, Lat. 29° 53' S., Long. 31° 04' E., to T, Lat, 34° 48' S., Long. 138° 31' E., without crossing the parallel of latitude of 42° S. In the right-angled triangle PDF cos FPD = tan PD cot PF = cos Lat. of D tan Lat. of F. In the right-angled triangle PET cos EPT = tan PE cot PT = cot Lat. of E tan Lat. of T. Lcot 42° 00' - 10-04556 L tan 29 53 - 9 -75939 I, cot 42° 00' - 10-04556 L tan 34 48 - 9-84200 L cos FPD - 9-80496 L cos EPT EPT = Long. T Long. E - 9-88756 FPD = Long. F = 50° 20' 31 04 E. 39° 28' 138 31 E. Long. D 81 24 E. 99 03 E. Having now the latitudes and longitudes of D and E, we can calculate the latitudes of various points on the great circle arcs FD and ET in the manner explained in § 35. If we remember that the latitude of the limiting parallel is the latitude of the vertex for each great circle arc, we may very easily find the longitudes of D and E by Towson's tables. In the example above, entering the table with the latitude of the vertex 42° and latitude of F 29° 53', we find the longitude from the vertex is 50° 20' ; and with the latitude of T 34° 48', we find the longitude from the vertex is 39° 28'. 41 Arts. 38, 39. CHAPTER VI. THE DEAD RECKONING AND ESTIMATED POSITIONS. 38. The dead-reckoning position. — To find the position of the ship at any time when no observations for obtaining it are available, we have to utilise all the information that is at our disposal. The position of the ship depends primarily on the course steered and the distance run through the water, both of which should be known almost exactly, the first from the compass and the second from patent logs or other speed recorders, and from the revolutions of the engines. The position obtained from these data is called the dead-reckoning position, and is generally written D.R. The information relating to the above data is tabulated at intervals by the Officer of the Watch in the deck log. The Officer of the Watch Bhould be careful when making these entries that the course should In the average one which he considers the helmsman has been actually steering the ship on as indicated by the standard compass, to which frequent reference should have been made. As regards the distance run on each course, he should take into consideration the reading of patent log or speed recorder, the known revolutions of the engines, the condition of the ship's bottom, and the state of the wind and sea. 39. The estimated position. — The position of the ship depends second- arily on the direction and distance she has been moved by currents, tidal si reams, wind and sea. and imperfections in steering. The wind and sea combined have the effect of causing leeway, that is, of driving a ship to leeward of her course. Leeway is defined as being the angle between a ship's fore-and-aft line and her wake. In slow-moving sailing vessels this angle is allowed for as a correction tot he course steered. In steamers, owing to the difficulty or impossibility of measuring this angle, the amount a ship has been set to right or left of her course is usually estimated and allowed for. Another point to be considered when coasting is the possibility of an indraught into a deep bay or indentation of the coast. The methods of estimating the currents and tidal streams are fully dealt with in Part 111., and 1 lie effects of wind and Wad steering can only be est imated by experience. The position found, after taking all the above into consideration is the most probable position of the ship that can be ascertained from the data available, and is called the estimated position. When estimating the position of the ship, the greatest care should be taken that the fullest consideration is given to every factor which may influence her position, and it Bhould not be concluded that the estimated position is the actual position, although, when all available data have been allowed tor. it may be considered the most probable position. When shaping course from an estimated position to approach land or dangers, the grej pest i u now is neoessabi lnd soundings shoi ld 3TANTL1 BE TAKEN u nil THE SOUNDING MACHINE; al the earliest opportunity every endeavour should be made to check the estimated posit ion of t he ship by observat ioni It isobviouc that altera short run of two to three hour-; the estimated po it ion i- not bo likely to be in error as after a run of 24 hours ; therefore, Art. 40. 42 the longer the interval since the position of the ship was last fixed by- observation, the greater the distrust with which we should view the estimated position, particularly in localities where the currents are strong and variable. The dead reckoning and estimated positions can be obtained either by plotting on the chart or mooring board, or by calculation by aid of the traverse table ; this table is so called because it was originally con- structed to assist in finding the position of the ship after she had steered a number of different courses, when she was said to have made a " traverse." It is impossible to lay down any law as to when either method of working the reckoning — that is, of finding the estimated position, from all the above data — should be used ; but, as a general rule, it will be found that the most convenient method in any particular circumstances is the correct one to use. We must bear in mind, however, the degree of accu- racy required, and therefore the position should not be obtained by plotting on a chart on a small scale, because small errors in plotting would produce large errors in the position. When a chart on a large scale is not available, the position must be found by calculation. With reference to the term ' reckoning " it may here be remarked that a ship is said to be ahead of her reckoning when the actual position is found to be in advance of the estimated position, and astern of her reckoning when the actual position is found to be behind the estimated position. 40. Working the reckoning by chart. — As an example of working the reckoning by chart, let us take the following : — The position of the ship at 6 h a.m. was Lat. 49° 00' N., Long. 7° 30' W., and she steamed as shown in the following extract from the ship's log. During the whole time the current was estimated to be setting E.S.E. (mag.), 1 knot. The effects of tidal streams, wind, and sea were estimated to be nil. Hours. Patent Log. Distance Run. Miles. Tenths. Standard Compass Courses. Deviation of Standard Compass. Revolutions per Minute. Remarks. 7 175-0 15 S. 40° E. 4° E. 90-2 7.20 altered course to N. 60° E. P. Log. 180-0. 8.15 altered course to N. 80° W. P. Log 193-7. 9.0 altered course to N. 25° E. 9.40 altered course to N. 30° W. P. Log 215-0. 10.0 reduced to 12 knots. 10.30 altered course to N 68° E. P. Log 226-0. 8 190-0 / 5 \10 N. 60° E. 5> l lo y 89-9 9 205-0 / 3 7 3 N. 80° W. 4°W. 90-1 10 220-0 /10 \ 5 N. 25° E. N. 30° W. 2° W. 4° W. 90-0 11 232-0 / 6 \ 6 N. 68° E • 2°"e. 61-0 12 244-0 12 »' »j 60-0 43 Art. 41. It will be noticed from the above that from (i 1, a.m. to 7 h 20 m a.m. the ship steamed S. 4o E. by compass, 20 miles. From a reference to the variation, chart it has been found that the compass engraved on the chart in use (Fig. 32). for variation 1S : 1(5' YV.. is correct. W e have to lay off a course and distance S. 40° E. by standard compass, 2o miles, from the position on the chart marked (> \.u. ( lompass course - S. 40° E. Deviation 4 E. Magnetic course - - - S. 36 E. Place the parallel rulers on the engraved compass so that an edge lies on the graduations of S. 36° E. andN. 36° W. and on the centre of the compass. Transfer the ruler till its edge lies on the 6 h a.m. position, and from this position draw a line in the direction S. 36° E. (magnetic). From the scale of latitude on the chart, take with the dividers a length of 20' of latitude from that part of the scale which is in approximately the same latitude as the ship, and measure this distance from the 6 h a.m. position along the line already drawn. The position thus obtained is the D.R. position at 7 h 20 a.m. At 7 20™ a.m. the course Mas altered to N. 60° E. by compass, and this course was maintained till 8 h 16" a.m., so that the distance run on this course was 13-7 miles. Compass course Deviation N. 60° E. H E. N. 61i E ' Magnetic course Lay off this course and distance as above, and the position obtained will be the D.R. position at 8 h 15™ a.m. In a similar manner the other courses steered and distances run may be laid off, and the D.R. position of the ship obtained at any moment by reference to the scales of latitude and longitude on the chart. From the chart, Fig. 32, we observe that the D.R. position at Noon is Lat. 49° 23f X., Long. 6° r.sj' W. To obtain the estimated position of the ship at Noon, the available data are current E.S.E., t; miles: tidal stream, nil; wind and sea, nil. The estimated position is therefore found by laying off a course and dis- tance E.S.E. 6 miles from the D.R. position. We find thai the estimated positioE at Noon is Lat. 19 23£' V. Long. 6 19' \Y. 41. Working the reckoning by calculation. We will now show with the i-iiplc how the D.R. and estimated positions may be found by calculat ion. First ly, it us necesf u \ to correct all courses for deviation and variation, bhe traverse table should be entered with true courses; then, by refer- ence to the traverse table we find how much difference of latitude and departure the ihip has made >>u each course. The total difference ol latitude made i the algebraical sum <>l the various d Late. The total departure macb timed t<> be the algebraical sum of the departuree made on the variou courses. When- the distances run <>n the various com reat, or the latitude high, or both, the error due to this assump tion i con iderable, I >u t for a traverse which coven onl} a f<-w hours' ming no a pprecia U<- ei r< ir us im rodueed. 44 i \ e» « f.A ■ . s6\ ' 68 '■ '•■ ,lBk,ih •A s ro •? \ *>, 49 • m i: ' 1! 70» f» ' ■ ea 63 'S* B^ 3J1> ~^ _ 1 .Tii-Uth flfl ■ ; «8 \ 1& i. / : \ t ' 2&. i TO *"* / ma \ to io_ : • ro i f* \ *> *V«h 71 * \ " — 73 -' : V.. ? M g- ■tK .111 ' \ \ * ?8 ' 3 re " %-. \ 'I « J IS. 7* 7* W '■ yX y -? H ■ e.» is \jr \ ^"-"" * -J ? , 7-* /*&' "„^l<"^ \ «« ~? 74 Cgy.r.JreJ.' -_ ^^ *^- \ «> \ •*■»'> i 10. „ 7<9 f.w...»*.,'k / ^ J0? ^ Vi f.^ w -. '»■■■» >v ';. % 7^w ^ aj \ "M*i * \ f • ymA m J*<^ / e? / ijii X W7T — 1» 1 \ -Vfc 6. 74 /' • A /70 ..fi"»"»'\ 71 \ '•w"" f -A •■'"a ^' ■* •* \ 76 ■ f" 56 'i ■ 1 \ V 49° .» rs&OVA.M. 73 1 a 73 ?* lw « /• 7£ v » ' V \ \ ^^v" ''-s. rs ^ •■«■ 7S . It:-" 1 ^__^_- r a*/5'?' \ -" / 7J -— -— / \ / 74 / \ / o .k 55. 73 .' \ l 78 / 72 " ' ( \, / • ?2 C.W...A £■■».•. A \ f ~ * * 34 X V W / '.? >. Ul-Ji / •■* i so. / \ 77 zSLN /^ \ a« 74 * '*' '"^C t •/ 77 firk.dt >,/ 77 SI •«%.* 84 • WVJ ' *-"-..... BO • all 78 77 <•• 76 1 • l^k.t . r.» , 83 1 45. 79 "" 30' as' zo' is' i 10' 6' r< d o .'»5' fib' 45' Fig. 32. 45 Art. 41. The total d Lat. applied to the latitude of the last observed position gives the D.R. latitude required. With the total departure and the middle latitude (between the D.R. latitude and the latitude of the last position) we can, by aid of the table in Inman's for converting departure into d Lat., or by the traverse table, find the d Long, made from the last position; this d Long, applied to the longitude of the last position gives the D.R. longitude required. The working of the example is shown below : — Compass Course. De- Magnetic ,- . .. viation. Course. True Course. d Lat. Dis- tance. N. Dep. E. W S. 40 ; E. N. 60 E. N. 80 W. X. 25 E. X. 30 W. X. 68 E. 4 C E. HE. 4 \V. 2 W. 4 W. 2 E. s. 30° E. X. 6UE X. 84 u X. 23 E. X. 34 W. 1 X. 70 E. 181 W. S.544/E. 20-0 11-7 16-2 — 99 X.43JE. 13-7 10-0 — 9-4 — 99 S.77|W. 11-3 — 2-4 — 11-0 ?> X. 4JE 10-0 100 — 0-9 — >> N.52JW. 11-0 6-8 — — 8-7 >» X.51f E. 18-0 11-3 — 14-0 — 38-1 14-1 40-5 19-7 Total d Lat. 14-1 19-7 24 -OX Total Dep. 20.8E. Latitude at 6 h a.m. d Lat. D.R. Lat. Xoon Latitude at 6 h a.m. Middle latitude 49° 00' N. 24 N. 49 49 24 N. 00 2/98 24 49 12 With departure 20'-8 and middle latitude 4!> 12'. we find from the table in Inman's thai the d Long, is :vi' . Longitude at 6 1 l.m. - 7° 30' \Y. d Long. - - 32 E. D.R. Long. Noon 6 58 W. D.R. position at Noon, Lat. 19 24' X., Long. 6 ( 58' W. To find the estimated position al noon we must take accountjof the currenl in the interval, and consider another course, E.S.E., 6j miles; tin- i- equivalent to 8. 85| K. (true), 6 miles, since the current is always given a- magnetic. The d Lat. and departure for tin- are <>'■•> 8. and B'-O E. Arts. 42, 43, 44. 46 D.R. Lat. Noon. 49° 24' N. D.R. Long. Noon, 6° 58' W. dLat. - - 0-4 S., Dep. 6'-0 E. 5 d Long. - - 9 E. Estimated lati- ] 4f) 9o.p]u Estimated longi- \ „ >q ^ tude, noon. / - tude, noon. J 42. Current by difference between dead-reckoning and observed positions. — If the position of the ship is found by observation to differ from the estimated position, it is obvious that some of our data are incorrect. As it is impossible to determine which of the data has been wrongly estimated, the difference between the actual and the D.R. positions is attributed to the current alone, because this generally has the greatest effect in displacing the ship. For example, in the preceding article suppose that the actual position of the ship at noon was found to be Lat. 49° 27' N., Long. 6° 46' W. The difference between the D.R. position and this position is expressed by finding the course and distance from the former to the latter, and assuming that this course and distance were due to the set and drift of the current in the interval. D.R. position, noon - - - Lat. 49° 24' N., Long. 6° 58' W. Observed position, noon - - Lat. 49 27 N., Long. 6 46 W. d Lat. 3 N., d Long. 12 E. With middle latitude 49°| N. and d Long. 12' E., we find the departure to be 7' -8 E. With d Lat"! 3' N. and departure 7' -8 E., we find the course and distance to be N. 69° E., 8*4 miles, which gives the set and drift of the current as N. 69° E. (true), 1-4 knots. 43. Keeping the reckoning in a tideway. — The direction and rate of a tidal stream varies at different places and at different times of the day, so that, when a ship steers through a tideway, it is necessary to find the estimated position at frequent intervals. It is convenient to plot the estimated position hourly and on every change of course. An example of plotting the estimated position for a ship steering through a tideway for five hours is shown on the chart, Fig. 33. At 5 h a.m. the ship's position was Lat. 50° 10' N., Long: 4° 10' W., and from this position she shaped course S.W. (magnetic) at a speed of 7-8 knots. From 5 h a.m. to 6 h a.m. it is found from the tidal atlas that the tidal stream had probably set the ship N. by E. 1'. From the 5 h a.m. position lay off a line FA, S. 45° W., 7-8 miles. The D.R. position at 6 h a.m. is at A. From A lay off a line AB, N. by E., 1 mile, to allow for the tidal stream experienced between 5 !l a.m. and 6 h a.m. The estimated position of the ship at 6 h a.m. is at B. From B lay off BC, S. 45° W., 7-8 miles, and note that the direction and rate of the tidal stream between 6 h a.m. and 7 h a.m. has been E.N.E., 1| knots. Lay this off as before, and obtain the estimated position at 7 h a.m. Proceeding in a similar manner we find the estimated position at the end of every hour as shown on the chart. 44. Track of a ship while turning. — When a ship alters course, she does not turn instantaneously about a point on to the new course, but •describes a curve from the time when the helm is put over to the time 17 30 6 * 1* ,, - > / V.J. as '*7 ^J -^ " *5 M % er TO e.a SO .Hand Deeps "> 29 .3 ip : 1... , Art. 44. 48 when she is steadied in the new course, as shown in Fig. 34. AX is the original track of the ship, X is the point where the helm is put over, B the point where the ship arrives on her new course, having described the curve XDB in the interval. In order to lay off the new course of A* Fig. 34. the ship, we must know the position of B relative to X — in other words, we must know the length of XB and the angle EXB. Now from the turning trials of the ship, which are carried out with various angles of helm, her track while turning with any particular angle of helm may be plotted ; and the angle EXB and the length XB, which correspond to any particular alteration of course, may be measured. Now as the direction of AX is known, the direction of XB may be found; the direction and length of XB are called the intermediate course and distance. If, therefore, the position where the helm is put over be known, it is possible by means of the intermediate course and distance, to lay down the point B from which to lay off the new course. Another method of laying off the new course is to hiy it off from the point E, which is the intersection of the new and original tracks ; the distance XE is called the " distance to new course," and is tabulated for every ship for alterations of course up to 12 points; for larger altera- tions, this method should not be used, because the distance XE becomes inconveniently great, being infinite for an alteration of course of 16 points. The track of a ship while turning is different for different angles of helm,, and for a particular angle of helm, on a calm day and in smooth * water, is approximately constant ; wind and sea are liable to cause a ship to deviate considerably from her normal path. No rules can be laid down as to the effects of wind and sea on the path of a ship while turning, and they can only be allowed for after experience. In cases where the available manoeuvring space is very restricted it is desirable, before entering such a harbour or channel, to plot the approximate track of the ship, while turning, on the chart, and this 49 Art. 45. may be easily done by means of the advance and transfer. The advance is the distance the centre of gravity of the ship has advanced in the direction of her original course, measured from the point where the helm was put over — (the distance XF for the alteration of course shown in Fig. 34). The transfer is the distance the centre of gravity of the ship has been transferred in the direction at right angles to her original course — (FB for the alteration of course shown). The transfer for an alteration of course of 16 points is called the tactical diameter of the ship for the particular angle of helm which has been used. The advance and transfer for various alterations of course and angles of helm should be tabulated for every ship. To plot the approximate track, with half the tactical diameter as radius, describe a circle to touch the original track at J, Fig. 34, XJ being the advance for a 16 point turn. While a ship is turning through the first 16 points, her speed does not remain uniform, but becomes very much reduced; consequently, when steadied on her new course, some little time will elapse before the original speed is regained, and therefore, unless a patent log, which indicates the distance run through the water, is available, the mean speed of the ship to the time when the next alteration of course takes place has to be esti- mated. The percentage of the loss of speed during any alteration of course, and the times taken to complete various alterations of course at different speeds, should be tabulated for every ship. 45. Keeping the reckoning during manoeuvres. — When at fleet manoeuvres, the alterations of course are frequently so numerous, and the distance run on each course is so short, that the curves described by the ship while making the various turns form a large proportion of the traverse; these curves must therefore receive more consideration than is usually necessary for the ordinary methods of keeping the reckoning. On account of the possibility that at any moment it may be necessary for a ship engaged in manoeuvres to shape a course for a particular posi- tion, it is essential that the reckoning should be kept in such a manner, t hat the position of the ship at any moment may be plotted on the chart with the least possible delay. The method of keeping the reckoning < < msists in considering that a ship starts from a known position A, Fig. 34, runs a course and distance AX, then turns about a point X and runs the intermediate course and distance XB, and again turns about the point B and runs the course and distance HC, &c. In order to obtain the distance run on each course, it is convenient for an electric receiver from the patent log to be placed in the vicinity of the Standard compass. If the reading of the patent log be taken at the point A, which is plotted on the chart, and again when the helm i- put over for the alteration of course at X, the distance run in the direction AX a known. The intermediate distance XB is also known. but while the Bhip i passing from X to B she travels <>n the ourved path X />/; and t lie distance run, as indicated by the patent log, will be greater than the intermediate distance. It is impossible to tell the instant when th<- Bhip arrives ai B, and in order thai the reading of the patent log may be noted at that instant, the Length of the ourved are XDB is measured off from the plotted results of the turning trials, and is tabulated for various alterations of course. This length of the ourved are in the dbtanee through the water that the ship actually steams between the point X and /,', and, if added t<> the reading of the patent X 01 us 1) Art. 45. 50 log at X gives the reading of the patent log at B. This length of the curved arc is called the " Log correction " (Log. Cor.). In case of there being no patent log available, the distance run on each course must be calculated from the interval of time during which the ship was steering that course and from the estimated speed of the ship through the water. For the same reason as we required the Log correction we now require a time correction, which, if added to the time shown by a watch when the helm was put over, will give the time of arrival at B. This time correction may be found from the known length of the arc and the mean speed of the ship on that arc, and may be tabulated for various alterations of course and for various speeds. 10 S S 7 S S 4 3 2 1 ! K 1 | A _ .]. . ..-{-. 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( !\ ■:/■».';: X .■-■ s y \A .!-' ;/ .■• .'■ < . A ' / ' A ' ' i ■ -' ' ' t ^ '■ ' ' X s' - A i ■•" -•■' • / ■[■ ■■' : ' / , } . '£~ Z¥z ?= H\ : -\ ..-■ :■•- ..■ y y > / / / / ^zt^ztL 7 -; ■■^t~ ! rnir \ ' \,* >■■ ' yi / ■ .■ / / ; -• r : 4 ■ tjt : rn ft rr \ - -- 'l' ! j/ ,/ .■ £ .', / ' v // . 7 f ■■ ■ .' • f r; \- ' j^*^ ' If' J ^2 ,• ^^7^ : . . ■ '1 t! '' ' -' '1 (* • * /- i 4 ;. . .' / ■' .' ; '-] V p .• -'T , ■ / ' ■ 7 :tZ y" 7 """ i ■■ ^r-i — N<-4— -7' — -' ■ m ,■ /. / _,' ^ ■ v ■ • tz - Ctii ■•jh no' ^4; J^ — 'i^'-s' — / — ■- — ■— — — ^ \L' ^/ / .•' / T /~ : ,■ • 1 J . ' : * * / ■' : • \^ / ■ ■ / ~^ ;"cj ■■ "^ . 1 ■ r t-^- N^ -' J J T Z l-t^t^ i- ■■ tl r T~ *° ^„^_i X. L ; T ■ 7 • ^ 1 ■ ^ • _r •\[ • / t • r ~^7 2_ ■■ .- : "j I ; rt" X ' ', ., 1 A t-j J- ■ i i ,L4 LI ^? i T : j / ■■ t ; t l^ tt ^< J- ft '-i I 2 t-, Z LT_ 30* ^C_ -- y i ■ 4:1 ■ j._ II ^•s ^4^_ r ~i ~I ^■^-LJ/ '' ■ / 20° ""^---L ; ; ■ i i ■ I 2 2 * H 5 3 e 4 a to' 5 10 0" Fig. 35. A time correction should not be used when the alteration of course is greater than 16 points, because the wind and sea have a considerable effect on the time occupied by the ship in turning through very large angles. In such a case the time when the ship is steady on the new course should be noted and assumed to be the time at B. For alterations of course which are not greater than 30°, it may be assumed without appreciable error that the intermediate course is coincident with the original course. Therefore, for such alterations of course, the distance run on the original course is the difference between the readings of the patent log at A and B. Similarly, if there is no patent log available, the distance run on the original course is that found by the method described above with the addition of the intermediate distance. 51 Art. 45. If a gyro-compass, which indicates true directions, is used, the reckoning may be calculated as explained in § 41. If a magnetic compass is used, the following procedure is adopted. The distance on any magnetic course may be resolved into its components in, and at right angles to, the magnetic meridian. As the traverse table is simply the solution of a large number of right-angled plane triangles, it may be used for resolving the distance on any magnetic course in these directions. For example, a distance of 2- 84 miles on a magnetic course X. 35 \\\ may be resolved into its components 2-33 miles in the direction North (mag.). 1-63 ,, „ „ West (mag.). which, as may be seen from § 30, are the numbers given in the columns of the traverse table headed Diff. Lat. and Dep. respectively. In order to avoid the necessity for using a book, it is convenient to have a diagram, called a traverse diagram, as shown in Fig. 35, which may be pasted on a board. To use the diagram in the example given above, with a pair of dividers take off, from the right or top of the diagram, a distance equal to 2- S-i miles on any convenient scale ; with one leg of the dividers at the centre of the graduated arc mark with the other leg a point G on the radiating line marked 35°. Measure the vertical distance GK, which will be found to be 2-33 miles, and mark it N. because the course is named North, and measure the horizontal distance GH, winch will be found to be 1-63 miles, and mark it W. because the course is named West If the components of every distance in the North or South and East or West magnetic directions are tabulated in four columns headed X.. >.. E., and W., the sum of each column will give the distance the ship has moved in that particular direction. If the difference of the totals of the columns marked N. and S. be taken and marked with the name of the greater, the number of miles the ship has moved in the direction Magnetic North (or South) is known. Similarly, if the difference between the totals of the columns marked E. and W. be taken and marked with the name of the greater, the number of miles the ship has moved in the direction Magnetic East (or West) is known. The magnetic course and distance run in the whole interval may now be ' n from the traverse diagram, by marking the point on it such that OK is the difference between the columns marked N. and S., and OR tli" difference between the columns marked E. and W. The graduation where 00 cute bhe arc will be the magnetic course and will be named X. or 8. and E. or \\\. according bo the quadrant in which fche ship has moved. The length of 00 pvee bhe distance run. Whenever the coin.,, [g altered, it is necessary fco find fche inter- lurse to fche position where fche ship i- steady on her new com i" do this if i- necessary to apply fche tabulated angle EXB, Pig. 34, fco the last course. To save time, diagrams may be constructed which show readily fche intermediate course without fche necessity for calcula- I ion. In order to explain fche construction oi these diagrams, it will be convenient fco oonstrucl them for fche ship, whose turning circle is shown in Pig, 36. In Pig. 36, let /;, /;,, i: lr B 9l &c, be fche positions oi bhe ship when she hat burned through 30 i point-, r> points, s point . &c, respectively, D I Art. 45. 52 from her original course XE, and let X be the position where the helm was put over. The various measurements are made and the results are tabulated below. Tactical diameter 150yards. Scale 200 yards = I inch. Fig. 36. Alteration of Angle EXB. Length of XB. Intermediate Length of Arc XDB Log Mean Speed per cent, on Speed per cent. course. distance. correction. arc XDB. remaining atB. Degrees. Miles. Miles. 30° •14 •14 100 100 Points 4 14 20 .20 95 90 6 28 27 30 92 82 8 39 33 38 90 75 10 48 37 45 85 74 12 57 38 51 80 73 14 67 39 57 78 72 16 76 38 64 77 70 18 85 37 71 — 70 20 96 •33 78 — 70 22 106 28 85 — 70 24 117 22 92 — 70 26 124 15 1 00 — 70 28 124 09 1 06 — 70 30 67 03 1 12 — 70 32 14 •08 1-19 — 70 53 Art. 45. M S Alteration greater t/ian /6 points. Alteration leSi than 16 (■ Fio. 37. Art. 45. 54 The upper diagram of Fig. 37, called the compass diagram, represents a compass card, and forms a scale for the construction and use of the lower diagrams. We will first construct the lower diagram marked ''Alteration less than 16 points." Draw two parallel lines, MN and ST, at any convenient distance apart, and at right angles to a base line MS. From the compass diagram, measure off the chord for 4 points with a pair of dividers, and lay off this distance MP on the left hand line. Along ST lay off SU the chord for 14° which is the value of the angle EXB, corresponding to an alteration of course of 4 points ; join PU. Similarly, lay off MQ the chord for 6 points and SV the chord for 28° and join QV and so on. Lay off M J the chord for 30° and join JS. Tabulate the log correction, the intermediate distance and other data, as shown in the diagram. The diagram for alterations greater than 16 points is constructed in a similar manner. It will be seen that the chords for alterations of course of more than 16 points become successively less, whilst at first the chords for the angle EXB become successively greater, so that the fines joining corresponding points in some cases cross one another. To use the diagrams for finding the intermediate course and distance and log correction, corresponding to any alteration of course, let us take the following : — Example. — A ship is steering S. 60° W. (Mag.) and the helm is put over for an alteration of course to starboard to N.W. The reading of the patent log when the helm was put over was noted to be 37 • 2. It is required to find the intermediate course (magnetic) and distance and the log correction. Place the legs of the dividers on the graduations of the compass diagram corresponding to the old and new magnetic courses, then the distance spanned by the dividers is the chord for the alteration of course. On the diagram for alterations less than 16 points lay off this chord MR, and note that against the point of the dividers at R are tabulated Log Cor. *33 miles and Int. Dist. -29 miles. The eye being guided by the transverse lines, note that the corresponding point to R on the fine ST is Z. Place one leg of the dividers at S and the other at Z, then the distance spanned by the dividers is the chord for the angle EXB corre- sponding to the given alteration of course. Place one leg of the dividers on the graduation S. 60° W. (the original course) on the compass diagram, and with the other sweep an arc to intersect the circumference of the compass diagram on the side to which the course was altered, in this case on the right as the alteration was to starboard, and note that the graduation at which it intersects is N. 86° W. which is the intermediate course required. oo Art. 46. In the case of alterations greater than 1C points, the transverse lines cross one another and it appears to be difficult to determine the point in the line ST, but if care be taken to note between which transverse lines the point R is situated, and if these hues are followed to the line ST, the point may be easily determined. In the case of turns which are not greater than 30°, it is only necessary to note the intermediate distance tabulated against the point B, for, as explained above, in such a case, the intermediate course is practically the same as the original course. 46. Examples oi keeping the reckoning during manoeuvres. — The method to be adopted depends on whether a patent log (or other distance- recording instrument) is available, or the distances have to be calculated from the time and speed. It is preferable to use a patent log, because it is extremely difficult to make allow ance for the loss of speed occasioned by the helm being put over. A reliable assistant should always, when possible, be employed to keep the reckoning, in order that this very important matter may have the undivided attention of one individual. The reckoning should be as carefully kept when manoeuvring in sight of land as when in the open ocean. Only by constant practice in sight of land, where the results can be checked by observation, is it possible to be certain that the reckoning is kept in such a methodical manner, that the resulting position of the ship is free from all errors, other than those due to wrong estimation of the effects of tidal streams, currents, &c. It should be understood that the various entries tabulated in the following examples would, in practice, be written down in the note-book as each incident occurs. It is advisable to add up the four columns marked X.. S.. E. and W. as each page of the note-book is completed, and 1" transfer the totals to the head of the next page in order to simplify the addition when the position of the ship is required. Example. Talent log available. The ship, for which the diagrams in Fig. 37 have been constructed, « i ■ 1 1 1 ■_• North (Mag.), and at J) h a.m. her position was plotted on the chart and the reading oi the patent log was noted to he IT-."). Subsequently, Various alterations of course were made; the reading ot tin- patent log and the time to the nearest minute wen- noted on each OOCasiOl] ot putting tin- helm over, and tin- letters R or L w ere noted in the margin ot the note-hook against each entry, according a- to whether the turn was made to righl or lett (to starboard or port). At L0 36' a.m. the magnetic course and distance run since 9 h \.m. wen- required in order to plot the position <>t (lie -hip on the ohart. In order to render the working ot the example dear, the Intermediate cour-e- and distances, log correction* and readings ot the patent log Art. 46. 56 depending on them are printed in italics; the readings of the patent log, the difference between which is the distance run on each course, are bracketed together. The reckoning is kept as shown below. — Time. P. Log. Course. Distance. N. S. E. W. R \ h.m. 9 00 9 18 9 25 9 41 10 04 10 14 10 36 17-5 21-9 •26 N. N. 25° E. N. 60° E. E. S. 32° E. S.W. S. 10° w. S.E. S. 48° W. N. 4-40 •25 1-58 3-76 •38 4-99 •33 1-82 •34 4-44 4-40 •23 •79 4-44 •32 3-53 •32 1-29 •23 •11 1-37 376 •20 1-29 ■{ 22-16 23-6 •14 • »{ 23-74 27-5 ■51 / 28-01 33-0 ■38 3-53 •06 R \ 33-38 352 ■76 •25 / \ 35-96 40-4 9-86 5-69 5-69 6-73 3-84 3-84 4-17N. 2-89 E. ! From the traverse diagram, Fig. 35, with the above results 4' -17 .N. and 2' • 89 E. it is found that the course and distance run since 9 h a.m. is JN. 35° E. (Mag.), 5*1 miles. This course and distance may now be drawn on the chart from the 9 h a.m. position, and thus the position of the ship at 10 !l 33 m a.m. is found. The arrangement in which the entries should be written down, as shown in the above example, should be carefully studied, because only by following a regular procedure is it possible to be certain of avoiding mistakes. It will be seen that each course, whether a course actually steered or an intermediate course, is entered against the reading of the patent log when the ship commenced to steer that course, or was supposed to commence to steer that course, as the case may be; therefore, the distance run on each course steered is the difference between the readings of the patent log shown against that course and that shown against the next. Should there be any error in the patent log, which, as will be explained in Fart IV., is always stated as a percentage of the distance shown by the log, it must be applied to the resulting distance run in the whole interval as a percentage of that distance. For example, suppose that in the case considered above the error of the patent log was " under- logging 5 per cent." Then the resulting course and distance would be N. 35" E. (Mag.) (5-1 + ^ X 5- 1) = JN. 35" E. (Mag.), 5-4 miles. 57 Art. 46. The following is the working of the same example when no patent log is available ; in this case the distance run on each course is calculated irom the times and the estimated speed of the ship. The nominal speed of the ship was 15 knots; the mean speed while steering any course has to be estimated, not only from the known per- centage of the speed which remains when the ship is steadied on that course, but also from the interval of time during which the ship was steering that course ; the distance run on any course cannot, therefore, he tilled in until after the next alteration. It is convenient to note the estimated speed in brackets underneath each course as shown below. The time at which the helm was put over should be noted to the nearest tenth of a minute. Time P. Log. Course. Distance. N. E. W h. m. 9 00 R R R J 9 17-6 11 9 18-7 9 25-2 •5 9 25-7 9 40-7 25 9 432 10 03-8 1-7 10 055 10 13 t, 10 17-6 10 36 26 14 51 38 N. (15) N. 25° E. U3-9) N. 60° E. (13-25) (15) E. S. 32° E. (12) S.W. (14-5) S. 10° W. (13-5) S.E. (13-5) S. 48° W. X. (14-5) 4-40 •25 1-44 •14 440 •23 •79 1-58 3-70 •38 4-99 •33 1-82 •34 4-44 4 44 11 1-37 •32 353 •32 1-29 •23 3-76 •20 353 •06 1-29 26 9-8G .VG9 : 0-73 3-84J 5*69 ::•*! 4-17 X. 2-89 i:. In older to render the working of the example clear, the intermediate courses and distances, Log and calculated time corrections and times depending on the Latter are printed in italics: the two entries Ln the time column, the difference between winch gives the interval during which the ship was steering each OOUTSe, are joined by brackets. As before, the total course and distance run between '.»'' \.m. and 10 36" a.m. is found to be N. 35 K. (Mag.), 5« I milt It it, i- expected thai a tidal stream or current exi I . the magnetic direction and the distance, which it \a supposed that the tidal stream <>r c ur rent will have moved the ship in the whole interval, may be tabulated Art. 46. 58 and dealt with as another course and distance; the final position obtained will be the estimated position. However much care may have been taken in keeping and working the reckoning, it must be borne in mind that the greatest caution must be exercised when it is necessary to make a landfall, or to shape a course to avoid a danger, from an estimated position so obtained. Even under the most favourable conditions, when the ship has been steaming on a steady course, and at a constant speed, it is sometimes found that the estimated position is many miles in error. Therefore, when there have been many alterations of course or speed, it is obvious that too much reliance should not be placed on the estimated position. 50 Arts. 47, 48. CHAPTER VII. POSITION LINE BY OBSERVATION OF TERRESTRIAL OBJECTS. 47. Unreliability of the estimated position. Position line. — The estimated position of the ship, which has been discussed in the previous chapter, is so called because it is not necessarily the actual position, and for the following reasons. In the first place, the data for finding the dead reckoning position, namely compass course, variation, deviation and distance run through the water, may all be more or less in error. However carefully the ship ma}' have been steered, and however much care may have been taken in ascertaining the error of the compass and estimating the distance run through the water, yet these can only be obtained approximately : although the errors considered separately may be insignificant, they may so combine as to produce considerable error in the dead reckoning position derived from them. \\\ the second place, the estimated position depends, not only on the dead reckoning, but also on the degree of accuracy with which the tidal streams, currents, and the effects of wind and sea have been estimated. As the tidal streams vary considerably both in strength and din ction, and as in some parts of the world there are currents whose drifts vary between 10 and 50 miles per day, it is obvious that little reliance can lie placed on an estimated position, even when the utmost care has been taken in making an estimate of the factors involved. From this unreliability of the estimated position, we see the necessity for obtaining the position of the ship by other means, and this is done by reference to some object or objects whose position is accurately known. This reference must take the form of a measurement which can only be made, either by observing some angle, or by obtaining the distance of the ship from an object. An observation of an angle or distance gives certain data from which we obtain a line (which may be drawn on the chart ) somewhere on which the Bhip must lie to satisfy the data of the observation. This line is • ailed a position line. if two observations are taken, two position lines are obtained, and if these line- are drawn on the chart, the point where they intersect i- t he position of the ship. There are various observations which may he taken with different navigational instruments to obtain the data to enable as to draw a position line on the Chart, each of which will now be dealt with Bepa lately. 48. Position line by compass bearing. If the bearing of an object is taken with the COmpaSS, and the OOmpaSS error is applied, the tine bearing of the object from the observer is obtained. -Now there are an infinite number of positions tram vrhich the true bearing of the object Art. 48. 60 is the true bearing thus obtained, and if all these points were joined, it would be found that they all he on a curve. In Fig. 38, let the true bearing of the object A be N. 60° W. Let ABCD .... be the position line resulting from this observa- tion : then, if the observer were at D, and DA were the arc of the great circle joining him to the object A, the angle PDA would be 60° ; similarly, the angle PC A would be 60°, and so on for all points on the curve. If a point be selected close to A, it will be seen that the arc of the great circle joining the observer and the object is coincident with the curve, and therefore the position line makes an angle of 60° with the meridian of the object observed. For this reason, and owing to the very large radius of curvature of this curve (when represented on the Mercator's chart), which can never, at the object observed, be less than the radius of the earth, it is sufficiently accurate in practice to lay off the line ABCD .... on the chart as a straight line making an angle with the meridian equal to the true bearing ; therefore the position line is drawn Fig. 38. on a Mercator's chart as if it were a rhumb line, and is generally called a line of bearing. The error in a position obtained by this approximation under the worst conditions is 1 mile when the distance is 63 miles and the latitude is 60°, and the error is less in lower latitudes, being less than • 4 mile for the same distance in latitude 30°. In practice it is convenient to draw the line of bearing on the chart by means of the magnetic bearing of the object observed, the method being similar to that employed when laying off a magnetic course (§ 40). As a large number of charts are now published on the gnomonic projection, it may be remarked that lines of bearing may be sufficiently correctly laid off on these charts by laying them off as straight lines, using the compass rose nearest to the estimated position of the ship. As these charts do not embrace a very large area, the errors involved are not great. When correcting an observed compass bearing, that deviation should be used which corresponds to the direction of the ship's head at the time the bearing was taken, and it should be remembered that allowance should be made, when necessary, for the amount by which the variation as shown on the compass rose, is in error. til Arts. 49-51. Fia. 39. 49. Position line by horizontal sextant angle. — If an angle is observed which is subtended by two objects .4 and X, the observer must lie some- where on the circumference of a circle which contains this angle. In Fig. 30, if the angle observed between the two objects -4 and X is 30 . the observer must lie somewhere on the segment of a circle at every point of which the line AX subtends an angle of 30°. The segment of the circle AOBX is, therefore, the position line obtained from this observation. This position line may be repre- sented on the Mercator's chart as a circle without appreciable error. 50. Position line by distance from an object. — If the distance of an object can be obtained, the ship must be situated on the circumference of a circle described with the object as centre and with the distance as radius. This circle is, therefore, the position line. The distance from an object may be found in the following ways': — (a) By rangefinder. If the object is well denned, the rangefinder, provided it is in good adjustment, is by far the quickest and most accurate method of obtaining the distance, within the limits of the instrument. (b) By sextant. When the height of the object is known, the distance can be found by aid of the sextant. The sextant is an instrument for measuring angles and is described in Part IV. ; angles measured with it have to be corrected for an instrumental error, called index error, which is denoted by I.E. Before explaining the method of finding the distance of an object by sextant angle, we have to explain what is meant by terrestrial refraction, altitude and depression, sea and shore horizons, dip of the sea horizon and dip of the shore horizon. 51. Terrestrial refraction. — Since the density of the atmosphere diminishes as its distance from the sur- face of the earth increases, a ray of ]i_ r ht. | i.i --i i ig from one point to another, does not travel in a straight line, but in a curve, which lies in a vertical plane containing the points, and is concave to the earth's centre; thus, in Fig. 40, an observer aees the point X in the direction OT, because the ray of IL r lii from .V i i.i \ il along I he oun e XYo, and OT is the tangenl to the curve at 0. This apparent change in t be direction of I In- terresi rial point X — namely, the angle TOX is called Hhe terrestrial refraction of the ray XTO. If the tangent at X to the ray "I Fig. i" Arts. 52-55. 62 light intersects the tangent at in T, the angles TOX and TXO are found to be approximately equal, and from a large number of experi- ments it has been found that the mean value of either of these angles is about jJgth of OCX. Therefore, terrestrial refraction = OCX 13 approximately . Now the angle OCX, expressed in minutes of arc, is the number of nautical miles between A and B. Therefore, terrestrial refraction = distance, 13 approximately. 52. Abnormal retraction. — The refraction is said to be abnormal when it differs from the value as found by dividing the distance by 13. Refraction is likely to be abnormal when the temperatures of the water and air differ considerably, where currents of different temperature meet, and where the sun is shining on large expanses of sandbanks or coral reefs. It is found to exist at times in a marked degree in the Red Sea, in the Persian Gulf, in the vicinity of the Gulf Stream, on the West Coast of Africa and in the Mediterranean. 53. Altitude of a terrestrial object. zontal plane through the obser- ver's eye, its apparent altitude is the vertical angle between the apparent direction of the point and the horizontal plane passing through the observer's eye. In Fig. 41, let X be the point, OX the ray of light from X to the observer's eye, and OT the tangent to the ray at ; then the apparent direction of the object is along the line OT, and the angle TOR is the apparent altitude of X. Now the angle TOX is the refraction for the ray OX, and the angle XOH, which is the apparent altitude diminished by the refraction, is called the true altitude of the terrestrial point X. -When a point is above the hori- Fig. 41. 54. Depression of a terrestrial object. — When the point is below the horizontal plane passing through the observer's eye, as S in Fig. 41, the apparent depression of the point is the angle HOK, and the true depression is HOS. 55. The observer's sea and shore horizons. — The observers sea horizon is the small circle of the earth where the sea and sky appear to meet. The observer's shore horizon is the irregular line in which the sea and land intersect. On board ship there is nothing to define the horizontal plane through the observer's eye, and it is impossible to directly measure an altitude or depression ; consequently, the altitude has to be measured to the observer's sea or shore horizon, and this measurement is called the 63 [Art. 56. observed altitude. Therefore, if we know the apparent depression of the sea or shore horizon which is called the dip. the apparent altitude of a point is equal to its observed altitude diminished by the dip of the sea or shore horizon. Thus, in Pig. 41. OK is the apparent direction of the sea horizon S, HOK is the dip, OT is the apparent direction of the point X, TOK is the observed altitude. TOH is the apparent altitude, and XOII is the true altitude of the point X. 56. Formula for the dip of the sea horizon. — In Fig. 42, let be the observer's eye at a height h feet above sea-level, SO the curved ray by which the sea horizon is seen at S, TO and T8 the tangents to the ray at <) and S. Let OH be the horizontal line passing through the observer's eye and in the same vertical plane as S. The angle TSO = TOS = the terres- trial refraction for the ray OS = r, say. As the curved ray touches the earth at S, the tangent TS also touches it at S ; therefore, OSC = 90° - r. Now COS = 180° - OCS - OSC. = 180° — OCS — 90° -f r. Therefore, denoting the angle OCS Fig. 42. COS = 90° 4- r — C. Again, HOT = 90° - COS - SOT = 90° - (90° + r — C) — r = C - 2r. Q Now HOT is the dip, and as r= we have SO that, in order to find the dip we must find C. In the triangle OCS. in COS SC R sin C80 CO " R + b where I! is t he earl We radius in teei . Now Bin COS Bin (90 • /■ C) cos (C - /•). and Bin 0£C (00° - r) coj ( • of the tide should be made when necessary. For example, suppose an observer, whose height of eye is 50 feet, sees the Bass Rock Lighl | L50 feet above high water) just showing over his sea horizon, the height of the tide at the time being (» feel below the level of high water of spring tides. The height of the light aboVe the sea level is L56 feet. I'i'oin the table for the distance of the sea horizon in Inman's tables, 150 feet gives BS as 1-4 -3 miles, and ,, t q 50 feet gives .4»S as s l miles; there- fore the distance AB is 22-4 miles, from which it may be concluded that the distance of the lighthouse is about 22 mil< 58. Formula for the dip of the shore horizon. — In Fig. 44 let 8 be a point of the shore horizon, and the observer's eye at a height of h feet above sea-level. Let OT be a tangenl to the curved ray 08, then if Oil is horizontal, the angle HOT i^ t lie dip of the shore horizon. Denote HOT by ft and the refraction TOS by r. In the triangle OSC, sin CSO I! h suTOO/S A' where fi is the earth's radius in feet. XoW ( 'SO = 180° - G (90 - r - ft) = 90° + r + cos (r + 6 - ' Jl h ' ' COS (/■ + ft) R ' .*. cos C Bin C tan (r - = « + 1- Fro. 41. C. sinCtan(r 0) ^ 2 sin 5 ^? .-. tan (/• /.' sin f 2 Therefore, since r, ft and t ' arc all small angles (r 0)'sin I' ~ [ 2 si,, I'. Lei d be tbc distance in nautical miles between .1 and 8, then iV Therefore ^ // C C 6080 rf sin I' 2 13' Now the number of minutes in Cia the same as the number of nautical miles in d. .•. I )i|> of -bore horizon in minutes of arc RC 6080rf. Abo, itt. I I I ■/. •5654 3 • 12 a where h i- in feet and il is in'n.i utie.i I mil x UIoh The dip of the shore horizon is tabulated in Inman's tables for various distances and heights of eye. 59. Distance by vertical sextant angle. — Case 1. — When the point observed is vertically over the shore horizon. In Fig. 45, let BC be a vertical cliff of height H feet above the sea- level C. Let be the observer's eye at a height h feet above the sea-level A. Let the angle sub- tended by BC at the observer's eye be a. Let a circle described about the triangle OBC cut AC in D and AO produced in E. The horizontal distance of the ob- server from the foot of the cliff is AC. Now AC --DC + AD — H cot a + = H cot a -\- AO.AE AC h(H h) AC Now if AC is greater than H, that is. if the distance of the ship from the shore horizon is greater than the height of the cliff, the second term is less than h. Therefore, if we assume that the distance is H cot a, the error will be less than h provided that AC is greater than H. In this and the following case, refraction and the curvature of the earth have been neglected; no appreciable error is caused thereby, because the distances involved are necessarily very small. Case 2. — When the point observed is not vertically over the shore horizon. In Fig. 46, let F be the shore horizon and BOF the observed angle a. Let a circle described about the triangle OFB cut AC in D, AO produced in E, and CB produced in G. Then AC =-- DC + AD = H cot a AO.AE „ . CG + (H-h) AF -- ft cot a + h - AF Now Therefore CO = DC . FC H (H--h\ , , DC .FC AC II cot a. -hi -— - ) + /i. -j-= ■ AF J AF . H ffcota+*( AF )+* y/ ( FC (AF - AD -[-FC" AF = // col a - h II h AF + * FC H AD AF FC AF Now if AF > H, and H > FC, then AF> FC and the second term on the right is less than h, while the third term is less than 2h, i\: Art. 59. Therefore, if we take the distance as // cot a, the error will be less than3A provided .1/' > II > FC ; that is. if the distance of the short- horizon is greater than the height of the point observed, \j« rH-h. and the height of the point observed is greater than its horizontal distance from the shore horizon. It will be seen that the error due to taking the distance as // <<>t a places the ship nearer the object observed than is really the case. When the observed angle is than 3 the following modi- FlG. 46. fixation of the formula Distance // cot a may sometimes be found useful : — // . // I distance // cot a = nearly Bin a a" sin I" Therefore if // is expressed in feet, the distance is given in nautical miles b\ // = H x 34 a" 6080 sin i" " a" Therefore 1 1 » « - distance in nautical miles = Height in Eeel x .*U ( Ibsen ed angle in seconds ( 'at 3 When the base of the object observed is below the observer's horizon. In Fig. 47 let II be the summit of a mountain, \\ hose height DB is // feet above level. Let the observed altitude of l>. as measured from the horizon, when diminished i>\ t he dip, be a. Then a is the apparent altitude of l> TOR in Fig.). Suppose r to be I lie refrac- t ion for the pay OB, t hen t he true altitude "I /<'. \i/... the angle BOK, U e T f H ~ h Let-j: == — R log,, 10 then log x = log (H — h) — log (R \og e 10) = log (H — A) — log (20890550 X 2-30285) -log {H -h) - 7-682215. Therefore we have log cos (C + a — r) = log cos (a — r) — x where log a; = log (H — h) — 7-682215 Example : — The observed altitude of a mountain peak, 10,000 feet high, was 1° 01' 30", the height of the observer's eye being 50 feet and the index error of the sextant (I.E.) — 1' 30"; required the distance Observed altitude I.E. Dip for 50 ft. from Inman's Tables - Apparent alt. (a) 1° or 30" — 1 30 1 00-0 - 7-0 53 • til. Iii this example, II ft = 9950 feet. log 9950 = 3-997823 7-682215 Art. 59. 4-315608 = log -000207 0002i r, log cos 53' x I -999948 •000207 log cos (C 53') = i -999741 = log cos 1 58'-75. ,.C 53' -I 58'-75 =118'-75. Therefore C 65'-75. With this approximate distance we find, by dividing by 13, that the refraction is 5', and consequently the true altitude (a — r) is 48'. log cos 48' I -999958 •000207 log cos {C + 48') 1*999751 = log cos 1° 56'-5. Therefore G f 48' I 56'-5 = 110' -5. Then-fore C (is-."». which is the distance required. If we can estimate the distance of the object observed, either from the reckoning and the chart, or by eye, the refraction obtained from this estimated distance will probably be sufficiently accurate to enable the actual distance to be found directly from the formula. Case. 4. — When the sea or shore horizon can be seen beyond the object, and the height of the observer's eye is considerable, the distance from the object ina\ be found from the observed angle of depression of the water line of the. object. Here, as in cases I and 2, the distance if necessarily so small thai refraction and the curvature of the earth may be neglected. In Fig. 18, let be the observer's eye at a height h feet above the sea Level .1. and let 08 be the apparenl direction of the sea or shore horizon. Horizontal H ■ I'l. Is. \ Lei 80B be the ol I angle a between the sea or shore horizon and t he water line B of ' he objeel Prom the Figure it is clear thai the angle [BO BOH a I dip. Therefore AB 10 i o1 a dip) Tin i ef< ire distance l< col (a di] Art. 60. 70 60. Lecky's Off-Shore Distance Tables. — These tables give in tabular form the solutions of the trigonometrical equations found in the three cases above. In Part I. are given solutions of the formula distance = H cot a for distances up to 5 miles at every 1 1 th of a mile for heights varying from 50 to 1,100 feet and the corresponding observed angles. In Par II. are given the solutions of the formula r> I 7. cos (C + a -- r) = „ „ cos (a — r) for distances varying from 5 miles to 110 miles, and for heights varying from 200 to 18,000 feet and the corresponding observed angles, h being taken as 0. The rinding of distances by means of a vertical sextant angle is, therefore, much simplified by the use of these tables, and as the heights of most prominent peaks, lighthouses, &c. are given on the charts, the method of finding a position line by vertical sextant angle is of very considerable value in navigation. It should be remembered that the heights given on the chart are given above high water of spring tides, and so, when necessary, allowance should be made for the height of the tide at the time of observation. The tables show readily when a small error in the height of the object observed produces appreciable error in the distance. It should also be remembered, when taking altitudes of lighthouses, that the height of a light given on the chart or elsewhere, is the height of the centre of the lantern and not of the summit of the lighthouse. When using Lecky's tables for case 1 the error will not exceed the height of the observer's eye if the distance from the shore horizon is greater than the height of the point observed. When using the tables for case 2 the error will not be appreciable — (1) if the distance from the shore horizon is greater than the horizontal distance of the shore horizon from the point observed ; (2) if the latter distance is less than the height of the point observed; (3) if the observed angle is less than 45°. Now, from the above, it will be seen that the error in each case depends on the height of the observer's eye ; therefore in cases where the conditions stated above are not fulfilled and it is still desired to take the observation, it is advisable that the height of eye should be as small as possible. 71 Arts. 61, 62. CHAPTER VIII. POSITION BY OBSERVATION <»i- TERRESTRIAL OBJECTS. 61. To fix the position of a ship. Having shown how a position line may be drawn on the chart, we now have to show how the position of the -hip may lit.- found by drawing two or more position lines on the chart. Tw<. or more position lines obtained at the same time give the most satisfactory position, provided that their angles of intersection are not -mail, and the position so found is called a [< fix." Whenever the position of the ship is fixed, a small circle should he drawn round the position on the chart and the time written against it. When drawing position lines on the chart, unnecessarily long or heavy lines should not he drawn, because thej have to be eventually rubbed out and a considerable amount of rubbing out deface- the .-hart. 62. Position by cross bearings. -When a ship's position is fixed by the intersection of two or more lines of bearing, the position is said to he fixed io cross bearings. Two objects should he selected, the bearings of which give as near a right-angled cul as possible. The bearing of a third object should lie taken when possible, not only because it i- a cheek on the observations, hut because it ensures as against the possibility of laying off a position line from t he w rong point. Objects abeam and before the beam should he used in preference to objects abaft the beam which the ship has already passed. < Objects should be selected that arc near to the ship, in preference to those far away, because au\ error in the bearing of a near objecl has less '•tied on the position than the same error in the bearing of a distant objecl : and moreover, as chart- are slightly distorted in printing, lone liui-- of bearing are never so accurate as short ones. When taking cross bearings the name- of die objects should firsl be written in the note hook, after which the bearings fiould he observed as quickly a- possible with due regard to accuracy the object whose bearing i- changing most rapidly being observed last. The bearings should he written against the names of the objects in t he note book; the time of the which should he that .ii which the last bearing was observed, should also he note. |. should the objects be changing their bearings quickly, ii is impossible t<> 'jet a satisfactory cut it some time elapses between taking tin- bearings of the different obje< When, owing '" tnall errors of observation, or bo the points observed being incorrectly placed on the chart, the three line- of bearing d<> not intersect at .< point, the m.ill triangle formed is called a cocked hat. • nid in the case tin- central point of tin cocked li.it -h.-uld he taken as t he posit i' 'ii of I he hip .i liow n in Fig . 19. When it i known that the cocked lial i due to an incorrect deviation liaving been u ed or. in other word t" all three hue oi bearing having the . • iit* error, it i po iblc to give ■ > geomt trical eon tructioii for finding Art. 63. 72- the position of the ship, but it is better to obtain the two horizontal angles subtended by the objects by means of the differences of theirbearings / , Beacon i$* Church Fig. 49. and to plot the position of the ship with the aid of the station pointer as explained in § 05. 63. Position by bearing and horizontal sextant angle. — It may happen that only one conspicuous object can be observed from the standard com- pass. In this case a fix can often be obtained by taking the bearing of that object, and at the same time observing the sextant angle between it and some other object from a position near the standard compass. Thus in Fig. 50, if a bearing is taken of B and the horizontal sextant angle a subtended by BC is measured, then the observer is at the inter- section of the line of bearing A B and the segment of the circle BAC which S*vi Church 8 30A.M Fig. 50. contains the angle a. In practice it is not usual to draw the segment of the circle, because the intersection of the position lines can be more rapidlv found as follows. 73 Arts. 64, 65. If the horizontal -extant angle a is applied to the observed bearing of B, the bearing of ( ' La obtained and the position may be plotted by cross l>ea rings. In Fig. 50, the Hill bore N. 30 E. and the angle to the Church is i5 J . A> the Church is to the right of the Hill, the bearing of the former must have been N. 75 I The position of the ship is therefore at .1. which is the point of inter- section of the lines of bearing. When selecting the object C it is advisable that the observed angle should be as nearly 90 as possible, and in no case less than 25°; when possible a second angle or bearing should be obtained as a cheek, because any error in either the bearing or the angle would not othen* 186 be apparent . When two objects arc seen to be in linen ith one another they are said to be in transit, generally denoted by 0. so that when an observer sees two objects in transit, and these objects are marked on the chart, his position line is the straight line which passes through the two object.-. When cruising in narrow waters or near land, care should always be taken to note the transits of any conspicuous objects, since a transit by itself gives a position line. At the moment of the transit coming on, if the bearing of, or an angle to, some other object situated so as to give- as near a right-angled cut as possible, be taken, a good fix is obtained, provided that the distance apart of the objects In transit is sufficient to under the transit a sensitive one. as explained in Part II. As before, check angles or bearings should be taken when possible. Fig. 51. 64. Position by bearing and distance. When only one object is in sight, if we can obtain its distance, either by rangefinder or by vertical ixtant angle, as explained in §§ 50 and 59, and at the same time take it* bearing, the position of the ship must be .it the intersection of the line of bearing and the circle described with the object as centre and the distance as radius. Thi if an i Kceedingly useful method of fixing the pi • ition of the ship quicklj . 65. Position by horizontal sextant angles. The method of fixing the ship's position by the intersection of two or more position lines, obtained by observing the horizontal sextant angle- subtended l>\ three or more object • bremerj u eful in navigation when great accuracy is essentia] or when no compa ailable, a the observation* can be taken from any posit ion in t he ship. Art. 65. 74 The position is more exact than the position found by bearings, because the angles can be measured with a sextant with greater precision than the compass will permit. This method is especially valuable when the objects available are at a considerable distance from the observer, when the drawing of long lines of bearing introduces error which is difficult to avoid. Another advantage is that the observer is not tied to any one spot, and can therefore place himself in the most advantageous position to see the objects clear of masts or other obstacles which ordinarily obscure so many points. In Fig. 51, let A, B, C be three objects, and let the horizontal sextant angles subtended by AB and BC be a and ft respectively; then the observer is at the point D which is the intersection of the three position lines corresponding to the angles a, ft, and (a + ft) ; the segment of the circle corresponding to the angle (a + ft) is not shown in the Figure. The drawing of the circles is a matter which occupies some time, and requires great care when accuracy is desired; but tracing paper on which the angles may be plotted, or preferably the station-pointer, affords the means of ascertaining the position readily, quickly, and accu- rately, provided that the angles of intersection of the circles are not less than 60°. Tower Lighthouse Fig. 52. The station -pointer, which is described in Part IV., consists of three legs, two of which are movable, radial to a common centre, with an arrangement for setting them at the required angles from the central nxed leg. The right leg being set for the angle measured between C and B and the left leg to that between B and A, the instrument should be placed on the chart with the chamfered edge of the central leg directed to B, and the instrument moved until the chamfered edge of the right leg falls on C and that of the left on A. The centre of the instrument will then be on the position where the two circles, if drawn, would intersect, because from no other position would all the legs, when set at the proper angles, coincide with the objects. A dot made with a sharp pencil at the centre of the instrument marks the position of the sliip. It is important to so select the objects that the circle passing through them does not pass through or near the position of the ship. Should the circle pass through the position of the ship, it will be seen from Fig. 52 t hat, since angles in the same segment of a circle are equal to one another, 7.". Art. 65. the ship might be situated at X or )' or at any point on the segment of the circle, for at every point on this segment the angles between Rock and Tower and between Tower and Lighthouse are the observed angles a and [i respectively. By attending to the following rules 1 1 1 i - may be avoided. (I) Tin middle object may be on the ship's side of the line joining ilu other two, as shown in Fig, ■">.">. If the central object is very close to the ship, the method should not be employed unless the whole angle between the right and left objects can be observed, and then either the right or left angle, because the angles adjoining the central object are changing very quickly as compared with the whole angle. Flagstaff Lighthouse Fig. 53. (2) The thret objects ihi be in or near a straight line as shown in Fig. 54. ' In this case the angles observed should not be too acute that is, neither of the angles should be less than 30 . Tower Beacon Monument I' ». Art. 65. 76 (3) The ship may be inside the triangle formed by the three objects, as shown in Fig. 55. Church Lighthouse .Fig. 55. In all doubtful cases, either a bearing should be taken of one of the objects, or a check angle should be taken to a fourth object. When a check angle is taken, it should always be taken from the central object to a fourth object, and if a second check angle is taken, it should be taken from the central object also. This facilitates plotting because, after having placed the legs of the station-pointer on the three original objects, the centre of the instrument and the fixed leg can be held steady, and one or both of the movable legs can be moved to show the check angle or angles. When writing down a station-pointer fix, the names of the objects should be written from left to right, as they were situated when observed, and the check angle written below. For example :— Lighthouse 10° 15' Beacon 85° Church 50° Flagstaff, which indicates : — Left-hand angle between beacon and lighthouse - 10° 15' Right-hand angle between beacon and church - 85° 00' Check angle between beacon and flagstaff (to right of beacon) - - 50° 00' When plotting with a station-pointer, if the objects were well placed according to the foregoing rules, the lightest movement of the centre of the instrument will immediately throw out one or more of the legs. Conversely, when the centre of the station-pointer can be moved without the legs being thrown off the objects, it indicates that the objects are badly placed and the fix unreliable. As a general rule, the greater the difficulty in plotting the position with a station-pointer, to a person accustomed to its use, the more unreliable is the fix. The station-pointer should not be used on charts which indicate, as explained in Part II., that the survey was not made in great detail. In such a case it is preferable to fix by cross bearings. If bearings of several objects are observed, and the lines of bearing do not intersect at 77 Art. 66. a point, it shows that one or more of t he objects is incorrectly charted or that an error was made in the observation of one or more of t he bearings. Where the distances, as represented on the chart, are very small, it frequently happens that the central part of the instrument obscures one or more of the points observed : in such a case it is convenient to plot the angles on cither a Douglas' protractor, a Cust's station-pointer, or a piece of tracing paper and to use it in the same manner as the station- pointer. The Douglas' protractor and the Cust's station-pointer are graduated celluloid sheets on which lines may be drawn. 66. Running fix.— We have shown above how the ship's position may be found by the intersection of position lines from simultaneous observations, and we have now to show how the position may be obtained when only one object is in sight whose distance we do not know. This is done by obtaining two position lines from two observations with a considerable interval of time between them, the position so found being called a " running fix." The value of a running fix is manifestly dependent on the accuracy of the reckoning kept, and on the correct estimation of the tidal stream or current experienced during the interval: for this reason, it is desirable when possible to obtain absolute fixes. A running fix depends on the following principle. In Fig. 56, suppose the ship to be at any point P on the position line AB, and suppose that in a given time she steams a given course and distance repre- sented by the line PP' to P'. Again, -appose the ship to he at Q on the position line - 1 B, and t ha1 in t he same time Bhe steams the same course and distance repre- sented by QQ' to Q', then the line P'Q' is parallel to AB. From this we see that, wherever the ship may be on the line AB, -he will, after steaming the given course and distance, he on the line .17; . Tin- line i- called the first position line transferred, to the tune of t he second observal ion : — Every running fix maj be plotted as follow- : (1) Draw the first position line on the chart. (2) From any point on the first position line laj of! the course and distance run between the observations, and from 'he e\ fcremitj of tin- hue tin- estimated direction and amount of the current or I idal st ream in t he inten a!. (3) Through the point so found draw a line parallel to the first position line; this is the first position line transferred, ;mf| the ship niii-t be situated somewhere on tin- line pro \ id<-d the course and distance made good between the observations baa been correctl) estimated ami laid off. i) l)raw the second position line on the chart . the point at which tin- Hue iiit-- the first position line transferred is the position <>f t In- -hip. Fig. :.<'. Art. 66. Example 78 -(Ship's course East, 8 knots. Estimated current, S.E., 3 knots. At 4 h p.m. the lighthouse bore N. 34° E. At 4 h 30 m p.m. the liehthou.se bore N. 22° W. Lighthouse \ \ \ \ ft *■ v~ 4-3 o p.m. of East 4' Fig. 57. In Fig. 57, A is any point on the first position line. AE is the course and distance run in 30 minutes. EC is the direction and amount of the current in 30 minutes. The position at 4 h 30 m p.m. is as shown in the Figure. In this example, the bearings of the same object have been taken with which to obtain the position lines ; but the same method holds good if two different objects have been observed, in either case the difference in bearing should exceed 25°. A special case of this problem is called fixing by doubling the angle on the bow. By the angle on the bow is meant the angle at the observer between the ship's course and the direction of the object ; it is measured from right ahead to starboard or port, from 0° to 180°. Lighthouse Fig. 58. In Fig. 58 it will be seen that the distance of the observer from the object when the angle on the bow has been doubled is equal to the distance run over the ground in the interval, 79 Art. 67. When the first angle observed is - points (22| ). the distance of the object when abeam is the distance run over the ground multiplied by •". The position by tour point bearing i- another special case when the first bearing is -t points on the how. and the second when the object is on the beam. The method of fixing by doubling the angle <>n the bow should not he employed when there is a tidal stream or current whose direction i- not the same a- the ship's course, or contrary to it : therefore, in general, when there is a tidal stream or current, the lix should he plotted as an ordinary r unning tix. 67. Use of soundings in obtaining the position. \\ hen only one object is in sight, an approximate position can be obtained by observing the bearing of the object and taking a sounding at the same time. The sounding must he reduced to the level <>r datum to which soundings on the charts are reduced, and. if a chemical tube has been used, should he corrected for the height of the barometer as explained in Part IV. Little reliance can he placed on this fix unless the soundings shown on the chart are such that tin- fathom line of the depth obtained can be drawn with confidence, it- mean direction makes a good angle with the line of bearing, and the depth lias been verified by two or more soundings. It is sometimes possible to estimate the -hip's position approximately >llo\\ - : Sound at regular intervals, noting the depth and nature of the bottom at each 30Unding ; these soundings must lie collected as mentioned above. 1 haw a tew Lines on a piece of tracing paper to represent true meridians, and on it lay off the course made good (allowing for tidal streams or currents). On the line which represents the ship's track, plot the ob- served soundings anil natures of the bottom at their correct distances apart, according to the scale of the chart. Place the tracing paper on the chart in the vicinity of the ship's esti- mated position, and. keeping the meridians drawn on it parallel to those on the chart, moveit ahout and see if the soundings on the tracing paper can he made to coincide with those on the chart. If they do coincide. the position of the ship at the time of the last sounding was at the point of the chart underneat b I he last sounding on the tracing paper. 'I'll.- utmost caution should he observed in estimating the ship's position from the coincidence of a line of soundings with the soundings on the chart, because -mall error- may give very erroneous results. particularly where the water ahoals gradually. Arts. 68-72. so CHAPTER IX. THE HEAVENLY BODIES AND THEIR TRUE PLACES. 68. Necessity for astronomical observations. — As stated in § 47 , the position of the ship should be frequently determined by observation , not only as a check on the accurate steering of the course and on the estimated speed, but also to guard against a wrong estimation of currents, tidal streams, &c. When it is impossible to determine the ship's position by observations of fixed objects on shore, as, for instance, when there is a haze over the land, or when the ship is in mid-ocean, we have to find it by observation of the heavenly bodies ; but before proceeding to explain how this may be done, it is necessary to give some account of the heavenly bodies, with special reference to those which are suited to the purpose of navigation. The heavenly bodies may be classified into two groups, the stars and the solar system. 69. The stars. — The stars are bodies comparable in size and physical conditions with the sun, shining by their own light as does the sun. and emitting a radiance which cannot be distinguished from sunlight. Some of the stars are much larger than the sun and some are much hotter, some are smaller and some cooler. 70. The constellations. — In ancient times the stars were grouped into constellations, partly as a matter of convenient reference, and partly out of superstition. These groups were given fanciful names, mostly of persons or objects conspicuous in the mythologies of the times. In some cases a vague resemblance to the object which gives the name to the con- stellation can be traced, but generally it is difficult to assign a reason as to why the constellations have been so named or so bounded. The names of the constellations are given in a Latinised form, such as Leo, Taurus, Argus, &c. 71. Designation Of bright stars. — The stars in a particular constella- tion are designated by letters of the Greek alphabet, assigned usually in order of brightness. Thus the brightest star in the constellation Taurus, is a Tauri, the next brightest star is /? Tauri, and so on. Some of the bright stars have names of their own, the majority of the names being of Greek or Latin origin, as, for instance, Arcturus (a Bootis), and Procyon (a Canis Minoris) ; some, however, have Arabic names, as, for instance, Aldebaran (a Tauri). 72. Magnitudes of stars. — The term " magnitude." as applied to a star, refers simply to its brightness. The magnitudes of the stars have been determined on the assumption that the magnitude of a particular star, called the Pole star, is 2-15. Magnitudes are assigned to stars according to their brightness, the brighter the star the lower being the number assigned to its magnitude. Those stars whose magnitudes are less than 2 are called stars of the 1st magnitude, those whose magnitudes are 2 and above but less than 3 are called stars of the 2nd magnitude, and so on. 81 Arts. 73, 74. Those stars which can only just be seen by the naked eye on a clear night are stars of the 6th magnitude. 73. The Solar System. — If we now confine ourselves to that particular star which is called the sun, we find that there are several bodies which revolve round it in definite periods. These bodies arc called the sun's planets, and one of them is the earth. For the purposes of navigation, we need only consider five of the planets, namely, Venus, The Earth. .Mars, Jupiter and Saturn. The planets revolve round the sun in planes which are little inclined to one another, and they have a common direction of revolution which is the same as that of the earth on its axis. They have also a common direction of rotation on their axes, which is the same as that of the sun. The earth moves round the sun in an orbit which is an ellipse, the plane of the ellipse being inclined at an angle of about 23 27' to the plane of the earth's equator. In the same way as the earth revolves round the sun. so the moon rev lives round the earth, the plane of the moon's orbit being inclined at about 5 to that of the earth. The moon is called the earth's satellite. Similarly .Mars. Jupiter, and Saturn are attended by their respective satellites in their motion round the sun. and. in addition to satellites, Saturn is surrounded by three revolving rings. The following table gives details of the sun, planets, and the moon, which, together with other bodies which are of no value in navigation, form what is called the Solar System :— Sun. Venus. The Earth. Moon. .Mars. Jupiter. Saturn. 1 1 dist ance 67 92-7 from in millions of i oil* 3, ■r in i,000 7,660 7,918 1 Time of i\ial 25-3 23h. 21m. 23h. S6min rotation. -lays. Time of orbital — •62 1 revolution in ire. ■ Mill of 23 27' nrliii the ttor. Number i lit' l>cr, - • 92 l ..i 23 ntl.lt the ecliptic. 141 is: ssi 4,200 85,000 71,000 :' Ih. 37m. 9h. 55m. lOh. 1 In.. 1-88 11-86 29-46 24 50 I., 0.1 ■23 I is' 26 19 s and I! hiil:*. •11 2 29 The mean di tance of the moon from the earth is 239,000 statute mil' 74. The Nebular Theory. i\ if so important to realise the rapid movera it the moon and planets in distinction to the comparative fixity "t the that in order to empha i i the matter b brief account of the nebular theory ot Laplace may not be withoul value. Laplace conceived that the matter now conden ed into the various member _,. Sj, and S 4 are the apparent places of the sun as realk Been from F r E a , E 8 , and F 4 respectively. ( (wing to the real movement of the earth in t he direction of the double arrows. Fig. 63, the centre of the sun appeals, in the course of a complete revolution (year), to describe a circle on the celestial concave, Fig. 64; this circle is called the ecliptic. Since the planes of the orbits of the moon and planets are but little inclined to that of the ecliptic, the moon and planets are always seen near the eeliptic. An imaginary belt of the heavens, extending 8° on either side of the ecliptic and in which all the planets are situated, is termed the zodiac. The plane ot the earth's equator, if extended, would intersect the celestial concave in a great circle, which would intersect the ecliptic in two opposite points. This great circle on the celestial concave is • ailed the celestial equator (or equinoctial), and is evidently inclined to the ecliptic at the same angle as the plane of the earth's equator is inclined to that of its orbit; this angle (23° 27') is called the obliquity of the ecliptic. The axis of the earth remains, for all practical purposes, parallel to itself during every revolution ; therefore the two opposite points of in- rsection of the ecliptic and celestial equator are practically fixed points on the eelestial concave. They are known as the first points of Aries and Libra, because in early age> they occupied positions in these constellations. ('n March 21st. when the earth is at E l5 the centre of the sun occupies on the eelestiai concave the same apparent position as the first point 01 Aries, and this position is called the vernal equinoctial point; for a similar reason, when the earth on September 23rd is at E 3 , the sun apparently occupies the first point of Libra, and this position is called the autumnal equinoctial point. Therefore, the first point of Aries i the position of the sun on the celestial equator as it moves from South to North : it is denoted by the symbol T, Fig. 65. A difficulty may occur to the reader that the plane of the equator when the earth is at E 2 j Pig. 63, is not identical with thai when the earth is at K.|. and that, i hereto re, the points of intersection of the plane of the equator with the fixed plane of the ecliptic are not the same in the two cases. This is strictly true, and would be appreciable ai a finite distance, but is not bo ai the infinite distance of the eelestial concave. The celestia] poles being ai an infinite distance are unaffected by the • ii '- motion in ite orbit, and may, therefore, be regarded as fixed points. The ecliptic and celestial equator intersect a1 the equinoctial points. and are, therefore, mo I widely separated at positions midway between these point-. These positions are known as the summer and winter Bolstitial points, and the sun appears to occupy them when the earth is .it \\ 2 (June _-iid) and it E 4 (December 22nd), respectively. 78. Positions of heavenly bodies. The celestial equator being a fixed circle on th< cele fcial concave, and the first point of Aries vet} nearly a fixed point on that circle, the positions of the heavenly bodies maj Art. 78. 86 be expressed by reference to them, in precisely the same way as places on the earth's surface are expressed by reference to the equator and the meridian of Greenwich. The true place of a heavenly body is the point where the line joining the centre of the earth to the centre of the body meets the celestial concave. In Fig. 65 X is the true place of the body S. ( lelestial meridians are semi-great circles which join the celestial poles, PXP', Fig. 65, and they correspond to terrestrial meridians. Parallels of declination are small circles whose planes are parallel to that of the celestial equator BX in Fig. 65, and they correspond to terres- trial parallels of latitude. Fig. 65. The declination of a heavenly body is the arc of the celestial meridian. which passes through the true place of the body, intercepted between the celestial equator and the true place of the body, or it is the angle at the centre of the earth subtended by this arc ; it is measured from the celestial equator from to 90°, and is named North or South according as the body is North or South of the celestial equator. Declination on the celestial concave corresponds to latitude on the earth. In Fig. 65. AX or ACX is the declination of the body S. The polar distance of a heavenly body is the arc of the celestial meridian, which passes through the true place of the body, intercepted between the elevated pole and the true place of the body, and is, therefore, !)(> r declination. In Fig. 65 PX is the polar distance of the body 8 bo an -observer in North latitude, and P'X to an observer in South lati- tude. 87 Art. 79. The right ascension (R.A.) of a heavenly body is the arc of the celestial equator intercepted between the first point of Aries and the celestial meridian which passes through the true place of the body; it is measured Eastward from the first point of Aries, increasing from 11 in 360* (or 24 hours). In Fig. (>r>T -I is the right ascension of the body • s '. Right ascension on the celestial concave corresponds to longitude on the earth. 79. Variation in right ascension and declination. In the case of the sun it wiil be seen from Fig. (34 that its right ascension on March 21st is or hours); on June 22nd. ".hi (or 6 hours); on September 23rd, I 80 na' 12 hours) ; and on December 22nd it is 270° (or 18 hours). Since the planes of the ecliptic and celestial equator are inclined at an angle of about 2M 27', it follows that the sua s declination on March 21st is o : on June 22nd. 23 27'N. ; on September 23rd, 0° ; and on December 22nd, 23 27' S. In a similar way it may be shown that there are considerable periodic changes in the right ascensions and the declinations of the moon and planet-. The stars are so distant that their positions are unaffected by the annual change of position of the earth, and their declinations and right ascensions only change by a small yearly amount, dependent principally (•n the slight annual movement of the first point of Aries. The right ascensions and declinations of the centres of heavcuk bodies are obtained by the fixed Instruments of astronomical observatories, and are tabulated in the Nautical Almanac for each year. In this book the general abbreviation for the right ascension of a heavenly body is R. A. ■>!»-. Arts. 80-83. 88 CHAPTER X. THE GREENWICH DATE AND CORRECTION OF RIGHT ASCENSION AND DECLINATION. 89. The year and the month. — It has just been shown how the posi- tions of heavenly bodies are referred to the celestial concave by means of their right ascensions and declinations. As the right ascensions and declinations are continually changing, we have to show how to find these elements at any instant of time, from the particular values tabulated in the Nautical Almanac; in other words, we have to find the right ascension and decimation at a particular date. Now the date, at which an observation is taken, is the interval of time that has elapsed since some particular event ; this interval is measured in various units of time which depend on the intervals occupied by the earth in its revolution round the sun and its rotation on its axis. The largest unit is the mean solar year, which is the interval between two successive passages of the sun through the first point of Aries. The next unit in order of magnitude is the calendar month. A lunar month is the interval occupied by the moon in revolving round the earth with reference to the sun ; as the mean solar year contains about twelve lunar months, but not an exact number, it has been found convenient to. divide the mean solar year into a series of twelve periods, each having a fixed number of days : these periods are the calendar months now in use. In order to explain the smaller units of time we must first explain how the rotation of the earth on its axis is made use of to measure them. 81. Celestial meridians of observer and heavenly body. — The earth rotates on its axis from West to East ; consequently the heavenly bodies appear to us to revolve round the earth from East to West. For this reason we regard the earth as fixed and the heavenly bodies as rotating round the earth together with the celestial concave, so that the plane of each celestial meridian coincides in turn with the plane of the meridian of the observer. That particular celestial meridian whose plane coincides with that of the meridian of the observer at any instant, is called the celestial meridian of the observer at that instant. The celestial meridian of a heavenly body is that celestial meridian which passes through the true place of the body. 82. The day. — When the celestial meridian of a heavenly body and the celestial meridian of an observer coincide, the body is said to be on the observer's meridian, to pass the observer's meridian, or to be in transit, and the interval between two successive meridian passages of a body is used as a means of measuring time ; this interval is called a day. There are different kinds of days, which take their names from the different bodies to whose meridian passages they refer. 83. The solar day. — The solar day is the interval of time between two successive passages of the sun's centre over the same meridian. 89 Art. 84. The solar day begins when the sun's centre is on the meridian of the observer, and at this instant it is said to be apparent noon at his meridian. Observations show that this interval is not the same for any two days in succession. This is due to two causes : — (a) The sun does not move in the celestial equator, but in the ecliptic. (6) The sun's motion in the ecliptic is not uniform, the velocity of the earth in its orbit varying with its distance from the sun. The Length of the solar day is, therefore, variable, and clocks cannot be regulated bo measure it. 84. The mean solar day and mean soiar time. — In order to obtain a uniform measure of time, an imaginary day is employed, called a mean soiar day. which is equal in length to the mean or average of all the solar days in a mean solar year. There are 365*24219 mean solar days in a mean solar year. The mean solar day refers to the meridian passage of an imaginary Min. called the mean sun. which is conceived to move in the celestial equator with the true sun's mean rate of motion in right ascension. The mean sun is regulated with regard to the true sun by means of a fictitious body, which is conceived to move in the ecliptic with the average speed of the true sun, and to coincide with the sun when the earth is nearest to the sun. When this fictitious body passes the first point of Aries, the mean sun is -apposed to start from that point and to move in the celestial equator with the same uniform speed as the fictitious body in the ecliptie. A mean solar day at any place is considered to begin when the mean sun is on the meridian of that place (mean noon), and is measured by the interval which elapses between two successive passages of the mean sun over that meridian. This interval is divided into 24 mean solar hours, each being again subdivided into minutes and seconds. A clock regulated to keep this time is called a mean solar clock, and the time shown by it is called mean time. For convenience the civil day begins at midnight and ends at the uc.Nt midnight, midnight being the instant at which the mean sun is on that meridian t he longitude of which differs by 180° from that of the place. It comprises 24 hours, which, however, arc counted in two series of o hours to 12 hours; the first is marked a.m., extending from mid ru'ghl to noon, and the second is marked p.m., extending from noon to midnight. The astronomical day begins at noon on the civil day of the same date. It also comprises 24 hours. bu1 these are reckoned from hours to 24 hour-, and extends from noon of one da\ to noon of the next. It follow- that, whereas ~ u p.m., January 9th civil time is January 9th, 2 hour- astronomical I ime ; 2 h a.m. January 9th civil time is January 8th, l t hour as1 ronomical time. ThUfl we gee that the date at which an ohservat ion is taken may be expn aed in hours, minutes, and seconds of a particular mean solar day of a particular month of a particular mean solar year; and that the mean solar day may he civil or astronomical. The mean -oia>- time a! any place is denoted l>\ ftf.T.P. (mean time ai place) and on board a ship by S.M.T. (ship mean time). The lime kept by clocks in England is the mean solar time ,n Greenwich, and is denoted by G.M.T. Chronometers are carried on Art. 85. 90 board ship and from them the G.M.T. can always be found. To avoid the necessity of moving the chronometers, a watch called a deck or hack watch is used for noting the time at sea, and its error on G.M.T. is found by comparison with the chronometers. 85. Change of time for change of longitude. — With regard to the mean sun M, in Fig. 66, 24 mean solar hours will elapse between two successive passages across the same meridian, and, therefore, if we suppose 24 meridians to be drawn at equal distances apart / 360° \ ( — — = 15° |, they will by the rotation of the earth pass successively under the mean sun at intervals of one mean solar hour. If one of these 24 meridians be that of Greenwich, PG in Fig. 66, the first of those Eastward of that meridian, PE, will evidently pass under the mean sun one mean solar hour before, and the first Westward of Greenwich, PW, one hour after the mean sun has crossed that meridian. In other words, at Greenwich mean noon, the mean time at every place on the meridian PE will be l h p.m., and similarly at the same instant the mean time at every place on the meridian PW will be ll h a.m. From this it follows that time is converted into arc at the rate of 15° to an hour, which is the same as 1° to 4 minutes, or 1' to 4 seconds, or J" to rsth of a second of time. Inman's tables give the Log. Haversines for angles expressed either in arc or time; consequently time may be converted into arc, or vice versa, by inspection of these tables. To avoid the risk of arithmetical mistakes, this method should always be employed. In the event of no tables being available, arc may be converted into time and vice versa by remembering the relations stated above. It will be seen that at every place on the meridian of Greenwich, PG in Fig. 66, the time will be mean noon (G.M. Noon) ; at every place on the meridian PE the M.T.P. is l 1 ' p.m., and at every place on the meridian P W the M.T.P. is ll h a.m. From this we see that the difference in time at the two meridians, expressed in arc, is the difference of longitude of the two meri- dians : thus the difference between the M.T.P. of the meridians PE and PW is 2 hours, which, expressed in arc, is 30°, and this is the d Long, between the two meridians. When one of the meridians considered is that of Greenwich, the difference between the longitudes becomes the longitude of the other meridian, and so the longitude of a place expressed in time is the difference between the G.M.T. and the M.T.P. at any instant. In Fig. 66, the longitude of PE is 15° E., and the G.M.T. is hours or 24 hours. The M.T.P. of the meridian PE is ] hour, so thai, ? Fig. 66. .since the longitude expressed in time is 1 hour, we see that M.T.P. G.M.T. Long, of PE. 91 Arts. 86, 87. Similarly with regard to the meridian PW, M.T.P. = G.M.T. Long, of PW. Thus, when finding the S.M.T. or M.T.P., we add or subtract the Longitude of the ship or place, expressed in time, to the G.M.T. or from it. according as the plan- is in East or West longitude. This is easily remembered by aid of the following rhyme : — Longitude East, Greenwich tinn least : Longitude West, Greenwich time best. * 88. The Greenwich date. —All the elements tabulated in the Nautical Almanac are given for various hours of Greenwich mean time, some being given for G.M. Noon only and some for every two hours. In order to take out the elements for any date it is necessary to find the < r.M.T. corresponding to that date, and to find this we apply to the time shown by the chronometer, or deck watch, the error of the instrument on G.M.T. The G.M.T. is always expressed in astronomical time and, since the dials of most ehronometers and watches are marked from to 12 hours, it may sometimes be necessary to add 12 hours to the chronometer or watch time, and to put the day of the month one day back. To deter mine whether this must be done, an approximate G.M.T., called the Greenwich date (G.D.), should always be found by applying the estimated longitude (in time) to the S.M.T. or M.T.P. expressed in astronomical time. Example 1 : — August 3rd, at 5 1 ' 32'" p.m. (S.M.T. nearly) in estimated longitude 150° 30' W. a chronometer showed 3' 1 23 m 15 s . its error on G.M.T. being 10 m 20- slow. Required the G.M.T. S.M.T. 5 32 m Aug. 3rd Chron. - 3 23 m L5 S Long. +10 02 (W.) Error on G.M.T. 10 20 slow G.D. 15 34 Aug. 3rd 3 33 35 " Add - 12 00 00 G.M.T. - - 15 33 35 A ug. 3rd Example 2 : March loth, at 2 11 lo m a.m. (S.M.T. nearly) in estimated longitude 20 43' B., a chronometer showed h 2 m 50 . its error on G.M.T. being i.v 16 slow. Required the G.M.T. - M.T. M 1 ' 10'" Mar. 9th < 'limn. - 02™ 50 Lor I 23 (E.) Error on G.M.T. 45 16 slow G.D. 12 47 Mar. 9th 48 06 \(kl L2 00 00 G.M.T. - - L2 18 06 Mar. 9th 87. Correction ot right ascension and declination. {«) The Sun. \ will be presently understood, alter reading Chapter XI.. i< is un in- 1 ■ . io find the righl ascension of the sun. The declination <>f the un is given in the Abridged Nautical Almanac on page I. every month. The name of the declination ia indicated by X. or s. prefixed to it al e\ ery third noon, and also at oach "I the two Art. 87. 92 noons between which it changes name. The value of the declination for any G.M.T. other than noon is found as follows : — Take the interval between the G.M.T. and the nearest noon ; express it in hours and decimals of an hour. Take the value of the declination and its variation in one hour at that noon. Multiply the variation in one hour by the interval. Apply the product as a correction to the noon value, additive or sub- tractive as indicated by inspection of the Almanac. When a change of name in declination occurs during the interval, it is made evident by the fact that the correction is greater than the noon value and is subtractive. On pages III. to VI. of every month the value of the declination is given for every even hour of G.M.T.. and it may be taken out at sight. In the following examples. the multiplication is not shown. Example 1 : — Required the sun's declination at G.M.T., April 12th, 1914, 5 h 41 ra . The nearest noon is that of April 12th, and the interval is 5-7 hours. The variation in one hour is 0'-92. By inspection the value required is greater than the noon value. At April 12th, G.M. Noon, Sun's Dec. 8° 28' -5 N. Add 5-7 X 0'-92 +5-2 At G.M.T. required - 8 33 -7 N. From page IV. an estimate, made between the values for four and six hours on April 12th, gives the same result. Example 2 : — Required the sun's declination at G.M.T., March 20th, I!) 14, 19 h 53'". The nearest noon is that of March 31st, and the interval is 4- 1 hours. The variation in one hour is 0'-99. By inspection a change of name may occur. At March 21st, Noon, Sun's Dec. - 0° 00' -8 N. Subtract 4-1 X -99 - - —4-1 At G.M.T. required - 03 -3 S. The correction is subtractive and exceeds the noon value, so that there is a change of name. From page V. the same result may be estimated. (6) The Moon. — The right ascension and declination of the moon are given on page.-; VII. to X. for every month for every even hour of G.M.T., and the two hourly differences enable the value for any intermediate G.M.T. to be readily obtained by inspection of the table of proportional parts ; this table will be found at the end of the Almanac, the arguments being, at the top of the page, the two hourly differences, and at the left-hand side of the page, the interval from the nearest even hour of G.M.T. Example :■ — Requrred the right ascension and declination of the moon for G.M.T., March 5th, 1914, 9 h 36'". The nearest even hour is 10 and the interval is 24 minutes. With 288, the difference between 8 hours and 10 hours, at top of page, and 24 minutes, at left-hand side of page, as arguments, it will be found that .IS seconds should be subtracted from the R.A. for 10 hours. Similarly 93 Art. 88. 0'-6 is found to be the amount to be subtracted from the declination for 10 hours. At March 5th, 10 h R. A. Moon - 5 h 26™ 59* Dec. 28° 29'-5N. Proportional parts for 24 m - — 58 —0-6 At G.M.T. required - - 5 26 01 28 28-9N. (c) The Planets. — The right ascensions and declinations of Venus, Mais. In niter, and Saturn are given on pages XI. and XII. of every month for G.M. Noon of each day; the values for any other G.M.T. can be found by means of the table of proportional parts, using as argu- ments the difference in 24 hours at the top of the page and the interval from the nearest G.M. Noon at the right-hand side of the page. (d) The Stars. — The right ascensions and declinations are given of all stars, of magnitudes 3 and upwards, at intervals of 90 days; the approximate values for any day can be taken out by inspection. 88. Adjusting ship's clocks for change oi longitude. — It is convenient for many reasons to keep the ship's clocks adjusted so as to show S.M.T. as nearly as possible. Suppose a ship starts from the meridian of Greenwich with her clocks showing G.M.T. On arriving at the meridian of L5 C E. she will have changed her longitude (expressed in time) by 1 hour, so that the time at this meridian is 1 hour in advance of G.M.T.; consequently, when a ship steams East it is necessary, in order to keep her clocks adjusted to S.M.T., to pnl them on by an amount equal to the (/Long. expressed in time. Similarly, when steaming West, it is necessary to put i be clocks hack. It is customary to adjust the clocks of a man-of-war during the night, or in the morning watch, so as to interfere with the work of the mip as little as possible, and to adjust them so thai they will show correct time at the following noon. It may be convenient, when a ship is on a long voyage, to adjust the clocks so that they will show XII. at the next apparent noon, in order that observations of the sun. when on the meridian, can be made at noon by the ship's clocks. Lit us again consider the change of time on board the ship which is ateaming East. When in longitude 180° E. the S.M.T. will be 12 hours in advance of the G.M.T. at any instant, and this introduces an important complical ion. Suppose the ship to be in longitude 179° 45' E. (ll h 59 m E.) at _' i'.w. on January 4th, and that her longitude alter an interval of one tiour is 179 16' W. (ll h 59 ra \V.). Now the G.M.T. at 2' p.m. is given by 8.M.T. 2 h no 1 " January 4th. Loi - - - 11 59 (E.) G M T. - M ni^ January 3rd. One hour later her G.M.T. i 15 01 ni January 3rd, and her S.M.T. at t he aame instant \& given by G.M.T. - IS 1 ' oi 1 - Januarj 3rd. Long. -II 59 (W.) S Vf.T. :5 ol' January 3rd. Art. 89. 94 Therefore the S.M.T. has changed in one hour from 2 h p.m. January 4th to 3 h 02 m p.m. January 3rd. From this we see that when crossing the meridian of 180° from East longitude to West longitude, the date will alter one day back. Similarly it may be shown that when crossing the meridian of 180° from West longitude to East longitude the date will advance one day. When navigating in the vicinity of the meridian of 180°, the possi- bility of using a Greenwich date with an incorrect day of the month may be avoided by noting that the sequence of the days of the month used in the Greenwich date, from day to day, remains unbroken. 89. Standard times. — If every place in the same country kept the time appropriate to its meridian — that is, M.T.P. — difficulties would arise in the transactions of ordinary life, in particular as regards railways. For this reason a system of standard times has been adopted, by which all places in one particular country, or division of a country where it is a large one, keep the same time— which is that of some important place or meridian ; in the latter case the time is generally regulated by Greenwich mean time, and is a certain number of hours in advance, or behind it, depending on the average longitude of the country. In England, Scotland, and Wales, G.M.T. is kept in all ports, and this time is also kept in all the ports of France, Belgium, Spain, and Portugal. The time at the meridian of 15°E.is one hour in advance of G.M.T. ; this time is called Mid-European time and is kept by Germany, Austria, Denmark, Sweden, Norway, Italy, Malta, and other countries which are situated in about the same longitude. East European time is two hours in advance of G.M.T. It is the time for the meridian of 30° E., and is kept by Egypt, South Africa, and Asia Minor. Similarly other times, which are a certain number of hours in advance or behind that of Greenwich, are kept in other parts of the world ; for example, New Zealand's standard time is 11 hours 30 minutes fast on G.M.T. A few countries keep the M.T.P. of a particular place : for example, Ireland's standard time is that of the meridian of Dublin, which is 25 minutes 21-1 seconds slow on G.M.T. The standard times kept in any particular country are given in the sailing directions, in a table towards the end of the unabridged edition of the Nautical Almanac, and in the Admiralty List of Lights and Time Signals. When, therefore, a ship steams from one port to another, at both of which the same standard time is kept, it is generally unnecessary to alter the ship's clocks during the voyage. The meridian of 180° passes through several groups of islands, so that it is possible for the dates at two islands in any particular group to differ. To avoid the inconvenience arising from a difference of date in adjacent islands, the meridian of 180°, in the vicinity of each group, is broken and replaced by a zig-zag line which leaves the whole group to one or other side of it. This line is called the date or calender line, and countries, situated on opposite sides of it, keep different dates. Infor- mation relating to the date line will be found in the Admiralty List of Lights and Time Signals. When proceeding to a place, which docs not keep the date corre- sponding to its longitude due to the position of the dato line, care must 95 Art. 89. be taken when working observations to use the correct (!.D. The possibility of error may be avoided by noting that the sequence of the days of the month used in the Greenwich date, from day to day, remains unbroken; after the meridian of 180 has been crossed, the Greenwich date may be found by remembering that, if the date has not been changed on crossing the meridian of 180 c , the name of the longitude must not be changed. Example : — Suppose a ship to leave a New Zealand port, the longitude of which is 17.V E. on January 3rd, on a voyage to the Friendly Islands (Long. 175 \\\). On this voyage the ship will not cross the date line, because in this vicinity the date line coincides with the meridian of 172 30' W. ; therefore it is not desirable to change the date. On January 7th, at about 7 h a.m., in estimated longitude 177° W., an observation for finding the position of the ship was taken. The G.D. of the observation is found as follows : — M.T.P. (according to date used in ship) l ( .» h 00™ January 6th. Long. (183° E.) - 12 12 (E.) G.D. - - - - - - 6 48 January 6th. Art. 90-93. 96 CHAPTER XI. THE ZENITH DISTANCE AND AZIMUTH AT THE ESTIMATED POSITION. 90. Connection between a position on the earth and a heavenly body. — Having shown how a position of a heavenly body on the celestial concave may be found at any instant, we have now to find how the body is situated with regard to the estimated position of the ship, and to do this we have to bring the estimated position into relation with the true place of the body by referring the estimated position to the celestial concave. The zenith of a position on the earth's surface is the point where the normal to the earth's surface at the position intersects the celestial concave, Z in Fig. 67. The celestial meridian which passes through the zenith is in the same plane as the meridian of the position on the earth's surface. Great circles of the celestial concave which pass through the zenith are called circles of altitude. The connection between a position on the earth and a heavenly body, which we require to find, is the connection between the two points Z and X on the celestial concave, X being the true place of the heavenly body. In Fig. 67, P is the celestial pole, Z the zenith of the estimated posi- tion E, and X the true place of the body S. The spherical triangle PZX formed by the celestial meridian of the estimated position (PZ), the celestial meridian of the heavenly body (PX) and the circle of altitude (ZX) is called the astronomical or position triangle. The connection between Z and X is known if we can determine the angle PZX and the side ZX ; in other words, the bearing and distance of X from Z. 91. The azimuth. — The azimuth of a heavenly body, at any instant at any place, is the angle at the zenith of that place between the celestial meridian of the place and the circle of altitude which passes through the true place of the body at that instant. It is measured from that part of the meridian which is on the polar side of the zenith towards East or West from to 180°. In Fig. 67 the angle PZX is the azimuth of the body S at the estimated position E. 92. The zenith distance. — The zenith distance (z) of a heavenly body, at any instant at any place, is the arc of a circle of altitude intercepted between the zenith of the place and the true place of the body at that instant. In Fig. 67, ZX is the zenith distance of the body S at the esti- mated position E. 93. The astronomical triangle. — In order to find the azimuth and zenith distance we must know three elements of the astronomical triangle PZX. The side PZ which measures the angle PCE, that is 90° - - ECQ, is the co-latitude of E, which is obtained as explained in Chapter VI. The side PX is the polar distance of the body S, that is 90° + the declination of the body, and is obtained from the Nautical Almanac. u: Arts. 94, 95. Therefore, PZ and PX being known, if we know the angle ZPX three elements of the triangle are known, and any one of the others can be found. 94. The hour angle. — The hour angle (H) of a heavenly body, at any instant at any place, is the angle at the celestial pole between the celestial meridian of the place and the celestial meridian of the body at that instant. It is measured from the celestial meridian of the place Westward from to 24 hours. It may also be regarded as the arc of the celestial equator intercepted between the two celestial meridians. In Fig. 67, ZPX is the hour angle of the body S at the estimated position E. In Fig. 6S, let PZ be the celestial meridian of the estimated position, PX the celestial meridian of the heavenly body at any instant, and M the position of the mean sun on the celestial equator; then, since the mean sun revolves at a uniform rate, the hour angle of M (ZPM) is the mean solar time at that instant at the estimated position (M.T.P.). Fig. 67. Similarly the hour angle of the mean sun at the position of the ship is the mean solar time at the ship (S.M.T.). The apparent solar time, at any instant at any place, is the hour angle of the sun at that instant at that place (A.T.P. or S.A.T.), ZVX ID Big. 68, X being the true place of tin- sun. 95. The equation of time. — The equation of time (Eq. T.), at any instant at any place, is the difference between the apparenl solar time and the mean solar time at that instant at that place. It is, therefore, the difference between the hour angles <»f the ran and mean sun ; thai is, the angle at the pole between the celestial meridians of the sun and mean • uii a Arts. 96, 97. 98 sun. In Fig. 68, the equation of time is the angle XPM, X being the true place of the sun. The equation of time is tabulated in the Nautical Almanac for every day of the year. Since the mean sun is sometimes ahead and sometimes behind the sun S.A.T. = S.M.T. + Eq. T. or, hour angle of the sun at any place = M.T.P. + Eq. T. 96. The right ascension of a meridian (or sidereal time). — When X is the true place of any heavenly body other than the sun,. the hour angle is found by reference to the first point of Aries. The right ascension of the meridian (R.A.M.), of any place, is the arc of the celestial equator intercepted between the first point of Aries and the celestial meridian of that place, and is measured to the East- ward from the first point of Aries. In Fig. 68, TQ is the right ascension of the meridian PZ. Now ZP T (or QT) is the hour angle of the first point of Aries at the place, and is also called the sidereal time at that place. Thus it will be seen that the sidereal time at any place and the right ascension of the meridian of that place are identical. 97. Formula for the hour angle of a heavenly body. — Suppose that all points of the celestial concave are projected on to the plane of the celestial equator, from a point on the fine of the earth's axis which is at an infinite distance beyond the north celestial pole ; then in the following figures, TQ represents the celestial equator, PZQ the celestial meridian of the estimated position, and PX the celestial meridian of the body whose true place is X. In Fig. 69, XPZ or AQ = TQ - TA. Now XPZ or AQ is the hour angle of the body, TQ is the right ascension of the meridian of the estimated position, and TA is the right ascension of the body. Therefore, tf^R.A.M.-R.A.-* Fig. 68. Q Fig. 69. In Fig. 70, XPZ or AQ = TQ + AT. 99 Art. 98. Now AT is 24 hours — the right ascension of X. Therefore, # h = 24 + R.A.M. — R.A.^. Now the right ascension of a heavenly body may be taken from the Nautical Almanac, so that we have now to find the right ascension of the meridian, and this is done by reference to the mean sun. In Figs. 71 and 72 let M be the mean sun. In Pig. 71, TQ = ?M -f MQ. Now TQ is the right ascension of the meridian (R.A.M. ), TM is the right ascension of the mean sun (R.A.M.S.), and MQ is the mean time at the estimated position (M.T.P.),. and may be found from G.M.T. + estimated longitude; therefore R.A.M. = R.A.M.S. + M.T.P. • In Fig. 72, TQ =■ MQ - Mr = M.T.P. - (24 h - R.A.M.S.) = M.T.P. + R.A.M.S. - 24 h . Combining the formulae for H and R.A.M. we have H = M.T.P. + R.A.M.S. - - R.A.-fc ± 24 h as necessary. In the case of the sun, R.A.M.S. — R.A. is the angle at the pole, between the celestial meridians of the mean sun and the sun, and is therefore the equation of time ; and the formula for H becomes // = M.T.P. + Eq. T. The right ascension of the mean sun is tabulated in the Nautical Almanac for every day of the year. 98. Correction of the equation of time. — The equation of time is given in the Nautical Almanac, on page I of every month, for G.M. noon; Its sense La indicated at the head of the column by precepts, "Add to apparent time " or " Subtract from apparent I im<\" w hieli iiiusl be Under- stood also to imply respectively subtract from mean time or add to mean time. When a change of precept OCCUrS in the course of a month, the heading ■ , and the black line between two noon values 3 subtract from indicates thai the change occurs at some time between the two noons. The value of the equation of time at any G.M.T., other than noon, is found in a similar way to the declination (§ S7a). (i L' Arts. 99, 100. 100 When a change of precept in the equation of time occurs during the interval, it is made evident by the fact that the correction is greater than the noon value and is subtractive. On pages III to VI of every month the value of the equation of time is given for every even hour of G.M.T. and its value for any G.M.T. can be taken out at sight. The note at the bottom of the page denotes how the sign, placed against the equation of time, is to be interpreted. Example 1 : — Required the equation of time for G.M.T. March 20th 1914 19 h 53 m . The nearest noon is that of March 21st, the interval is 4*1 hours. The variation in 1 hour is • 75 second. By inspection the correction is additive. At March 21st Noon, Equation of time - - 7 m 29«-3 - to A.T. Add 4-1 X -75 s +3-1 At G.M.T. required ----- 7 32-4 — to A.T. From page V the same result may be estimated. Example 2 : — Required the equation of time for G.M.T. April 15th 1914 15 h 25 a . The nearest noon is April 16th. The interval is 8-6 hours. The variation in 1 hour is -61 second. By inspection a change of name may occur. At April 16th Noon Equation of time - - m 02 s - 7 — to A.T. Subtract 8-6 X -61 s - — 5-2 At G.M.T. required 02-5+ to A.T. From page IV the same result may be estimated. 99. Change in the right ascension of the mean sun. — In a mean solar year the mean sun travels through 360°, or 24 hours of right ascension, along the celestial equator. Therefore, since there are 365*242216 mean 24 solar days in a mean solar year, the mean sun moves through ^ 9A99]( { hours of right ascension in one mean solar day ; that is, through hrs. 3 mins. 56-6 sees., which is the change in the right ascension of the mean sun in a mean solar day. In the Nautical Almanac the last column of page I of every month gives the change in the R.A.M.S. for various intervals of mean solar time up to 24 hours. 100. Correction of the right ascension of the mean sun. — The right ascension of the mean sun is given on page I. of every month for G.M. noon. On pages III to VI of every month the R.A.M.S. is given for every even hour of G.M.T. ; its value for any other G.M.T. is found by adding, to the value for the preceding even hour, the correction for the remaining interval, from the auxiliary table on page I of each month headed " Add for hours." Example 1 :— Required the R.A.M.S. for G.M.T. March 6th 1914, 10 h 42 ra . At March 6th G.M.T. 10 h R.A.M.S. - - 22 h 55 m 08 8 -4 Add for 40 minutes 6-6 Add for 2 minutes *■ -3 At G.M.T. required 22 55 15-3 101 Art. 101. Example 2 .-—Required the R.A.M.S. for G.M.T. March 22nd 1914, 21 h 36'". At March 22nd G.M.T. 20 h R.A.M.S. - - 23 h 59" 51 s - 8 Add for 1 hour 9-9 Add for 30 minutes 4-9 Add for 6 minutes 1-0 24 00 07 -G Subtract 24 00 00 At G.M.T. required 00 00 07 • 6 101. Calculation of the zenith distance and azimuth at the estimated position. — In the astronomical triangle PZX, Fig. 67, we know PZ, the co-latitude of the estimated position, PX, the polar distance of the body, and ZPX, the hour angle of the body at the estimated position. The zenith distance ZX may be found from the formula : — hav ZX = hav {PX ~ PZ + hav 6 where hav = sin PZ sin PX hav ZPX. If the latitude (L) and the declination (D) are of the same name, PZ = 90° — L and PX = 90° — D and the f ormulae become :— hav z = hav (L ~ D) -f- hav 0, where hav = cos L'cos D hav H. If the latitude and declination are of different names, PZ = 90° — L and PX = 90° + D and the formulas become : — hav z = hav (L + D) + hav 6, where hav = cos L cos D hav H. Thus we have hav z = hav (L + D) + hav 6, where hav = cos L cos D hav H, the sign ~ or -j- being used according as L and D are of the same or different names. Having found the zenith distance ZX, the angle PZX, which is the azimuth, may be found from the formula : — hav PZX = cosec PZ cosec ZX ^Eav (PX + ZX - PZ) hav (PX - ZX + PZ). The following examples show the method of calculating the zenith distance and azimuth : — Example 1 :— On March 30th 1914 at about 6 h 20"' p.m. (S.M.T. nearly) in <'s1irna1<-d position Lat. 21° 10' N., Long. 168° 15' \\\, a deck watch showed 2 1 ' 54 m 33 B and was slow on G.M.T. 2 h 03'" 25 s . Required the zenith distance and azimuth of Venus at the estimated position. S.M.T. Long. d 1 ' 2• 2 h 2 54 m 03 33 s 25 102 Add 4 12 57 00 58 00 • G.M.T. Long. 16 10 57 33 58 Mar. 30th. 00 (W.) M.T.P. R.A.M.S. 6 24 30 58 54-3 + R.A.M. R.A* 6 1 55 20 52-3 14- H. 5 35 38 • 3 L hav 9-65025 Lat. Dec. 21° 7 10' 29- N. L cos 2 N. L cos 9-96966 9-99629 (L-D) 13 40- Nat Nat Nat r Z -PZ I + PZ 8 L hav l > hav 8 , hav (L - D) hav ZX ZX = 81° 39'-2 68 50 ? 961620 •41325 •01418 •42743 81° 39'-2 ZX ■ PZ - £cosec 10-00463 L cosec 10-03034 ZX -Pi PX - 12 49-2 82 30-8 PX +Z1 PX - Zl 95 20 69 41-6 iLhav 4-86878 \L hav 4-75692 lav PZX 9-66067 PZX = 85° 09' h Add for 50m „ „ 8m R.A.M.S. 30 m 44 s -8 8-2 1-3 30 54 3 Since the hour angle is less than 12 hours, Venus is West of the meridian ; therefore the azimuth is N. 85° 09' W. Therefore, at the estimated position, the zenith distance of Venus is 81° 39' -2, and the azimuth N. 85° 09' W. Example 2 :— On March 4th, 1914, at about 8 h 20 m a.m. (S.M.T. nearly), in estimated position Lat. 34° 31' N., Long. 127° 15' E., a deck watch showed 9 h 57 m 53 s and was slow on G.M.T. l h 54 m 31 s . Required the zenith distance and azimuth of the sun. Eq. T. + to A.T. 12 ra 08 9 - 3 S.M.T. - Long. - 9 h 1 57™ 54 - 20 h - 8 20 m Mar. 29 (E.) Dec. 3rd. 6°50'-6S G.D. - - 11 51 Mar. 3rd. D.W. Slow 53 9 31 ) L hav G.M.T. Long. 11 8 52 29 24 00 (E. M.T.P. Eq. T. 20 21 12 24 08-3 H. 20 09 15-7 9-36680 103 Art. 102. Dec. 6° Lat. 34 50' 31 •6 S. N. L cos L cos L hav < ■6 (L + D) ZX ZX = 17'-7 29-0 9-91591 9-99690 L~D) 41 21 PZ PZ 6 Nat hav Nat hav Nat hav 68° 55 J 9-27961 •19038 •12470 •31508 68° 17'-7 ZX PZ - L cosec L cosec £ L hav i L hav lav PZX PZX = 10- 03193 10-08409 ZX - PZ PX - 12 96 48 7 50-6 PX + ZX - PZ - ZX + 109 84 39-3 01-9 4-91244 4-82565 L\ 9-85411 = 115° 25' Therefore the sun's azimuth is N. 115° 25' E. Therefore, at the estimated position, the zenith distance of the sun is 68° 17' -7 and the azimuth N. 115° 25' E. 102. Azimuth tables and azimuth diagram. — When great accuracy is not required, instead of calculating the azimuth as in the previous examples, it is customary to obtain it by reference to a book of tables or a diagram. Burdwood and Davis's azimuth tables, and Captain Weir's azimuth diagram, are supplied to all H.M. Ships ; the diagram has the advantage that the azimuth can be taken off directly and no interpolation is necessary, as is usually the case when using the tables. Directions for using the tables are given at the beginning of the book and those for the diagram are printed on it. Art. 103. 104 CHAPTER XII. THE TRUE ZENITH DISTANCE AND ASTRONOMICAL POSITION LINE. 103. The true zenith distance. — We have shown how to calculate what the zenith distance and azimuth of a heavenly body would have been had the observer been at the estimated position of the ship ; now if an observer obtains the zenith distance of the body by observation, comparison of these two zenith distances (the calculated and the true) together with the azimuth of the body, will provide sufficient data for drawing a position line on a chart, as will be explained later. We have now to show the connection between the observed altitude of the body above the sea horizon and the corresponding true zenith distance. Fig. 73. In Fig. 73, which is on the plane of a circle of altitude, let be the observer's eye, Z his zenith, and OH the observer's horizontal plane. Let S be the centre of a heavenly body whose true place is X. The rational horizon is the great circle on the celestial concave whose plane passes through the centre of the earth, and is parallel to the observer's horizontal plane, RR' in Fig. 73. The true altitude of a heavenly body is the arc of a circle of altitude intercepted between the true place of the body and the rational horizon, XR in Fig. 73 ; or it is the angle at the centre, XCR. 105 Art. 104. The observer sees the upper edge M of the body S in the direction OT, due to astronomical refraction, and he sees the sea horizon in the direction OK, due to terrestrial refraction, so that the angle TOK is the observed altitude of the point M . Now the true zenith distance of the body S is ZX, and this is measured by the angle ZCX, which is the complement of XCR, that is, the comple- ment of the true altitude ; therefore to find the true zenith distance we require the true altitude XCR. Now XCR = XBH = SOH + OSC = (MOH - MOS) + OSC = {TOH - TOM) - MOS + OSC = (TOK - HOK) - TOM - MOS + OSC. Now TOK is the observed altitude of the upper edge of the body above the sea horizon, HOK is the dip of the sea horizon, TOM is the astronomical refraction for the ray OM , MOS is called the semi-diameter of the body and OSC is called the parallax in altitude of the body; therefore we have true zenith distance = 90° — [Obs. altitude — dip — refraction — semi-diameter -f- parallax in altitude]. Had the lower edge of the body been observed the semi-diameter would have been additive to the observed altitude. Formulae for astronomical refraction, semi-diameter, and parallax in altitude will now be given. 104. Formula for astronomical refraction. — Refraction, as explained in § 51, is the bending of a ray of light in passing obliquely through media of different din ii Bui f«>r tin- existence of the atmosphere surrounding the earth, n ray of light emanating from a point M of a heavenly body 8 (V\'J. 74) would proceed in a straight lino to the eye of Art. 105. 106 an observer 0, and he would see it in the direction M ' . The atmosphere, however, causes every ray from S to be deflected from a straight line to a curve, which is concave to the centre of the earth, so that the ray which renders M visible to the observer has really pursued the curved track MRQPO. The limit of the atmosphere is shown by the outer circle in Fig. 74, and the observer sees the point M in the direction OT which is a tangent to the curve at 0. On account of the great distance of the body, the straight line from O to M, OM', is parallel to MR, and hence the apparent altitude of a heavenly body is greater than the true altitude by the angle M'OT, which is called the astronomical refraction for that apparent altitude. The rays which proceed from a body in the zenith undergo no refraction, because they enter the layers of the atmosphere perpendicu- larly. When the body is not in the zenith, the refraction increases as the altitude diminishes, and attains its maximum value of about 34' when the body is on the horizon. The astronomical refraction is found to vary approximately with the cotangent of the altitude, and, for an atmospheric pressure of 30 inches of mercury and a temperature of 50° F., is given by r = 58" -36 cot (a + 4r ) where a is the apparent altitude of the point observed. The refraction r is called the mean astronomical refraction and is tabulated in Inman's Tables. It is assumed that the refraction varies with the density of the air at the earth's surface, so that, if the pressure of the atmosphere is p inches and the temperature t° F., the corresponding refraction r is given by p /460 + 50\ J Ip Therefore **0 30 \460 + t J r — r _ 460 + t — \lp *o 460 + t 250 + t — lOp 460 +t from 30. Therefore , J- nearly, since p differs very little 760 + t — lOp J> * r n —r '™ + ho ^ 76 + fo The value of r — r is tabulated in Inman's Tables under the heading 'Correction to Mean Refraction" for various values of (tt\ — P) and a. 105. Semi-diameter. — In almost all cases of bodies which do not appear actually as points, such as the stars, it is necessary to observe one or other of their limbs — a term applied to the upper, lower, or any other edge of a circular disc ; hence almost every observation of a body having a sensible disc requires the semi-diameter to be either added to or subtracted from it, in order to reduce it to what it would have been if the centre had been observed. When the upper and lower limbs have 107 Art. 106. both been observed, the mean altitude is taken as that of the centre. The upper and lower limbs of a heavenly body arc denoted by U.L. and L.L. respectively. An observed altitude of the sun is denoted by the symbol obs. alt. © or obs. alt. © according as the U.L. or L.L. has been observed, and the corresponding observed altitudes of the moon are denoted by obs. alt. "]) or obs. alt. J).. For the purposes of navigation telescopes of only weak magnifying power are used in sextants ; consequently it is impossible to observe the altitude of a limb of a planet, and therefore only the semi-diameters of the sun and moon require consideration. The semi-diameters (S.D.) of the sun and moon are tabulated in the Nautical Almanac for G.M. Noon of each day; in either case the semi- diameter is the angle subtended at the centre of the earth by a radius of the body. .JThe semi-diameter of the sun requires no correction ; that of the moon, however, on account of the moon's rapid change of distance, changes appreciably during the day, and, when required for any G.M.T. other than noon, should be corrected in a similar way to the declination of the sun (§ 87a). The moon's semi-diameter requires a further correction as will be explained in § 107. 106. Parallax. — In Fig. 75 the true altitude of the centre of the heavenly body S is SCR, where CR is the rational horizon. Let S' be the body when it is in the observer's horizontal plane, then SCR = SBS' = SOS' + OSC. Now the angle SOS' = observed altitude -- dip — refraction + S.D. (§ 103). = apparent altitude corrected for refraction. The angle OSC is the parallax in altitude of the body S. The angle OS'C is called the horizontal parallax of the body. Now in the triangle OCS' . nQ , n CO CO sin CSO SmCSO = CS' = ~CS=sinCOS .-. sin CSO = sin CSV x sin COS. Therefore, since the parallax in latitude and the horizontal parallax are both small angles, we have Parallax in altitude = horizontal parallax X cos (apparent altitude corrected for refraction). The horizontal parallax of a heavenly body depends on the 'li -lance of the body from the (•••litre of the earth ; for the stars it is extremely minute, and for the sun its mean value is B*- 8. On account of the small distance of the moon from fche in t h, and t he variai ion in I his distance, there is an apprecia ble daily change in lli<- horizontal parallax of the moon ; it is < here- fore tabulated in the Nautical Almanac for ( l.M. noon of each day, and when required for any G.M.T., other than noon, it should be corrected. Fig. 15, Art. 107. 108 The tabulated values are for an observer situated on the equator, and the horizontal parallax for any other latitude may be found by applying the correction called " Reduction of horizontal parallax for latitude of place " (given in Inman's Tables), but the correction is so small that it is of no practical importance. The parallax in altitude is tabulated in Inman's Tables for the sun, moon, and planets. 107. Augmentation of the moon's semi-diameter.— When the moon is above the observer's horizon, as at S in Fig. 76, its distance OS, from an observer at 0, is less than its dis- tance OS' when it is in the observer's horizontal plane. Since the horizon- tal parallax OS'G is small, OS' is nearly equal to CS', and therefore DS' is less than OS' by nearly the earth's radius. Hence, if two observ- ers are situated at O and D, one would see the moon, when at S', in the horizontal plane, and the other observer would see it in the zenith; but, from the observer at the moon will be more distant than it is from the observer at D by about 4,000 miles, and the diameter would appear to the former about 30" less than to the latter. It is evident that at any intermediate altitude the distance OS is less than OS' , and therefore the moon's diameter at S appears greater than the true or hori- zontal diameter at S' ; therefore the diameter at S is augmented. This increase in the moon's semi-diameter is termed the augmentation. In Fig. 77, S is the centre of the moon, whose radius is r; ON and CM are tangents to the moon, from O and C respectively, in the vertical plane of the observer. Let SCM and SON be denoted by s and (s -j- x) respectively, then x is the augmenta- tion of the moon's semi-diameter. Let the apparent zenith distance of the moon, ZOS, be denoted by 90° — a so that a is the apparent altitude, and let the corresponding parallax in altitude OSC be denoted by p, then Fig. 77. sin (s + x) = OS sin s CS 109 Art. 108. Therefore, since s and a are small angles s -f- x __ CS _ sin SOC _ cos a s " OS ~~ sinOCS ~ cos (a + p). ' x cos a — cos (a + p) s cos (a + p) .-. a: = 2s sin ( a +"^) &in ^ sec (a +#)• Let CJ/' be a tangent to the moon from C when the moon is in the observer's horizontal plane, then sin OS'C = II, Go where R is the earth's radius, and sin s CS'' Therefore OS'C R 11 , ,»-„, -- = — = — nearly, (fc 73.) Now 05'C is the horizontal parallax of the moon and p is the horizontal parallax x cos a, therefore 11 p = — 5 cos a ; therefore the augmentation of the moon's semi-diameter is given by x = 2s sin (ft> + ? ) s" 1 o sec ( a + ^)> where p = s cos a. The augmentation of the moon's semi-diameter is given in Inman'a Tables for various apparent altitudes and semi-diameters. The great distances of the other heavenly bodies renders any augmen- tation of their semi-diameters too minute a quantity to be considered. 108. Examples of the correction of altitudes. — Example 1 .—On March 1st, the obs. alt. was 20° 18' 30"; height of eye (H.E.), 50 feet; I.E., — V 20". Required the sun's true altitude. Obs. Alt. sun's L.L. - I.E. - Dip • Refraction - B.D. - Parallax True \M. - - 23 20° 18' - 1 30' 20 20 17 -G Ml 58 20 10 _ 2 12 37 20 07 + 1 ,; 35 10 2i) l>:{ •ir» + 8 Art. 108. 110 For a given height of eye and altitude of the sun, the dip, refraction, and parallax remain the same, while the semi-diameter varies by a small amount during the year from its mean value, 16'. For this reason a total correction in minutes of arc for dip, refraction, parallax, and semi-diameter is tabulated in Inman's Tables with arguments, height of eye, and observed altitude of the L.L. ; a supplementary table gives a small correction for the variation of the semi-diameter. Except when very great accuracy is desired, observed altitudes should be corrected by means of this total correction, which should be applied as shown below. Obs. Alt. sun's L.L. - - - 20° 18' 30" I.E. - - - - - 1 20 Total Corr. True Alt. 20 17' + 6' 2 •7 20 23 •9 When the upper limb of the sun has been observed the same table may be used, but twice the sun's semi-diameter must be subtracted from the result. Example 2: — The observed altitude of Aldebaran was 18° 20' 40"; height of eye, 50 feet; I.E., + 1' 30". Required the true altitude of Aldebaran : — Obs. Alt. star I.E. - - 18° 20' + 1 40" 30 Dip - 18 22 - 6 10 58 Refraction - 18 15 -2 12 55 True Alt. - - 18 12 17 A total correction (in minutes of arc) to a star's altitude is tabulated in Inman's Tables, and is applied as follows : — Obs. Alt. star - - 18° 20' 40" I.E. - - - - + 1 30 Total correction True altitude 18 22-2 -9-9 18 12-3 As it is never required to work observations of the moon to a very great degree of accuracy, the observed altitude of the moon should always be corrected by means of the total correction. Example 3 : — March 11th, 1914, the observed alt. of the moon's ILL. was 35° 13' 20"; height of eye, 50 feet; I.E., — V 10". Required the true altitude of the moon, the G.D. being 10 hrs. Horizontal parallax - 60' 56" Semi-diameter - 16' 38" Correction - - - +11 Correction - - +3 61 07 16 41 ■ Augmentation - +11 16 52 Ill Art. 109. Obs. Alt. moon's U.L - I.E. .... 35° 13' 20" - 1 10 Total correction - 35 12-2 -8-3 Semi -diameter 35 03-9 - 10- 9 Parallax in alt. for 61' 7" 34 47-0 + 50-1 + -1 True altitude 35 37-2 109. The geographical position of a heavenly body.— To understand the theory of the position line, as obtained from the observed altitude of a heavenly body and the G.M.T., it is necessary to understand what is meant by the geographical position of a heavenly body. If a straight hue is drawn from the centre of a heavenly body perpen- dicular to the earth's surface, the point where this line intersects the surface is the geographical position of the body. In Fig. 78, U is the geo- graphical position of the body S. We will now show how the latitude and longitude of this point may be found. (a) To find the latitude : — In Fig. 78 let S be the centre of a heavenly body and U the geographical position, and let SU intersect the plane of the earth's equator in K ; then the angle UKQ is the latitude of U. Join C, the centre of the earth, to S. Then UKQ = QCS + CSK. On account of the great distances of the heavenly bodies, the angle CSK is inappreciable ; therefore, since QCS is the declination of the body (§ 78), we have Latitude of geographical position = declination of body. (6) To find the longitude : — In Fig. 79, let P'<< and PZ be the meridian and the celestial meridian of Greenwich respectively, Z being the zenith of Greenwich. Let PZ' be the celestial meridian of the body S, Z' being the zenith of the geographical position of 8, namely U. Let P'U be the meridian of U. Let PT be the celestial meridian of the first point of Aries, then \\V-< longitude of U=* GP'U = ZPZ' = TPZ - ?PZ' = R.A.IM. Greenwich - R.A.-X- = R.A.M.S. -I-G.M.T. KA* Wheaa I he body considered is i he sun, the difference l>ei ween U.A.iM.S. and the R.A. of the sun La the equation of time, and in this oase we have West longitude of U = G.M.T. ± Eq. T. = G.A.T. Art. 110. 112 When it is found that the West longitude of U exceeds 12 hours (180°) it must be subtracted from 24 hours (360°), and the result is the East longitude of U. Fig. 79. 110. The true bearing of the geographical position.— If we neglect the spheroidal form of the earth, the azimuth of a heavenly body is P Fio. 80. ciearly the same as the angle at the place between the meridian of the place and the great circle which joins the place to the geographical 113 Art. 111. position of the body ; in other words, the true bearing of the geographical position of a heavenly body is the same as the azimuth of the heavenly body. 111. The circle of position. — In Fig. 80, let X be the true place of a heavenly body and U its geographical position. Let z be the true zenith distance of the body, as obtained from an observed altitude. Let ZiZ.Z.j etc. be a small circle of the celestial concave whose centre is X and whose radius is z; then the observer":, zenith must lie somewhere on the circumference of this circle. Let O v 0. 2 . 3 . etc. be the geographical positions of Z v Z. z , Z 3 , etc. respectively; then the observer is somewhere on a curve x 2 Zi etc. of the earth's surface, such that every point of the curve has its zenith on the circle Z x Z$ Zl etc. This curve is very nearly a circle, whose centre is the geographical position of the body, and whose radius is the true zenith distance expressed in nautical miles, and it is called a circle of position. From this we see that t lie information derived from observations of the altitude of a heavenly body, and the time shown by the deck watch at the same instant, is : — (a) The observer is situated somewhere on the circumference of a circle whose radius is the true zenith distance of the body expressed in nautical miles; this distance is obtained from the observed altitude. (6) The centre of the circle is the geographical position of the body at the G.M.T. of the observation; its position is obtained from the time shown by the deck watch and the Nautical Almanac. A circle of position when represented on the Mercator's chart becomes ;i curve, and takes one of three forms according as the circle of position lies between the poles, passes through a pole; or encloses a pole. Km;. 81. In l'i- s- th<- curves marked I, 2, '■'> are the representations of the corresponding circles oi position marked I. -, •'* m Fig. 81. When the zenith distance is extremely in. ill, the ova] type <>i curve becomec approximately •> circle on the Mercator' chart, bul it should x 6108 JJ Art. 112. 114 be noted that the centre of this circle is not the geographical position of the body, except in low latitudes. Fig. 82. 112. The astronomical position line.— In practice it is only necessary to consider a small portion of the circle of position in the neighbourhood of the estimated position. In Fig. 83, let E be the estimated position of the ship, and U the geographical position of the heavenly body observed, whose true place is X. Let the great circle arc EU, produced if necessary, intersect the circle of position J Y in J, then EJ is called the intercept. The small arc of the circle of position which contains J is the position line, and is at right angles to EJ, so that, if we know the magnitude and direction of EJ, the position line is determined with regard to E. RlfLet Z and Z' be the zeniths of E and J respect- ively; then, if the earth is assumed to be a sphere, the lines ZE, Z'J, and XU inter- sect at C, the centre of the earth. The error involved in this assumption is extremely minute and of no import- ance. We have EJ = EU ~ JU = ECU ~ JGU ■ = zx ~ zx. Now Z\ is the zenith distance of [the body at the estimated position at the instant of observation, as calculated in the manner 115 Art. 112. explained in § 101, and Z' X is the true zenith distance as found Jfrom the observed altitude. .•. Intercept calculated zenith distance true zenith distance. Again, the direction of EJ is the same as that of ZX, or in the opposite direction, according as the true zenith distance is lc.ss or greater than the calculated zenith distance : in ot her words, the direction of the intercept . as regards the estimated position /•„'. is the same as the azimuth of the body at the estimated position or in the opposite direction, "towards or "away." according as the true zenith distance is less or greater than the calculated zenith distance. Now the intercept is a small arc of a ureal circle, and is, therefore, practically coincident with the rhumb line drawn through the estimated position in the direction of. or opposite to, the azimuth of the body. The position line, being the small are of I he circle of po.-iii.in in the vicinity of J. provided the zenith distance i- not \ er\ small, may also he regarded as coincident with a rhumb line, and lies at right angles to 1 lie azimuth of the body. Since angles on the earth's surface are correctly represented on the Mercator's chart, it follows that, when the intercept and azimuth have been obtained, the point J may be found by laying off, from the estimated position, a course and distance corresponding to the direction and magnitude of the intercept (§ 40). The position line may then be drawn through J perpendicular to the intercept EJ. The point •/ may also be found by aid of the transverse table (§41). The following example shows the method of determining a position hue from the observed altitude of the sun's lower limb, by plotting, and also by aid of the transverse table : — Example :— On March 7th. L 914, about 9 h A.M. (S.M.T. nearly), in estimated position bat. 20° 15' \.. Long. 160° 39' E., when the deck watch was slow on G.M.T. 2 h IT 1 " 27 s ; I.E., + 1' 30"; H.E., 50 ft. the following observation was taken : — ohs. Ait. __ :>,{■>' :;.v nr Obs. Alt. 36 35' 10* Hoc. r, ii!'- 7 8. I.K. +1 30 Eq.T.ll m 29' toA.T. ' !orr, D.W. 8 h 02'" 36' S.M.T 2] 00 Mar. 6th Long. 10 42 36 (E.) Mar. <..h. In 17 6th. D.W. 9 02 True t Slow L' 17 U7 36 36-7 8-0 36 44-7 63 15*3 G.M.T. in 20 03 Lon lo u 36 i M.T.P. _'i iil' 30 T. - ) I //. 20 .".I in /. ha . 0-20602 H Art. 113. 116 Lat. 20° Dec. 5 15' N. 42-7 S L cos 9 L cos 9 • 97229 99784 (L + D) 25 57-7 Nat. Nat. Nat. L hav 6 9 •17515 hav 6 hav (L + D) • 14968 ■ 05046 hav z •20014 20014 Calc. z 53° 09' Trues 53 15-3 Intercept 6 • 3 away. From the azimuth tables the sun's azimuth is N. 114° E. Sun Fig. 84. Fig. 84 shows the position line obtained from this observation. The point J, through which the position line is drawn, may be plotted directly on the chart by laying off a line N. 66° W. (true), 6-3 miles from the estimated position E. The point J may also be found by aid of the traverse table as follows : — Estimated position Lat. 20° 15' N. Long 160° 39' E. N. 66° W. 6' • 3 d Lat. 2 • 6 N. Dep. 5' • 8 W. d Long. 6 • 1 W. Lat. 20 17-6 N. Long. 160 32-9 E. The position line is now drawn in a N "F 1 direction ' 24° ' (true) through the position of J thus found. 113. The most probable position from a single observation.— The error of the estimated position is always known within certain limits. If it be assumed that the estimated position is not in error by more than n miles, in Fig. 85, let E be the estimated position and let a circle with centre E, and radius n miles] intersect the circle of position at A and Fig. 85. 117 Art. 114. B\ then, since the ship's position lies within the circumference of this circle and on the arc AB, it must lie between the points A and B; therefore the best point to assume as the position of the ship is J, which is the mean of all the positions which she might occupy, because it is the middle point of AB. 114. The value of a single position line. — The information obtained from an observation of a heavenly body is that the ship is situated somewhere on the resulting position line. In the vicinity of land this information is often very valuable, for if the position line, when produced, intersects the land, its direction indicates the course to steer in order to reach the point of intersection; whereas, if it. passes clear of land and all dangers, its direction indicates a safe course to steer. Again, if an observation is taken of a body which is on one beam or the other, the resulting position line indicates whether the ship is on her intended track or to starboard or port of it : and. similarly, if an observation is taken of a body which is either ahead or astern, or nearly so, the resulting position line indicates whether the ship is ahead or astern of her reckoning. The following examples illustrate the value of a single position line : — Ex miles from the Seven Stones. Lay off from ./ a line in the direct ion s. -i:\ E. (true), intersecting CD in C\ then JC IS found to be 27 miles. Therefore, if the ship Steers BOae to make good S. 23 E. (tine). 27 miles, and then alters course so at to make good S. 10 E. (true), her trad, will then be along the line CD. Art. 114. 118 Fig. 86. LIO Arts. 115, 116. CHAPTER XIII. POSITION BY ASTRONOMICAL POSITION LINKS. 115. Position from two or more observations. — The position of a ship is found from the intersection of two or more position lines. It is im- portant to obtain the position from two or more simultaneous or nearly simultaneous observations, in order that the accuracy of the position may not be dependent on that of the reckoning, and this is particularly the case in a man-of-war. where there is always the possibility of the ship being engaged in manoeuvres or other exercises which may complicate the keeping of the reckoning between two observations. The best time for taking observations is at morning or evening twilight . when the stars and planets are just visible and the horizon is usually very clearly defined; it should, therefore, be made a rule that, whenever the ship's position is not accurately known, observations of two or more -tars or planets should be taken at morning and evening twilight. When -fleeting heavenly bodies to observe, it should be remembered that the accuracy of the position depends largely on the angle at which the position lines cut one another; this angle is the same as the difference of the azimuths of the bodies, so that bodies should be selected the difference of whose azimuths is as near a right angle as possible, and never less than 30°. When the intercepts have been found for two observations, the position of the ship, which is at the intersection of the two corresponding position lines, may be found by plotting or by calculation. When the chart is on a sufficiently large scale the method by plotting on the chart li;is the advantage that the position of the ship with regard to the land is immediately known. When 1 he chart is on too small a scale, the position lines may be [dotted eit her on t he diagram supplied for t he purpose or on squared paper. The diagram consists of a mounted sheet on which are drawn meridians and a large compass graduated in degrees. At the side is -i scale of differences of meridional parts corresponding to the scale of longitude of the plan. When finding the position by plotting on squared paper, the relation between departure and difference of longitude Bhould be carefully borne in mind.' 116. Examples of finding position by plotting and by calculation. - The method of finding the position bj plotting the position lines will be understood bom the following examples. In examples (I) and (.'{) the position line are plotted on ;i chart, and in example ( I ) on squared paper. It i sometimes convenient to find the position i>> calculation; in t hi- ca >■ t he traverse table i employed ae shown in examples (2 ) and(3). The order in which the work i- arranged in the following examples Bhould he carefully noted. It will he ecu thai there are two distinct arrangement ih.it mown In example ( I ) being applicable to simultaneous Art. 116. 120 observations when it is intended to plot the position lines ; that shown in examples (2) and (3) being applicable to successive observations, and also to simultaneous observations, when it is intended to find the position by calculation instead of plotting. It is of the utmost importance that observations should be worked out in a systematic manner, because the chance of making mistakes is very much minimised by following set methods. Example (1) : — Position by plotting (a) on chart, (6) on squared paper. Simultaneous observations. On April 27th, 1914, at about 7 h 30 m p.m. (S.M.T. nearly) in estimated position Lat. 49° 55' N., Long. 7° 15' W., the deck watch was slow on G.M.T. 2 h 29 m 34 s . I.E., + 1' 30". H.E., 40 ft. The following observations were taken to determine the position of the ship : — Deck watch 5 1 ' 27 m 54 s 5 29 51-2 Obs. alt. Procyon „ „ Capella 37° 28' 30" 44 51 20 S.M.T. Long. 7" 30 m Apri 29 (W.) 1 27th. i 1 27th. 91601 80882 99803 a Obs. alt I.E. Cor. True z Dec. R.A. D.W. Slow G.M.T. Long. M.T.P. R.A.M.! For l 1 ' „50™ „9* R.A.M. R.A. H. Lat, Dec. (L-D) %pella. . 44° 51' 20" + 1 30 G.D. 7 59 Apri Procyon. Obs. alt. 37° 28' 30" I.E. + 1 30 Cor. for G.M.T. L hav 8 ■ L cos 9' L cos 9 ■ L hav 6 8 Cor. 37 30-0 -7-4 44 52-8 -7-2 37 22-6 44 45-6 Trn» z 52 37-4 45 14-4 Dec. R.A. D.W. Slow 5° 26' -7 N. 7 h 34 m 49 s 5 b 27 m 54 s 2 29 34 45° 55' N. 5" 10 m 21" 5 h 29 m 512 s 2 29 34 G.M.T. Long. 7 57 28 29 00 (W 7 59 252 29 00 (W.) M.T.P. R.A.M.S For l b „ 50 m „ 7-5" 7 . 2 28 28 19 29-7 + +9-9] + 8-2 I + 1-2J 7 30 25-2 3.2 19 29-7 + Is '9 l Cor - for +11 J GMT - R.A.M. R.A. 9 7 48 17-0 34 49 9 50 14-3 5 10 21 H. 2 13 280 4 39 53-3 Lhav 9- 51688 Lat. Dec. 4S i° 55' N. i 26-7 N. 49°55'N. Lcos 9- 45 55 N. Lcos 9- 80882 84242 (L-D) 44 = 28-3 •72286 4 00 £hav0 9 •16812 121 Art. 116. Nat. hav 6 -05i\s;; Nat. hav (L-D) -14320 Nat. hav • 14727 Nat hav (L-D) -00122 Nat. hav z 52 33-6 52 37-4 •19G03 Calc. z True z [nteroepl Nat hav z ■ 14849 Calc. 2 Tnv 45 19' -8 45 14-4 [atercept 3 • 9 away. 5- 4 towards. Azimuth from Tables N. 136 W Azimuth from Tables N. 67° \Y. 30 85' 80* i:> W 5' 7 °- 61 Si (73 o'i 6;.' f > .1 st A- vpcb tii 3.9 62 7-30 A/W. Observed Posttion [^ ' S0 ¥,t N - (Long. 7 /9 W. 64 61 63 , L 36 i . 46 30P.M/^E. Estimated Position t >Y" • c gr« 6« 6S 63 r . .i. £ 67 ^ k J '> - X / 1 V J \ T Ijv r~ s^ 7 s^ 7" V | 4. ... .. — — f,. . - -. ....... -; — . "'NV' ^-. ' v> v J- Z> c *£^%*6^ -t i • v ,^g>,^ 7 ....... T^ Z i ^r>,> r i 7 f ' ^ y t>^ Z Z<-2^" v, i,^ „S-Z r x ^ J 1 -\e>y y '■**■>£■« i ' ws 4—/ ^t ^^&/J ~r- A .V -J- T 7 r*^ o V/ Z_ l i... ssii- c>j'' «t^ /\ i I ^^ ! 'i -*'"fz \ / "^-^ ) • MI77.-. \ai hav z 37653 (ale. z 76° 12'-2 True .-. 7:, 35 -2 Intercept - - 7' towards Azimuth from Tables X. 103 E. (S. 77 E.) Estimated position Lat. :: 20 38 s 15 Obs. I.E. Cor. 17th S.D. Par. alt. C True z 16° 23' 00" + 1 30 R.A. Dec. S.D. Aug. 16" 37 m 25 s + 2 03 16 12 47 00 53 00 16 24-5 — 9-4 16 39 28 G.M.T. 4 24 47 00 53 Mar. 00 16 15- 1 — 16-0 27° 25'- 6 S. + 3-8 Long. 28 9 47 19 53 38 (W.) 15 59-1 + 55-8 + 0-5 27 29-4 S. 16' 01" -3 M.T.P. R.A.M.S. For 40" „ 8 m 19 23 28 15 37 31-3 + .+ 6-6 + 1-3 16 55-4 15 58 + 5 73 04-6 R.A.M. R.A. H. Lat. - Dec. - (L + D) 43 05 54- o 24 00 00 19 05 54- 2 16 39 28- - 2 26 26- 2 36° 48' •4N 27 29 ■4S. 64 17 •8 S.D. 16 03 Hor. par. 58 41 - 10 58 31 Lhav 8-99403 L cos L cos 9-90344 9-94796 L hav 8-84543 Nat hav 6 Nat hav (L -f Nat hav z •07006 D) -28317 35323 Calc. z 72° 55' -7 — True z 73 04-6 Intercept 8 • 9 away Azimuth from Tables N. 146° W. (S. 34° \V.) Fig. 89. 125 Art. 116. The position lines should now be sketched as shown in Fig. 89, where OJ is the first position line. J J' the second intercept, and OJ' the second position line. The position of can be calculated if we know the length and direction of JO. Now JO is in the direction of the first position line, X. 13° E. and JO --= J J' sec OJJ' =8-9 sec 21°, which is found by the traverse table to be 9* 5 miles. Thus, if we apply 9 - 5 miles in a direction N. 13° E. to the latitude and longitude of J, we can find the latitude and longitude of 0. JLat. - - - 36°48'-5N. Long. 139° 54' -5 W. X. 13° E. 9'- 5 d Lat. 9 -3 N. Dep. 2'-l d Long. 2 -7 E. Ship's position Lat. - 36 57-8 N. Long. 139 51 -8 W. Example (3) : — Position by calculation and by plotting on the chart. Successive observations. On March 21st, 1914, at about 8 h a.m. (S.M.T. nearly), in estimated position Lat. 4$° 58'- 2 N., Long. 7° 31' W., the deck watch was slow on G.M.T. 5 1 ' 20 m 15*. I.E., + 1' 30". H.E., 40 ft. The following observations were taken : — Deck watch 3 h 09™ 10* Obs. alt 17° 29' 50" 3 09 44 17 34 50 3 10 06 17 38 10 The ship was steaming S. 32° E. (comp.) at 11 knots, and at about II 15 m a.m. (S.M.T. nearly) the following observations were taken : — Deck watch 6-- 25 m 48- Obs. alt. 39° 08' 10" 6 26 12 39 09 00 6 26 33 30 10 10 Required the position of the ship at 1 L h I5 ra a.m. 3" 09"' 10' 17° 29' 50" 3 09 44 17 34 50 3 10 06 17 38 10 3 /29 :; 09 00 40 3/102 50 it ::4 17 S.M.T. Long. 20" 00'" Mar. 20th. 30 04- (W.) Obs. alt. Cor. True z - 12268 it :;r 17" Dec (i + 1 30 Eq. T. \ 17 35 s 7*0 <;.!>. lMi 30 Mar. 20th 3--09 10 5 20 16 D.W. Slow 17 42-8 72 17*2 8 29 56 12 00 00 G.M.T. Long. JO 2U 30 hi (\\ .) M.T.I'. i:.,. t. L9 59 -l - 7 31-9 //. I'.i :,i 19' I /, li.iv Art. 116. 12G Lat. - 49°58'-2N. L cos 9-80834 Dec. - 02-7 S. L cos 10-00000 (L + D) 50 00-9 L hav B 9-23102 Nat hav - - -17024 Nat hav (L + D) - • 17869 Nat hav 2 - - -34893 Calc. z 72° 24' -7 Trues 72 17-2 Intercept - - - - - 7-5 towards. Azimuth from Tables N. 112° E. (S. 68° E.) Estimated position Lat, 49° 58'- 2 N. Long. 7° 31' W. S. 68° E. r -5 d Lat. 2 -8 S. Dep. 6'- 9 d Long. 10-8 E. Lat. 49 55 -4 N. Long. *7 20-2 W. Compass course S. 32° E. Run for 3 h 15'" at 11 knots is 35'- 7 Dev. from table 4 W. Mag. course - S. 36 E. Var. from chart 18| W. True course - S. 54i E. J ... Lat. 49°55'-4N. Long. 7°20'-2 W. S. 54£° E. 35'- 7 d Lat. 20-7 S. Dep. 29-1 d Long. 45 -0 E. Est. Pos. ll h 15 ,n a.m. 49 34-7 N. Long. 6 35 -2 W. 6 h 25 ra 48 s 39° 08' 10" 6 26 12 39 09 00 6 26 33 39 10 10 3 / 78 33 3 / 27 20 6 26 11 39 09 07 S.M.T. 23 h 15 m Mar. 20th. Obs. alt. Q 30° 09' 07" Dec. 00'- 5 N. Long. 26 21 s (W). I.E. - + 1 30 Eq. T. 7'" 29 s • 5 + to A.T G.D. - 23 41 Mar. 20th 39 10-6 D.W. - 6 h 26 m 11 s Cor Slow - 5 20 15 11 46 26 12 00 00 True z +8-6 39 19 -4 50 40 -6 G.M.T 23 46 26 Long. 26 20-8 (W.) M.T.P. 23 20 05-2 Eq. T. - — 7 29-5 H. - 23 12 35-7 L hav 8-02767 127 Art. 117. Lat. • 19 Dec. - ii 34'- 7 \. 00 -5 X. L • /. COS L hav 6 e (L D) '.t* 81184 10-00000 /. D 19 34 -2 • hav Xat hav Nat \w\ 7-83951 ■00691 • 17.">7.~i ■18266 Calc. : 50 36'-2 True : .30 40 • (> Latercepl i • l away. Azimuth from Tables X. L64 c E. (S. 16 E. E'O = E'J' see OE'J' = 4' -4 sec 38° = 5'" 6 (from traverse table). Fig. 90. E timated position at ll h I5 m a.m.: — X. 22 E. 5'*6 Position at II L5 A..M. L.I. VY 34'5N. d Lat. 5 -2 N. Dep. 2'-l Long 6° 35'- 2 W. tfLong. 3'-:; E. Lat. 49 39 -7 X. Long. 6 31-9 W. Fig. m Bhowa the method of finding the position by plotting on the chart. 117. Error in a position due to error in the observed altitudes. Suppose thai we can estimate thai the observed altitude is too .ureal or too mall bj an amounl no1 exceeding n minutes, then the true zenith distance XCJ, Fig. 92, ie too small or too greal h\ an amounl uol eeding n minut< thai the actual zenith distance, at the observer, musl lie between XCB and XCA, JA and JB being each equal to n nautical miles. Therefore the observer's position lies between the two circles of posil ion w hose radii ar< ( B and / - 1 . Art. 117. 128 Consequently the observer's position on the chart lies between two parallel position lines situated on either side of the position line obtained from the observation, and at a distance of n miles from it. In Example ( 1 ) (§11 6), suppose that we assume that the altitudes were each not more ' s 8 ' «L 1 **%. |? ' \ S-U* N S Si. CI Qs B C -J O 3* > s.« Fig. 91. than 2' in error, due to uncertainty in the position of the sea horizon or to errors of observation; then, corresponding to the altitude of Procyon, the observer's position lies between the position lines CD and FG, Fig. 03, and, corresponding to the altitude of Capella, his position 129 Art. 118. Fig lies between the position lines CF and DG. It follows, therefore, that his position lies within the parallelogram CDGF, which may be referred to as his area of position, and, although is the most probable position of the ship, if a course lias to be shaped to clear a danger, consideration should be given to the possibility of the ship being situated anywhere within the area of position. For example, suppose that it is desired to shape a course up Channel to pass ai least 5 miles off the Bishop Rock ; it will l»e seen that, if the course is shaped from the point G, it will have been shaped from the most disadvantageous position and is the safest to steer. In a ease where it is possible to assume that in one altitude the error does not exceed m', and that in the other it does not exceed ??', the parallelogram may be constructed in a similar manner by drawing the sides at their respective dis- tance- [in' and n') on either side of the position lines obtained from the observa- tions. Now, the error, to which an altitude is most liable, is that due to the uncertain position of the sea horizon. and tlii- may to some extent he guarded against by taking observa- tions of four heavenly bodies, A, B, G, D, the azimuths of A and jB and of CandD being approximately opposite. In this case il is probable thai the four position lines will form a quadrilateral figure, when the most probable position of the ship is at a central point within the quadrilateral. When three heavenly bodies are observed, and the position lines form a cocked hat, the most probable position of the ship is, in the absence of all information within the triangle at a point whose distances from the three sides are proportional to the lengths of the sides respectively. II ii he assumed thai the errors in the three observed altitude arc equal and in the same direction it is possible to give a geometrical con BtniCtion for Bnding 1 he position of the ship, hut one can never he certain thai the dip of the sea horizon is the same in all direction-, and therefore it i- never safe to assume thai the error in each position line is the same. " 'I"' ship is in the vicinity of land, position line-, parallel to the -ides ot t he triangle, should he draw n externa] to the triangle, and ;it distances equal to the maximum estimated error ; the course should t hen be shaped by considering the relative position <>l the land and the triangle thus formed. 118. Error in a position due to uncertainty of the error of the deck watch. In Pig. 94 let be the observer at the intersection of two circles of position. Then if there is an error in the G.M.T. as found from the deck watch, tin- observer, instead of regarding tin meridian <>i Greenwich in its true position POP' regard il ;>t -• me position /'<■"/". the angle '■!''■ being the error in the <. \i t The consequent of tin- is that, since the error both observations equally, the observer regards x r, io 1 Art. 118. 130 himself as being at the intersection of the two circles of position (shown in broken lines in the figure), which are of the same radii as the former but displaced in longitude an amount equal to OPG', which is the error to the G.M.T. Thus is moved East or West in longitude by an amount Fig. 93. equal to the error, and the position lines are moved parallel to themselves through the same distance in longitude. The direction in which is moved will be seen from the formula for the longitude of the geographical position of a heavenly body (§ 100), (W. Long. = R.A.M.S. + G.M.T, - 131 Arts. 119, 120. R. A. .)(.). from which it is obvious t hat, if the G.M.T. is greater than it should be. is too far to the Westward, and if the G.M.T. is smaller than it should be. () is too far to the Eastward. Thus, in Fig. 95, if is the position obtained from the two position lines shown, and there is an unknown error in the observed time the maximum value of which is estimated to be + dH, the ship will lie on the line ()'()" where 0' and O" differ in longitude from by dil. In example (1) (§ 116) suppose that the error in the deck watch was estimated to lie between 2 29 m 30 s slow and 2 h 29™ 38 8 slow. The position of the ship was calculated using an error •1 29 m 34 s slow, and was found to be Lat, 50° 2' -8 N., Long. 7° 1!)' W. and we see that, due to this possibility of error in the G.M.T., the ship's position lies on the arc of a parallefof latitude r>0 3 2' -8 N. between the longitudes 7° IS' W. and 7 20' W. In these circumstances, if a course has to be shaped to make the land, it should as a rule be shaped from the most disad- vantageous position on the arc of the parallel named, but if shaped from the mosl probable position of ship, 0, it should be borne in mind that the aetual position of the ship may be nearer to the shore than the estimated position. 119. Error in a position due to error in the observed altitudes and to uncertainty of the error of the deck watch. — It has been shown above that if there is an error in each of the observed altitudes the observer is within a certain parallelogram; it has also been shown that if there is an error in the G.M.T. the observer is on a parallel of latitude intersected between two particular meridians ; therefore, if these two errors coexist, the observer is somewhere within an area traced out by moving the parallelogram East and West within the limits of longitude above-mentioned, as shown in Pig. 96 which refers to Example (l)(§ U6). 120. Error in a position due to error in the reckoning between the observa tions. -When their is an interval of time between the two observations for findings position, we tran fer the posi- tion line obtained at the first observation, parallel to Itself, through ;> distance equal to the run of t he ship bet ween I he two obsen at ion ; i hen, if t he reckoning in the interval is correct the ship is <>n the transferred position line ;>t the time of the second observation. In Pig. '.it. /■; i- the estimated position at the first observation, E' the [ 2 Art. 120. 132 estimated position at the second observation, E'O the first position line transferred, so that, if the course and distance made good have been correctly estimated, the ship is some- where on the line E'O at the time of the second observation. Let us assume that it is possible for the reckoning to be in error by an amount not exceeding # % of the dis- tance run, then the transferred position line at the second observation may he on either side of E' and at a distance from it not exceeding x % of the dis- tance run. Therefore, if we describe a circle with centre E' , and radius X run, and draw two tangents to x 100 this circle parallel to the first position line, the ship must lie between these tangents. Let the second observation, worked out with E' as estimated position, give a position line which intersects the tan- gents h\X and Y, then the ship must lie on the line X Y intercepted between the two tangents. • Therefore unless the reckoning between the two observations is absolutely correct, the information from two successive observations is that the ship is situated on a terminated portion of the second position line, the length of which varies directly as the error in the run and inversely as the sine of the angle between the first and second position lines. Fig. *« Fig. 97 133 Arts. 121-123. In Example (3) (§ 1 1G) let us assume that it is possible for the reckoning to be in error by an amount not exceeding 5 per cent, of the distance run (35-7 miles), then the radius of the circle mentioned above is 1-8 miles. The ship is therefore on the second position line XT, which lies and passes through the point 0, the position N. E. in the direction , 74 _, of whi.h has been found to be Lat. 49° 39' -7 N., Long. 6° 31' -9 W. Now XO = 0Y = l'-8 cosec 52° = 2-28 miles. Therefore the length of the hue XY, somewhere on which the ship is situated, is 4-56 miles. 121. Error in a position due to error in the reckoning between the observations, and to the error in the observed altitudes. — If, in the last example, there had been a possibility of error in each altitude not exceed- ing 2'. it is necessary to draw lines iST and UV (Fig. 98) parallel to the Fig. 98. tangents and at distance- 2 miles from them, measured away from the circle, and to draw lines S V and TU parallel to and on eii her aide of A ) and 2 miles from it. The ana of position, taking the two errors into account, is the parallelogram 8TVU. 122. Error in a position due to error in the reckoning between the observations, to error in the observed altitudes, and to uncertainty of the error of the deck watch. -If, in addition bo the possible errors in the reckoning and altitude just mentioned (§ L20 121), there is a possible error of four seconds in the < I.M.T., it i obvious thai the area of position i- the a re; i traced out l>\ moving the parallelogram 8TXJV (§ 121) Mast and \\ • -i t hrough l' of longil ade. 123. Particular case oi very large altitudes. The following method of plotting the position lines, although it can seldom be applied, brings out the theorj o\ po ition tin rj clearly. When in low latitudes an observation is taken ol a body which i pa ing nearly overhead, the circle of position may be drawn as a circle on the Meroator's chart ; the centre Art. 123. 134 of the circle is the geographical position of the body, and the radius is the true zenith distance. When two observations are taken, two circles of position may be drawn, and the position of the ship is at one or other of their points of intersection ; to determine which of the points of inter- section is the position of the ship, the observer should note whether he is North or South of the body as it passes his meridian. If there is a run of the ship between the two observations, as is generally the case, the position line at the first observation must be trans- ferred for the run of the ship ; this is done by transferring the geographical position at the first observation through a distance equal to the run of the ship and in the same direction. The following example, in which there are three observations and consequently three circles of position, shows how the position of the ship is found, the circles being drawn on squared paper. In Fig. 99, A, B and C are the three geographical positions of the sun at the times of the three observations, their latitudes and longitudes being found in the manner shown below; AD is the run of the ship between the first and third observations, that is N. 60° W. l'-5; BE is the run of the ship between the second and third observations, that is N. 60° W. 0' • 6. The three circles are described with centres D, E and C. Example:— On April 28th, 1914, at about 11> 55 m a.m. (S.M.T. nearly) in estimated position Lat. 14° 30' N., Long. 85° 10' E., the deck watch was slow on G.M.T. 2 h 12 m ; 34 s , I.E., + 1' 30"; H.E., 40 feet. The ship was steaming N. 60° W. (true) 18 knots. The following observations were taken to determine the position of the ship, and the observer was North of the body as it passed his meridian. Deck watch 4 h 01 m 40 s © „ 4 04 24 „ 4 06 34 S.M.T. 23 h 55™ Apr. 27th Dec. 13° 53' -9 N. Long. 5 41 (E.) Eq. T. 2'" 25 s -9 - to A.T 89° 03' 00" 89 15 10 88 57 50 G.D. 18 14 Apr. 27th. D.W. - - 4 h 01 m 40 Slow - 4 12 34 6 14 12 00 14 00 18 14 + 2 14 25-9 18 16 24 00 39-9 00 5 43 85° 50 20-1 ' E. G.M.T. - Eq. T. - G.A.T. - Geographical \ Lat. 13° 53' -9 N. Long, of A. 85° 50' E. pus. at 1st Obs. \ Long. 85° 50' E. 135 Art. 124. D.W. at 1st Obs. 4'" 01™ 40 s D.W. at 2nd Obs. 4 04 24 Interval - 2 44- 41' (W.) Dep. 39' -8 (W.). D.W. at 1st Obs. 4 01 40 D.W. at 3rd Obs. 4 06 34 Interval - - 4 54 = 73'-5 (W.) Dep. 71'-3 (W.) Run between 1st and 3rd Obs. N. 60° W. 18 * 4 ' 9 = N. 60° W. 1'- 47. 60 Run between 2nd and 3rd Obs. 18-4-2-2 _ _ A , TT „, „„ X. GO W Obs. alt. I.K. Cor. '" 60 89° 03' 00" + 1 30 89° 15' 10" + 1 30 88° 57' 50" + 1 30 89 04-5 + 9-7 89 16-7 + 9-7 88 59-3 + 9-7 89 14-2 89 26-4 89 09-0 45-8 33-6 51-0 True z (Radii) - Draw a line on the squared paper, Fig. 99, to represent the parallel of I.J 53' • 9 NT., which is the latitude of the three geographical positions, and on this line select a point .4 to represent the geographical position at the 1-1 observation. On any convenient scale, 10 miles to the inch in this example, plot the geographical positions at the second and third observations by means of 1 be departures found above, and mark them B and C respectively. From A lay off AD, N. 60° W., 1-47 miles, and from B lay off BE. X. 60 \V., -66 miles. With cent res D, E, and C describe circles of radii 45' -8, 33' -6, and 51' respectively. The intersection of these three circles at is the position of the ship. Measure the d Lat. and Dep. between O and A, convert the Dep. into '/ Lou-, and BO find the latitude and longitude of the ship. Lat. .1 13 63'-9N. Long. A 85° 50' E. d Lat. 33 -r, X. Dep. 33'-5 (W.) (/ Long. 34-4 (W.) Lat. O 14 27'-4N. Long. 85 15-6E. 124. Position by astronomical and terrestrial position lines. (1) By combination of an astronomical position line and a line of bearing. Suppose thai ■> bearing of a terre trial object is taken al the same time ,i .mi observation "t .i heaven!} body, then obviouslj the position of the ship i- .it tin- inter ection "i Hie line ,,i bearing and the astronomical position line. The accuracy oi thi position depends mi the angle <1 Art. 124. 136 S4°J W. -j— _r 3 i i 7 r< ie A te <~ 'die n ]JH- »- V n 3Q >> «=■: .f (T i 1 - u /I ^-3 Z c' -a t. 3 3' 6 A ■ 53^ - — r f £ 7 £S - I • t 1 ^v- _x -■l * ^ ij t \ t-» ^ r» i o. o i 5 • 95 °c £ / c ou > -4 ol & i 1 I .IE Fig. 99. 137 Art. 124. intersection of the two position lines, so that the bearing of the object and the heavenly body should be as nearly as possible the same or opposite to one another. The position can be obtained from two such observations when there is a run in the interval between them, the position in this case being obtained as explained above by transferring the first position line for the run of the ship. (2) By an astronomical position line and a sounding. If a Bounding is taken at the same time as an observation of a heavenly body an approximate portion can be obtained, provided that t lie soundings shown on the chart are such that the contour line of the depth obtained eau be drawn with confidence, and that its mean direction makes a good angle with the astronomical position line. The depth should be verified by two or more soundings, and these should be corrected as explained in Part IV. Art. 125. 138 CHAPTER XIV. OTHER METHODS OF DETERMINING AN A NOMICAL POSITION LINE. 125. Meridian passages of heavenly bodies. — Besides the general method of determining an astronomical position line, there are various other methods which have advantages over the general method in special circumstances, and these will be described in this chapter. We will first explain the method of obtaining the position line from the altitude of a heavenly body when the body is on the observer's meridian, but, before doing so, we must show how to find the observer's mean solar time at which the observations should be taken. A body is said to have its upper meridian passage when it passes the observer's celestial meridian, and to have its lower meridian passage, sometimes called its meridian passage below pole, when it passes the meridian which differs from that of the observer by 180°. In this book, whenever meridian passage is mentioned, the upper meridian passage is to be understood unless otherwise stated. (a) The Sun. — The sun passes the meridian of any place at apparent noon at that meridian, and has its lower meridian passage at apparent midnight. In order to find the time by the chronometer or by the ship's clocks at which the sun passes the meridian, we proceed as follows :■ — ■ Example : — Required the time by ship's clocks on March 3rd, 1914, at which the sun will pass the meridian of a place in longitude 25° 17' E., the ship's clocks being set to Eastern European time which is 2 hours fast on G.M.T. Eq. T. 12 m 15 s + to A.T. S.A.T. Long. 24 h 00" 1 Mar. 2nd. 1 41 (E.) G.D. 22 19 Mar. 2nd. S.A.T. Long. 24 h 00 m 1 41 (E.) G.A.T. Eq. T. 22 19 + 12 G.M.T. Clock 22 31 2 00 fast on G.M.T 24 31 24 00 31 p.m. Time by ship's clocks. (b) The Slavs. — When a .star is on the observer's meridian the right ascension of the star is equal to the light ascension of the meridian, and the latter, by the formula in § 97, is equal to R.A.M/S. -|- S.M.T. 139 Art. 125. Therefore, R.A.-fc (when on the meridian) = R.A. M.S. S.M.T. or &.M.T. R.A.*- R.A. Ms. Now the R.A. of a star nui\ he taken directly from the Almanac. The R.A. .M.S. should be taken oul for G.M. Noon, and then with these two elements we can find an approximate S.M.T. By applying the longitude in time to this approximate S.M.T. we can find the Greenwich date, with which to correct the R.A. M.S. and then rind a more correct S.M.T. Example: Find the S.M.T. at which Canopus (q Argus) will pass the observer's meridian (Long. 45 W.) on March 5th, L914. G.D. R.A.* Add 6 h 24 — — 00 03 s 00 R.A. Canopus 6 1 ' 22 m 03 R.A. M.S. 22 ID 33-3 Add for L0 h . 1 38-6 „ „ 30"' 4-9 „ ■• 2 3 R.A. M.S. 30 22 22 49 03 33 S.M.T. Long. 7 3 32 00 30 (approx.) 00 (W.) 22 51 17 1 10 32 30 Mar. 5th. R.A.# -24' R.A. M.S. S.M.T. 30 22'" 03 s 22 51 17-1 7 30 45-9 Therefore Canopus will pass the meridian at approximately 7 h 31 in r..\i.. March 5th. Since the right ascensions of the stars are practically constant, and the daily increase of Jhe R.A. M.S. (3 UI 56 B ) is nearly 4 minutes per day, it follows that the stars cross the meridian of any particular place about 1 minute- earlier every day. When a star passes the meridian below pole, its R.A. differs l»y Fig. LOO. 12 hum- from thai of the meridian. Iii Fig. LOO, since right ascension i mea ared to 1 he East cvard, T/'Z T/'A 12 loon .-. RAM. R. A -£ 12 bout Therefore once R A M R.A M.S. S.M.T. we liave S.M.T. R.A.-fc 12 1 R.A M Art. 126. 140 Example : — Find the S.M.T. at which Canopus will pass the observer's meridian (Longitude 45° W.) below pole on the night of March 5th, 1914. RA^ 6 h 22 in 03 8 R.A. Canopus 6 h 22 m 03 8 Add 24 00 00 R.A.M.S. 22 49 33-3 Addfor22 h 3 36-8 30 22 03 „ „ 30 m 4-9 R.A.M.S. 22 49 33 „ „ 2™ -3 S.M.T. 7 32 30 (approx.) 22 53 15-3 Add 12 00 00 — ■ S.M.T. 19 32 30 (approx.) Long. 3 00 00 (W.) G.D. 22 32 30 Mar. 5th. R.A.-* + 24 1 ' 30 h 22 m 03 9 R.A.M.S. 22 53 15 7 28 48 Add 12 00 00 S.M.T. 19 28 48 Therefore Canopus will pass the meridian below pole at approximately 7 h 29 m a.m., March 6th. It is sometimes desirable to find what stars pass the observer's meridian above and below pole between two given times; in this case we proceed as follows. Example : — It is required to find what stars of the first magnitude pass the meridian of 45° W. on March 11th above, and below pole, between the hours of 5 h and 6 h p.m. (S.M.T.). S.M.T. 5 1 ' 00™ Mar. 11th. S.M.T. 6 h 00™ Mar. 11th. Long. 3 00 (W.) Long. 3 00 (W.) G.M.T. R.A.M.S. S.M.T. 8 23 5 00 15 00 Mar. 11th 28 24 15 00 R.A.M. 4 15 G.M.T. 9 00 R.A.M.S. S.M.T. 23 6 15 00 29 24 15 00 R.A.M. 5 15 Therefore, since the R.A.-X- (when on the meridian) = R.A.M., we require the names of all stars of the first magnitude whose R.A.s lie between the two values of the R.A.M. just found. On inspection of the Almanac, they will be found to be Aldebaran (a Tauri), Capella (a Aurigse), and Rigel (a Ononis). If 12 hours are added to each of the R.A.M.s, we find the R.A. of the meridian below pole at 5 h p.m. and at 6 h p.m. Therefore, all stars of the first magnitude whose R.A.s he between 16 h 15 ni and 17 h 15 m pass 141 Art. 125. the meridian below pole between 5 h p.m. and 6 h p.m. It will be found that there is only one star of the first magnitude, namely Antares (a Scorpii), whose R.A. lies between these limits. (c) The Moon. — Owing to the rapid change in the right ascension of the moon, it is a lengthy operation to find the time of the meridian passage by the method which has been given above for the stars, because it is necessary to correct the right ascension of the moon several times. For this reason the times of the upper and lower meridian passages of the moon are tabulated in the Abridged Nautical Almanac, on page II. of every month. The times given are the astronomical G.M.T.s at which the moon crosses the meridian of Greenwich, and the meridian of 180°. When two asterisks are shown, as on March 11th and 26th, in the columns headed " Moon's Mer. Pass." it indicates that there is no lower or upper meridian passage respectively on those days. The moon passes the meridian of Greenwich later each day by the number of minutes in the column headed " diff.'' Since, in the interval between two meridian passages, the moon passes over 360° of longitude, it follows that the astronomical mean time of meridian passage, over any meridian of West longitude, is later than that over the meridian of W. Long ° Greenwich bv 0rtrt0 X diff. Similarly, the astronomical mean time 360 of meridian passage, over any meridian of East longitude, is earlier than that over the meridian of Greenwich by " „„ X diff. In West J 360 longitude, the " diff." between the day and the following day should be used ; in East longitude, that between the day and the preceding day. \ table for \^ X diff. is given in lnman's Tables under >( Correction of moon's meridian passage." Example : — Find the S.M.T. of the moon's meridian passage on March 9th, 1914. in longitude 60° E. From the Abridged Nautical Almanac the moon's upper meridian passage takes place at 10 h 15™ on March 0th. The diff. between this ini I the preceding meridian passage is 55 minutes. With arguments 60 and 56 m , a correction is found in lnman's Tables to be 9 m *2 Bubtractive. Mer. Pass. I0 h 15 m March 9th Correction — 9*2 S.M.T. 10 05- 8 -March 9th or, the moon pa the meridian of 60° E. at S.M.T. I0' 1 06 m p.m. March '.'Hi. ('/i 77/' Planets. The time of meridian passage <»f a planet may be found as in the case of a Btar, but, for convenience, the time of meridian of each of I be four navigational planets is tabulated on pages X I . and XII. of the Abridged Nautical Almanac for each month. The time given i- the a tronomical G.M.T. of passage over the meridian of enwich, which for all practical purposes may be taken as the mean time <>f passage over any Other meridian. If the exact S.M.T. is required it can be found at in the case oi the moon. The difference between the times of two oonsecutive passages is the ohange while the planel pass* over 360 of longitude; the correction of the meridian Long ,.. T pae age, I aereiore la . ( ain. Art. 126. 142 If the times of consecutive meridian passages are getting later, as in the case of the moon, add for West longitude and subtract for East longitude ; if the times of meridian passages are getting earlier, contrary to the case of the moon, subtract for West longitude and add for East longitude. 126. Position line by meridian altitude. — If an observer takes the altitude of a heavenly body when on his meridian, the observer and the geographical position of the body are on the same meridian. In Fig. 101, let U be the geographical position of the body whose altitude has been observed when the body was on the observer's meridian. Let AB be the circle of position resulting from this observation, then, as the bearing of the body must have been either North or South, the position line must lie East and West through one or other of the points B or A . As the position line in this case runs East and West it coincides with a parallel of latitude, and therefore, from this observation, the latitude of the observer is determined. Let UQ be the declination of the body, then if the body crossed the meridian North of the observer the latitude of the observer is the latitude of B, and therefore UQ - UB Lat. = Declination — true zenith distance. If the body crossed the meridian South of the observer the latitude of the observer is the latitude of A, in which case Lat. - UQ +AU = Declination -\- true zenith distance. In order to find the latitude from this observation it is advisable to draw a figure, an inspection of which will show at once how the latitude is obtained when the meridian zenith distance (m.z.d.) and the declination of the body are known. A very convenient figure for this and other problems is obtained by supposing the celestial concave to be projected on to the plane of the observer's rational hori- zon, from a point at an infinite distance vertically above the zenith. In this case any point of the celestial concave is re- presented on the plane of the rational horizon by the foot of the perpendicular dropped from that point. Thus, in Fig. 102, the circle NESW represents the rational horizon of a position on the earth whose zenith is Z, NZS the celestial meridian, P the elevated celestial pole, and WQE the celestial equator. If X be the true place of a heavenly body, XX' is its parallel of declination, PXD the celestial meridian of the body, XD the declination of the body, PX the polar distance, ZPX the hour angle, PZX the Fig. 102. 143 Art. 126. azimuth. ZX the zenith distance, X A the altitude of the body, and the triangle PZX is the astronomical or position triangle. The points of the rational horizon where it is intersected by the celestial meridian of the observer are called the North and South points. The circle of altitude which is at right angles to the celestial meridian of the observer is called the prime vertical, WZE, and it intersects the horizon in two points called the East and West points. Case 1. — Latitude N. Declination N. Azimuth S. From Fig. 103 we have Lat, = ZQ = ZX + XQ = m.z.d. + Dec. Case 2.— Latitude N. Declination N. Azimuth N. From Fig. 104 we have Lat, = ZQ = QX - ZX -Bee. - - m.z.d. Case 3. — Latitude X. Declination S. From Fig. 105 we have Lat. = ZQ = ZX - QX = m.z.d. - Dec. N n w / 1 -p \ "Z s / x / w X*~*\ / / / / / ' < 'P ! \ / \ / \ 1 \ / \ 1 v ^- • \ z vH Q / s Flo. 106. Fig. 106, A body is -aid i<> be circumpolar when its parallel <>l declination does 1 1 « > i intersect the horizon. In such a case the altitude of a bodymay be observed when on the meridian below poles. < n i \ When a body pa e the meridian belo^a f »< >1< * . From Fig. 1 06 n e have Lat. ZQ 90 PZ PN PX V v Polar distanoe altitude. h should be observed that /'A is the altitude of the pole, bo thai the altitude "t the pole .it any place is equal to the latitude of that place. Art. 126. 144 Example (1) : — On April 28th, 1914, in estimated position Lat. 30° 11' S., Long. 84° 13' E. ; I.E., - 1' 10"; H.E., 50 ft. The following observation was taken to determine the latitude of the ship : — Obs. Meridian altitude sun's L.L. 45° 50' 10" (Azimuth North). S.A.T. - 24 h 00 m Apr. 27th. Obs. alt. £? 45° 50' 10" Dec. - 13° 54' N. Long. 5 37 (E.) I.E. 1 10 Eq. T. - 2 m 26 s - to A.T. G.A.T. - 18 23 Eq. T. - - 2 Cor. ZX - QX - ZQ - 45 49-0 + 8-1 G.D. - 18 21 Apr. 27th. 45 57-1 44 02-9 13 54 Lat. 30° 08' -9 S. 30 8-9 S. N Fig. 107. $ Example (2) : — On March 7th, 1914, in estimated position Lat. 55° 26' N., Long. 50° 18' W. ; I.E., - 1' 10"; H.E., 50 ft. The following observation was taken to determine the latitude of the ship : — Obs. Meridian altitude moon's L.L. 00° 17' 30" (Azimuth South). Time of Moon's nier. pass, at Greenwich - 8 1 ' 22'" Mar. 7th. Dec. Cor. for Long. +8 Obs* Alt. -in c hav // = cos (p ~ c) — cos (#> ~ c) cos y + sin (^> - c) sin */, = 2 cos (p ~ c) hav y A- sin (p ~ c) sin ?/, 2 sin p sin c hav H sin y = — •.cos 1/ = 2 hav # = Now let sin //! = sin (p ~ c) 2 -in j9 sin c hav H — 2 cot (p ~ c) hav //. and sin (j) ~ c) sin y t - -1 cot (y, c) hav 1/, in which (# c) may be regarded as equal to c ami // as equal to //, ; then, since //, and y., are small angles, y — yx- Hi ,„iw .. - '"~ /- ' "- D ha^ // whore sin //. = — " sin (L . I)) and sin y % - 2 tan (altitude) hav //,, the Bigns or being used according ae /.and D are of the same or of different names. I hi- vain.- .,r , jx ;m ,| ,, m ;iv be Found from [nman's Tables: Ex- Meridian Tables I.. II.. and III. give the value of //, and Table IV. gives the value of //,. . When y has been found it should be added t<> the true altitude ; the meridian altitude tine obtained, when combined with the deelin.i I ion in K 2 Art. 128. 148 the manner previously explained (§ 126), gives the latitude of the point through which the position line may be drawn. Therefore the position line is drawn on the chart through the point A, whose latitude is the latitude thus found and whose longitude is the estimated longitude, and in a direction at right angles to the azimuth of the body. When the heavenly body is near the meridian below pole the formulae above are the same except that instead of H we have 12 h — H. In this case the altitude is decreasing as the body approaches the meridian, so that the correction y is subtractive from the true altitude. The limits within which an observation may be worked by the ex- meridian method are defined by the scope of the tables. When an observation is taken of a heavenly body which is near the meridian, and it is found that it is impossible to work it out by means of the ex-meridian tables, it should be worked in the ordinary manner which has-been described in the previous chapters. Example (1) :— On March 2nd, 1914, at about ll !l 30 m a.m. (S.M.T. nearly), in estimated position Lat. 49° 17' N., Long. 38° 15' W., the deck watch was slow on G.M.T. 2^ 15 m 10 s ; I.E., + 1' 40"; H.E., 40 ft. The following observation was taken : — Deck watch, ll h 48 m 53 s . Obs. alt. 32° 24' 40". Required the latitude of the point through which to draw the position line. S.M.T. • Long. 23 h 30 m . . 2 33 Mar. (W.) Mar. 53 s 10 1st. 2nd. (W.) Obs. alt. i I.E. - Cor. - True alt. y Mer. alt. M.Z.D. Dec. - Lat. - Azimuth fi Tables 2 32° 24' 40" + 1 40 Dec. 7° 23' -OS. Eq.T. 12 m 25 8 -8 + to'A.T. Tab. I. - - 9-890 Tab. II. - - 7 • 909 G.D. 2 03 - ll h 48" - 2 15 32 26-3 + 8-6 D.W. Slow - 32 34-9 - +43-1 1 7-799 Tab. III. - - 43'- 3 Tab TV • - -2 14 04 12 00 03 00 - 33 18-0 90 00 y - - =43-1 G.M.T. Long. - 2 04 - 2 33 03 00 - 56 42-0 - 7 23-0 M.T.P. Eq. T. - 23 31 - - 12 03 26 - 49 19-0 N. •om - S. 12J° E. H. - 23 18 37 N W / i >p \ z a" / s Fig. 113. Lat. 49-/$ Long.38°/5 149 Art. 128 Therefore, the position line is drawn through the point whose position N. E. is Lat. 49° 19' N., Long. 38° 15' W. and in a direction 77i° , as shown S. " W. in Fig. 114. Example (2) :— On March 28th, 1914, at about 4>> 20 m a.m. (S.M.T. nearly), in estimated position Lat. 56° 51' N., Long. 17° 25' W., the deck watch was slow on G.M.T. 3 h 47 m 19 8 , I.E., — 1' 50"; H.E., 40 ft. The following observation was taken : — Deck watch l h 43 m 47 s . Obs. alt, Capella (below pole) 13° 02' 40". Required the latitude of the point through which to draw the position line. Lat.SG°44--3N\ 8? LonqJ7?ZS'W.r~'^ Position Line Fig. 115. S.M T. 16 h 20- Mar. 27th. Long.- 1 09 40' (W.) Obs. alt. I.E. \ 27th. Cor. - True alt. y Fig. 110. G.D. - 17 30 M D.W. Slow - 1" 43 ra - 3 47 47 19 5 31 12 00 06 00 G.M.T. Long. - 17 31 - 1 09 06 40 13° 02' 40" - 1 50 13 00-8 - 10-3 12 50-5 - 11-3 Mer. alt. - 12 39-2 Polar dist. 44 05-0 Lat. 44 • 2 N. M.T.P. - 16 21 26 R.A.M.S. 18 55-1 + For 1'' „ 30" ,, 1" R.A.M R.A. II. 12" + 9-9 + 4-9 + -2 Azimuth - N. 5J° W. from Tables. R.A. Dec. Polar dist. Tab. I. Tab. II. Tab. III. - Tab. IV. - 5 h lO- 21' - 45° 55' N. 90 00 ?/ - 44 05 - 9-591 - 7-624 7-215 - 1T-3 - 00 = 11-3 . - 16 - 5 m 10 36- 1 21- - 11 12 30 00 15-1 no //. 2!l 14*9 Therefore, the position line is drawn through the poinl whose position N. I is Lat. 56° 44'-3 N., Long. 17 25' W.. and in a direction 84f , as s. " w. Hhown in F\sin (R.A.M. -- R.A.-&)] 2 tana. The second and third terms on the right are tabulated in the Nautical Almanac for constant values of p and R.A.-X-; Table I. gives the value of p cos (R.A.M. - - R.A.-fc) and Table II. the value of \ sin 1" \p sin (R.A.M. -R.A.fc)] 2 tan a. Table III. gives a correction for the change of the declination and right ascension during the year, increased by 1'. The actual correction is sometimes positive and sometimes negative, therefore if 1' is always subtracted from the altitude the numbers given in Table III. are always , additive. It will be noticed that the elements in the Nautical Almanac are tabulated for local sidereal time, but, as explained in § 96, this is the same as the right ascension of the meridian. The azimuth of Polaris is tabulated in Inman's Tables for various latitudes and right ascensions of the meridian. Example. :— On March 14th, 1914, at about 6 h 30 m P.M. (S.M.T. nearly), in estimated position Lat. 29° 42' N., Long. 126° 30' E., the deck watch was slow on G.M.T. 5 h 06'" 47% I.E., + 1' 30" ; H.E., 30 ft, The following observation was taken : — Deck watch, 4 !l 57'" 05 s ; obs. alt, Polaris, 30° 18' 40". Required the position line. S.M.T. - 6 1 ' 30™ Mar. 14th Obs. alt. Long. - 8 26 (E.) I.E. <:.!). - 22 04 Mar. 13th Cor. D.W. - 4 1 ' r>7'" 05 Slow 5 or, 47 Tine alt. Subtract 10 (13 f>2 li> 0(1 (III G.M.T. - 22 03 52 Long. 8 26 no (I-;.) 1st cor. 2nd cor. .M.T.I'. o 2«.i 52 3rd cor. R.A.M.S. 23 i\ i 2-5 + For 4" +0-7 L ;i t. i".t :>i :;.vl> l'I on on go 3 18' 40" + 1 30 •M) 20- 2 - 7- 1 30 13- 1 1 ■ 30 12- 1 27 • 1 29 1 1- — ,,. ••{ 1- ■1 29 Hi 2 N . R \..\1. Art. 130. 152 From Inman's Tables the azimuth of Polaris is found to be N. l|-° W. ; therefore the position line is drawn on the chart through the point whose position is Lat. 29° 46' -2 N., Long. 126° 30' E., and in a direction N. _.„ E. S. 881° W. 130. Position line by "Longitude by chronometer" problem consists of finding the longitude of one of the points where the estimated parallel of latitude intersects the circle of position. In Fig. 119 let the parallel oi latitude AB intersect the circle of position in A and B, and let the body be West, of the observer's meridian at the time of observa- tion. Then, if we can find the longitude of A, the position line can be drawn on the chart through the point the longitude of which has been found, and the latitude of which is the estimated latitude used in the calculation. This Now longitude M.T.P. ~ G.M.T. [H + R.A.-X- - R.A.M.S.] G.M.T. or in the case of the sun, Long. = [H ± Eq. T.] ~ G.M.T. In each case the only unknown quantity on the right-hand side of the equation is the hour angle of the body, so that, to find the longitude of A, we have first to calculate the hour angle of the body. In the triangle PZX, Fig. 102— hav ZPX = cosec PZ cosec PX ^hav [ZX + {PX-PZ)] hav [ZX~(PX~PZ~)l Now PZ = 90° - L and PX = 90° + D ; therefore hav H — sec L sec D Vhav [z + (L + D)] hav [z ~ (L + D)] the sign + being taken in the usual manner. When looking out the hour angle from the haversine table it should be borne in mind that, if the body is West of the meridian, the hour angle is less than 12 hours, and if East of the meridian, the hour angle is greater than 12 hours. Having found the hour angle, the longitude of A may be obtained from the formula given above. The position line is drawn on the chart through the point whose latitude is the latitude of the estimated position, and whose longitude is the longitude thus found; its direction is at right angles to the azimuth of the body. Example (1) :— On March 3rd, 1914, at about 4 h 30 m p.m. (S.M.T. nearly) in estimated position Lat. 30° 21' N., Long. 160° 25' E., the deck watch was slow on G.M.T. 3 h ll m 21*; I.E., + 1' 20"; H.E., 30 ft. The following observations were taken : — Deck watch 2 h 33 m 52 s Obs. alt. „ „ 2 34 20 „ „ „ )! 51 & 04 41 ,,51)5 18° 27' 30" 18 18 50 18 12 30 153 Art. 130. Required the longitude of the point through which to draw the position line. 2 h 33 m 53 s 18° 27' 30" 2 34 20 18 18 50 2 34 41 18 12 30 3/102 2 34 54 18 _ 3/ 18 58 50 19 37 - 7° 07'- 12 m 17»-7 12 S.M.T. Long.- 4 h 30™ Mar. 3rd. 10 41 40' (E.). Obs. alt, I.E. Cor. True alt. True z L sec L sec L hav L hav Lhav H 18° 19' 37* + 1 20 Dec. Eq. T. H Eq. T. M.T.P. G.M.T. Long. >> OS. + to A.T G.D. 17 48 Mar. 2nd 18 21-0 -f 8-0 D W 2 h 34' n 18^ 3 11 21 Slow - 18 29-0 5 45 39 12 00 00 71 310 - 0-06401 0- 00337 4-91069 4-46637 G.M.T. 17 45 39 L D - 30°21'-0 N. - 7 07-9 S. {L + D) - 37 28-9 z - - 71 31-0 z + {L+D) 108 59-9 z ~ {L+D) 34 02-1 9-44444 42" 17-7 4 26 17 45 69-7 39 10 41 160° 20' 20-7(E.) •2E. Azimuth N. 110° W. from Tables. Therefore tin position line is drawn through the point whose position is N. W. Lat. 30° 21' N., Long. 100° 20' -2 E., and it runs 20° ^ . S. E. If two observations are taken and two position lines found, the position of the ship may be obtained by plotting the position lines. If the azimuth of the body is '.>0°, that is, if the body is on the prime vertical, the position line runs North and South and is coincident with the meridian the longitude of which lias been obtained from the observation ; in such a ease it is obvious that the longitude obtained is the longitude of the ship, irrespective of the latitude used in the calculation. When the latitude of the ship is known at the time of the observation the longitude obtained i- the longitude; of the ship; therefore when an altitude of a body on the meridian can be taken simultaneously, or nearly simultaneously, with that of a body whose a/.imuth is not less than 30°, tin- position of the ship can be immediately obtained from the Art. 131. 154 observations, without the necessity of plotting the position lines or having recourse to the traverse table ; this is illustrated by the following example. Example (2) :— On March 28th, 1914, at about 7 h 15 m p.m. (S.M.T. nearly), in estimated position Lat. 42° 41' N., Long. 40° 20' W., the deck watch was slow on G.M.T. 3 h 39 m 15*. I.E., - 1' 30"; H.E., 45 ft. The following observations were taken to determine the position of the ship : — Obs. meridian altitude Procyon 52° 48' 30" (Azimuth South), Deck watch 6 h 16 m 08 s . Obs. alt. Regulus (E.) 46° 02' 00". Obs. alt. Procyon - 52° 48' 30" Dec. 5° 26' -7 N. I.E. - - - I 30 Cor. ZX QX ZQ Latitude 52 47-0 -7-4 52 39-6 - 37 5 20-4 26-7 - 42 47-1 42° 47'-l N N W / "P \ K z A [V -^ •=24 « y s Fig. 120. S.M.T. 7 h 15 m Mar. 28th. Long. 2 41 20* (W.) G.D. 9 56 Mar. 28th. D.W. 6 h 16 m 08 s Slow 3 39 15 G.M.T. 9 55 23 L ■ D - - 42°47'-l - 12 23-2 (L-D) - z - 30 23-9 44 07-1 Obs. alt. Regulus I.E. Cor. True z L sec L sec 46°02' 00" - 1 30 46 00- - 7- 5 6 45 52 •9 44 07 •1 R.A. Dec. R.A.M.S. For l h „ 50 m „ 5 m 13436 01023 H R.A.* 10 h 03 m 49 s -8 12°23'-2N. h 21 m 32 s -9 9-9 8-2 •8 21 51-8 21 h 31 m 51 8 10 03 49-8 31 35 40-8 24 00 00 z + (L -D) - 74 31-0 z - (L - D) - 13 43-2 | L hav J L hav L hav H 4-78205 4-07718 9-00382 Position of ship : Lat. 42° 47'- 1 N., Long. R.AM. R.A.M.S. 7 35 40-8 21 51-8 S.M.T. G.M.T. 7 13 49 9 55 23 Long. 2 41 34 (W.) 40° 23' -5 W. 40° 23' -5 W. 131. Longitude by equal altitudes. — The following method of finding the longitude, although not strictly belonging to the theory of position 1 .-).-» Art. 131. lines, is given on account of the extreme brevity of the calculations involved. Suppose that the times, shown by the chronometer, when a heavenly- body has the same altitude before and after its meridian passage, are t x and t 2 respectively ; then, if we neglect the motion of the ship and the change in the declination of the body, the meridian passage of the t 4- t body takes place when the chronometer shows — - ~. Therefore the G.M.T. of the meridian passage is known, and this, compared with the S.M.T. of passage, obtained as shown in § 125, gives the longitude of the ship. When we take into consideration the motion of the ship and the change in the declination of the body, the body may be assumed to be at its maximum altitude (§ 127) at the mean of the chronometer times, provided that the altitudes are taken within 30 minutes of the time of the meridian passage. If, therefore, we can find the interval between the times of meridian passage and maximum altitude, this interval applied to the mean of the chronometer times will give the chronometer time of the meridian passage, and hence, as explained above, the Longitude of the :-hip. In Rg. L21, let Z be the zenith of the ship and X the true place of a heavenly body when at its maximum altitude. Let t he velocities of the ship in latitude and Longitude be vj, and vq respectively, BO that the velocity of Z in a direction perpendicular to the meridian i L. where /> is the latitude of the ship. Lei the relocitiee of X in declination and hour angle be 1'/, and \'<, respect tvely. When the body is at its maximum altitude, the relative velocity of it- true place X, along the circle of altitude XX. is zero. There) ore. Vq COS l> BUI I'XZ |„ cos I'XZ Vq COS L sin PZX + )/, cos PZX 0. Art. 131. 156 Since the angles PXZ and PZX are small, we may put cos PXZ = \ y and cos PZX = — 1. Also . „ v „ sin # cos L , . „<7 V sin # cos i) sin PXZ - and sin PZX = - . - . sin z sin z F COS D COsL . „ T/ F 22 4 2 5 38 1-5 L6 43 4 :* 5 59 1-0 16 04 4 4 6 21 I -7 10 25 4 5 6 43 1-8 10 45 1 6 7 06 1-9 17 06 1 7 7 27 20 17 26 1 8 7 19 2- 1 17 17 4 9 8 12 2« 2 is 07 5 34 45 10 35 no 10 7 35 i;» 10 8 35 30 10- 9 35 46 1 1 36 (in 1 1 • l Art. 131. 158 Lot D — L or D. — Lor D. L or D. — 36° 15' 11-2 39° 17' 12-5 42° 05' 13-8 44° 40' 15-1 36 29 11-3 39 31 12-6 42 18 13-9 44 51 15-2 36 44 11-4 39 44 12-7 42 30 14-0 45 02 15-3 36 58 11-5 39 57 12-8 42 42 14-1 45 13 15-4 37 12 11-6 40 10 12-9 42 54 14-2 45 25 15-5 37 20 11-7 40 23 13-0 43 06 14-3 45 36 15-6 37 41 11-8 40 36 131 43 18 14-4 45 47 15-7 37 55 11-9 40 49 13-2 43 30 14-5 45 58 15-8 38 09 12-0 41 02 13-3 43 42 14-6 46 08 15-9 38 23 12-1 41 15 13-4 43 54 14-7 46 19 16-0 38 36 12-2 41 28 13-5 44 05 14-8 46 30 16-1 38 50 12-3 41 40 13-6 44 17 14-9 46 41 16-2 39 04 12-4 41 53 13-7 44 28 150 46 51 16-3 To use the table, take out the numbers corresponding to the latitude and declination; add these numbers together when L and D are of different names, and take their difference when L and D are of the same name. Multiply the result by the relative speed of the ship and body in latitude. This gives the interval, disregarding the motion of the ship in longitude. To correct the interval for this motion, multiply it by • 002 times the speed of the ship in longitude and apply it to the interval just found + according as the ship's course is a Westerly or an Easterly one. The following examples show how the longitude is obtained by aid of this table. Example (1) : — On March 2nd, 1914, in estimated position Lat. 2° 10' N., Long. 71° 15' E., the deck watch was slow on G.M.T. b 56 m 38 s , and the ship was steaming N. 35° W. (true) at 18 knots. The following observations were taken to determine the longitude of the ship. The sun had equal altitudes at the following times by deck watch : — (a.m.) 6 !l 04 m 58 s . (p.m.) 6 h 55 m 01 s . S.A.T. 24 jl 00'" Mar. 1st. Dec. 7°29'-2S. Long. 4 45 (E.) Eq. T. 12^ 29 m + to A.T. G.A.T. Eq. T. G.D. 19 15 Mar. 1st. + 12 19 27 Mar. 1st. N. 35° W. 18' = d Lat. 14'- 74 N., Dep. 10' -32 W., d Long. 10' -32 W. Speed in latitude - 14-74 knots (N.) Speed in declination - -95 knots (N.) Relative speed 13*79 knots (parting). From table 2° 10' N gives 0-6 ) L and D different names ; — 7° 29' S. „ 2-0 add. 2-6 2-6 x 13-79 = 35 9 -85. 159 Art. 131. Speed of ship in longitude is 10-32 knots (W.) 35-85 x -002 x 10-32 =0^74. 35 s -85 •74 Interval between times of max. and mer. alts. 36*59 DAY. (a.m.) - - - 6 h 04™ 58 s D.W. (p.m.) - 6 55 01 Mean D.W. time Slow G.M.T. at Max. Alt. Interval - G.M.T. at Mer. Pass. Eq. T. G.A.T. at Mer. Pass. S.A.T. at Mer. Pass. - 2/12 59 59 6 12 29 00 59 00 18 29 56 59 38 19 26 37 + 37 19 27 - 12 14 29 19 24 14 00 45 00 4 71° 45 18'' 15 (E.) ■75 (E.) Longitude Example (2) :— On April 27th, 1914, at about 7>> 45™ p.m. (S.M.T. nearly) in estimated position Lat. 19° 23' N., Long. 7° 15' W. the deck watch was slow on G.M.T., 3 h 13 m 27 s and the ship was steaming S. 62°E.(true) at 15 knots. The following observations were taken to determine the longitude of the ship. Regulus had equal altitudes at the following times by deck watch : (E. of Mer.) 4 1 ' 40" 20 s . (W. of Mer.) 5 h 18™ 46 8 . S.M.T. 7 1 ' 45'" Apl. 27th. R.A.# 10'' 03' n 50 s Long. 29 (W.) G.D. 8 14 Apl. 27th. Dec. 12° 23' -2 N. R.A.M.S. For 10" 2 I!) 1 " 49 8 + 1 + •5 •6 •7 2 l!) 51 •8 2 E. I5' = d Lat. T-04 s.. Dep. l3'-24 E., d Long. 14' E. Speed in latitude - - 7*04 knots (S.) Speed in declination - 0-00 Relative speed - 7*04 knots (nearing). Art. 132. 160 From table 19° 23' N. gives 5-4 \ L and D same names „ 12° 23' N. „ 3-4) subtract. 2-0 2-0 x 7-04 = 14 s -08. Speed of ship in longitude is 14 knots (E.) 14-08 x -002 x 14 = s -39. Interval between times of Max. and Mer. Alts. R.A.^f - 10 h 03 m 50 s D.W. (E. of Mer.) - R.A.M.S. - 2 19 52 D.W. (W. of Mer.) - S.M.T. of Mer. Pass 7 43 58 14 s -08 - -39 13-69 4 h 40™ 5 18 20* 46 2/9 59 06 4 59 3 13 33 27 8 13 00 - 14 8 12 7 43 46 58 28 7° 12' 48(W.) W. Mean D.W. time Slow G.M.T. of Max. Alt. Interval - - - G.M.T. of Mer. Pass. S.M.T. of Mer. Pass. Longitude 132. Notes on observations for determining position lines. — The accuracy of all altitudes depends on the degree of exactness with which the position of the sea horizon is known, in other words on the dip, which, as explained in § 52, occasionally differs considerably from the tabulated values on account of abnormal refraction. In addition, the accuracy of an altitude depends on the distinctness with which the sea horizon can be seen by the observer. When mist causes the horizon to appear indefinite, it is advisable to take an observation from a position where the height of eye is as low as possible, and so bring the sea horizon nearer to the observer (§ 57). The difficulty caused by the sea horizon being obscured can be over- come approximately, when ships are in company, by using for shore horizon the water fine of another ship which has the same bearing as the sun, care being taken to measure the distance of the ship by range-finder at the time of observation. As the dip of the shore horizon (§ 58) cannot be easily and accurately obtained from the tables it should be calculated from the formula, which, for convenience in this case, may be put in the form : Dip (in minutes of arc) = H46^ + -0002 d, where h is the height of eye in feet and d the distance in yards. 161 Art. 132. The best time for taking observations for obtaining the position of the ship is when the stars tirst become visible or just before they disappear, at evening and morning twilight respectively, as the horizon is usually very well defined at those times. The altitudes of Venus and Jupiter may sometimes be observed in daylight when the bodies are near the meridian. In order to locate the body which it is wished to observe, it is advisable to previously calculate its approximate altitude and to set the altitude on the sextant. With the sextant telescope (Erected to the correct point of the horizon the body should be seen in the field of the telescope. Observations should not be taken from positions where the ray of light from the body observed has to pass through hot air or steam. When the heavenly body is not near the meridian three or five observa- tions should be taken in quick succession and their mean used to work out the observation; this procedure should not be followed in the case of a body which is near the meridian, because in that position the altitude of the body does not vary directly as the time. The minute hand of the deck watch should always be looked at by the observer immediately after taking the last observation, to see if the correct minute has been written down by the time-taker. The time by the ship's dock should always be noted, and also the reading of the patent log or speed recorder. It is as necessary for the time by the deck watch to be taken accurately as tor the altitude to be correctly measured. The method of taking time by the deck watch is given in Chapter XVI. W hen observing, give the time-taker a warning of about 5 seconds and call top at the instant of making the contact. The sextant telescope of the highest power that will give clear images oi the body and the horizon should always be used. When the body appears very bright the eye is strained and the exact instant of contact is difficult to detect ; consequently the darkest sextant shade that will give a clear image of the body should be used. The index error of the sextant should be determined just before observations are taken or just afterwards. Whenever a star or planet is observed its compass bearing should be taken, to assist, if necessary, in determining the name of the body observed, as will be explained in Chapter XV. [t is always advisable to take observations of 1 he sun in the late after- noon, even if if is intended to take observations of stars a little later on ; the observations of the sun need not necessarily be worked out, but they serve as a 'stand by" in case the stars are obscured. For a similar on observations Bhould be taken when land is about to be made. for it a fog comes on these observations may be worked oul and will prove most valuable. The estimated position with which to find the position line should be ascertained as accurately as possible, although the position line can be found equally well by using an estimated position which is many miles iu error. The reasons for \\\\< are: (l) the necessity of developing a habit of always making as careful an estimate as possible of the ship's position : (2) n as the magnitude and direction of an intercept has been ascertained, the difference between the ship's probable position and the estimated position is immediately apparent . When observing the meridian altitude of a bodj which is passing nearly overhead, ii i advisable <<» note bi compass the position <»n the x 611 L Art. 132. 162 horizon of either the North or South point, depending on whether the body is passing to the North or South of the observer, and, at the correct time, to observe the altitude above that point. It may happen that the supplement of the altitude has been observed, either inadvertently or because the horizon was partially obscured ; in such a case it should be corrected as shown in the following example. Example: — On March 28th, 1914, the supplement of the altitude of the sun's L.L., measured to the North point of the horizon, was observed to be 94° 16' 30" ; I.E., + 1' 30" ; H.E., 50 feet. Obs. alt. Q_ to N. point of horizon - - 94° 16' 30" I.E. - ' ' - - - - - - - + 1 30 94 18-0 Dip -------- - —6-9 App. alt. © to N. point of horizon - - 94 11-1 180 00 App. alt. to S. point of horizon - - 85 48-9 Refraction - — • 1 85 48-8 S.D. (U.L.) -16-0 True alt. sun's centre to S. point of horizon - 85 32-8 103 Art. 133. CHAPTER XV. [USING AND SETTING OF HEAVENLY BODIES, TWILIGHT, &g. 133. Hour angles of heavenly bodies when on the rational horizon. — At sea it may frequently be necessary to determine whether there will be sufficient light at a particular time to enable objects to be recog- nised, and for this reason we have to consider the times at which a heavenly body rises and sets. The times of rising and setting of a heavenly body are the times at which its centre is on the rational horizon East am I West of the meridian respectively. In Fig.' 122. let X' and X be the true places of a heavenly bod} - when on the rational horizon East and West of the meri- dian respectively, then 24 h — ZPX' is the hour angle of the body when rising, and ZPX is the hour angle when setting. In order to find the times of rising or setting of a heavenly body it is first necessary to deter- mine this angle (ZPX' or ZPX). Let L be the latitude of the observer, and D the declination of the heavenly body. L and D being of the same name, that is, both North or both South. In the triangle PZX cos ZPX = cos ZX - cos PX cos PZ sin PX sin PZ therefore, denoting the hour angle by H and remembering that when a body is on the rational horizon its zenith distance is 90°, we have cos H = - cot PX cot PZ. Now, PX = 90° - D, and PZ = 90° ■ - L. Therefore cos // : — tan I) tan />. or cos (I2 h — H) tan I) tan L. If L and 1) arc of different names PX is !)()° -f- /'. and if we denote the hour angle in t his case by //' we have cos //' = tan D tan L. Prom these formula' we see thai //' I2 h //. The hour a null- .it Betting {II \ are tabulated iii t he Abridged Nautical Almanac for values of I. from to To and of D from to 30°, when /. and l> are "I the 3ame name. The hour angles at rising are found by subtracting the tabulated results from 24 hours. When /. and /> are <»f different names the hour angles at setting are found by subtracting the tabulated results from L2 hours. The hour angle at rising is found by subtracting this amount from 24 hours. The table takes no account < >f dip, semi diameter, refract ion or parallax. so it must not be expected that a heavenly bodj becomes visible, or disappear exactly when ite hour angle is that given in the table. Art. 134. 164 134. S.M.T. of visible sunrise and visible sunset. — In the case of the sun the tabulated hour angle is the S.A.T. of sunset, and when subtracted from 24 hours the result is the S.A.T. of sunrise. Now let us consider what is the observed altitude of the sun when it is on the rational horizon, that is, when its true altitude is zero. Sun's true altitude - - 0° 00' Refraction and parallax - +29 Apparent altitude - - 29 From this we may see that at sunset or sunrise the sun's centre appears to be about 29' above the horizon, and taking the semi-diameter as 16', the sun's L.L. at sunset or sunrise is about 13', or about a semi- diameter, above the horizon. Therefore the times at which the sun is seen to rise and set, that is, the times of visible sunrise and visible sunset, differ by a small amount from the times at which the sun is on the rational horizon, so that, by applying a small correction to the time given in the Abridged Nautical Almanac, we can find the time of visible sunset or the time of visible sunrise. The following investigation shows how this correction is obtained : — ■ Obs. alt. sun's U.L. - 0° 00' 00" Dip for 20 ft, - - - 4 24 Refraction Parallax S.D. - and assuming 20 feet as the average height of the observer's eye, the correction required is the time the sun takes to change its altitude 55' • 8 at the time of rising or setting. In Figs. 123 and 124, let X be the true place of the sun when on the rational horizon West of the meridian. In Fig. 123 L and D are of the same name, and in Fig. 124 they are of different names. Let BX' be the change in altitude = dz (55-8') and XPX' the corresponding change in hour angle = dH. In the triangle XBX' , the sides are so small that the triangle may be considered a plane triangle right-angled at B. Now dH = XX' sec D (§ 12) ; also XX' = BX' cosec BXX' = BX' cosec PXZ =. dz cosec PXZ. Therefore dH = dz sec D cosec PXZ. In the triangle PZX, ZX — 90°, and therefore by the rule of sines, cosec PXZ = sec L cosec H. Therefore dH = dz sec D sec L cosec H dz sin H cos D cos L -0 04 -35 24 32 -0 39 56 + 9 -0 39 - 16 47 00 -0 55 47 165 Art. 134. Now, as H is the hour angle at sunset, cos H = + tan D tan L r. sin H = v /l - cos- // = % /i - tan 2 D tan*L x /coPZ) cos 2 L ""- sin 2 Z) sin 2 L cos Z) cos L. N sin /Z = /y/co s (Z> + L) cos (D — L) cos 2) cos L .'. sin ZZ cos D cos L = ^/cos (Z) -f Z>) cos (D — L). dz . ITT " ,/cos (Z) + L) cos (Z) - L). Therefore, if dH is in minutes of time and dA in minutes of arc, we have dH = 7£*/sec (D + L) sec (D - L). dflcooD Fio. L24. Tin- following table baa been calculated from this formula, dz being taken a 55'*8, which corresponds to a height of eye of 20 feet; the Art. 135. 166 numbers given in the table are the minutes that should be added to the S.A.T. of sunset, or subtracted from the S.A.T. of sunrise, to obtain the S.A.T. of visible sunset or visible sunrise. The purpose for which this problem is most often required is to find the time at which to fire the sunset gun when in harbour ; the error, due to the height of eye being more or less than 20 feet, is very small and need not be considered. Latitude. 0° 10° 20° 30° 40° 50° 60° 65° Declination. 0° 3-7 3-8 4-0 4-3 4-9 5-8 7-4 8-8 10° 3-8 3-8 4-0 4-4 5-0 6-0 7-9 9-7 20° 4-0 4-0 4-2 4-7 5-4 6-8 10-2 15-2 23° 40 41 4-4 4-8 5-6 7-3 11-9 23 1 Example : — On April 29th, 1914, at Bermuda, Latitude 32° 22' N., Longitude 64° 30' W., it is required to find the time at which to fire the sunset gun. Rough S.A.T. sunset - 6 h 00 m April 29th. Long. 4 18 (W.) G.D. 10 18 April 29th. Declination for G.D., 14° 25' N. Equation of time for G.D., 2 m 41 s — to A.T. From the Abridged Nautical Almanac, the hour angle at setting is found to be 6 h 38 m . S.A.T. sun's centre on rational horizon - 6 h 38 m Correction from preceding table - - - +4-6 S.A.T. sun's U.L. on sea horizon - Eq. T. - - 6 42-6 -2-7 S.M.T. sun's U.L. on sea horizon - - 6 39-9 The time of visible sunset is therefore 6" 40 m P.M., and this is the time required. 135. Twilight. — Owing to the reflection of light from the atmosphere a certain amount of light is received from the sun when below the horizon, and this is called twilight. There are two periods of twilight, evening twilight and morning twilight. Astronomical twilight is assumed to begin in the morning and to end in the evening, when the sun's centre is 18° below the horizon. During this time stars of the 2nd magnitude are not visible to the naked eye. Civil twilight is assumed to begin in the morning, and end in the evening, when the sun's centre is 6° below the horizon, and during this time stars of the 1st magnitude are not visible to the naked eye. The duration of civil twilight is about one-third of the duration of astronomical twilight, but is less than one-third when the latter is very long. 167 Art. 135. Astronomical twilight lasts all night when the latitude and declination are of the same name and their sum is not less than 72°. Twilight is necessarily short within the tropics, because the apparent path of the sun is there more nearly perpendicular to the horizon than in higher latitudes. The times of cessation and commencement of twilight may be calcu- lated from the astronomical triangle PZX, the zenith distance being taken as 108° for astronomical twilight, and as 96° for civil twilight. Example :— On April 27th, 1914, in Lat. 50° 00' N., Long. 45° 00' W., it is required to find the duration of astronomical evening twilight. As a general rule the time will not be required to any great degree of accuracy ; it is therefore sufficient to take out the declination of the sun for the G.D. of sunset. Rough S.A.T. sunset - - - 6 h 00 m April 27th. Longitude 3 00 (W.) G.D. 9 00 April 27th. Declination for G.D., 13° 46' N. From Abridged Nautical Almanac, the hour angle at setting is 7 h 07 m . S.A.T. sun's centre on rational horizon - 7 h 07 m Correction from table (§ 134) - - - +0-3 S.A.T. sun's U.L. on sea horizon 7 13-3 In Fig. 125, let X be the true place of the sun when 18° below the rational horizon, so that ZX = 108°. Then in the astronomical triangle PZX, the S.A.T. (H.) is calculated from the formula : — hav H = sec L sec D Vhav [z + (L +~Z>)] hav [z — (L + ~D)l Lat. Dec. Fig. 125. 50° 00' N. L sec 13 46 X. /vsec (L 1>) - z 36 14 ins 00 z + (L D) - z - (/, - I>) - l 1 1 II 71 10 H - 27 -6 | /. Ii;iv | L hai L hab // 10- L0193 [0*01266 1-97849 4*76799 !i- 95107 Art. 136. 168 S.A.T. at end of twilight - - 9 h 27 m -6 S.A.T. visible sunset * - - - 7 13 -3 Duration of astronomical evening twilight 2 14 -3 -0 04 -35 24 32 - 39 + 57 56 30 17 — 15 34 45 01 49 136. S.M.T. of visible moonrise and visible moonset. — Let us first consider what is the altitude of the moon's centre when the observed altitude of the moon's U.L. is zero. Observed altitude moon's U.L. - - 0° 00' 00" Dip for 20 feet — 4 24 Refraction Average parallax ----- Semi-diameter ----- True altitude moon's centre - - - From this we see that the appearance of the moon's U.L. on the sea horizon at rising, and its disappearance at setting, takes place very nearly (within less than one minute in Lat. 60°) at the same time as the arrival of the moon's centre on the rational horizon. The times of moonrise and moonset are constantly required, but seldom to a great degree of accuracy, the time to the nearest two or three minutes being generally sufficient. The table in the Abridged Nautical Almanac, for rinding the times of rising and setting of a heavenly body, does not give the interval in solar hours between the times of rising or setting and the time of meridian passage of any heavenly body, other than the sun. As the moon takes roughly 24 h 50 m from one meridian passage to another, or while changing its hour angle 360° or 24 hours, the interval of mean solar time in passing through any hour angle is greater than that hour angle, by an amount depending on the mean solar interval between two successive meridian passages of the moon, as shown in the following example : — Example :— On March 12th, 1914, in Lat. 60° N., Long. 150° W., it is required to find the S.M.T. of moonrise and moonset. M.T. of upper meridian passage at Greenwich - - 12 h 52 m Mar. 12th. Correction for 150° W. and diff. 52 m - 22 S.M.T. meridian passage - - - 13 14 Mar. 12th. Longitude in time - - - 10 00 (W.) G.D. of meridian passage - - - 23 14 Mar. 12th. Moon's declination for above G.D., 6° S. 169 Art. 137. From Abridged Nautical Almanac, hour angle, 5 G.M.T. of meridian passage - Hour angle - G.D. of rising 5 h 18 m 23 14 5 18 G.D. of setting 4 32 Mar. 13t h. Rising. Setting. G.D., 17 h 56™ Mar. 12th. G.D., 4 h 32"' Mar. 13th. Declination, 4° 36' S. Declination, 7° 40' S. Hour angle from table 5 1 ' 28 m Hour angle from table - 5 1 ' 06' Correction for 5 h 2S m and Correction for 5 h 06 m and diff. 52" 12 and diff. 52 m Interval between mer. 11 Interval between rising and meridian passage - 5 40 passage and setting 5 17 S.M.T. meridian passage - 13 14 S.M.T. meridian passage S.M.T. moonset 13 14 S.M.T. moonrise 34 18 31 137. Identification of stars. — It frequently happens that the sky is partially obscured by clouds and that only a few of the heavenly bodies are visible, and sometimes only one star in any particular constellation can be seen. Under such conditions it is impossible to ascertain the name of any particular body, that may be visible, by means of imaginary lines in the heavens such as were described in § 75. A book entitled " What Star is it '. " (Harvey), a copy of which is supplied to each of H.M. Ships, affords a means of identifying any heavenly body from its altitude and compass bearing. The book consists of the solutions of a large number of spherical triangles. On the left-hand page are tabulated the hour angles and on the right-hand page the declinations corresponding to the three known data— latitude, altitude, and azimuth. These hour angles and declina- tions are tabulated for every 5° of latitude from 0° to 65°, and for every 5° of altitude from 10° to 65°, and for every 10° of azimuth. Thus, if a body's altitude is observed, and at the same time its bearing is note I by compass and so its true bearing obtained, the hour angle and the declination nf t lie body can be obtained. In Pig. 126, which is on the plane of the celestial eipiator, l>Z IS the meridian of the observer, X and )' arc the true places of two Stan W'e-t and Easl Of the meridian respect [very, T U the firsl point of Aries. XPZ is the hour angle of X ae obtained from t he tables, )'/'/. is 21 hour angle of F B obtained from the tables, and we have i:..\.ot.v rrz XPZ RAM. R.A. of F TPZ Z/'Y B .A.M. Thus we have I lie follon ing rule ; — Star E . add hour angle to It \ M Fig. 126. hour angle oi X. hour angle of F from tallies. for bai - R.A. Star W.. subtract hour angle from R.A.M. for star's R.A. Art. 138. 170 Example :— On March 26th, 1914, in Lat. 50° N., Long. 45° W., at 5 h 55 m p.m. (S.M.T. nearly), the altitude of a star was observed to be 50° 10', and the compass bearing to be S. 76° W. Required the name of the star. S.M.T. - - 5 h 55 ra Mar. 26th. R.A.M.S. - h 14 m Long. - - 3 00 (W.) S.M.T. - - 5 55 G.D. - - 8 55 Mar. 26th. R.A.M.- - 6 09 Compass bearing Deviation - s. 76 c 1 W. W. - s. 75 33 w. w. - s. 42 w. 6h 09 m 1 46 4 23 Magnetic bearing - Variation from variation chart True bearing - Entering the tables with Lat. 50° and altitude 50° 10' we find, opposite star's true bearing 42° (latitude and bearing contrary names), that the hour angle is l h 46 m and the declination is 16° N. r.a.m; H (Star W. subtract) R.A.* From the list of stars at the end of the book we find that Aldebaran has right ascension 4 h 30 m and declination 16° 3' N. and that this is the only star that will satisfy the data. Should there be no star whose right ascension and declination agree with the calculated right ascension and declination it is probable that a planet has been observed, and in such a case search should be made among the planets in the Nautical Almanack. Should there be two or three stars whose right ascensions and declina- tions are so near to one another as to make it difficult to determine which has been observed, it will be necessary to interpolate between the numbers given in the table, in order to find the star's right ascension and declination more exactly, but this is seldom necessary. As one of the arguments, with which the tables are entered, is the true bearing of the body, it should be made a rule, whenever a star is observed, to note the compass bearing at the time of observation. The name of an unknown star may be more easily found when a Star Globe or Star Finder is available. This instrument is particularly useful, not only for the purpose for which it is designed, but for general instruction in astronomy. 138. Torrid, Frigid, and Temperate zones. — The declination of the sun varies from 23° 27' N. to 23° 27' S. ; therefore since the latitude of the geographical position of a heavenly body is equal to the declination of the body (§ 109), the sun is always in the zenith of some place on the earth's surface situated between the parallels of latitude 23° 27' N. and 23°27'S. 171 Art. 138. That part of the surface of the earth which is bounded by the equator and the parallel of latitude of 23° 27' N. is called the North Torrid zone : similarly, that bounded by the equator and the parallel of latitude 23° 27' S. is tailed the South Torrid zone. These two zones are frequently spoken of as the Tropics. That circle of position, whose centre is the geographical position of the sun at any instant, and which corresponds to a true zenith distance Sun Fig. 127. of 90°, is called the circle of illumination at that instant, because the sun is visible at every point within it. It divides the surface of the earth into two hemispheres, the illuminated and the dark. At any point on the circumference of the circle of illumination the sun is on the rational horizon of that point. Sun Fig. 128. When tli'' geographical position <>l the sun is on fche equator, thaf is. when the declination is . fche circle of illumination passes through both polr .i iii Pig. 127. When flu- geographical position of (lie sun is in Lat. ~:'> 27' .V. that is, when i he sun has its maximum North declination, the illuminated bemi phere (bounded by the circle of illumination AB, Pig. 128) contain* fche North Pole. As the earth revolves in the direction show n bj fche arrow, i he points .1 and /: which are fche points on fche circle Art. 138. 172 of illumination of maximum latitude North and South, trace out the parallels of latitude 66° 33' N. and 66° 33' S. Therefore, when the declina- tion of the sun is 23° 27' N., the sun will not set at any point North of the parallel of 66° 33' N., and will not rise at any point South of the parallel of 66° 33' S. When the declination of the sun is 23° 27' S. the converse takes place. That part of the surface of the earth which extends from the North Pole to the parallel of 66° 33' N. is called the Arctic zone, and the corresponding part in the Southern hemisphere is called the Antarctic zone. These two zones, when referred to together, are termed the Frigid zones. The area which is included between the parallels of 23° 27' N. and 66° 33' N. is called the North Temperate zone, and the corresponding part in the Southern hemisphere is called the South Temperate zone. 173 Arts. 139, 140. CHAPTER XVI. THE ERROR AND RATE OF THE CHRONOMETER. 139. Meaning of the terms error, rate, and accumulated rate. — The principle and description of the chronometer will be found in Part IV. ; we are here concerned with the problem of finding the error and rate of t he chronometer. By the error of a chronometer we mean the difference between the time shown by it at any instant and the G.M.T. at the same instant. It is convenient always to consider that a chronometer is slow, in order that the G.M.T. may be found by adding the error to the time shown by the chronometer. The error of a chronometer varies from day to day, and in a good instrument the daily change in the error remains approximately constant. This daily change is called the rate of the chronometer, and is said to be a gaining or losing rate according as the chronometer is gaining or losing. All H.M. Ships are supplied with three chronometers and one deck watch. When supplied to a ship, the chronometers are accompanied by tabular statements showing their rates during the past few weeks, and from these, estimates may be made as to their reliability. It is customary to label the chronometers A, B, C, &c, according to the estimate made, A being considered the most reliable and adopted as the standard. In order to obtain the G.M.T. at any instant, it is necessary to know the error of the chronometers at that instant, and this error depends on the error determined at some previous date, and on the accumulated rate, which is the increase or decrease of the error of the chronometer in the interval. Thus the accuracy of the G.M.T., found from a chronometer at any instant, depends on the accuracy of the accumulated rate. Now accumulated rate in an interval = daily rate x number of day-, bo that the accuracy of the G.M.T. depends on the accuracy with which the chronometer has maintained its daily rate. 140. System Oi daily comparisons.— In order to determine whether the chronometers are working steadily, recourse is had to a system of daily comparisons, the results of which are entered in a book called the chronometer journal. This system 'consists of comparisons between the A chronometer and all the other chronometers and deck watches in the ship, and i- carried OUt as follows : — [Chronometers heat every halt second, chronometer watches and dech watcln- u-ii. illy heat live limes in two seconds. | When about to compare, only open the lid of .1 chronometer, so thai it tick mi.i\ SOUnd loudly and that of the others may he deadened. Write down .i time which .1 i< going to show, say, I Mi 1 " .'{(l ■<», and start counting the beats when the second hand i_ r ets to -<• seconds, thus : — Half, one, half, two, halt, three, &c. ; in a lew moments the beats can easily be counted; t hen -till counting the heats t urn the eye to the other chronometer, and note exactly what it- second hand shows at the instanl Art. 141. 174 y ou hear A beat the exact second decided on. Write down the comparison as follows : — • A - 4 h 16 m 30 3 -0 B - 4 27 28 -5 B - 11 49 01 -5 slow on A. Compare again as a check on the first comparison. The comparisons are usually all shown as slow on A ; this saves confusion, and enables the time by any other chronometer or deck watch to be converted into time by A by using addition instead of subtraction. Similarly, all chronometer errors should be shown as slow on G.M.T. and not some fast and some slow. With practice, chronometers can be easily compared to a quarter of a second, and accurate comparison is most important when finding the errors by observation. The daily difference between the comparisons of any two chronometers is the difference between their daily rates ; any alteration of the daily difference shows that one or both of the chronometers is going irregularly. If the daily difference of comparison between A and B remains constant at the approximate algebraic sum of their previously obtained daily rates, and that between A and C alters, it is probable that the rate of C chronometer has altered; thus, when finding the error of the deck watch from the chronometer journal in order to determine a position line, it is necessary to examine as to whether all the chronometers agree, and this is done as follows. Apply to the estimated error of B, found as explained above, the comparison between A and B, and thus find the error of A on G.M.T. , as indicated by the B chronometer. Similarly the error of A on G.M.T. as indicated by other. chronometers may be found. Thus we find three or more possible errors for the A chronometer, an inspection of which will show the most probable error of A, and from this the error of the D.W. is determined. In the event of no one error appearing more probable than another, their mean should be assumed to be the error of A. If a landfall has to be made, or a danger to be cleared, from a position obtained by astronomical observations, when there is a con- siderable disagreement between the several chronometers as to the error of A, that error should be selected which places the ship in the most disadvantageous position (§ 118). 141. How to take time accurately with a deck watch. — Accurate time-taking is of special importance when taking observations for obtaining the errors of chronometers. A practised time-taker can take time with a good deck watch to one-fifth of a second. A deck watch beats five times in two seconds ; the beats are therefore ■ 4 second apart, and consequently the beat of a watch coincides exactly with every even second. Beginning at, say, 8 seconds the 1st beat afterwards would be 8 • 4 55 2nd 55 55 55 8 -8 55 3rd 55 55 55 9 -2 55 4th 55 55 55 9 -6 55 5th 55 55 55 10 -o I7f. Arts. 142, 143. The time-taker looks at the watch and starts counting from an even second, every time the watch beats, until the next even second is reached, 4, 8, 2, 6, o. 4. 8. 2. 6, 0, 4. 8, 2, 6, and so on, until he hears the observer call " ; ' top. 1 " If the " ' top " coincides exactly with one of the beat-, the time-taker can exactly recognise from his counting which decimal of a second corresponds to the " ' top," and his eye tells him which second. With practice it is possible to interpolate between the beats. When taking time for any kind of observation, the time-taker should insist on the observer looking at the watch, after the last observation of the set has been taken, to satisfy himself that the correct minute has been put down. 142. Error of the chronometer by time signal. — The error of a chrono- meter may be found, either by comparison with a clock whose error is exactly known, or by astronomical observation. The standard clock at every observatory is regulated daily by means of observations taken with a transit instrument, and this clock can be placed in electrical communication with the telegraphic system ; by this means, at a certain hour every day, a signal is transmitted to telegraph offices and port authorities for the purpose of regulating their clocks. In the United Kingdom the signal is transmitted from Greenwich at 10 a.m. This signal automatically adjusts certain clocks so that they show G.M.T., and from each of them a time signal is worked. At most important ports a signal is made for the convenience of shipping, and this usually consists of the automatic release of a ball from the yard-arm of a signal station; the release is actuated electrically by the standard clock at the place, or direct from the observatory. The whereabouts and times of time signals are given on the charts and in the sailing directions ; full details of each signal are given in the Admiralty List of Lights and Time Signals. When observing a time signal the following procedure should be adopted. Holding the deck watch in one hand, take up such a position that the time signal is clearly visible, and about ten seconds before the signal is expected begin counting as explained (§ 141). Write down the time shown by the deck watch at the instant the ball begins to fall. Immediately proceed to the chronometer room and compare the D.W. with the .4 chronometer, and the other chronometers with the A chronometer. From these comparisons the errors of all t he chronometers may be found. Time signals are also transmitted from various high power wireless telegraphy stations, and comparison with such signals is a very con- venient method of finding the error of the chronometers, when at a phut- where no time signal exists; when using this method consideration should he paid to the table of safe distance- given in Tart IV. When 3ome considerable time must elapse between the finding of the error of the D.W. and the subsequent comparison, such as when the D.W. has to be conveyed ashore for comparison with a standard clock, consideration should be given to the following article. 143. The mean comparison. M is of no use obtaining the G.M.T., however accurately it may be done, unless it can be conveyed accurately to the chronometers. Suppose .1 has b stead} gaining rate of 7 seconds per day and the D.W. a losing rate <.i io seconds per day, it is obvious that the comparison between, them cannot remain con-taut for even an hour. When the rate arc steady, it follows that il comparisons are Art. 144. 176 made before landing, when necessary to do so to obtain the error, and again after returning, a comparison may be deduced which would be correct for any particular instant between the two comparisons actually taken; this calculated comparison is called a mean comparison, and is found as follows : — Comparison before landing : — Time by A - ..... 8^ 39 m 00* „ „ D.W. 8 24 07-2 D.W. slow on ^1 14 52-8 Comparison after return : — Time by A - - 10 h 40™ 00 s „ „ D.W. - 10 25 10-0 D.W. slow on A 14 50-0 Elapsed time between comparisons by D.W. = 2 h 01 m 03 s = 121 m D.W. time at which error was observed 9 h 57 m 20 s D.W. time of last comparison - - - 10 25 10 Elapsed time 27 50 =27™ -8 By first comparison D.W. is 14 m 52 s * 8 slow on A, „ second „ „ „ 14 50 „ „ A ; therefore in 121 m the D.W. has gained 2 s - 8 on A and in 27 s - 8 the D.W. .,. . 27-8 x 2-8 will gam - -^nri = ' " 4 • & 121 By the second comparison the D.W. was 14 m 50 s slow on A ; there- fore, at the time at which the error was observed it was h 15 m 50 s ' 64 slow on A, which is the mean comparison. 144. Error of the chronometer by astronomical observations. — To find the. error of the chronometer if there is no time signal available — that is, to find the difference between the time shown by the chronometer at any instant and the G.M.T. — necessitates our finding the G.M.T. by observation. In the case of the sun, G.M.T. = M.T.P. + Long. = A.T.P. + Eq. T. ± Long. In the case of other heavenly bodies G.M.T. = H. + R.A.*. - R.A.M.S. ± Long. From these equations we see that the only unknown term on the right hand side is the hour angle of the body. Now if we know the latitude, longitude, and altitude exactly, the hour angle of the body can be calculated as explained in § 130. The altitude of a heavenly body should be observed as accurately as possible when it is desired to obtain the error of the chronometer. Any error in the altitude not only affects the error of the chronometer deduced from the altitude, but affects every position of the ship that subsequently depends on that error. For. a similar reason the observa- tion is usually taken on shore at a place the latitude and longitude of 177 Art. 145. winch are exactly known. The altitude is not taken above the sea horizon because of the unreliability of all altitudes measured from it, but the observer has recourse to an instrument called the artificial horizon, one or more of which are supplied to each of H.M. Ships. In the event of it being impossible to go on shore the altitudes may be observed above the sea horizon, but in such a case the results must be considered as approximate only. 145. The artificial horizon. — This usually consists of a shallow rectangular trough, BC t Fig. 129, filled with pure mercury, the surface of which forms a perfectly horizontal plane, except near the edges. A ray of light from a body X is reflected from BC in the direction AO, which makes an angle OAB with the plane of the mercury = angle XAC in accordance with the law in optics " the angle of incidence is equal to the angle of reflection." An observer whose eye is at 0, sees, on looking into the mercury, an image of X proceeding apparently from the point X' along the straight %;' Fig. 129. line AO, and he measures the angle XOX', which is the observed altitude in the artificial horizon. Since fche angle OAB X'AC, the angle X'AC = XAC, so that the angle XOX' = XAX' = 2 XAC = twice the apparent altitude of A '. From this we see that, provided that fche surface of fche mercury is horizontal, an observed altitude of a heavenly body in an artificial horizon, after instrumental errors of fche sextant have been applied, is twice fche apparent altitude of fche body, and that fche dip is not involved. To obviate fche disturbing effects of wind on fche surface of fche mercury, a -h - rout'. Kig. L29, is placed over fche artificial horizon. The two sheets of glass in fche roof tit Loosely in the frame so as fco avoid the possibility of fche glass being warped due to fche unequal coefficients Of expansion Of fche metal frame and fche glass. The surfaces of fche - plates are ground ae nearly parallel as is possible, but, owing fco fche ribility of their nol being quite parallel, it is advisable fco mars one side of fche roof with a while paint mark and to fcake half fche observations x r.ios M Art. 146. 178 with this mark on the right, and half with the mark on the left; the practice varies with different kinds of observations, and this point will be dealt with further on. The artificial horizon does not admit of observations being taken when the altitude is less than 15°. When taking observations with this instrument, the eye should be in such a position that the image of the body appears in the centre of the mercury. Practical rules which should be followed when taking observations on shore for obtaining the error of the chronometer, together with remarks on the selection of the position for setting up the artificial horizon, will be found at the end of this chapter. 146. Observations in the artificial horizon. — We will now consider how the observation is taken. The observer 0, Fig. 130, sees the sun at X and sees the reflected image of the sun at X' . If U and L represent the upper limb and lower limb respectively of the sun, then U' and L' represent the reflected images of the upper limb and lower limb respectively. u Fig. 130. Suppose that an observer takes the altitude of the sun's lower limb in an artificial horizon (obs. alt. 0j. The angle measured is LOL' (Fig. 130). Now— LOL' = LAL' =2 LAC = 2 App. Alt. 0. Similarly, when the altitude of the upper limb (Obs. Alt.©) is taken, we have UOU' = UAU' = 2 VAC = 2 App. Alt. 0. Therefore, in either case, the measured angle is twice the apparent altitude of the limb observed. The observed double altitude is written D.Alt. Suppose that "observations are being taken in the morning, that is, when the altitude is increasing, then from Fig. 130 we see that, if the lower limb is being observed, the two reflected images, one L from the mirror of the sextant and the other L' from the artificial horizon, are separating; similarly, if the upper linib is being observed the two images are closing. The opposite takes place when observations are 179 Art. 146. being taken in the afternoon. This may be briefly expressed as follows : — A.M. P.M. I Closing suns - - - - U.L. \ Opening suns - - - L.L. ( Closing suns - - - - L.L. ( Opening suns - - - U.L. Attention to this rule will prevent a mistake being made as regards which limb of the sun has been observed. Observations should be taken at equal intervals of altitude as follows. Set the index of the sextant to an exact 10' of arc and call " 'top " when the contact takes place; then set the index 10' forwards or back- wards, according as the body is rising or setting; watch for the contact and call 'top " again, and so on until the set is complete. If the body is moving so fast that it is impossible to set the sextant at every 10' of arc, the observations should be taken at every 20' of arc. By following this mode of procedure, all the observations will have been taken at equal intervals of altitude and the time interval between successive observations should be nearly the same. An inspection of the time intervals between successive observations will make it plain whether the set is reliable or not. An odd number of observations should be taken to simplify taking the mean of the results. In observations at sea very great accuracy in calculation is not only unnecessary, but is a waste of valuable time when it is desired to obtain the position of the ship as rapidly as possible. In shore observations for time there is no such necessity for haste, and, as mentioned above, the accuracy of all positions subsequently obtained depends on the time. Therefore, in working out shore observations, every care should be taken that the elements and corrections are as accurate as possible, and interpolation should be made use of when taking out the logarithms. For this reason when working out these obsevations, the elements should be taken from the unabridged Nautical Almanac, one copy of which is supplied to each of H.M. Ships. In this Almanac the declination of the sun is tabulated to decimals of a second of arc ; the equation of time and the right ascension of the mean sun are tabulated to the second decimal place of a second of time. The declination and equation of time should be taken from page II. of the month, where they are tabulated for Greenwich mean noon; the right ascension of the mean bud should be taken from the column headed Sidereal Time," and should be corrected by means of the table at the end of the Almanac for converting intervals of mean solar time into equivalent intervale of sidereal time; this table La simply an extension of t hat given on page t. of the month in the Abridged Nautical Almanac for the correction of the R.A.M.S. The elements for the planets should be taken from that pari of the unabridged Almanac where they are t a hii late. I ui n ler t he heading .Me. in Time " ; the elements for t ln> stars should !><• taken from thai pari where they are tabulated for every tent h day. The double altitude observed should be corrected for index error; it should aUo he eorreefed for another instrumental error of the sextant called centering error c'.K.). The result divided by 2, as explained above, gives the apparent altitude of the limb which has been observed. The mean refraetion for this altitude should then he applied and its M 1 Art. 147. 180 correction for barometer and thermometer; the semi-diameter should then be applied, and, lastly, the parallax in altitude. It is most important that the latitude and longitude of the spot where the observations are taken should be correctly known. If the " observation spot " is used, which is a point marked on the chart whose latitude and longitude were accurately determined during the survey of the locality, the latitude and longitude of this spot will be found in the title of the chart. If any other place is selected, its position must be fixed on the chart ; this can generally be done by sextant angles, the d Lat. and d Long, between the place and the observation spot being measured off and applied to the known latitude and longitude of the latter. Observations for error of chronometer are of two lands : — (a) Absolute altitudes, by which is meant observations on one or both sides of the meridian worked in a manner similar to the " longitude by chronometer " method. (§ 130.) (6) Equal altitudes, by which is meant noting the times when the body had equal altitudes E. and W. of the meridian. 147. Error of the chronometer by absolute altitudes. — Under abso- lute altitudes are included three kinds of observations : — (a) Absolute altitudes of the sun or a star on one side of the meridian. (b) Mean of the results of absolute altitudes of the sun taken a.m. and p.m. (c) Mean of the results of absolute altitudes of stars taken East and West of the meridian. The following examples show (1) the method of working a single set of absolute altitudes of the sun and (2) the method of working absolute altitudes of stars East and West of the meridian. Example (1) :— On March 3rd, 1914, at about 8 h 5 m a.m. (M.T.P. nearly), on the Observation Spot at Aden, Lat. 12° 47' 11" N., Long. 44° 58' 31" E., the deck watch was slow on G.M.T. (approx.) 25 m 06 s . I.E., - 1' 50". Barometer, 29-7 inches. Thermometer, 87° F. The following observations were taken to determine the error of the chronometers on G.M.T. (Opening suns) : — ■ D.W. Diff. Obs. alt ,. 4 h 37 m I73 •2 20-0 49° 10' Mark right. 4 37 37 •2 21-2 49 20 4 37 58 •4 20-8 49 30 4 38 19 •2 22-2 49 40 4 38 41 •4 23-0 49 50 4 39 04 •4 20-4 50 00 Mark left. 4 39 24 •8 20-8 50 10 4 39 45 •6 20-4 50 20 * 4 40 06 •0 22-0 50 30 4 40 28 •0 20-0 50 40 4 40 48 •0 50 50 11/- - 4 429 30 •2 •75 50 00 Mean 39 02 181 Art. 147. M.T.P. 20 h 05™ 0' Mar. 2nd. Long. 2 59 54-1 (E.) G.D. 17 05 Mi D.W. 4 h 39" Slow 25 03' 06 5 04 12 00 09 00 G.M.T. approx.17 04 09 Obs. alt. I.E. 50° 00' 00' - 1 50 Dec. 7° 01' 59' -8 S. + 6 37-5 57-36 6-93 «'.!•:. 48 58 10 + 40 7 08 37-3 S. 17208 51624 34416 App. alt. © 2/49 58 50 App. alt. 24 59 25 Mean ref. - 2 05 6' 37* -5 60/397-5048 «. L D Cor. to Mean ref. S.P. 24 57 20 -f 13 12' Eq. T. ■ 14* -52 4- to A.T. + 3-60 52 6-93 1396 3465 24 57 33 + 16 09 12 18-12 -4. to A.T. 25 13 42 — 8 Parallax - 3-6046 True alt. O 25 13 50 True z 64 46 10 - 12' 47' ll'N. Lsec - 7 08 37 S. L sec 0-01091 0-00338 (L + D) - - 19 55 48 z - - - 64 46 10 t + (L + D) - 84 41 58 \ L hav 4-828437 z — (L + D) -44 50 22 J L hav 4-581367 L hav H. 9 -424094 A.T.P. 19 h 51 ro 52'-10 Eq. T. + 12 18 -12 M.T.P. 20 04 10 -22 Long. 2 59 54-1 (E.) G.M.T. 17 04 16 -12 D.W. 16 39 02 -75 Slow 25 13 -37 The fleck watch was 25 m 11* -55 slow on G.M.T. The following comparison- were made : — I tefore landing .1 7'' 11'" 00- D.W. 3 47 15-2 D.W. slow - - . . :; 23 W-8 on .1 Afti-r r.t urn on bonnl A B fc 20" 00" A i\ nir I 9 h 21" 30 D.W 6 56 13-2 B 7 14 4 11 13 10 Slow 8 23 46-8 m 2 M 15 Slow 10 08 L9-5on.fl, <"hnnp* in r'.rnpnrii^in*' between D.W. and 1 in Art. 147. 182 D.W. at 1st comparison - - - 3 h 47 m 15 s -2 2nd „ - - - - 3 56 13-2 Elapsed time by D.W. - - - 2 08 58 = 129 m D.W. at middle observation - - 4 39 02-75 D.W. at 2nd comparison - - - 5 56 13-2 Elapsed time by D.W. - - - 1 17 10-45 = 77 ra - 77,2 X2 ^l 10 129 l iy E.W. slow on A return 3 h 23 ra 46' • 8 —1-19 Mean comparison, D.W. slow on A - - - 3 23 45-61 D.W. slow on G.M.T. 25 13-37 A fast on G.M.T. ' 2 58 32-24 — 12 00 00 A slow on G.M.T 9 01 27-76 B slow on A 2 06 15 B slow on G.M.T. 11 07 42-76 A slow on G.M.T. 9 01 27-76 C slow on A - - - 10 08 19-5 C slow on G.M.T. 7 09 47 • 26 Example (2) :— On April 29th, 1914, at about 6 h 45 m p.m. (M.T.P. nearly) at Hobart, Lat. 42° 53' 22" S., Long. 147° 20' 28" E., the deck watch was slow on G.M.T. (approximately) ll h 53 m 00 s . I.E., + 1' 10". Barometer, 28-3 inches. Thermometer, 43° F. The following; observations were taken to determine the errors of the chronometers on G.M.T. : — Spica (E.). Rigel (W.). D.W. Diff. Obs. D. Alt. D.W. Diff. Obs. D. Alt 8 h 54 m 08 s -8 27-6 51° 40' 9* 02 m 50 s -8 28-4 54° 40' 8 54 36-4 28-0 51 50 9 03 19-2 28-0 54 30 8 55 04-4 27 • 6 52 00 9 03 47-2 29-2 54 20 8 55 32-0 27-6 52 10 9 04 16-4 27-6 54 10 8 55 59-6 28-0 52 20 9 04 44-4 28-4 54 00 8 56 27-6 27-6 52 30 9 05 12-4 28-4 53 50 8 56 55-2 52 40 9 05 40-8 53 40 7 /38 44-0 7 /29 51-2 8 55 32-0 71 5 April 2 10 9 04 15-89 54 10 M.T.P. - 6 h 45' 29th Long - 9 49 2P-87 (E.) April 28th G.D. - 20 56 183 Art. 147. Spica (E.). Rigel (W.). D.W. Slow • 8 h 55 m - 11 53 32 s approx. R.A. L3 h 20 m 42-03 D.W.- Slow - G.M.T. Obs. D. all I.E. C.E. - t Mn. Ref. Cor. z L 42° 53' D 8 17 9 h 04 m - 11 53 15' -89 G.M.T Obs. E I.E. - - 20 48 ». alt. 52° 10' 00' - + 1 10 32 1 F( 7 > i se< / sei hav hav H. 19 h 13 - 20 57 t.54°10' 00" - + 1 10 15-89 approx. R.A. 5 h 10 m 24' -39 C.E. • 62 11 10 + 40 Dec. L0° 43' 03* -8 S 54 11 10 + 40 Dec. 2/52 11 50 5/54 11 50 27 05 55 + 1 54 8° 17' 58"- 2 S 26 05 55 Mn. Ref. - 1 59 R.A.M.S. 2 h 22 m 27 s -18 )r20 h 3 17-13 , 48 m 7-88 , 32 s -09 R.A.M.S. Cor. - 26 03 56 + 3 27 04 01 + 3 2 b 22 m 27'-18 For20 h 3 17-13 „ 57 m 9-39 „ 16' -04 26 03 59 27 4 04 z - 63 56 01 2 25 52-28 ■ 82 55 56 2 27 53-74 L 42° D 10 53' 22' S. / 43 04 S. I ?. 0-13509 2. 0-00764 4-871432 4-437179 22" S. L i 58 S- L. sec. 0-13509 sec. 0-00457 32 z 63 10 18 56 01 34 2 62 35 55 24 56 96 31 06 19 \L 45 43 \L 97 28 31 20 20 J L hav 4-876199 32 I L hav 4 • 388844 H. - R.A. L hav 9-451341 43 m 0P-98 20 42 03 L hav H. - R.A. R.A.M.S. M.T.P. - Long. G.M.T. - D.W. - D.W. slow on G.M.T. H. 9-404703 4 h 02 m 04" • 26 5 10 24-39 R.A.M :.s. ilowonG.M.T. i-ii-' .r, alow 33 2 03 44 01 25 52-28 9 12 28-65 2 25 53-74 M.T.P Long. 6 9 37 51-73 49 21-87 (E.) 6 46 34-91 9 49 21-87 (E.) Q.M T D.W. 20 8 is 29-86 r>:> 32 00 20 57 13 04 9 04 15-89 D.W.< 11 11 :,l> 57-86 52 57-15 11 52 '.7 15 Mean 11 2/11501 52 57*5 'llif? following comparisons were miwlo : — I tefore landing — ,i D.W.- 7 :: I 00- 7 20 12-8 I >.\\'., slo* (il 47 -2. .ii I Art. 148. 184 After return — A - 10 h ll m 00' A - 10 h 12 m 00' A - 10 h 12 ra 30" D.W. - 10 06 12 B - 7 11 31-5 C 9 56 14 D.W. slow 04 48 B slow 3 00 28-5 C slow 16 16 on A Change in comparison between D.W. and A is 0-8 second. D.W. at 1st comparison 7 h 26 m 12' -8 2nd „ - - - - 10 06 12 Elapsed time by D.W. - - 2 39 59 -2 = 160 m , D.W. at mid observation Spica - Mean D.W. time of observation - D.W. at 2nd comparison Elapsed time - 07 18-06 == 67 m - 3. 67-3 X -8 __ 160 D.W. slow on A on return - - - - h 04 ra 48 s 2 39 59 -2 : 8 h 9 55 m 04 32° 15-89 2/17 59 47-89 8 10 58 06 53-94 12 1 07 18-06 34 11 04 52 47-66 57-5 11 3 48 00 9-84 28-5 2 48 38-34 11 48 16 9-84 16 04 25-84- Mean comparison D.W. slow on A - D.W. slow on G.M.T. .... A slow on G.M.T. B slow on A B slow on G.M.T. A slow on G.M.T. C slow on A C slow on G.M.T 148. Errors involved in absolute altitudes: Absolute altitudes on one side of the meridian. — In this observa- tion the following errors are involved : — Instrumental error, shade error, roof error, error due to irradiation, error due to abnormal refraction, and personal error. Instrumental error. — This includes all unknown errors of the sextant, and its effect cannot be eliminated. Shade error. — This is due to the fact that the two rays, from the horizon glass and artificial horizon, pass through different shades before reaching the eye, and these shades may have different errors. The possibility of shade error is avoided by using a dark eye-piece on the telescope, for both rays will then be affected in the same manner whatever may be the error of the eye-piece. For this reason a dark eye-piece should always be used when taking these observations in preference to the sextant shades. Roof error. — This is due to lack of parallelism between the face of the glass used in the roof of the artificial horizon, and may be eliminated by reversing the roof of the artificial horizon half way through the set of observations. 185 Art. 149. Error of irradiation. — This is due to an optical illusion, strongly illuminated objects on a dark ground appearing much larger than they really are. This error is eliminated by taking two sets of observations, one of the upper limb and one of the lower limb, working each separately and taking the mean of the results, and by using the darkest eye-piece through which the limb of the body can be clearly distinguished. Error due to abnormal refraction. — This cannot be eliminated. Personal error. — This is due to a peculiarity of habit of the observer and cannot be eliminated. Mean of the results of absolute altitudes of the sun taken a.m. and p.m. — We have seen above that the instrumental error, and the error due to abnormal refraction, cannot be eliminated in absolute altitudes on one side of the meridian ; if, however, absolute altitudes are taken on both sides of the meridian when the sun has about the same altitude, these errors to some extent cancel one another. Mean of the results of absolute altitudes of stars taken East and West of the meridian. — The most accurate results are obtained from absolute altitudes of two stars, one East and the other West of the meridian and of about the same altitude, the interval between the observations being as brief as possible. The effects of errors in this and in the preceding case are as follows: — Instrumental error. — This has an approximately equal and opposite effect on the error of the deck watch obtained from the two observations, and therefore nearly disappears in the mean of the results. Roof error. — When observations are taken on both sides of the meridian, it is unnecessary to reverse the roof of the artificial horizon half way through each set of observations ; but the observer should be careful to note that the mark on the roof is in the same relative position at each observation, i.e., mark right or mark left a1 each observation. Abnormal refraction. — This has an equal and opposite effect on the error of the deck watch at the two observations, provided that the at mospheric conditions have no1 changed. For this reason the econd of the above two methods of obtaining the error of the chronometers is regarded as the more accurate. Personal error. — The personal error cannot be eliminated. 149. Error of the chronometer by equal altitudes. To ascertain the error of the chronometer as exactly as possible with -extant and artificial horizon, we must endeavour to gel rid of the instrumental and other errors, and this is attained l>y observing a1 equal altitudes East and \\ i i of the meridian. It will be evident thai whatever be the instru- mental and other errors, supposing them to remain unaltered, the middle time between the ob ervations will be tin same; f<>r whatever tend make the observed altitude more or le in the forenoon will act in the same manner in the afternoon, and a- we do nol want to knoTH what ih.it altitude is, bul men ly to en ure that it is the same l.m. and p.m., the amount of the error i immaterial. The method of equal altitudes therefore should be used whenever we wish to get the error very exactly. Art. 150. 186 Equal altitudes of the sun can be taken either in the forenoon and afternoon of the same day so as to find the error at noon; or in the afternoon of one day and the forenoon of the next to obtain the error at midnight. Theoretically these two are equally correct, but it is better to get the error at noon because in this case the elapsed time is less and gives less latitude to the chronometers and deck watches for eccentricity. The principle of finding the error of chronometer by observation of equal altitudes is that, as the earth revolves at a uniform rate, equal altitudes of a body on either side of the meridian will be found at equal intervals from the time of the meridian passage of the body, and there- fore the mean of the times of such equal altitudes gives the time of the meridian passage. In the case of stars, the declinations are practically constant, so that this is strictly true, and the calculation of the error of a chronometer is confined to taking the difference between the mean of the times shown by the chronometer and the calculated time of the meridian passage (§ 125 (6)). Thus, let t x be the time by the chronometer at the first observation, and t 2 the time at the second, then 1 "T 2 is the chronometer time of the meridian passage of the body, which, compared with the true time of meridian passage (R.A.^f — R.A.M.S.) gives the error of the chrono- meter at the time of the meridian passage of the body. In the case of the sun, however, the declination is constantly changing ; the altitudes are thereby affected, and an altitude equal to that observed before meridian passage will be reached after meridian passage, sooner or later according to the direction of the change in declination. It is therefore necessary to make a calculation of the correction resulting from the change in declination, to be applied to the middle time in order to reduce it to apparent noon. This correction is called the " equation of equal altitudes." 150. Formula for the equation of equal altitudes. — In Fig. 131, let X x and X 2 be the true places of the sun at the times of the a.m. and p.m. observations respectively, and let (D -f- dp) and (D — dp) be the declina- tion's at those times, dp being the change of polar distance (or declination) in seconds of arc in half the elapsed time. Let the celestial meridian PA bisect the angle X X PX 2 , then if t x and t 2 are the chronometer times at the two observations, the sun will «be on the meridian PA when the chronometer time is 1 2 , and therefore, if we apply the angle APS to the mean of the chronometer times, we obtain the chronometer time at which the sun is on the meridian of the observer. This angle APS is the equation of equal altitudes and will be denoted by e. Let ZPX 3 be a triangle equal in all respects to ZPX V then since PS bisects the angle X X PX 3 and PA bisects the angle X 1 PX 2 , e = \ X 2 PX 3 . Let PX be a celestial meridian bisecting the angle X 2 PX 3 ; let X 2 X 3 be the arc of a small circle whose centre is Z and intersecting the celestial meridian PX in X, then e = XPX 2 or XPX 3 . 187 Arts. 151, 152. Since PX is the mean value of PX 2 and PX. 3 , the declination of X is D, which is very nearly the declination of the sun at apparent Noon. Let the parallel of declination through X intersect PX 2 in K ; then, since the triangle XKX % is so small, it may be considered a plane triangle right-angled at K, and we have e = XPX 2 -- ■■ XK sec D KX» cot KXX sec D = KX 2 tan ZXK sec D .'. e = dp cot PXZ sec D ; or, if e is expressed in seconds of time dp 15 cot PXZ sec 2). Therefore the time shown by the chronometer at the instant when the sun is on the meridian of the observer is dp 16 *»""*■- : cot PXZ sec D (seconds). When applying the equation of equal altitudes to the mean of the chronometer times, care should be taken to give dp and cot PXZ their proper algebraical signs, dp being positive when the polar distance is increasing, and vice versa. 151. Errors involved in equal altitudes.- The effects of errors in this obscrwif ion arc llic same as in the case of Stars observed Kast and West of the meridian, except as regards the instrumental error, which has do <-ti<-'( provided that it has remained constant in the interval between t be "i' en ations. 152. Example of error of chronometer by equal altitudes.— Example: - Qn April 28th, 1914, at Zanzibar, Lat. b°09' 43" S., Long. 39° 1 1' 08* E., Art. 152. 188 the following observations of the sun were taken to determine the errors of the chronometers on G.M.T. : — A L .M. P.M. D.W. Diff. Obs. alt.O D.W. Diff. Obs. alt lh 33ir 1 52 s . 8 21-6 68° 10' 8 ! ' 28 m 54 s -0 21-6 69° 50' 1 34 14-4 21-6 68 20 8 29 15-6 22-0 69 40 1 34 36-0 22-0 68 30 8 29 37-6 21-2 69 30 1 34 58-0 21-2 68 40 8 29 58-8 21-6 69 20 1 35 19-2 22-0 68 50 8 30 20-4 21-6 69 10 1 35 41-2 21-2 69 00 8 30 42-0 21-2 69 0) 1 36 02-4 21-6 69 10 8 31 03-2 22-0 68 50 1 36 24-0 21-6 69 20 8 31 25-2 21-2 68 40 1 36 45-6 22-0 69 30 8 31 46-4 22-0 68 30 1 37 07-6 21-2 69 40 8 32 08-4 21-6 68 20 1 37 28-8 69 50 8 32 30-0 68 10 11/392 30-0 11/; 337 41-6 1 35 40-91 8 30 41-96 Comparisons A.M. :- Before landing- A. - - D.W. D.W. slow A - D.W. D.W. slow ns between D.W. mparison comparison ' D.W. - and 4 h 33™ 00' 27 49-2 4 05 10-8 on A After returning- 6 h 2 47 m 00 s 41 50-4 4 05 09 -6 on A Change in compariso D.W. at first co: D.W. at second A is 1-2 seconds. h 27™ 49 8 -2 2 41 50-4 Elapsed time hx 2 14 01-2 = 134 D.W. at mid comparison - D.W. at 2nd comparison - Elapsed time by D.W. l h 35 m 40-91 2 41 50-4 1 06 09-49 - 66 ra -l 66-1 x 1-2 "134 59 ! D.W. slow on A on return Mean comparison A.M. D.W. slow D.W. at mid observation - Mid observation by A 4 h 05 m 09'-6 •59 4 05 10-19 on A 1 35 40-91 5 40 51-1 ISO Art, 152. Comparisons at apparent noon : — A ■ 9" 09 m 00- D.W. - 5 03 51-8 Slow 4 05 08-2 .4 - 9 h 10 m 00' -4 B - 7 11 46-5 C Slow - 1 58 13-5 Slow 9 h 10 m 30' 6 05 29-0 3 05 01-0 on ,4 Comparisons P.M. : — Before landing — After returning — ■ .4 D.W. - - 11" - 7 31™ 25 00 s 53-2 D.W. slow - - 4 05 06 • 8 on .4 .4 D.W. - - l h - 9 4(i m 40 00' 54-8 D.W. slow - - 4 05 05 • 2 on A Change in comparisons between D.W. and A is 1 • 6 seconds. D.W. at 1st comparison D.W. at 2nd comparison Elapsed time by D.W. D.W. at mid observation D.W. at 2nd comparison Elapsed time by D.W. 7 h 25 m 53 s -2 9 40 54-8 2 15 01 -6 = 135" gh 30 m 4 p. 96 9 40 54-8 1 10 12-84 = 70 m -2 70-2 X 1-6 135 83" D.W. slow on A on return Mean comparison p.m., D.W. slow D.W. at mid. observation - Mid. observation by A A.T.P. Long. (appx 24" 2 00 m 36 00' Apl. 27tb. 44-53 (E.) G.A.T. Eq. T. 21 ■) 23 - 2 15-47 G.D. 21 21 Apl. 27th G.A.T. Eq. T. 21 h 23 ra - 2 l.V-47 27 04 Q.M.T. 12 20 48-43 Dec. 4 h Q 5 m 05 ,. 2 •83 4 05 06-03 on A 8 30 41-96 35 47-99 13° 58' 21'- 1 N. -2 06-1 47-60 2-65 13 56 15 N. 23800 28560 9520 60/126-1400 2'06'-l Eq. T Mj'l. observations a.m. by A Mid. ol i r- a( Lon - p.m. by 1 time by i lapsed 1 ime by .1 - 2 28" - 1 •117 •03 - t( 2 27 04 t< 6* 40 2 36 51' 17 ■ 10 •'.tO to A.T to A.T. ■: we have dz = XY sin KXY = XY cos PXK = XY sin PXZ cos L sin A = 17 where A is the azimuth of the body. .*. dz = dH cos D cosD ' cos L sin A cos D = dH cos L sin A. Therefore if dH is expressed in seconds of time andjcfo in minutes of arc we have dz cos L sin A dH = ~T~ This is the speed of the body in altitude, expressed in minutes of arc per second of time. When the altitude of a heavenly body changes 5' (10' of double altitude on the sextant) in 35 seconds of time, that is when the speed is r — •, satisfactory results are obtained, and when there is any choice, 193 Art. 154. observations of bodies whose speed is less than this should not be taken. Therefore, from the formula, we have cos L sin A . . , I - is not less than - 4 7 or .v . . , , 4 sin A is not less than sec L. To summarise these three conditions : — The altitude of the body should lie between 15° and 60°, and if A is the azimuth of the body, A should be as nearly 90° as possible, and in no case should sin A be less 4 than - sec L. In the winter in moderately high latitudes the sun will not fulfil the conditions above, but stars can always be found which will more nearly do so. In England and corresponding latitudes the sun is useless for some months, and at midwinter its altitude is so small that it cannot be observed in the artificial horizon even when on the meridian. In Inman's Tables there is a table which gives the hours, depending on the latitude and declination, between which it is possible to take observations of the sun in an artificial horizon for error of chronometer, having regard to the conditions stated above. When about to take observations, select a place remote from traffic and sheltered as far as possible from the wind ; the ground should be -olid or the mercury will tremble; avoid artificially made ground. If possible use the observation spot given on the chart; if not, fix your position by sextant angles and station pointer, plot it on the chart, and then measure off its exact latitude and longitude. When selecting a place for observations on both sides of the meridian, do not go so close to buildings, trees, or hills which may obscure the body when at the required altitude on the other side of the meridian. See that the horizon trough is clean and free from dust ; place it in the direction of its shadow (if using the sun), and put the roof over it except at one end. Remove the cover and screw-plug from the mercury bottle and screw the cover on again ; put a finger on the hole, invert the bottle and keep it in this position for a time so as to allow the scum and impurities to rise through the mercury; then fill the trough, but do not pour in all the mercury or the scum will flow in also and cloud the surface ; then put the roof on properly. When packing up a mercurial artificial horizon, put the mercury bottle in the wooden box before lifting up and emptying the trough; if any mercury is spilled, it is then caught in the box and can be recovered. Before taking observations remove any existing side error (Part W., Chapter KXVI1I.) from the sextant, and take and record the index error. It taking index error on any occasion when the sun is low, measure the diameter between the right and Left limbs, and not between the upper and lower limbs, on account of refraction. For 'he -mi age the inverting telescope with the highest power eye- piece; the bigger the sun's image appear in the telescope the better can a contact of the limbs be observed. The loss of light due to a high power i of no importance. Bring tin- images together roughly before orewing in the telescope, and see that the tangent '-ivu ha been run hack in the right direction. x 6108 N Art. 155. 194 The image which moves in the field of view when the index bar is moved is the reflected image ; if this is above the direct image when using the inverting telescope, you will be observing the upper limb, and if below, the lower limb, whether the body is rising or setting. Take sets of upper limbs and sets of lower limbs alternately and take an equal number of sets of each ; this obviates the effect of irradiation (§ 148). Seven, nine or eleven is a good number of observations to take in a set. At the end of each set of observations look at the deck watch and see that the right minute has been written down. Twilight is the best time to observe stars if suitable stars can be found ; for if it is dark a lantern or light is required by the time-taker, and this is liable to disturb the observer's vision. When getting a star down it is best to approach very close to the artificial horizon, as there is then less chance of observing the wrong star. It is often useful to calculate what the altitude of the star, will be and to set twice that altitude on the sextant. A star has no appreciable diameter, and the contact occurs when the reflected and direct images flick across one another. The surface of the mercury in the artificial horizon is perfectly horizontal at any place where the direction of gravity (the plumb line) is normal to the earth's surface at that place. In the immediate neigh- bourhood of mountains the direction of gravity slightly deviates from the vertical, and the surface of the mercury is consequently not truly horizontal ; therefore such a locality should be avoided when observations with the artificial horizon are required. 155. The rate of the chronometer. — As regards the rate of the chronometer, it would at first appear that it is only necessary to obtain errors at the same time on two successive days, and that the difference between these errors would be the daily rate. This would be so if we were able to guarantee that the errors found were exactly correct, but as each may be inaccurate by some small amount, it is obvious that the resulting rate would be vitiated by the sun or difference of the inaccuracies in the errors. For this reason we obtain the errors at an interval of some days, and the resulting rate will then only be in error by the sum or difference of the inaccuracies of the observed errors number of days. Thus it appears that to obtain the rate as accurately as possible the interval between the observations should be large. This would be true if the chronometer were always to maintain a steady rate, but the rate of a chronometer seldom remains steady for many days together; it varies with change of temperature, and is often different according as the ship is at sea or in harbour. Taking the above into consideration, it is generally accepted that the interval between observations for error of chronometer, in order to obtain the rate, should not be less than six days or more than ten days. To obtain the rate as accurately as possible, the observations should be taken in such a manner that the sum or difference of the inaccuracies in the observed errors is as small as possible. It is obvious that, if the 195 Art. 155. inaccuracy of each error is in the same direction, the resulting rate will be in error by the difference of the inaccuracies in the observed errors number of days, and the observations should therefore be taken in such a maimer that the inaccuracies are likely to be in the same direction. For this reason, the two observations for a rate should always, if possible, be of the same nature, and it would be imprudent to obtain the rate from the difference of the errors obtained by absolute altitudes a. m. on one day and absolute altitudes p.m. on another day, for in such a case the rate would probably be in error by the sum of the inaccuracies in the observed errors number of days. To illustrate the above, suppose that the error of the chronometer was found from absolute altitudes a.m. on March 3rd, and that equal altitudes of the sun were observed on March 10th. The error of the chronometer on March 10th was found in the ordinary way from the equal altitudes, but the rate was found from the difference between the error calculated from the absolute altitude taken on March 3rd. and the error found by working the a.m. set of observations taken on March 10th as absolute altitudes. It is important that the interval between the observations, often called the epoch, and expressed in days, should be determined as accurately as possible. When observations are taken at different places, it should be remembered that the difference of longitude is involved, and consequently it should always be made a practice to find the epoch from the Greenwich dates, thus : — Epoch = G.D. 2nd observation — G.D. 1st observation. Example. : — On March 3rd, 1914, at about 6 s 45 m p.m. (M.T.P. nearly) at Yokohama. Long. 139° 39' 13" E.. a chronometer was found to be slow on G.M.T. 3 h 14 m 57 s -34 (from observations of stars E. and W. of the meridian). On March 11th, 1914, at about 6 h 15 m a.m. (M.T.P. nearly), at Honolulu, Long. 157° 51' 53" W., the chronometer was found to be slow on G.M.T 3 b 15"' 14 s - 71 (from similar observations). Required the rate of the chronometer. \8t error. 2nd error. M.T.P. 6 1 ' 45 ,n Mar. 3rd. M.T.P. 18 h 15 m .Mar. 10th. Long. 9 18 36' -9 (E.) Long. 10 31 27" -5 (\V.) G.D. 21 26 Mar. 2nd. 28 46 Mar. 10th. 24 00 G.D. 4 46 Mar. 11th. G.D. at 2nd Obe'n 11" 04 h 46" Error at 2nd Obs'n. 3 h 15" 11 7 1 G.D. at 1st Obe'n. 2 21 26 Error at 1st Obs'n. 8 14 »7 -34 Epoch - - 8 07 20 Accumulate! rate 17-37 = 8-306 days. 17*87 I >aily rate s . ., )l( . 2 09 1 leoouda I N 1' Art. 156. 196 PART H.— PILOTAGE. CHAPTER XVII. THE ADMIRALTY CHART AND ARTIFICIAL AIDS TO NAVIGATION. 156. Coasts. — In Part I. navigation has been treated without special reference to dangers, such as rocks, shoals, &c. ; that part of navigation which is particularly concerned with the conduct of the ship when in the neighbourhood of such dangers is called pilotage, and will be dealt with in the two chapters comprising this part of the book. To conduct a ship in the neighbourhood of dangers, that is to pilot a ship, necessitates a knowledge of the coasts, dangers, and artificial aids to navigation such as buoys, fights, and fog signals. The coasts of countries take various forms ; a coast may consist of vertical cliffs with deep water adjacent to them so that the coast fine is very sharply defined, or it may be low with the adjacent water very shallow and the coast line indefinite. Between these two extreme forms there are many others too numerous to mention. On approaching land it is important to be able to recognise the coast which may come into view. To facilitate this, the nature of the coast and the prominent features of the adjacent land are indicated on the chart by a system of conventional signs and abbreviations, as shown below : — &J& ffhiffh,) >(360) Steep coast. Islands and Rocks. The figures within brackets express the heights in feet above the level of high water of an ordinary spring tide, or above the level of the sea in cases where there is no tide. Cliffs. Sandy shore. Stony or shingly shore. DrieaSfl Dr.3ft. -.V Dries 2 it: Rocky ledges and isolated rocks, dry at low water of ordinary spring tides. The underlined figures, on the rocks which uncover, express the heights in feet above the level of low water of ordinary spring tides unless otherwise stated. 197 Art. 156. Breakers along a shore. Dr.zn.i A .*»•; .-&■ %%* *.* § Z>ri<"#2rt. ^ Stones, shingle, or gravel, dry at low water of ordinary spring tides. Mud banks, dry at low water of ordinary spring tides. *> Sand and gravel, or stones, dry at low water of ordinary spring tides. Sand and mud, dry at low water of ordinary spring tides. .«A % i'*w„ *& I i >ra1 reefs, -* - - rapy, marshy, i >r most} land. Drir*m Sandy beach and banks, dry at low water of ordinary spring tides Sand hills or dunes. Cultivated land. Firs Paltns Casuarums Trees. Mangroves. * \COOQEZ1. Towns, villages, or houses. Villages or houses. * ( 'hurehes or chapels Temples. Windmills. Triangulation Station. • • I :. iron, chin m. \ . flagstaff, «>r other axed point. Roi Track or \'t ic itpath Railway I ramwaj i — — l ■ - Art. 157. 198 The configuration of the land is shown on the charts by the heights of various points, the heights of the summits of prominent hills and other elevated points being shown by figures within brackets. Heights given on the charts are those above the level of high water of ordinary spring tides, unless otherwise stated in the title of the chart. On some charts the configuration of the land is delineated by means of contour lines, which are lines drawn through all points of the same height on the same undulation. These lines are drawn for various heights, the difference between any two consecutive lines being the same, so that the proximity or otherwise of the contour lines indicates at a glance the slope of the land. Views of prominent points, entrances to harbours, &c, are shown on some charts; the positions from which the views are taken are also shown. Views are shown in Fig. 142, Chapter XVIII. (page 251). 157. Dangers. — In the vicinity of coasts (and sometimes at a con- siderable distance from them) small isolated rocks frequently exist, some of which are well above the surface of the sea while others are just below it, or at one time above and at another time below it according to the state of the tide. An indication of submerged rocks is sometimes given by the presence of kelp or seaweed on the surface of the water. Rocks and dangers, with the floating beacons, &c, which sometimes mark them, and reported dangers, called vigias, are shown on the charts by means of the following conventional signs and abbreviations : — * or {*•: Rock awash at low water of ordinary spring tides. .'ei'- Wreck ■&..< (1311) Wreck, the depth over which is known. ♦ or (V: Rock with less than six feet of water over it at low water of ordinary spring, tides. On small scale charts this symbol is used for rocks with greater depths of water over them. ( * " : 'c! «fc • • • • ••-...♦♦ *.-■*. e y Rocks with limiting danger lines. Rock or shoal, the position of which is doubtful. (*)e.d Qe.d Reported rock or shoal, the existence of which is doubtful. ... Wreck, J * L (I9H) Wreck, partially or wholly submerged, the depth over which is unknown. «s (F '""////, 'limn, Fishing stakes. Kelp. jo. i till 1.1 I 1 I t 1 Fixed or floating beacons. Light vessels or floats. The actual position of a floating beacon or light vessel is the centre of the water line as depicted on the chart, and is often marked by a small circle. 199 Arts. 158, 159. 158. Depth of water. — The depth of the water at any spot, as found from the soundings taken at the time of the survey, is indicated by a number which shows the depth in feet or fathoms (as stated in the title of the chart) when the level of the surface of the water is at a certain height. This level or datum is that of the surface of the water at low water of ordinary spring tides, unless otherwise stated in the title of the chart. A bench mark is a mark on a dock wall, or in some convenient position, to the level of which the datum of the soundings may be referred in case of necessity. When a sounding is taken and the bottom is not reached by the lead the depth to which the lead actually descends is shown thus ^o* , which indicates that the bottom was not reached at depths of 70 fathoms and 100 fathoms respectively. If a line is drawn on the chart through all points at which the depth is the same, the line is called a fathom line. Fathom lines for different depths are indicated on the chart as shown below. Siqnxfle* 1 fathom, line Aim'Uni «n iv''-'" f v. ■;-,- ■!■'■;■. ■ • ** -* » ^.-W v,v,.A'A..v-.* . . .rt*rtWii\* 4..,,.... .... - - a - ,- Jo « , „ 20 m „ so 159. Quality of the bottom. — The quality of the bottom at any spot, as found when soundings were taken, is printed in an abbreviated form below the number which indicates the depth at that spot ; the abbrevia- tions for the various qualities of the bottom are shown below : — Quality of the bottom. b ... blue gy • •• grey s ... sand blk . . . black sc ... scoriae br ... brown h ... hard sft ... soft brk ... broken sh ... shell i ... large shin ... shingle c ... coarse lv ... lava sm ... small cal ... calcareous It ... light sp ... sponge chk ... chalk spk ... specks. choc ... chocolate m ... mud Speckled (in ... cinders mad ... madrepore st ... stones cl ... clay man ... manganese stf ... stiff crl ... coral ml inns . . . marl ... mussels St k ... sticky d ... dark t ... tufa di ... diatom oys ... oysters « oy. ... ooze Vol ... volcanic f ... fine for ... foraminiftra peb ... pebbles w ... white P< ... pteropod wd ... weed - r ... gravel pum ... pumice gl ... globigerina y ... yellow gn ... green r ... rook grd ... ground r.i'l ... radiolaris Art. 160. 200 The quality of the bottom, as indicated by the arming of the lead when a sounding has been taken, may be of considerable value in estimating a ship's position. When a spot is to be selected at which to anchor a ship consideration should be given to the quality of the bottom as shown by the abbrevia- tions on the chart ; thus it is inadvisable to anchor a ship where the bottom is shown as rocky or hard, because of the risk of breaking the anchor, or of the anchor not obtaining a firm hold on the bottom. Good holding ground such as mud, clay, or sand should be selected when possible. On many charts the most suitable places for anchoring large and small vessels are shown by means of the following signs : — Anchorage for large vessels ... ,+, 3 j yj Slllcill * y ••• ••• ••• Hf \JL* 160. Tides and tidal streams. Currents. — Full information regarding these matters is given in Part III. The following abbreviations are used on the Admiralty charts : — H.W.F. & C.LX> 25™.. .High Water Full and Change. The hours are expressed in Roman figures, except 2 h . Equin 1 Equinoctial. m minutes. F1. 5 fl Flood. Np Neap Tides. *H.W High Water. ford ordinary. •j-H.W.O.S High Water, Q r Quarter. Ordinary Springs. Sp. Spr Spring Tides. h hour, hours. kn knot, knots. , ~ *L.W Low Water. -TT^} Current. •j-L.W.O.S LowW T ater, Flood Tide Stream. Ordinary Springs. ,. Ebb Tide Stream. M.H.W.S Mean High Water Springs. M.L/W.S Mean Low Water Springs. * H.W. or L.W. always refers to Mean High Water or Mean Low Water of Spring Tides, unless otherwise stated. t These terms will not appear on new charts or new editions of charts published subsequent to June 1914. The period of the tide, at which the streams are running in the direction of the arrows, is denoted as follows : — (1) 1 st Q r ., 2 nd Q r ., &c. for the Quarters of each Tide ., o^qp ™* t> . „ (2) ]>, IP*, IIP, &c. for l*t, 2 "d 5 3rd ^ _^ •__ hours after High or Low Water (3) Black dots on the arrows, the number of hours after High or Low Water. (The reference being to High or Low Water in the locality, unless otherwise stated on the chart) 3 hours after High Water, and 3 hours Ebb are both indicated by . .. . 4 hours after Low Water, and 4 hours Flood ' are both indicated by The Velocity of Currents and Tidal Streams is + . 1 hn **,. ^X?, . expressed in knots, thus : — The Rise of Tide is given above the Datum of the chart. The Datum to which soundings are reduced, unless otherwise stated, is approximately Mean Low Water of Spring Tides. 201 Art. 161. 161. General abbreviations. — Besides the abbreviations which have been enumerated above there are a number of others, of a general character, which are given on the charts as shown below :— General Ajbbre\ cations. A. (Agios) ....Saint (Greek) Fl ne . (Fluene) Sunken Rocks (Nor- ab 1 about wegian) Anch p Anchorage F ,n . F mB Fathom, Fathoms Anc* Anci< nt F.S Flagstaff Approx Approximate f*., ft foot or feet Arch Archipelago F l Fort %'•;•' ; ? 1 ay \ B ,H uk . , G a . (Gawa) ...River (Japanese) *• ( 5f Se) , Shoal (FrenC ? ) G*., G*.. (Grand) Great (French) B". (Bana) ...( ape or point , (Gunong) Mountain (Malay) (J»P— ) Gt J (Gusong) Shoal (Malay) ' mt ..Jttattery Goyt Government Bg - < Bei «) ( -;r DnTcM crman) Grd - ( Gn,nd) shoaj (German) - i5v t>w I tape (Dutch) (Norwegian) ] *Vl • 5 anl V U1 t S Gt.,Gr' Great BM - ( A) Bench Mark ( Great Trigonometrk . al B".,Bn- Beacon, Beacons GTg j s , Station Bo. (Bogha) Sunken Rock (Gaelic) d lii\ B'. (Besar) ...Great (Malay) [ } Br Bridge n > nrs hour, hours B<. (Bukit) ...Hill (Malay) Ha - (Hana) ...Point (Japanese) H (1 Head (' Cape H»\ (Holm) ..Island c as Castle H no .(Holmene)Islands (Nor- Cath Cathedral wegian) C.G Coast Guard H n Haven Ch Church or Chapel Ho House Chan Channel H r Harbour, Higher ( '' Chimney 1 p Island, Islet r,,,ls I ,lc Conspicuous l8 Islands, Islets r,,v Covers, Covered in j h Cr Creek J., Jeb. (Jebel) Mountain (Arabic) J) Doubtful J 8 - (Jima) ....Island (.Japanese) dist distant Jea*. (Jezrirat) Island (Arabic) Dr " flr |)| " * Kk. (Kampong) tillage (Malay) _ ., ,_.. ... K«. (Karang) Coral Reef (Malay) :, B». (Eilean) Maud, [dands RI (Kechil) ... Small (Malay) " Eil n . J (Gaelic) K.D Existence doubtful L Lake Lock. Lough Ens" ( Ensenada | Bay or ( Ireek (Norwegian | (Spanish) L . (Lilla).... j ,„,,,. Estab* Establishment Lit i Est . | Estero)E8t nary (Spanish) I- I Lagoon F. (Fiume) ...River (Italian) Lag" F' 1 Fiord (Norwegian) Lai Latitude Fl. (Flu.) Sunken Rock (Nor L.B Life Boat wegian I L.B.S Life Boat Station Art. 162. 202 T d f Leading (Lights or Beacons) \ Landing (Place) L e ., L es Ledge, Ledges Long Longitude L r Lower L.S.S Life Saving Station L l . Ho. Lighthouse L l . Ves Light vessel m miles, minutes rain minutes Mag Magnetic Mag z Magazine Mid Middle Mon* Monument Mony Monastery MK, M te Mountain M th Mouth N° Number Obs n . Spot + Observation Spot Obsy Observatory Occas 1 Occasional Off Office Ord Ordinary P., Pto Port, Porto, Puerto Pag Pagoda Pass Passage P.D Position doubtful Pen la Peninsula Pt Peak P°. (Pulo) ....Island (Malay) P.O Post Office Pos n Position Promy Promontory Prov 1 Provisional P*., P ta ., P te . Point P. A Position approximate Pv River R.C Roman Catholic R f Reef R d ., R ds Road, Roads Rem ble Remarkable Rk.,Rks Rock, Rocks R.S Rocket Station Ru. (Rudha) Point (Gaelic) Ru Ruin Ry Railway S^ < s seconds St.', S*!, S'o. } Saint f (Sima or Shima) Island J (Japanese) S a . "] (Serra or Sierra) Mountains |^ (Spanish) S d Sound Sem Semaphore S.B Submarine Bell Sg., Sg r . (Sgeir) Rock, Rocks (Gaelic) Sh Shoal f(Sidi)...Tomb (Arabic) J (Sungi) River (Malay) (Saki) ..Cape or Point (Japanese) Sig Signal Sk ne . (Skierene) Rocks (Norwegian) Sk r . (Skar or Skier) Rock (Norwegian) St. (Stor) Great, Street (Norwegian) St n Station Str Strait S.F.B Submarine Fog Bell Tel Telegraph Tempy /Temporary ( lemporarily Ts. (Tanjong) Point (Malay) T k . (Telok) ...Bay or Cove (Malay) T r ., T« Tower Ujg. (Ujong). Cape or Point (Malay) Uncov Uncovers, Uncovered V a . (Villa) ....House or Town Var 11 Variation Vel Velocity Vil Village Vol Volcano W. (Wadi) ...River (Arabic) Wh f Wharf W.T. Wireless Telegraph Station Y a . (Yama)... Mountain (Japanese) Y ds . ." Yards Z'. (Zaki) Cape or Point (Japanese) 162. System of buoyage in the United Kingdom.— The positions # of rocks and shoals are generally indicated by buoys. The shape and colour of a buoy depend on its position relative to the danger which 203 Art. 162. Black. Fig. 133. Red and white chequers. Fie. 134. it marks, and buoys should be used so as to conform to the following rules : — A By the term starboard hand is meant that side which will be on the right hand when going with the main stream of flood tide, or when entering a harbour, river, or estuary from seaward. T>\ the term port hand is meant that side which will be on the left hand under the same circumstances. Starboard hand buoys, that is buoys which mark the starboard side of a channel as above defined, show the top of a cone above water and are called conical buoys; they are painted one colour; in England, red or black; in Scotland and Ireland, red only. In order to distinguish readily particular starboard hand-buoys in a channel, certain of them are sur- mounted by a topmark, consisting of a staff and one or more globes as shown in Fig. 133. Port hand buoys, that is buoys which mark the port side of a channel as above defined, show a flat top above water and are called can buoys ; they are painted as follows : — in England red and white or black and white, showing chequeis or vertical stripes, Figs. 134 and 135; in Scotland and Ireland, black. These buoys are distinguished by a topmark consisting of a staff and cage as shown in Fig. 135. Buoys on the same side of a channel are distin- guished from one another by names, numbers, or letters. A middle ground, which is a shoal with a channel on either side of it, has its ends marked by buoys ^P which show a domed top above water ; these are called spherical buoys and are coloured with hori- ^^^^^ zontal stripes. A spherical buoy surmounted with a ^^^^^\\ staff and diamond (Fig. 136) marks the outer end of a middle ground, and a spherical buoy surmounted by a staff and triangle marks the inner end. There are various other buoys which are used for special purposes, as shown below : — Black and white it ical stripes. Fig. 135. Black and white horizontal >t ri] es. Pig. 136. Shape and colour. Name Where used. Remarks Pillar buoy Spar buoy. Watch buoy. Generally to Generally carries mark a fair- a light. \\a\ in a channel. In s ]> e e i a 1 posit ions. In vicinity of To indicate to lightships. lightship keep ers if their \' el i< main- taining its position. Art. 162. Shape and colour. Name. 204 Where used. Remarks. Telegraph buoy. Over a telegraph cable. Green. Wreck buoy. Near a wreck. Moored on that side of the wreck which is nearest mid- Green, channel. Spoil ground To mark limits By a spoil ground buoy. of a spoil is meant an area ground. where dredgers and hoppers discharge. Yellow and Green. These buoys are not for the purposes of naviga- tion, and may be of any shape. Any buoy may carry a light, an automatic whistle, or a bell. A wreck may be marked by a wreck-marking vessel which is painted green with the word wreck painted in white letters. A wreck marking vessel carries three balls suspended from a yard, two in a vertical line from one yardarm and one from the other, the single ball being on the side next the wreck. By night such a ship carries three fixed white lights similarly arranged but does not carry the ordinary riding light. It is manifestly impossible that any reliance can be placed on buoys always maintaining their exact positions. Buoys, especially when in exposed positions, should therefore be regarded as warnings and not as infallible navigating marks, and a ship should always, when possible, be navigated by observations of fixed objects and not by buoys. The lights shown by buoys cannot be implicitly relied on, because if they happen to be extinguished a long interval may elapse before they are relit, particularly in bad weather. Buoys are depicted on the charts as shown below : — LightBuoys _£ & A Bell Buoys £ / JQL .EL JgL Can Buoys B w H I M- M JB. HS V.S Cheq / A A A Conical Buoys [ * ™ * J I A j! A H.S V.S Cheq Spherical Buoys j© -Q Buoys with Topmarks Q 0- i X I Spar Buoys J. J Mooring Buoys -£& &- -&■ 205 Art. 163. The little circle shown in the centre of the water line of a buoy as depicted on the chart indicates the actual position of the buoy. The following abbreviations shown below buoys on a chart indicate the characteristics of the buoys : — B., Blk Black ( heq CheqiU'i v I G Green Gy Gray H.s Horizontal Stripes Xo Number R Red S.B Submarine Bell (Sounded by wave action). S.F.B Submarine Fog Bell (Mechanically sounded). V.S Vertical Stripes Y Yellow W., Wh White 163. System of lighting. — Lighthouses and light vessels are placed, for convenience in navigation, to mark various prominent points of the coast and certain rocks and shoals; full details respecting them are given in a book entitled " The Admiralty List of Lights and Time Signals." The light shown may be a continuous steady light, or it may be varied by the introduction of flashes, eclipses, &c. Lights are generally divided into two classes, namely : — ( 1 ) Lights whose colours do not alter throughout the entire system of changes. (2) Lights which alter in colour. The abbreviations used in the Admiralty List of Lights, as well as the characteristic phases of the lights, are given in the following table :- Lights whose colours single Qs h of relatively greater brilliancy at regular inten al ■ The fla ih maj or may not , l>e preceded and i. >11( m > • I by .in eclip Alt.Occ. Alternating occulting. \li.( lp.< ice. Alternating group ocoult ing Alt.F.Fl. Alternating Qxed and Sashing. Art. 163. 206 Lights whose colours do not alter. Lights which alter in colour. F.Gp.Fl. Fixed and group flash- ing. Rev. Revolving A fixed light, varied at regular inter- vals, by a group of two or more flashes of relatively greater bril- liancy. The group may, or may not, be preceded and followed by an eclipse. Light gradually increasing to full brilliancy, then decreasing to eclipse. Alt.F.Gp.Fl. ing fixed flashing. Alternat- and group Alt. Rev. Alternating revolving. The letter (U), against the name of a light in the Light List, indicates that the light is unwatched. Caution should be exercised when expecting to sight an unwatched light, because some interval may elapse before it is re-exhibited if it should become extinguished from any. cause. The period of a light is the interval between successive commence- ments of the same phase. The order of a light is a conventional term which refers to the focal distance of the apparatus, the focal distance being the distance from the centre of the illuminant to the inner surface of the lens. Lights are divided into six orders ; the power of the lights however does not vary directly with the order, and whenever obtainable the candle power is given in units of 1,000 candle power. The small letter in brackets, which follows the name of a light in the Light List, indicates the authority responsible for that light. All bearings of lights given in the Light List are true and are given from seaward. In the case of lights which do not show the same characteristics or colours in all directions, the areas over which the different character- istics are shown are indicated on large scale charts by sectors of circles. The arcs of the circles do not denote the distance at which a light may be seen. All the distan3es given in the Light List, and on the charts, for the visibility of lights are calculated for a height of an observer's eye of 1 5 feet. The table at the beginning of each Light List for the distances at which lights should be visible due to height, or the table in Inman's Tables for the distance of the sea horizon, (§ 57), affords a means of ascertaining how much further the light might be visible should the height of the eye be more than 15 feet. The glare of a powerful light is often seen far beyond the limit of visibility of the actual rays of the light, but this must not be confounded with the true range. Refraction may often cause a light to be seen at a greater distance than under ordinary circumstances (§ 52). When looking out for a light at night, it should not be forgotten that the range of vision is much increased from aloft. By noting a star immediately over the light, a very correct bearing may be afterwards obtained from the standard compass. The intrinsic power of ' a light should always be considered when expecting to make it in thick weather. A weak light is easily obscured by haze and no dependence can be placed on it being seen. The power of a light whose candle power is not given can be estimated by remarking 207 Art. 163. its order, as given in the Light List, and in some cases by noting how- much its visibility in clear weather falls short of the range due to the height at which it is placed. Thus a light standing 200 feet above the i. and only recorded as visible at 10 miles in clear weather, is mani- festly of little brilliancy, because its height would permit it to be seen at a distance of over 20 miles provided that its candle power were sufficient. The distance from a light cannot be estimated by either its brilliancy or it- dimness. On first making a light from the bridge, by at once lowering the eye several feet and noting whether the light dips, it may be determined whether the vessel is in the circle of visibility corresponding to the usual height of the eye, or unexpectedly nearer the light. The following abbreviations with reference to lights are employed on the Admiralty charts : — i5r * • ' Lights, Position of L^L 18 Light, Lights L l . Alt . Light Alternating L'.F. „ Fixed L l .Fl. ,, Flashing TAOcc. ,, Occulting L'.Rev. ,, Revolving Lt.F.Fl. ,, Fixed and Flashing L'.Gp.Fl.(3) „ Group Flashing L'.F.Gp.Fl.(4) „ Fixed and Group Flashing L t .Gp.Occ.(2) ,, Group Occulting Alt. alternating ev. every fl.fl 8 . flash, flashes G.,G n . Green Gp. Group hor 1 horizontal (Lights placed horizontally) irreg. irregular m. miles min. minute or minutes o I isc' 1 . obscured occas 1 . occasional R. Red sec. second or seconds (U) Unwatched vert*. vertical (Lights placed vertically) vis. visible \V.,\Vh White The number in brackets after the description <>t' Group Flashing or (.ion], Occulting Lights denotes tin- number f»l dashes or eclipses in each group. Alt. | Uternating) signifies a Light which alters in oolour. The height given against a light is tin- height <>i the local plane of th<- light above High Water of ordinary Spring Tides, or above Hi'' i level in oa ' w here t here is no tide. \- an example it will i»" found that the Eddystone Light is marked ..n I. M ile chart - : — Lt.Gp.Fl. (2) ev. 30 1 1 L39 feet iris, it m. Arts. 164, 165. 208 This signifies that the light shows a group of two flashes, the period between the commencement of consecutive groups being 30 seconds ; the centre of the lantern is 133 feet above the level of high water of ordinary spring tides ; and at this state of the tide, on a dark night with a clear atmosphere, the light is visible up to a distance of 17 miles to an observer whose height of eye is 15 feet. Light-vessels in English and Scottish waters are painted red with their names in white letters ; in Irish? waters they are painted black. The approximate height of the day-mark (a distinguishing mark carried at the masthead) above the water-line and the description of the light- vessel is given in the Light List. Light-vessels carry riding lights to indicate the direction in which they are swung. If a light-vessel is adrift from her moorings, or out of position, by day her day-mark is lowered ; by night her ordinary lights are lowered, a red light is shown at each end of the vessel, and a red flare-up is shown every 15 minutes. If, from any cause, a light-vessel is unable to exhibit her usual lights whilst at her station, the riding light only is shown. 164. Fog-signals. — There are various kinds of fog-signals : — gun, explosive report, siren, horn, bell, gong, automatic whistle, and submarine bell. Signals by gun or explosive report are generally employed in light- houses and light-vessels which mark outlying rocks, and sometimes on important headlands. The siren, sometimes distinguished by high and low notes, is generally employed on headlands and important light- vessels. It has been found that, under certain conditions of the atmosphere, when a fog-signal is a combination of high and low notes one of the notes may be inaudible. The horn and gong are also used in light-vessels and light-houses. Bells are sometimes established in light-houses and light-vessels but more frequently on buoys. Submarine bells are fitted in light-vessels, and at certain positions on the sea bottom where they are electrically operated from a station on shore. Buoys, when provided with a sound signal, are generally fitted with a bell or automatic whistle. Submarine bells are fitted to some buoys, in which case they are rung by the action of the waves. Wreck-marking vessels sound a bell and gong alternately during fog. When listening for a fog-signal, from a buoy or an unwatched light- vessel, it should be remembered that the signal is worked by the motion of the sea; consequently, in a calm, the signal will probably not be heard. 165. Reliability of fog-signals. — Sound is conveyed through the atmosphere in a very capricious way. Apart from wind or visible obstructions, large areas of silence have been found, in different directions and at different distances from the origin of sound, even in the very clearest of weather and under a cloudless sky. From a long series of observations it has been discovered that sound is liable to be intercepted by streams of air which are unequally heated and unequally saturated with moisture, in fact by a want of homogeneity in the inter- posed atmosphere. Under such conditions the intercepted vibrations are weakened by repeated reflections, and possibly may fail to reach 209 Art. 166. the ears of person* although well within the ordinary limits of audibility. The observations clearly proved that rain, hail, snow and fog have no power to obstruct sound, and that the condition of the air associated with fog is favourable to the transmission of sound. Therefore while "iic may expect to hear a fog-signal normally both as to intensity and place, the foregoing should be taken into account and occasional aberration in audition prepared for. It has been found that when approaching a fog-signal with the wind one should go aloft, and when approaching it against the wind the nearer one is to the surface of the water the sooner will the signal be heard. The apparatus for sounding the signal frequently requires some time before it is in readiness to act. A fog often creeps imperceptibly towards the land, especially at night, and is not noticed by the lighthouse keeper until it is upon him ; whereas an approaching ship may have been for many hours in the midst of it. 166. Submarine bell. -Sound-waves in air travel at the rate of about 1,130 feet per second, but as stated above (§lt>.">) the progress of serial sound-waves is very variable. In water sound-waves travel about four times as fast as in air and their progress is far less variable; when discharged, they spread out in all directions, but are deflected bj' shoals, land, and breakwaters, and possibly by strong tidal streams and currents. The present form of submarine sound signal consists of a bell, worked electrically, which is either suspended under the keel of a light - vessel or is slung from a tripod resting on the bottom of the sea in the vicinity of a light-house. Submarine bells are also litted to buoys. but in this case, when listening for the sound, it should be borne in mind that the bell is only worked by the motion of the sea. Details "I submarine bells are given in the remarks column of the Light List. The various light-vessels, light-houses, &c, give signals Avhich arc distinguished from one another by the number and combination of -"•ikes. The receiver is the bottom plating of the vessel. The vibrations are conveyed froin the bottom plating of the vessel to the chart house by means of the receiving gear, which consists of micro phoi cured to the ship's side at about IS feet below the water line and »i«i bet from the bows. The microphones are generally in pairs, marked A and B, and are connected electrically to two telephone in the chart house, a two-way switch enabling the operator to listen on cither side of the ship at will. The sound i^ heard loudest when it is at right angles to the microphone or about 2 points before the beam, and thesound is lost when it is about 4° Oil the bow or about 6 points abafi the beam, according to the class of the vessel. It i- essentia] ill order to obtain good results that all aoise in the compartment in which the microphones are situated should be stopped, and that the -hip -hould In- as quiet a- p08Sible. for this reason it i found that the be I result* are obtained when the speed of the Bhip I- low. I •> obtain the bearing of b submarine bell listen on either sid< "i tie hij, alternately till the jound of the bell i beard, then, still listening on the side w here the sound w.i first beard alter oourse slowly towards the bell and note the direction oi the hip bead when the Bound "I the bell • immediaterj put the -witch over, U te i the other side x '■!• O Art. 167. 210 and note the direction of the ship's head when the sound of the bell is again heard. The mean of the two directions of the ship's head should be the bearing of the bell. As a check the operation should be repeated whilst turning back to the original course. With a little practice the bearing of the bell can be found with considerable accurac}', the distance at which this can be done varying from about 2 to 15 miles. 167. Printing of the chart. — Charts are printed from engraved copper plates, but, as copper is a comparatively soft metal, constant printing wears down the surface of the plate and the engraving soon becomes shallow and indistinct ; to meet this difficulty and prolong the life of the plate a method of electrically depositing steel on its surface has been adopted. Although the deposit is almost an immeasurable quantity, the effect is such that 10,000 copies can be pulled from a steel- surfaced plate with less damage to it than 1,000 copies when the plate has not got a steel surface. To print or pull an impression from a copper plate the printer first cleans the surface thoroughly, then dabs the whole surface over with printing ink until he is satisfied that every cut in the plate is filled. He then rubs the surface of the plate over quickly and lightly with his hands until all the surface ink is removed. The plate is then rubbed over with whitening and polished, after which it is placed on the bed of the printing press and a sheet of paper laid on it ; it is then drawn through the press and considerable pressure is applied. When the plate emerges from the press the paper is carefully lifted from it and the necessary proof is obtained. Charts used in navigation are printed on paper that has been slightly damped in order to take a good impression ; this damping causes a slight distortion due to shrinkage when the paper dries, the amount of which can be easily obtained by measuring the proof between the inner border lines and comparing the measurements with those engraved in the bottom right-hand corner of the chart. As a general rule the distortion is not sufficient to cause an appreciable error in the position of a ship, and the larger the scale of the chart the smaller is the error ; for this reason, as well as for others, that chart of the locality which is on the largest scale should always be used. In addition to the wear and tear of the plate, printing from copper is a long and expensive method of obtaining chart proofs ; it is very much more economical to print from lithographic stones. This is achieved by obtaining a proof from the copper plate in a greasy ink, specially made for the purpose, on a specially prepared paper. Care having been taken that every detail is shown, the proof is laid face downwards on a lithographic stone, which, owing to its nature, takes the impression of the wet greasy ink and thus gives, after certain treatment by the litho- grapher, another means of obtaining copies of the chart. Printing from lithographic stones is very inexpensive, for about 2,500 copies can be printed from a stone in an hour, with a steam or electrically- driven printing machine ; whereas only half a dozen copies can be printed from a copper plate in the same time, and the work has to be almost entirely manual. Owing, however, to the great weight, to the necessary care in handling to prevent breakage, and to the large amount of space required for storing lithographic stones (they are usually from 1\ to 3 inches thick) zinc plates specially prepared with a granulated surface 211 Arts. 168, 169. - have been found to answer the same purpose, and to possess advantages over the stone as regards handling, breakage, and storage. The process of transferring to, and printing from, zinc plates are practically the same as when using stones. Admiralty charts arc constructed either on the Mercator's or gnpmonic projections, the latter being used when the scale is greater than two inches to the mile and where areas in high latitudes have to be represented. *©* 168. Chart correction.— Charts are kept up to date in the following manner. When information has been received at the Hydrographic Department that a chart requires correction, the information relating to the correction is published in the "Notices to Mariners," which are despatched weekly to all Officers in charge of charts; it is the duty of these Officers to forthwith make the necessary correction with pen and red ink to the chart- which are affected. When making corrections on a chart the instructions issued with the chart set should be carefully followed. The correction is also placed on the chart plate, the date of such correction being engraved in the left hand lower corner of the margin, under the heading " Small corrections." When a correction i> too large to be conveniently placed on a chart by hand, such as when there nave been large alterations in soundings or in a coast line, a reproduction of the portion so corrected is sometimes inserted in a Notice to .Mariners: this reproduction is printed in two colour-, red ami black, the correction being in red. When this is not done a new edition of the chart is issued, the date of this new edition being printed on the margin at the bottom of the chart against the words " New eilit ions." A chart is described by means of its number (in the right hand lower corn* r), together with tic title and date- of publication or new edition, and la-1 .-mull correction; thus. No. 2 British [slands, New edition. 26th June 1912, last -mall collection, 1. 13. 169. Reliability of charts. The value of a chart manifestly depends on the accuracy of the survey on which it is based, and tin- becomes more important tin- larger the scale of the chart. To estimate tin-, the date of the survey, which is always given in the title, is a good guide. Besides the changes that, in water- where sand or mud prevail, may have taken place -inee t he date of the survey, the earlier survej - were mostly made under circumstances that precluded great accuracy of detail, an. I until a plan, founded on such a survey, i- tested, it should ho regarded with caution, h ma\ indeed be -aid that, excepl in well frequented harbours and their approaches, no surveys yet made have been minute in their examinations of the bottom as to make it certain that all dang( i - lci\ e been found. The fullness or scantiness of the soundings is another method of estimating the completeness of a chart. \\ ben the soundings are spi or unevenly distributed it may be taken for granted that the survey wa- no' in i ■!<■ in vie o detail. The degree of reliance which iei; be re i oiiablj placed upon an Admiralty chart even in surveys of modern date, is mainly dependent on the scale <>n which the survey iva m i le and it should not be a umod that the original survey wa made on a larger cale than thai published. I i ! Art. 169. 212 It should be borne in mind that the only method of ascertaining the inequality of the bottom is by the laborious process of sounding, and that in sounding over any area the boat or vessel which obtains the soundings is kept on given lines ; that each time the lead descends only the depth of water over an area equal to the diameter of the lead, which is about two inches, is ascertained, and that consequently, each line of soundings, though miles in length, is only to be considered as representing a width of two inches. Surveys are not made on uniform scales, but each survey is made on a scale commensurate with its importance. For instance, a general survey of a coast, which vessels only pass in proceeding from one place to another, is not usually made on a scale larger than one inch to the nautical mile ; surveys of areas where vessels are likely to anchor are made on a scale of two inches to the mile ; and surveys of frequented ports or harbours likely to be used by fleets, are made on a scale of from six inches to ten inches to the nautical mile. Little assistance in detecting excrescences on the bottom, when sounding from a boat, is afforded by the eye, even in clear weather, on account of the observer being so close to the surface of the water. If, therefore, there is no inequality in the soundings to cause suspicion, a shoal patch between two lines may occasionally escape detection. Lines of soundings, plotted as close as is practicable on a scale of six inches to the nautical mile, would be 100 feet apart, and each line would be only two inches in actual width. Thus, in a chart on a scale of one inch to the nautical mile, an inequality of some acres in extent rising close to the surface, if it happened to be situated between two lines, might escape the lead; while in a chart on a scale of six inches, inequalities as large as battleships, if lying parallel to and between the lines of soundings, might exist without detection if they rose abruptly from an otherwise even bottom. General coast charts should not, therefore, be looked upon as infallible, and a rocky shore should on no account be approaced within the ten- fathom line, without taking every precaution to avoid a possible danger ; and even with surveys of harbours on a scale of six inches to the nautical mile, vessels should avoid, if possible, passing over charted inequalities in the ground, for some isolated rocks are so sharp that the lead will not rest on them. Blank spaces among soundings mean that no soundings have been obtained in these spots. When the surrounding soundings are deep it may reasonably be assumed that in the blanks the water is also deep ; but when they are shallow, or it can be seen from the remainder of the chart that reefs or banks are present, such blank spaces should be regarded with suspicion. This is especially the case in coral regions and off rocky coasts, and it should be remembered that in waters where rocks abound it is always possible that a survey, however complete and detailed, may have failed to find every small patch. A wide berth should, therefore, be given to every rocky shore or patch in compliance with the following invariable rule : — instead of considering a coast to be clear, unless it is shown to be foul, the contrary shoidd be assumed. Except in plans of harbours that have been surveyed in detail, the five-fathom line on most Admiralty charts is to be considered as a caution or danger line against unnecessarily approaching the shore or banks within that line, on account of the possibility of the existence of undiscovered inequalities of the bottom. The ten-fathom line is, on a 213 Art. 170. rocky shore, as before-mentioned, another warning, especially for ships of heavy draughl . Charts on which no fathom linos are marked should be especially regarded with caution, for it may generally be concluded that the soundings were too scanty, and the bottom too uneven, to enable them to be drawn with accuracy. Isolated soundings, shoaler than the surroundings depths should always be avoided, especially if ringed round, for it is impossible to know how closely the spot may have been examined. Aiiows on charts only show the most usual or the mean direction of a tidal stream or current. It should never be assumed that the direction of the stream will not vary from that indicated by the arrows. In the same manner, the rate of a stream constantly varies with circum- stances, and the rate given on the chart is merely the mean of those found during the survey, possibly from very few observations. 170. Sailing Directions. The Sailing Directions are books which are supplied to II. .M. Ships for the purpose of giving detailed information respecting coasts, ports, tides, soundings, &c. Wherever the information given on the charts differs from that given in the Sailing Directions. the information given mi the chart of the largest scale, which should have been corrected from the latest information, should be taken as the guide for purposes of navigation. Art. 171. 214 CHAPTER XVII I. THE TRACK OF THE SHIP AND THE AVOIDANCE OF DANGER IN PILOTAGE WATERS. 171. The track. — Having studied the previous chapter the reader should now be able to read the chart — that is, to picture mentally the surroundings, in particular the relative positions of the various dangers in the vicinity of the ship's track, as well as the various artificial aids to navigation that may be expected to come into view. We have now to explain how the ship's track to a particular destination should be determined, so that the ship may steam in the vicinity of the dangers with the certainty of avoiding them. The first question to decide when laying off a course on the chart is — at what distance from any danger zone or from the coast is it most prudent for the ship to pass ? The governing factors in making a decision are, the nature of the dangers or coast and the depth of water in the vicinity, whether the dangers are marked by light-houses or other artificial aids to navigation, whether the coast is such that the position of the ship can be fixed while passing it, the state of the weather, whether it is day or night, and whether tidal streams or currents are strong in the vicinity. On short runs along well-surveyed coasts in daylight and clear weather, an offing of about five miles, where the depth of the water is over ten fathoms, is generally sufficient; but where a long distance is to be run along a more or less straight coast, the distance saved by steaming so close to the shore instead of having an offing of, say, ten miles, is of no moment, and a wider berth should be given than where the distance involved is short. The possibility of an indraught into a deep bay or indentation of the coast must also be borne in mind, for it is found that vessels, when passing such indentations, are frequently set inshore, although the normal direction of the current may be parallel to the general trend of the coast. A.nother point that has to be taken into consideration, when in much frequented waters, is the possibility of the ship being constantly compelled to alter course in order to avoid other vessels, and if the majority of the alterations of course are made to the same side, which is often the case, the cumulative effect of these may seriously displace the vessel ; conse- quently, disregard of this point may cause an otherwise carefully estimated position to be considerably in error. The general rule when coasting, that is when steaming along and in sight of a coast, is to pass sufficiently close to the coast to enable all prominent marks, such as lighthouses, &c, to be seen, and to fix the ship's position frequently, for only by so doing can one be certain of immediately discovering whether the ship has been set off her supposed track by an unexpected current, &c. To decide at what distance from dangers and coasts the ship should pass requires experience, but the course steered should as far as possible be such that, in the event of the marks being obscured by fog or mist 215 Art. 172. the ship could still be navigated with the certainty that she is not running into danger. When, of necessity, the track will lead the ship into comparatively shallow water, such as the estuaries of rivers or the approaches to harbours, it is essential to study the height of the tide as well as the draught of the ship. An ample margin of depth should always be allowed, and the importance of this margin is accentuated, if possible, when the naviga- tion is to be performed on a falling tide. It should be remembered that the draught of a ship is greater when steaming fast than when she is at rest.* and that the draught is vcv considerably increased when a ship rolls or heels heavily. The amount of the increase in a ship's draught due to rolling or heeling depends on thi" type of ship, being greatest in ships whose cross section below the water line is approximately rectangular, and it is further augmented when bilge keels arc fitted at the corners of the rectangle or if there is much "' tumble home " in the cross section above the normal water line. In certain classes of ships the increase is as much as 7 inches per degree of heel, so that for 10° the increase would amount to nearly 6 feet. In order to conduct a vessel in safety when in the vicinity of land or dangers, the principles of the terrestrial position line, explained in §§ 48, 49, and 50, are employed and the ship's track should, as far as possible. he so arranged that it coincides with a terrestrial position line, in ^ A order that repeated observations of the terrestrial point from which the position line results may indicate at once any deviation of the -hip from her intended track ; and, in addition, if the ship is known to be following her intended track, that a position line from a bearing of an object abeam may at once give her position. ^g 172. Leading marks. — When possible it is convenient to sd arrange the track that two objects in transit may be seen ahead or astern, in other words that the ship may steam along the position line resulting from this transit (§ 63). Provided the two objects are ~een to remain in transit certainty exists that the ship is following the arranged track, whereas, if they are seen to be not exactly in line with one another, it is obvious that the ship is to the light or left of the pre-arranged track. .Mark- are -aid to be open when they are not exactly in transit, thus in Fig. 137, two lights, A and II. are in transit to an observer at 0, but to an observer at C, A is said to be open to the right of A'. In many plans of harbours two marks are shown, which, being j,- |( , kept in transit, lead the ship clear of dangers, or in the best channel. [ ^~ Such marks air called leading marks, and their presence is indicated "ii t he chai t by a line draWE through t hem. Th" line is generally show n on the chart a- one Btraight line, but sometimes as two parallel lines close together. The line i- full lor a portion of it- length and then becomes dotted: thii signifies that it is only advisable to keep on it a- far .i tin' full line e\t"iid<. the dotted portion merely being drawn to guide 'he eye to i he objects which are to he kept in transit . The names of the objects and their magnetic and true bearings when iii transit are general I3 written along 'he line drawn through them. The magnetic bearing 1- only strictly correct during the year lor which the variation on 1 he chart i- given. * ,1 n record oj <> vessel haxttTuj grounded and sustained considerable '/"■ to her speed of 1 1 knots. 1 o c Arts. 173, 174. 216 When the objects are in transit, a bearing of them should be taken and compared with that given on the chart; this ensures that the two objects seen in transit are the correct ones, and is a necessary precaution to take when visiting a place for the first time. The distance between the leading marks should be roughly noted as a guide to the amount of reliance that can be placed on them, and to the amount of care necessary while watching them. When making use of leading marks, those which are a considerable distance apart, compared with the distance of the ship, are most trustworthy, and such marks are called sensitive, because the slightest deviation from the correct line will immediately open the marks, whereas, if the marks are close together they will still appear in transit when the ship is at some distance from the line. No absolute rule can be laid down as to the distance the marks should be apart ; but if it is a third to a quarter of the greatest distance for which they will be required, it will generally be sufficient. In Fig. 146 two leading marks are shown. (1) Red stripe on West end of coastguard building in line with beacon, N. 45° E. ; this leads clear of the dangers Harbour-rock and Carrig-a-bo, and as the distance between the marks is about a third of the greatest distance for which they will be required, this transit is fairly sensitive; (2) Dunboy turret in line with South extreme of Old Fort Point, N. 86° E. ; this leads in the deepest water, and the distance between the marks is half the greatest distance for which they will be required. When steadying the ship on leading marks ahead, the order " steady ' may be given when the ship's head is pointing exactly to the marks, but when the leading marks are astern, the ship must be steadied by compass in the required direction, when a glance astern at the marks will show whether the ship is on the correct line or not. 173. Lines Of bearing. — If no transit marks are available the track should be arranged, if possible, so as to coincide with a line of bearing (§ 48). In this case the track is drawn on the chart so as to pass through some well defined object, and the bearing of the object from any point of the track noted; the object selected should be ahead of the ship rather than astern. Provided that the bearing of the object remains constant at the bearing noted, the ship must be on the line of bearing which coincides with the pre-arranged track; should the bearing of the object be seen to change, it is obvious that the ship has been set off her track in that direction which is indicated by the change of bearing. When laying off a line of bearing an object should be selected which is not too far off ; the closer the object is to the observer, the easier it is to detect by the change of the bearing when the ship is being set off the line ; for example, if the object is one mile distant, the bearing will alter one degree if the ship is set about 30 yards off the fine, whereas, if it is ten miles distant, the ship will be set about two cables off the line before the bearing changes one degree. 174. Turning on to a predetermined line. — Having decided on the track proposed for the ship, it is necessary to consider how to deter- mine the instant at which the helm should be put over when altering from one course to another, so that the ship, when steadied on her new course, may be exactly on the pre-arranged track. To do this the distance to new course, or the advance and transfer, is made use of (§ 44). Thus, suppose a ship is steaming N.E., and that it is desired to alter course to North so as to steam along the line YZ* (Fig. 138) 217 Art. 174. From any point X on YZ lay off XP' in the opposite direction (S.W.) to the present course and equal to the . ii-tance to new course for the required alteration. Through P' draw a line P'Q' parallel to YZ, then the ship will turn on to the line YZ if the helm is put over when she is on the line P'Q', wherever she may be on that line, and she will follow a path such as P P or Q'Q till she heads North. Therefore, if the line P'Q' is drawn on the chart and it is found to pass through some object 0, the course should be altered when the ship reaches the position line OP'. Thus we have the rule for finding the position line on which to put the helm over — draw the estimated and new tracks, and from their point of intersection lay back along the estimated track the distance bo new course: this gives the point through which to draw the position line parallel to the new track. It cannot be expected that ships will always turn exactly as anticipated, for their paths are often much affected by wind, sea, depth of water, &c. The necessary allowances for disturbing influences can only be gained by experience and vary in different -flips, and can be determined only by experience. The rule stated above will be made clear by the three following examples. Example (1). — A ship is steaming N. 22° E. and it is desired to alter course to X. 45° W. on to the line YZ (Fig. 139). Let tip estimated track of the ■% ship intersect YZ at X. From the tabular statement re- lating to the ship's path while turn- ing, the distance to new course for a turn of 07° (from X. 22° E. to N. tfi \\ .) i- found to be 495 yards. From X lay back XA along the (+} estimated track equal to 4!»."> yards. Through .1 draw a dotted line IC parallel ic YZ. then if the helm i- put over when Ihe ship is on the line AC -he will t inn as required. Now it will he observed that AC, when produced, passes through the light housi < >. jot li.it t he helm should he put over when 1 he ship arrives on I he posit i"ii line resull ing from the observed bearing of the lighthouse being 8. 16 E. It i- seldom that an object can hi- found whose line of bearing cl ly coincides v. it h t he line A( '. hut frequently an object can be found w hose hue of In u [ng can he drawn parallel to AC and the principle of transferring a position line in el. II-- ..i .,u ii in Example C2). I'm. L39. Art. 174. 218 Example (2).— A ship is steering N. 40° W. at 10 knots; the position of the ship is uncertain and it is desired to alter course to North so as to steam along the line YZ, which is at a distance of 2 miles from the point (Fig. 140). Let the estimated track (N. 40° W.) of the ship inter- sect YZ in X. From the tabu- lar statement relating to the ship's path while turning, the distance to new course for a turn of 40° (from N. 40° W. to North) is found to be 400 yards. Lay back, along the esti- mated track, X.4 equal to 400 yards. Through A draw a dotted line AC parallel to YZ, 400Y *^ then if the helm is put over when the ship is on the line AC, the ship will turn as required. Through the point O draw a line parallel to YZ intersecting the estimated track at B, then it will be found that AB is 2' 9 miles. Note the instant when the point bears North, that is when the ship is on the position line OB ; then, since 2*9 miles is covered at 10 knots in 17*4 minutes, the ship will be on the line AC 17*4 minutes after the point bore North ; at this instant the helm should be put over and the ship will turn on to the line YZ as required. When a tidal stream or- current is being experienced it should be allowed for as shown in Example (3). Example (3). — A ship is steaming N. 60° W. at 10 knots ; her position is uncertain, and it is desired to alter course so as to make good a course North along the line YZ (Fig. 141), which runs through the channel MO at a distance of four cables from the point 0. A tidal stream is estimated to be setting West 1 knot. To find the course to steer in order to make good a course North, take any point X in the line YZ and lay off XG to represent one knot West on any convenient scale; with centre G and radius 10 knots on the same scale describe a circle cutting XZ in H, then the direction of GH, which is N. 6° E., is the course required. From the tabular statement relating to the ship's path while turning, the distance to new course for a turn of 66° (from N. 60° W. to N. 6° E.) is found to be 495 yards, and the time of turning is found to be two minutes. From A r lay off XK 495 yards S. 60° E. While the ship is turning, the tidal stream sets her to the westward a 2 000 x 2 distance of - yards or 67 yards. To allow for this set, from K lay off KA 67 yards East. Through A draw a dotted line AC parallel to YZ, then, if the helm is put over when the ship is on the line AC, Fig. 140. 21!) Art. 175. and the course altered to X. 6 E., she will turn so as to arrive on the line YZ. Through the point draw OB parallel to YZ. It is now accessary to linn the estimated track of the ship take any point E, and draw ED to represent lo knots X. 60° W. on any convenient scale: through /> draw />/•' to represent one knot West on the same scale, then KF represents the course and speed made good, namely. N. \\\. 10*8 knots. Let /•.'/•' produced intersect OB and .If 'in />' and C respectively, then the interval required is the time which the ship takes to cover the distance BC (34U yards) at 10*8 knots, namely. 57 seconds. The opportunity for the application of these problems frequently arises in pilotage, and the use of a stop watch is recommended. Tables, which give the times in which various distances arc covered at various speeds, are supplied to ELM. Ships. Fig. 141. When rounding a point which is very close to the ship, and it is desired to keep at a constant distance from it during the turn, the follow Lng method maj be employed : Put the helm over, an amount corresponding to the tactical diameter required, a little before ih<- point is on the beam, and subsequently continue to adjust the helm angle so that the object remain- abeam i hroughout t he i urn. 175. Clearing marks. Clearing mark- arc two marks shown on the chart, a straight hue through which runs dear of certain dangers; such a line is Bhown on the charl with the names of the marks and their magnetic and true bearings when in transit. When navigating mar a danger, care si Id be taken not to get inside the line of transit ot the clearing marks. A- long as the ship is kept outside this line, that is, jo long at the mark are kept open, she will he afe .i - in .i i li.it danger is concerned. Art. 175. 220 f ""• « / JOS 250 - ' ' MS iff* »«5 H*~ll -jC J" 4 5^ * ci" '■> *!> \>g ^***i. r u it <^0 * 5 «-.cr , .. o as tr <• g i&3 45 V 305 i* Ho 'V 3gQ .:?). When deciding on the track. Article 25 of the Regulations for Preventing Collisions al Sea should be remembered, namely:— "In i; narrow channels, every steam vessel shall, when it is safe and practic ' able, keep to that side of the fairwaj or mid-channel which lies on " the starboard side of such vessel." It should also be remembered that, on account of passing vessels, a ship may be compelled to leave the pre-arranged track, and conse- quently it may happen that a ship is forced to pass closer to a particular danger than was originally intended: for this reason, clearing marks or danger angles for all dangers, even for those at a considerable distance from the ship's track, and particularly for those situated on the starboard hand, should be included in the preparation of the chart. The position lines on which the helm should be put over should be drawn, and marks selected as explained in § 17 J. All courses, bearing-. &C, should be entered in a note book, so as to avoid the necessity of constantly leaving the compass in order to refer to t he char! . When piloting in waters like the entrance to the Thame.-, where the shore is distant and low lying, and it is difficult and sometimes impossible '■<• any objects on shore, the buoy- may be the only guide. Before arriving at Buch a locality, particularly if the weather is likely to be thick, when preparing the chart, the distances to be steamed on each course and the interval of time required to steam between oonsecu tive buoys should be noted, in order that, in the event of a foe coming on. the time maj be known beforehand when each particular buoy should be abeam, due allowance having been made for the effect of tidal stream . Should a buoy not be sighted and passed at the calculated time, i» should he assumed that the ship i- not passing along the pre arranged trick at the intended speed and the utmost caution should In- observed. The -hip mould be anchored it there is any uncertainty about her position, the depth of water at low tide having been fir I considered. Arts. 181, 182. 224 181. Selection of a position in which to anchor.— When selecting a position in which to anchor the ship numerous points have to be taken into consideration, namely, the depth of water and nature of the bottom, whether the bottom is good or bad holding ground (§ 159), whether the anchorage is in a landlocked harbour or in an open roadstead, the direction and probable strength of the prevailing wind, the strength and direction of the tidal streams, and the rise and fall of the tide. The length and draught of the ship, and whether she is to be at single anchor or moored, as well as the position of the landing place, have also to be taken into account. It is impossible to give any definite rule as to how near a danger a ship may be anchored, but in all cases an ample margin of safety should be allowed in order to meet the contingency of bad weather coming on and the ship dragging her anchors. If the ship is to be moored, the direction of the line joining her anchors should coincide, when possible, with that of the prevailing wind or tidal stream, and each anchor should be sufficiently far from dangers to enable it to be weighed without incon- venience whatever the direction of the wind may be. If no accurate chart of the anchorage is at hand, soundings should be carefully taken within a radius of at least three cables from the ship, in order to ascertain if there are any uncharted rocks or dangers. 182. To anchor a ship in a selected position. — Having selected the position in which to anchor the ship, the chart should be prepared as follows :— Select some conspicuous object on shore, the line of bearing of which from the selected position gives a possible line on which the ship may approach, and, if possible, select a second object on the same bearing hi order that the ship may approach the selected position with the two objects in transit. The remaining part of the chart should then be prepared as explained in § 180, the track being so arranged that the final course will be along this line, and that the ship will be turned on to it as far from the selected position as possible. Thus, in Fig. 144 let A be the position selected for the anchor, then the line which passes through Flagstaff and Church Spire (N. 22|° E.) gives a possible line of approach, because it passes through A and runs clear of all dangers ; the track of the ship should then be so arranged that her final course will be along this line. From A lay back AX along the line of approach etpial to the distance between the anchor bed and the standard compass, or between the stem and standard compass when the ship is fitted with stockless anchors; then X is the position of the standard compass at the instant the anchor should be let go. In order to determine the instant at which the standard compass will be at X, a position line should be laid off through the point X such that the angle which it makes with the fine of approach is as near a right angle as possible; this position line is generally a fine of bearing of an object, the object being on or nearly on the beam, but it may be a circle obtained from a horizontal sextant angle between two objects situated on either bow. Whichever position line may be selected it is important that the bearing or horizontal sextant angle should be altering rapidly, and for this reason a near object should be selected in preference to a distant one, even if the latter is more nearly on the beam ; for the same reason the horizontal sextant angle should not be small and the objects not too far away. The sextant being a more exact instrument 1 22:» Art. 182. for measuring angles than the compass, the position line by horizontal sextant angle should be preferred to the line of bearing, provided that the chart is based on an accurate survey. When about to anchor it is most important to so reduce the speed oi the ship that, when the anchor has been let go and the engines reversed. the Bhip may lie .-topped without any strain being brought on the cable- . for tins reason, when coming to with single anchor, it is customary to reduce the speed of the Bhip when at about a distance of one mile from the position selected for the anchor, and to stop the engines at a distaiu e of from two to four cables, according to the class of the ship, before arriving at the position for anchoring, and to reverse the engines at the instant of letting go the anchor. To find where to reduce speed and where to stop the engines, lay back from the point A' along the line of approach a distance XZ of on< mile and a distance X Y of from two to four cables according to the class of the ship ; the speed should be reduced (generally to six or seven knots over the ground) when the ship arrives at Z, and the engines should be -topped on arrival at Y. The instants of arriving at Z and Y are found in a similar maimer to that of arriving at X, as will he understood from the following example. In Fig. 144 the point A at which to anchor a ship has been selected, and it is noticed that the line which pas-.- through the Flagstaff and the Church Spire also passes through the point A and runs clear of all dangers ; it is therefore decided to approach A along this line (N. 221 E.), with the Church Spire and Flagstaff in transit ahead. From A lay back AX, 50 yards (the distance between the anchor bed :oid standard compass), then the anchor should be let go when the standard compass arrives at X. Lay the edge of the parallel rulers on the point X and in a direction at right angles to the line of approach, and note any conspicuous objects on shore that may be on or near the edge of the rulers ; it will be noticed that a monument lies very near the edge of the rulers, its bearing from X being S. 72° E. From X lay back XY, 2| cables, and XZ, 10 cables, and it will be found that the most suitable object at 7 is a white house bearing S. 80° E., and at Z a beacon hearing N. 50° W. Therefore the -hip. assuming that she has been turned on to the line of approach ZA, should be kept on this line by continually observing that the Church Spire remains iii transit with the Flagstaff, care having been taken when drat turning on to the line thai the bearing of the Church Spire Mud Flagstaff) was N. 22.1 E. (Mag.). When the beacon bears .\. 50 W. the ship- Bpeed should he reduced to, say, 7 knots. When the white house bears 8. 80 E. the engines should be -topped, and when the monument b< i 9 t:; E. the anchor should be let go and the engines ■ i ed. Should there he e tidal Btreaxn or ourrent, such a course should he steered that the course made good is along the line ZA (§ 25); the distance -V )' will obviously be greater or le according as the tidal stream i- v. it h t he ship or against her. It i- always advi able to have an alternative po ition line on which inchor, in oa e the object or object elected Bhould be obscured by tie,-, or ship already at anchor. When there i- not a ,,,l citable object whose bearing i roughly at right angle to the line of approach, b position hue by horizontal angle bould be employed; example, in Fig. 144a i gmenl ol a circle pa ing through the To* Bit P ' Art. 183. 226 the point X and the Windmill cuts the line of approach nearly at right angles and contains an angle of 101 1°, so that if this angle is set on the sextant, the instant of arrival at X will be the instant when the images of the Tower and the Windmill are seen in contact through the sextant telescope. A Church " Spire ■i^Tower Win dmill [^Monument 10CaH ( . s . Fig. 144. 183. To moor a ship in a selected position. — When mooring a ship the same principles are made use of as when anchoring, but in this case it is first necessary to decide what length of cable shall be out on each anchor when the ship has been moored. As a general rule, the amount of cable for a heavy ship is six shackles on each anchor. As explained 007 — . Art. 183. in the Seamanship Manual, one shackle of cable is usually required to go round the bow s in order that the mooring swivel may be -hackled on. and therefore the distance between the two anchors, when let go, is (G X 2 — 1) 11 shackles; therefore the distance of each anchor from 11 11 x -5 the point A should be shackles, that is or 137 yards. pf. Church Sp/re -- "y ^Windmill c House j' on \ ' 1 f- Fio. i 15. The distance «>f each anchor from the poinl .1 should be slightly less where the rise ->f the tide ia considerable or the depth of water great. m .1 Fig. 145, lay off AB and AC in both directions along the line of approach, each equal 1 i 1 37 yards, then B and C are the positions for Art. 184. 228 the two anchors. From B and C lay back BX and CX' each equal to 50 yards (the distance between the anchor bed and standard compass), then the first anchor should be let go when the standard compass arrives at X } and the second when it arrives at X' . To find when the standard compass arrives at X and X' we ascertain the bearings of the Monument from these points as when anchoring. The first anchor should be let go when the Monument bears S. 81|° E., or when the angle between the Tower and Windmill is 92|° ; the second anchor should be let go when the Monument bears S. 62|° E., or when the angle between the Tower and Windmill is 112°. The positions at which the speed should be reduced and the engines stopped are determined as in the previous example, the distance XY in this case being taken as H cables, because rather more way is required when mooring than when coming to single anchor. The weather anchor should always be let go first in order that the cable may be clear of the stem while the ship is being middled, and great care should be taken that the ship's head is kept perfectly steady till the second anchor has been let go, in order that the cable may be laid out in the straight line which contains the point A. 184. Example of the preparation of a chart with a view to anchoring. — The following example shows the method of preparing the chart for entering Berehaven by the Western entrance and taking up an anchorage off Mill Cove. In practice the large scale chart should be used, but for convenient representation in this book the example is shown on a portion of Admiralty chart 1840. (Fig. 146.) The necessary details of the ship are as follows : — Extreme length - 400 feet. Maximum draught - 26 feet. Anchor bed to standard compass - 150 feet. Alteration of course (in points) .... 2 4 I 1 6 1 8 ! 10 ! Distance to new course for 15° of helm (in yards) - 230 365 1 495 660 885 After consideration it has been decided that in this case a distance of 2^ cables from the five-fathom fine gives a sufficient margin of safety, and therefore the point A, whose minimum distance from the five- fathom line is 2\ cables, has been selected for the position of the anchor. Having the approach in view, lay the rulers on the five-fathom line between the Volage and Hornet rocks and also North-East of Sheep Island, and it will be seen that a fine in the direction S. 82° E., when drawn through the point A, is a safe course on which to approach A and, when produced, passes through the extremity of Carriglea Point (not shown in the Figure). Through A draw a line 82° - , and from A lay back AX equal to fe E 50 yards ; from X lay back X Y and XZ equal to 2| cables and 1 mile respectively. As explained above (§ 182) the pier head on a bearing S. 8° W. gives the position of X ; Corrigagannive Point on a bearing N. 13° E. gives 229 Art. 184. the position of Y ; and the Volage Rock buov abeam gives the position of Z. ( m examining the chart it is found that two leading marks are given and a track recommended for the Western entrance, and it is noticed that one of the leading marks leads in a depth of 4J fathoms just North Eastward of Harbour Rock, but this will not matter provided the state of the tide is not near low water of ordinary springs. It is therefore proposed to pass through the Western entrance making use of the leading marks. Let the line AZ intersect the leading mark " Dunboy Turret in hue with South extreme of Old Fort Point " in B, and let this leading mark intersect the leading mark 'Red stripe on \Y< •■ i Encl of Coast-guard building in line with Beacon " in ('. and lei the last -mentioned leading mark intersect the recommended track in D. The ship should therefore be steered so as to pass along the track EDGBX, due allowances being made for the effects of the tidal stream. In this example it is considered to be slack water, and it is now necessary to find the positions at which the helm should be put over. The course aiong ED is X. 27 e E., and along DC is N. 45° E. so that the alteration of course is 18°, and from the table above it will be seen that' the corre- sponding distance to new course is 210 yards. From D along DE lay ;; DF 210 yards, and through F draw a dotted line parallel to DC; if, therefore, the helm is put over when the ship is on the dotted line through F she will turn on to the line DC. It will be noticed that the • lotted line through F passes through the highest point of Dinish Island, -o that if the helm is put over when the summit of Dinish Island bears N. 45° E. or when Na-glos Point is just before the starboard beam, the ship will turn on to the leading mark ;i Red stripe on West end of C.G. building in line with the beacon on Dinish Island" bearing N. 45° E. ; ii l- obvious that the marks must be carefully kept on lill Harbour Rock has been passed. In a similar manner lay back CG along CD equal to 359 yards, the distance to new course for the next alteration, and note that the dotted line through G in the direction of the next course N. 86° E. passes through the Northern extremity of Sheep Island, so that if the helm is pul over when this point bears N. 86° E. the ship will turn on to the line CB, and Dunboy Turret will be in line with the South Extreme of Old Fori Point, astern. A- the ship will in this case be turning on to a stein mark, she musl be steadied on N. 86 E. by compass (§ 172). In a similar manner lay back Jill equal to l yards, and draw a dotted line through // in the direction of the new and final course S. 82 E. It will be noted thai this dotted line does not pass through or near any conspicuous object of which a bearing can be taken, but, if the ship is exactly on the leading marks, the helm should be pul over when Privateer Rock Perch bean N. I I W. If the ship is not exactly on the ling mark, her position Bhould be fixed and the helm put over when she arrives at the dotted line through H ; the ship should now be steadied on i" her final course S. B2 B. which coincides v\ith the bearing of < larriglea Point . The speed of the ship mould be reduced the engine stopped and t he anchor lei previou -l\ arranged. h will be noticed thai the -hip Bhould pase 100 yardi ofl Volage buoy and this bould prove a valuable oheck on the positi i x 611 Art. 185. 230 the ship, especially as Carriglea Point (not shown in the Figure) is rather distant for a line of bearing. 185. Conning the Ship. — In the majority of ships the officer, whose duty it is to direct the helmsman how the ship is to be steered (to con the ship), is situated in a position from which-a comprehensive view of the surroundings can be obtained, but from which he is often unable to see the helmsman ; consequently, it is most important that the necessary orders should be given to the helmsman in such a way that no ambiguity can arise. On arriving at the place where the helm is to be put over, the order to the helmsman, should be given thus :— " Port 25," ' Hard-a-Star- board," &c, particular care being taken to state the amount of helm required. At some time before the ship's head is in the required direction, depending on the rate at which the ship swings, orders should be given to reduce the helm and to put it amidships, thus " Ease to 20," ' Ease to 10," "Midships." In order that the swing of the ship may just be stopped when the ship arrives on her new course, an order for the requisite amount of opposite helm should be given ; or, the helmsman should be given the order " Meet her," when he will check the swing of the ship as rapidly as possible. When the ship's head comes exactly on to the new course the order 'Steady' should be given, and this order means: — keep the ship's head in the direction in which it is at the instant the order " Steady ' is received. After receiving the order " Steady " the helmsman should continue to keep the ship's head in the same direction until a further order has been received. When the helmsman receives the order " Steady " he should report the course, as indicated by the steering compass, to the officer conning the ship. The helmsman should repeat every order which is given to him- with regard to the helm. When giving orders for small alterations of course it is usual to name the actual degree which it is desired that the helmsman shall steer; for example, if the helmsman is steering N. 80° E. and it is desired to alter course so as to keep 5° further over to port, the order " Steer N. 75° E." should be given. If a ship is off her course the fact should be pointed out to the helms- man by saying ' You are 3° to the Northward of your course " or You are 3° to the Eastward of your course," as the case may be, care being taken to indicate that cardinal point to which the ship's head is too near. When altering course, orders should be given for sufficient helm to cause the ship's head to move immediately. If the alteration of course is small, the helm should be eased as soon as the ship's head is seen to be moving. To see if the ship is beginning to respond to the helm, the land or the horizon should be watched and the ship's head will be observed to move before there is any indication at the compass. If conning from forward any movement of the ship's head will be detected more quickly by looking aft, and vice versa. If, during an alteration of course, interrup- tions occur which make it necessary for the officer, who is conning the 231 Art. 186. ship, to direcl hi^ attention elsewhere, he should, before Leaving the compass, give the helmsman a course on which to steady the ship, thus Steady her on North Bast ": and subsequently, he should steady the ship on her proper course by standard compass as soon as possible. On taking charge of the ship the amount of helm which the ship is carrying should always be ascertained. H is Lmportanl to remember this, because, it the ship is carrying any helm, it is necessary to allow for it when altering course After steadying the ship by the standard compass on the new course, an interval of about five or ten minutes should be allowed to elapse, after which the ship should be steadied again so as to give the compasses time to settle down: this is a valuable check on an\ mistake thai may have been made when the original order " Steady " was given. When a ship i^ to be on a course for a few minutes only it is a waste of time to steady her very carefully, for a degree in cither direction is of little importance in a distance of a mile or two; but, if the ship is to remain an her course for a considerable time the greatest care should be taken that the ship is steadied on her course as accurately as possible. Arts. 186, 187. 232 PART III.— THE ATMOSPHERE AND OCEAN. CHAPTER XIX. THE WEATHER. 186. The atmosphere. — In Parts I. and II. navigation has been treated without special reference to the movements of the media, the atmosphere and ocean, through which the ship steams. These movements are ki^own as the winds, the rise and fall of the tide, the tidal streams and currents, all of which should be taken into careful consideration in the navigation of the ship (§ 39 and 47), and obviously no movement of the one can take place without some movement of the others. We shall first deal with the weather and forecasting the weather, weather being a general term for the state of the atmosphere with respect to its temperature, pressure, motion, humidity, and electrification. The atmosphere is a gaseous body surrounding the earth ; it is elastic, very sensitive to the action of heat, and is necessarily much denser in the vicinity of the earth's surface than above that level. Experience has shown that at a height of 7 miles the atmosphere is so rarefied that great difficulty is found in breathing, and at a height of about 40 miles the atmosphere is no longer capable of refracting the sun's rays. The atmosphere may be assumed to extend to about 200 miles above the earth's surface. The atmosphere always contains a certain amount of aqueous vapour, although it is seldom, if ever, completely saturated. The ratio of the quantity of aqueous vapour present in the atmosphere at any place to that which it would contain if it were saturated, the temperature remaining the same, is called its humidity. The humidity is measured by means of an instrument called a hygrometer, which is described in Part IV. 187. The pressure of the atmosphere.— Tf all parts of the atmosphere had the same temperature, there would be perfect calm and the surface pressure of the atmosphere would be everywhere the same. In conse- quence of the equatorial regions being at a higher temperature than the polar regions, the atmosphere over the equatorial regions rises and that over the polar regions falls ; at the same time the upper strata of the atmosphere flow from the equator towards the poles, and the lower strata flow from the poles towards the equator. If the earth had no rotation on its axis, this circulation would take place in the planes of the meridians. On account of the rotation of the earth, however, rising air is deflected to the Westward, and falling air to the Eastward ; also, as will be under- stood from the following article, air moving from the equator towards a pole is deflected to the Eastward, while in moving towards the equator it is deflected to the Westward. The result of this circulation of the atmosphere is that in high latitudes the atmosphere is moving faster than the earth's surface, its centrifugal force is consequently increased, and it tends to press on the atmosphere 233 Art. 188. in lower latitudes. Again, the expansion of the atmosphere over the equatorial regions due to the high temperature there causes it fco pi ob that in higher latitudes. The combined effect is bo raise the pressure of the atmosphere in about latitude 30°, above that in higher or lower latitudes, and the distribution of the atmospheric pressure is roughly as shown in Fig. 147. W hen : he temperature at any place is higher than t bat in the surround- ing area; the air over that place expands and rises, and the upper strata flow outwards; the result i^ that the pressure of the atmosphere at that place is reduced below that in the surrounding area. Due to this cause we may expect that the average pressure at any place will be different in summer and winter. Now the land is more susceptible to changes <>t temperature than the sea> and so we find that between summer and winter larger differences of pressure occur over the land than over the Tin- pressure of the atmosphere is measured by means of an instrument called the barometer, in which the pressure i- measured by the height, in inches, of the column of mercury p necessary to balance it. The baro- meter i- described in Part IV. The average pressure of the atmo- sphere is about 29*9 inches. Figs. 148 and 149 show the mean pressure of the atmosphere for i In- months of February and August respectively, by means of J line- drawn through all places where the mean height of the barometer during these months is the same. \ These lines are culled isobars and the charts on which they are drawn are 'ailed isobaric charts. On examining the charts it will een that the average pressure conforms fairly closely to what has □ said above. Thus, over the equatorial belt the pressure is everywhere relatively low ; over the various between the latitudes of -<» and 4r l"\\ pre one the centres of these ar often referred I ot high and low pressure respectively. 188. Cause and direction of wind. II a place lies between two area* whose barometric pressure* are different, the air il"\\ from the ■oca of relatively high prec lire to that of relatively l«»\\ . and wind ic experienced at that pi • The velocity of wind depends on the relative pre ure in adjoining irea and i- determined bj the iteepne I the barometric gradient; Art. 188. 234 in other words, the strength of the wind at any place depends on the diffe- rence in the heights of the barometer on either side of that place. To compare barometric gradients it is customary to reduce them to hundredths of an inch of mercury per fifteen nautical miles. The steepest gradient ever observed Avas at False Point in India, where it was 238, so that, in a distance of 15 miles, there existed a difference of barometer readings of 2 • 38 inches. For purposes of reference a scale, called Beaufort "s scale, is used to classify winds of various velocities, and is given in the beginning of the Ship's Log and in the Barometer Manual. The direction of the wind depends on its velocity due to the baro- metric gradient, and on that due to the rotation of the earth. If we suppose that the atmosphere is in a state of perfect calm, any small por- tion of it is moving Eastward at the same speed as the locality over which it is situated, so that, although there may be perfect calm over the whole earth, any particular portion of the atmosphere in contact with the earth in latitude L is moving East at 900 cos L knots ; this would be the condition of the atmosphere in the absence of disturbing influences. Let O, Fig. 150, be a centre of low pressure in latitude L North where the atmosphere has a speed of 900 cos L knots East and some upward velocity. Let A be a point in a higher latitude L' where the atmosphere is moving East at 900 cos L' knots and, on account of its pressure being higher than at 0, is moving South at a certain speed. The horizontal velocity of the atmosphere at A, relative to the centre of low pressure at O, may be found by reducing to rest and giving the atmosphere at A an addi- tional velocity 900 cos L knots West. Thus, relative to 0, the atmosphere at A has a velocity 900 (cos L -- cos L') knots West and a certain speed South ; consequently the direction of its resultant speed lies between South and West. Now the direction of the wind is named, not by the direction in which the atmosphere is moving but by the point of the compass from which it has come, so that an observer in the vicinity of A experiences a wind from between North and East, that is a North- Easterly wind. Similarly, if we consider another point B in a latitude lower than that of 0, and where the pressure of the air is greater than that of O, it will be seen that an observer in the vicinity of B will experience a South- westerly wind. From a consideration of a large number of points such as A and II, we conclude that, about the centre of low pressure 0, there is a circulation of the atmosphere in an anti-clockwise direction, inclined spirally inwards and rising. If the centre of low pressure were in the Southern hemi- sphere the circulation would be in a clockwise direction. Winds thus circulating about a centre of low pressure are called cyclonic winds. Conversely, if a portion of the atmosphere has its pressure increased above that of the surrounding areas, there is a flow from it to areas of relatively lower pressure. We conclude that, round an area of high pressure there is a circulation of the atmosphere in a clockwise direction in the Northern hemisphere, and in an anti-clockwise direction in the Southern hemisphere, and inclined spirally outwards. Winds thus circulating about an area of high pressure are called anti-cyclonic winds. From the above, it will be seen that at any place there exists a relation between the direction of the wind and the bearing of the nearest centre 235 Art. 189. of low pressure; this relation is known as Buys Ballot's law, and may In- enunciated thus : — In the Northern Hemisphere In the Soul hem Hemisphere Stand with your face to the wind, Stand with your face to the wind, ami the barometer will be lower on and the barometer will be lower on your right hand than on your left. your left hand than on your right. 189. Permanent winds. Trades and Westerlies. Reference to the charts, Figs. US and 149, shows that North and South of the equator there art- permanent areas of high and low pressure; therefore, in con- formity witli Buys Ballot's law, it may be expected that aboul these areas there arc winds whose speeds and directions arc more or less per manent. Lot us consider tin- effeel of the areas ,.| high and low pressure in the North Atlantic. The direction of the wind is as shown in Figs. 151 or 152; between the latitudes of :;<> and In X. there is a N.E. wind. while in the neighbourhood of the parallel of 40 X. the wind is more or A 900co5 L knots -<- s \ -*800 cos L! knots. SOOcosLknots <~ ^fJOOco^Lkr. Equator Fig. 150. Westerly. These winds are called the North-East Trade wind (Trades) and the Westerlj wind (Westerlies). Similarly it will be seen there are N.E. Trades and Westerlies in the North Pacific, and ,"• I le ai -I Westerlii i>. 'he South rn ocean. Owing to t he < (an pa rat ive absence of land in tb< Soul hern hemisphere the Westerly winds blow tin re with considerable violence, and t he region over which t hey blow, betwe< n the latitudes of 40 and BO s.. is called the " roaring fortie • en the Trades and Westerlies the winds are variable in direction, and th< over which these variable winds prevail are called, in the Northern hemisphere, the Variable* of Cancer and. in the Southern, t he V;i i i i bles <,t Capricorn i hey take th< ir name from those sometimes given to the parallels of latitude of 23 27 \ . and s. (the Tropic of < 'ancer and the Tropic o\ Capricorn). Between the N E. and the S.E. Trades then A calm* which \% known as the Doldrumi in thi^- region the weai hei i generall} characfr ri ed D3 clouds and rain, but occasionally h\ eddies or whirlwind- which form the nuclei of th( n tl tropical - toi ' The an b of low presnure over the equator and ho the limit "I the de wind . has a periodic movement North and South corresponding Arts. 190, 191. 230 to the movement of the sun in decimation. The following table shows the approximate Trade wind limits in the various oceans : — Ocean. In January. In July. North Atlantic - 2° N. to 25° N. 10° N. to 30° N South Atlantic - „ 30° S. 5°N. „ 25° S. North Pacific - - 8°N. „ 25° N. 12° N. „ 30° N South Pacific - - 4° N. „ 30° S. 8°N. „ 25° S. South Indian - - 15° S. „ 30° S. „ 25° S. Figs. 151 .and 152 show the areas where the Trades and Westerlies prevail. 190. Periodic winds. Monsoons. — Let us now consider the effect of the great change of pressure which takes place over the continent of Asia (§ 187, Figs. 148 and 149). In the Northern summer this continent becomes excessively heated and the pressure is reduced below that of the neighbouring equatorial regions ; the result is that a cyclonic wind system, with its centre over Asia, is introduced, and a South-Westerly wind, known as the S.W. Monsoon, prevails over the Indian Ocean and the China Sea. The centre of this cyclonic system is approximately over the Himalayas and, as the barometric gradient becomes steeper as the centre is approached, we find that the S.W. Monsoon in the Indian Ocean blows with great violence, while in the China sea it is a light wind. In the Northern winter, however, owing to the continent losing its heat more quickly than the ocean, the pressure of the atmosphere over the continent is raised above that over the neighbouring equatorial regions ; the result is that an anti-cyclonic system, with its centre over Asia, is introduced, and a N.Ely wind, known as the N.E. Monsoon, prevails over the Indian Ocean and China Sea. In this case the centre of the anti-cyclonic system is situated over Eastern Asia, and consequently the N.E. Monsoon in the China Sea blows with considerable violence, while in the Indian Ocean it is a light wind. From November to March the N.E. Monsoon blows across the equator, and, on account of the change of the speed of the earth's surface in different latitudes, changes its direction and becomes what is known as the N.W. Monsoon, which blows from a direction between N.W. and S.W. The following are the approximate seasons of the Monsoons :— S.W. Monsoon, March to September. N.E. and N.W. Monsoons, October to March. Figs. 151 and 152 show the areas where the Monsoons prevail. Another example of the effect of land is found in the winds round Australia. In the Southern summer a low pressure exists over Australia due to the heating of the land, and the winds round the continent are therefore cyclonic ; in the Southern winter the reverse takes place and the winds are anti-cyclonic. 191. Land and sea breezes. — The land and sea breezes which char- acterise the summer climate of nearly all sea coasts are analogous to the monsoons. The land becomes abnormally heated by day, a low pressure is produced, and a breeze draws in from seaward which continues until the evening. During the night the land loses its heat more rapidly than the water; the daytime conditions are therefore reversed, and a land breeze springs up which continues until the morning. 23 7 Arts. 192, 193. 192. Diurnal variation of the barometer. Apart from the effects of land, the changes of temperature by day and night give rise to a periodic variation of pressure, which is most marked hi the tropics. The baro- meter rises from about 4 h a.m. to 10 h A.M., falls during the heat of the day until about 4 h p.m., and then rises again until about 10'' p.m., when it once more falls till 4 U a.m. and so on. This diurnal variation has a range of about *07 of an inch in the tropics, but it is much less outside those regions where it may still be traced if the mean of a large number of observations is obtained. The regularity of this diurnal variation of the barometer in the tropics is of particular value, because, if the baro meter readings on any day do not conform to it, it is certain that some disturbance exists in the neighbourhood, as will be seen in the following chapter (§ 207). 193. Local winds. — On account of varying local conditions, the winds experienced in different parts of the world have special characteristics and usually have local names. The following table gives the most important local winds and the seasons at which they blow : — Name. Locality. Season. Remarks I [armattan T> irnado Cape Verde to Cape Lopez. West ( 'oast of Africa extending as far South as the River Congo. December, January and February. .March to June. October and Nov- ember. South- K Cape of Good Hope - October to April - \ i] t h -Wester Do. do. May to September Westerly North Coast of Winter. Africa. Easterly Do. do. - Summer. Scirocco (8.E.) Malta and Italy Do. - gale i X.E) Malta Winter. Boi i - Adriatic - Do. i.Mv.) Grecian Archipelago Summer. Mistral (N.W.) Gulf of Lyons - _ Norther Gulf of Mexico September to March I'.itnj Rio do la Plata July to September. terry Cape Horn April to July. Wilbwaw - Strait nf Magellan • Frequent Norther Bay of Panama I teoember t.> April. N.N.W. Red Sea, Southern part. D... do. - June i" September. 3 g E. • ( totober to May. 3hamaJ (N.W.) Persian Gulf - ■nil. K...: 3.E.) - Do. - 1 December 1 1 1 \pnl ii. ;.. t (N. to Arabia, South 1 1 1. villi- i i o March WWW.). Elephants [ndia, Malab itembei and ,,i .. ■ ■ Dauphin Vfad South < !c neral. N.E.). Km -i End, ■ i \.isl r.ili.i A very dry wind from the desert laden with fine sand. A violent squall off shoro followed 1>\ a downpour of rain. North-Easterly winds very seldom blow at the Cape of Good Hope. A hot. damp wind. The must, frequent wind, often bee. nnes a gale in w inter. Very heavy Bqual \li. rnates Willi Shamal during these HlMlltllS. A Strong land u in. I. Souther!] or South Easterly gale which the South- ion. Arts. 194, 195. 238 194. Causes Of clouds, rain, &C. — When the atmospheric pressure at any place is lower than that of the surrounding areas the air at that place rises, and, if situated over the ocean, the rising air carries with it a large quantity of aqueous vapour resulting from the evaporation of the water. As this column of air and aqueous vapour rises, it expands still further owing to the rarefied state of the upper regions of the atmosphere; this expansion is accompanied by loss of heat, and this loss together with a low temperature over the upper regions causes the aqueous vapour to be condensed, the condensed vapour combined with the multitude of small particles floating in the atmosphere presents the appearance known as clouds. Two theories of the formation of the clouds have been put forward :— (1) Condensation by cooling, which is the most general process and is that sketched above. (2) Condensation by mixing, which takes place when a mass of moist air encounters in its ascent another mass of moist air which is at a different temperature. The appearance of clouds depends on the way in which they have been formed and on the height at which condensation took place. Fig. 153 shows the four fundamental forms of clouds, namely : — cirrus, cumulus, nimbus, and stratus, as well as six others, together with their average heights. It is supposed that cumulus, nimbus and rain are due to process (1), that surface fog, which is only cloud in contact with the earth, is due to process (2), and that as regards the other forms of clouds it is impossible to say to which process they may be assigned. Rain always falls from the nimbus cloud and results from the con- densation being so great that water is precipitated. Should the con- ditions of the atmosphere be such as to condense and freeze the aqueous vapour in its ascent, the precipitation is in the form of hail. The conditions for the condensation of aqueous vapour in the form of snow are unknown. Dew is formed when the surface of the earth becomes sufficiently cold to condense the aqueous vapour in the atmosphere which is in imme- diate contact with it. The temperature at which this occurs is called the dew point. If the dew point is below freezing point, the deposited moisture is known as hoar frost. It is obvious that, when a wind is blowing, neither dew nor hoar frost can be deposited. When two winds, which are blowing in opposite directions at some distance above the earth's surface, come in contact a vortex is caused and a rain cloud is sometimes brought down to the earth's surface by the rapid gyrations of the air. This presents the appearance of a tapering funnel of water joining the surface of the sea to the cloud, and is known as a water-spout. Water-spouts are common in many parts of the ocean where the climate is warm, and particularly in the Western basin of the Mediterranean Sea. They should not be approached too closely. 195. Causes Of fog. — W r hen warm air which is greatly saturated with aqueous vapour passes over cold water, the temperature of the air is reduced, the aqueous vapour is condensed and fog is formed. When a cold wind blows over warm water the aqueous vapour which is evaporating from the water is chilled with the same result. When a deep ocean current is opposed by a shoal, such as, for example, the Davis Strait current by the banks of Newfoundland, the cold water NAMES. TYPICAL FORMS. MARE'S TAIL CIRRUS 27.000 to 50.000 (l. CIRRO-STRATUS RAGE 29,50'. Il MACKEREL SKY CIRRO-CUMULUS 10.000 to 23.000 ft. ALTO-CUMULUS !■' fl ALTO-STRATUS 10.000 to 23.000 ft. STRATO-CUMULUS ABOUT 6,500 ft. CUMULUS STORM CLOUD CUMULO-NIMBUS ii ■ HAIN CLOUD NIMBUS STRATUS (i HEIGHT. COMPARISON. OBJECTS. 9 a 7 h 4 :' \ I II ConcCor- < /It forest) AMP£S (Aconcaqma ) Mo*rr 8j.anc K-/TF Bosrosi » us SI \ •. : l //// j rt)>~ Jtwfll FORMS, HEIGHTS AND NAMES OF CLOUDS. f (tOM PHOTOOHAPHS UY COL H M 8AUNDEH8. Fio. L53. 230 Art. 196. from below is driven to the surface, and if its temperature is below dew point fog is formed. Another cause of fog is the interlacing of currents, the temperatures of which differ considerably, such as the Gulf Stream and the Davis Strait current. A bank of fog may be driven by the wind to a considerable distance from the place where it originated, provided there is little or no difference in the temperature of the air and surface water, hut such fogs soon disappear. Some fogs have a tendency to lie in a thin stratum which extend- only some .*>(» or 4t» feet above the surface of the sea, this probably oci ore when the water is colder than the air. It is quite possible to see over such fogs from 1 lie mast head. hut. on the other hand, there arc fogs w Inch have little density till they have attained a height of several feet. Thus we see the necessity of placing look-outs a- high up and as low down as possible when a ship is steaming in a fog. The following table shows the important localities where fogs are frequent and the seasons at which they occur : — Locality Season. British Islands At all seasons, hut most in quent ly in t he < Jhannel during January and dune. Wot Coast of Africa, north of the November to May. equator. West Coast of Africa, south of the June to August. equator. West Coast of North America - - Very frequent in the summer. Banks of Newfoundland - - At all seasons, hut most frequent in June and -Inly. ' of ( hina ----- January to April. Japan ------ April to dune. 196. Atmospheric electricity. The atmosphere is charged with elec tricity which is generally at a different potential to that of the earth: the cause of this electricity is uncertain, hut there is no doubt thai it exists in the minute partii les of aqueous vapour which, due to evapora tion. are continuously rising. Winn the difference of potential between a cloud and the earth is sufficiently great a discharge take place from the former to the latter, and it is accompanied by a brilliant Hash known as lightning and by a riolenl report known as thunder. Thunder ami lightning maj also he . .:, od bj an electrical discharge between two cloud Thunder cloud* are sometimes as near the earth's surface as Tun feet, hut more u uallj their height is between 3,000 and 6,000 feet. The distance oi •• thundi i torm from an observer ma} he estimated approxi mately by noting the number ol seconds which elapse between the Ha li ol lightning bein een and the" thunder being heard Remembering that sound travels al about 1,130 feet per second, we have the rough rule the distance oi the storm in cables i^ about twice the number <>i observed. In order to eliminate the po sibility ol danger in the evenl ol d hip being truck by lightning, h:_ditiiuiL r condu< i"i arc fitted on each ma Art. 196. 240 The effect of lightning striking the ship is usually very noticeable at the magnetic compass. Another effect of atmospheric electricity is the Aurora borealis, which is a brilliant light in the heavens in high North latitudes ; it is most frequent at the equinoxes, and least so at the solstices. The Aurora australis is a similar light visible in the Southern hemisphere. Still another effect is that known as St. Elmo's fire, which is some- times seen when a discharge of electricity takes place at prominent points, such as the extremities of a ship's yardarms ; it appears in the form of small balls of fire and is particularly noticeable on dark tempestuous nights. 241 Art. 197. CHAPTER XX. FORECASTING THE WEATHER. 197. The synoptic system of weather analysis. — In bhe previous chapter the effect of the more or less permanent areas of high and low pressure has been discussed. On account of temporary and local causes small areas of high and low pressure are found which are generally in motion, following more or less the normal direction of the wind, and bringing about variations in the normal weather at the various places which they pass. In this chapter we shall briefly indicate how to forecast the weather at any place on any particular day. To forecast the strength and direction of the wind and the type of weather likely to be experienced, a system, called the synoptic->y.M ein, is employed. A synoptic or synchronous char; of a region is one on which is shown the distribution of the various meteorological elements. namely the barometric pressure, the temperature.; of the air and water, the strength and direction of the wind, the weather, &c, over the region for the same instant of time. Simultaneous observations, taken at a large number of stations and also on board ships, arc placed on the chart . the barometer readings having first been reduced to sea level and to a temperature of 32° F. in latitude 45°. The isobars are then drawn, as well as a number of arrows which indicate the direction and strength oi the wind. All points at which the temperature is the same are joined by lines called isotherms. A specimen synoptic chart is shown in Fig. 154. From a study of a xery large number of synoptic charts, more than eleven hundred of which are constructed each year at the Meteorological ( Hlice, the following important generalisations nave been deduced. (1) In general, the configuration of the isobars take- one of seven well defined forms. (2) Apart from the form of the isobars, the wind alw ikes a definite direction relative to the trend of tin-.' lines and the direction of the nearest area of low pressure. (.*>) The velocity of the wind is nearly always proportional to the clo of the isobars, that i< to the steepness of the baro metric gradient. (4) The kind of weather, apart from the wind, depend; generally on the form of the isobars. Some forme an Lated with good and some w it h had weather. (5) The area mapped out by the isobars i constantly (lifting, so that as it drifts past any place, ohangeoi weal her is experienced. The motion oi an area mapped out by isobai follow a certain law which makes for< ble. Sometimes in the temperate zone, and constant!} in the tropin lam fall without any appreciable change in the i This kind of rain i called non isobaric rain. Arts. 198, 199. 242 198. The seven fundamental forms of isobars. — Fig. 155 shows in a diagrammatic form the broad features of the distribution of pressure over the North Atlantic on February 27th, 1865. In this Figure the seven fundamental forms of isobars are shown ; at the top we see two cyclones, the isobars round each of which are rather close together. Just South of the left hand cyclone the isobar of 29 • 9 inches forms a nearly circular loop enclosing an area, the pressure over which is lower than 29 • 9 inches ; this is called a secondary cyclone because it is generally secondary or subsidiary to some primary cyclone. Further to the left the same isobar bends into the shape of the letter V and encloses an area of lower pressure ; this form is called a V depression. Between the two cyclones the isobar projects upwards and encloses an area of higher pressure ; this form is called a wedge. Below all these there is an oblong area of high pressure, an anti-cyclone round which the isobars are very far apart. Between the two anti- cyclones there is a neck of relatively lower pressure which is called a col. Lastly, at the lower edge of the diagram an isobar rnajr be seen which does not enclose an area ; this is called a straight isobar. Cyclone 29 \29'7 ine Wec/q& ,'>»"> i ,--\ , ;-, / / \Cycions, •S' ! / / \ \ ! / '' /29 9 30-1 Anti r i „ .' / / Anti {cyclone Lycione i, j [~/ v - Stra/ght Isobar Fig. 155. It has been found that, in the temperate zone (§ 13S), cyclones, secondary cyclones, V depressions, and wedges usually move to the Eastward at about 20 miles an hour, while anti-cyclones are often stationary for days. 199. The cyclone. — Fig. 156 shows the kind of weather usually ex- perienced in a cyclone, the small arrows indicating the direction of the wind. The direction in which the cyclone is moving is indicated by the large arrow. It will be noticed that the isobars are oval and not cmite concentric, the inner ones being rather in the rear. As the cyclone passes an observer the barometer falls till the centre of low pressure has passed, and then begins to rise ; thus if, instead of supposing the observer s to be at rest and the cyclone to be in motion, we suppose the observer ^to be moving across the cyclone as shown in Fig. 157 and the cyclone|to be at rest, then the barometer will fall until he arrives at the point 'X when it will begin to rise again ; and it will be seen that wherever the path of the observer is with regard to the centre, he will experience some point of lowest pressure such as X. The line joining all such points passes through the centre of the cyclone and is approximately a straight line .perpendicular to the path. This line is called the trough 1>43 Art. 200. of the cyclone and i- associated with a squall or heavy shower, commonly known as the clearing shower, which is very marked in the Southern portions of the cyclones which occur in the North temperate zone. CirroStnattM (ffrro-Stratc As mentioned in § 1 i*7. the kind of weather experienced and the direction of the wind in a cyclone are approximately always the same, for these elements depend only on the forms of (he isobars, while the intensity of the weather and the strength of the wind depend on the closeness of the isobars. The sequence of weather experienced by an observer as a cyclone passes may be seen by reference to Fig. 156. \\ ind i> said to veer when its direction changes in the same way as 1 he hand- of a .lock ; and it is said to back when it changes its direction in the contrary way to the hands of a clock. Therefore it will be seen that in tin- Northern hemisphere the wind would veer to an observer situated in the Southern part of a cyclone. If the observer were to the Northward of the path, the wind would back, if the observer were in the oath of the cyclone the wind would remain steady, and then rapidly shift Hi points without either veering or backing; the direction of the wind would depend on the direction in which the cyclone was travelling. In the centre of a cyclone there is usually a small area of calms with a ver\ heavy dangerous sea. <-- Path of Ub$e (Cy 200. The secondary cyclone. Fig L58 shows the Kind .>l weather iisualh experienced in • > jeoondan cvclone. A secondary cyclone is generally found on th< of a cyclone, but frequently on thai oi an anti-cyclone. The isobar oi '■'• l> ' I inch »wn bcnl downward Art. 201. 244 enclosing an area of relatively low pressure, and it will be seen that the gradient between the isobars of 30- 1 and 30*0 inches is in consequence very much reduced and therefore the wind inside the bend is very light ; 30-00 30-10 Irregular Cumulus m ?ROHT > 36-20 Fig. 158. conversely, the barometric gradient between the isobars of 30-2 and 30 • 1 inches is increased and therefore the wind round the edges of the bend is stronger and blows in violent angry gusts and not steadily as in a cyclone. The motion of a secondary cyclone is usually parallel to the path of the primary, but when the secondary is formed on the edge of an anti-cyclone its motion is very obscure. Secondary cyclones are asso- ciated with a peculiar kind of thunderstorm, a special feature of which is calm and sultry weather. 201. The anti-cyclone. — Fig. 159 shows the kind of weather usually experienced in an anti-cyclone. The isobars are more or less circular 30 00 Fig. 159. and concentric, while the barometric gradient is slight. An anti-cyclone is frequently stationary for days, but sometimes moves on; it more frequently disappears and is replaced by isobars of another form. 245 Arts. 202-204. The distinguishing feature of an anti-cyclone is radiation weather, the theory of which is that, when the air is still, the heat from the earth's surface radiates into the surrounding atmosphere until the surface becomes sufficiently cold to condense the aqueous vapour in the air, or to form dew or fog. 202. The wedge. — Fig. 160 shows the form of isobars known as a wedge. The isobars of 29-8, 30-0 and 30-2 inches are shown bent upwards between two depressions. As the two depressions move onwards, the wedge moves on between them, so that there must be a line of stations where the barometer, after it has risen owing to the passing of the first depression, commences to fall owing to the advance of the second depression ; this line is called the crest of the wedge. In a wedge the gradient is never steep, so that the wind never rises above a pleasant breeze. Cyclone Cyclone 29-60 29-80 30 OO 30 a Fig. 160. 203. Straight isobar. Pig. 161 shows the kind of weather generally associated with straight isobars. The trend of the lines may be in any direct ion. Iii the Figure the barometer is shown high in the South and low in the North. The wind is usually strong or gusty but does uot rise to a gale, and when the barometric gradient i teep rain sometimes Falls in light showers w it h a hard ! 204. The V depression. Fig. 162 show* the kind of weather usually experienced in a V depression. In the Northern hemisphere the point ol the V Le generally directed towards the South. The trough (§ 199) is nearly always curved with it* convex side towards the ESa The wind does not veer in the usual manner, but, a the trough pa i over the observer, there is a udden bift of the wind accompanied bj a \ iolent squall. II] (IS l< Art. 205. 246 V depressions are generally formed along the prolongation of the trough of a cyclone to the Southward, or in the col between two anti cyclones. 29-70 Cold Rain Strstus Hate 23-80 Fig. 161. There are two kinds of V depressions, that shown in Fig. 162 being the more common in Northern Europe. The other kind differs from this chiefly in the fact that the rain is in the rear instead of in the front of the storm. From Fig. 162 it will be seen that the trough of a V depression is associated with a line of squalls. As the trough moves broadside on with the V depression to which it be- longs, there is a sudden shift of wind (from 8 to 10 points) with a violent squall continually taking place along the trough, so that a long strip of country may be visited by this disturbance at the same instant; this squall, which is characteristic of a V depression, is often called a line squall. 205. The col. — The col is merely an area situated between two or more anti- cyclones and of relatively lower pressure. No typical kinds of weather are expe- rienced in a col. The importance of this form of iso- bars lies in the fact that, since it lies between two anti-cyclones which are ' probably stationary, it is a line of weak- ' ness along which disturbances may be ;p IG \Q2 propagated. The movement of a cyclone after arriving at a col is uncertain ; sometimes it passes through the col, but more frequently the main body of the cyclone is deflected or dies away, while an irregular secondary /v 247 Art. 206. pushes its way more or less across the col. All that can be said with certainty is that the presence of a col is an indication of unsettled weather. 206. Revolving storms. — Although revolving storms of all kinds are called cyclones by the meteorologist, the very violent ones are known as hurricanes in the West Indies and Pacific Ocean, as cyclones in the Indian Ocean, and as typhoons in the China Sea. Revolving storms are seldom experienced within live or six degrees of the equator and never in very high latitudes; they are most severe in the West Indies. the Southern Indian Ocean (particularly in the vicinity of Mauritius), the Bay of Bengal, and in the China Sea. In the Northern hemisphere revolving storms occur between July and November, and in the Southern hemisphere from December to May. In the Bay of Bengal and in the Arabian Sea they are most common about the time of the change of the monsoon-. The following table shows the localities and seasons at which revolving storms occur : — Locality. Name. Season. WV-: Indies North Pacific China Sea - Arabian Sea and Bay of Bengal South Indian Ocean - South Pacific Hurricane Hurricane Typhoon Cyclone Cyclone Hurricane July to November. July to October. July to November. April and May. November. December to April. December to April. October and The following rhyme may be of use in remembering the seasons at which the West Indian Hurricanes may occur : — " June — too soon, July — stand by, August — look out, you must, September — remember, October — all over." When interpreting this rhyme it must be borne in mind thai many hurricanes occur in October, and the hurricane season cannot be said to be over till November. These storms, which originate in the tropics, at firsi travel about W.X.W. or W.S.W. .it Bpeeds varying between 50 and 300 miles a daj they gradually curve to a more polar direction along the edge of the great ocean anti-cyclone (Figs. 148, 149) which generally lie between the latitude 20 and 40 . They may continue travelling in a North We terry or South Westerly direction over tin- continents, but m [uently thej curve to the North Ea tward or South Eastward, along the polar edge oi the ocean anti cyclone, and eventually tnaj travel to the Eastward with the general movement of the atmo phere, or die out on meeting some high pressure an The path oi a torm i the trau h Followed bj il i entr Big I shows the norma] paths of revolving rtorms town the tropica into the temperate zon< It will be noticed thai in the Northern hemisphi the direction of the path changi in aboui Latitude 80 and m the Southern hemisphere in aboui Latitud< l: 2 Art. 206. 248 DIAGRAM SHEWING THE NORMAL SHAPE, AND TRACKS OF CYCLONIC STORMS. NORTH AND SOUTH OF THE. EQUATOR. 4-cr i l l • 10" NORTH LAT A ' '£ NORTH LAT.30" 40 20° ZO' 10* IO O EQUATOR EQUATOR 10" 2 0° t/V h^TIl) I J S 30- 40* o+°r*«*' 10' 20; SOUTH LAT.25' 30" 4cr Fig. 163. 240 Art. 207. The point of the path at which the direction changes is called the cod of the storm. The trough of the storm is the Hue through the centre at right angles to the path. That part of the storm which is on the right hand of the path in the direction of advance is called the right-hand semicircle ; the corresponding part on the left hand is called the left-hand semicircle. The trough of the storm divides each semicircle into two quadrants, called the front and rear quadrants. The right-hand semicircle is called the dangerous semicircle in the Northern hemisphere, and the left-hand semicircle is called the dangerous semicircle in the Southern hemisphere; these names arise from the fact that a vessel, if situated in the fore part of the semicircle, may possibly be drawn across the path of the storm. It will be seen that the dangerous semicircle is always on the inside of the curve which is the path of the storm. The diameter of the area covered by a revolving storm at a particular instant has been found to vary from 20 miles to several hundreds. In the Atlantic and South Indian Oceans these storms originate to the Eastward in about latitude 10° ; those of the Bay of Bengal originate near the Andaman Islands, and those of the Arabian Sea near the Laccadive Island-. The last two generally travel to the West and North-West, while those of the Bay of Bengal sometimes cross India. The typhoons of the China Sea generally move in a Westerly or North-Westerly direction at first: they then curve to North and then to North-East. In the earlier part of their season they often blow right home to the coast of China, whereas late in the season they often curve off before reaching the coast, passing outside -la pan and dying away in the Pacific. The rate of progression of revolving storms varies, but the average speeds in the various localities are : — West tidies - - - 300 miles per day. Arabian Sea - 2oo ,, ,, „ I Ihina Sea .... 200 ,, ,, ,, Bay of Bengal - - - 200 .. .. ,, South Indian ( Icean - 50 to 200 miles per da\ At the beginning and end of the hurricane, season in the South Indian Ocean a large proportion of cyclones aii- either stationary or move very slowly. The approximate average tracks of the revolving storms in the various oceans are shown on the pilot chart--. 207. The indications of the approach of a revolving storm. The approach of a revoh ing storm is indicated bj : — (1) A falling barometer, or an interruption of the usual diurnal range (§ 102 (2) An ugly threatening appearance ol the weather ami a rising gusty w ind. ('.'>) A long heavy swell or oonfu ed ea, which i- no1 caused by the then prevailing wind, but generally come from the direction in which t he i"i m i approachin Art. 208. 250 208. Rules for determining the path of and avoiding a revolving storm. — When in the region and in the season of revolving storms be constantly on the lookout for the indications just mentioned, and care- fully observe and record the barometer. If there is any indication of the approach of a storm it is necessary to know : — (1) The direction of the centre of the storm. (2) In which quadrant of the storm the vessel is situated. In order to ascertain these the observer must be stationary, so that it is necessary to stop or heave to. In a sailing vessel it is safer to assume that one is in the dangerous semicircle, in which case the ship should be hove to on the starboard tack if in the Northern hemisphere, and on the port tack if in the Southern hemisphere ; by so doing, every change in the direction of the wind will be from some direction further from ahead, as may be seen from Fig. 163, and so the danger of being taken aback will be guarded against. To find the bearing of the centre. — To find the bearing of the centre the observer should face the wind, and the centre of the storm will be from 12 to 8 points on his right hand in the Northern hemisphere, and on his left hand in the Southern hemisphere. At the beginning of a storm 12 points should be allowed; when the barometer has fallen three- tenths of an inch 10 points should be allowed, and when it has fallen six-tenths or more 8 points. To find in which quadrant the ship is situated. — To find in which semicircle the ship is situated the observer should face the wind; if it shifts to the right she is in the right-hand semicircle, and if it shifts to the left she is in the left-hand semicircle. To find in which quadrant the ship is situated he should note whether the barometer is rising or falling ; if it is falling she is before the trough of the storm, and if it is rising she is in the rear of the trough. The centre of a revolving storm is the region of greatest danger ; near it the wind is strongest, the direction of the wind changes suddenly, and the sea is most turbulent. If the wind remains steady in direction but increases in strength with a falling barometer, the ship is in the direct path of the storm. These rules hold good for both hemispheres. To avoid a revolving storm. — If it has been found that the ship is in the path of the storm she should run with the wind on the starboard quarter in the Northern hemisphere, and with the wind on the port quarter in the Southern hemisphere, until the barometer has ceased to fall. If it has been found that the ship is in the dangerous semicircle she should remain hove-to until the barometer begins to rise. If it has been found that the ship is in the safe semicircle she should run with the wind on the starboard quarter in the Northern hemisphere, and with the wind on the port quarter in the Southern hemisphere, until the barometer begins to rise. Careful note should be taken of any land that may be in the vicinity, as it may be possible to run into harbour or under the lee of land for shelter. In the Sailing Directions for the coasts of China a list of ports, called typhoon harbours, is given; in any of these a ship may safely ride at anchor during a typhoon. 251 Art. 209. It has been stated by Professor Mcldrum that in the South Indian Ocean it is often difficult to ascertain the hearing of the centre, owing to the difficulty of knowing whether the wind is a strong Trade wind or part of a stonn. When the wind lias shifted decidedly to East or South the centre may be approximately determined. In such a case, if the wind shifts from South-East directly to South, the ship should run to the North-West ; if the wind remains steady at South-Hast and the barometer falls, the ship is in the path of the storm and should run to the North- West. It has also been stated that iii cyclones of the South Indian Ocean. North-Easterly and Easterly winds often, if not always, blow towards the centre. 209. Weather in the British Islands and North Sea. — The British Islands and North Sea being situated between the parallels of 50° and 60°, Westerly winds prevail (§ 189), and Westerly gales are more prevalent than any other; they are most frequent in the winter months, between October and March, and often last three or four days; during May, June, and July they are rare. South-Westerly gales are most dangerous in the Eastern part of the channel, for when accompanied by rain they sometimes veer suddenly to North-West or North and cause a heavy sea. Winds from North to North-East are sometimes strong but seldom become gales in the central portion of the channel, except on the coast of France ; they do not usually last more than a day or two and the wind does not shift as it does with Westerly winds. In the channel, during winds from between North-North-East and Bast, the land is generally covered with a white fog which resembles smoke. Easterly winds are most common in the spring. South-Easterly winds accompanied by rain and a falling barometer almost always become gales. Moderate winds from North-West to North-East bring fine weather. During summer land and sea breezes frequently occur, at such times it usually falls calm at dark and a heavy dew* is formed. Little or no dew is a sign of an impending change in the weather. Prolonged calms are of rare occurrence, even in summer; they are generally precursors of bad weather, of which there are no more certain indications than swell in the offing and surf on the coast during a calm. The usual signs of an approaching cyclone are the wind backing to some point between South and South-East, and high cirrus clouds approaching from some Westerly point followed by cirro-stratus (§ L94), in which latter mock suns and halos round the moon are seen. The tracks followed by cyclones which pass over the British Islands are erratic, owing to the facl thai they are often deflected from then- course by the land. Those which pass between the Hebrides and [celand generally pursue a regular course t<> the North Bast, and it the position of the area of high prec are, a given in the dailj weather report- signalled to all II. M ship-, i tudied, it if po sible to forecast the path of a cyclone with a fair degree of aoouraoy. It is exceptional for the cent re of a cyclone to pa far South m the English Channel. Cyclones which past over the Briti h [glands almo I invariable pur lie an Easterly coui e. 'The wand therefore in these oyclones, wherevei their centres ma provided that thej are North of the observer, Art. 210. 252 begins between South and South-East and after a number of hours veers to some point between South and West. It has been found from a large number of observations that when the wind is between South and South-East the direction of the centre is about 120° from the direction of the wind, so that if the observer faces the wind the centre will be about 120° to his right (§ 208). When the wind has veered to some point between South-South-West and West the bearing of the centre is about 100° from the direction of the wind. The following table gives the mean angle between the direction of the wind and the bearing of the centre of the cyclone, for those cyclones which pass over or near the British Islands : — Direction of Wind. Mean Angle. Centre, close. I Centre, at a distance. N. N.E. E. S.E. S. s.w. w. N.W. 115° 118° 127 128 122 132 125 126 116 114 106 104 103 101 99 100 The following table, which has been made out for different months, gives the mean rate of progression of the cyclones which pass over, or near, the British Islands : — Month. Miles per hour. Month. Miles per hour. January - 17-4 July - - 14-2 February - - 18-0 August - 14-0 March - 17-5 September - 17 ?, April - 16-2 October - 19-0 May - - 14-7 November - - 18-6 June - - 15-8 December - - 17-9 210. Storm signals. — As explained in § 197, synoptic charts are pre- pared daily from observations taken at a large number of stations in the British Islands, Iceland, and on the continent, as well as on board ships at sea. From a study of these charts the Meteorological Office issue daily weather notices which, besides being signalled to H.M. Ships, are also transmitted by various commercial wireless telegraphy stations. Whenever bad weather is approaching the British Islands, information is telegraphed to numerous storm signal stations directing them to hoist a certain signal, in order to warn passing vessels of the weather that may be expected in their particular localities. Similarly, storm signal stations in other countries display storm signals from information received from their own National Meteorological Departments. In the majority of countries these signals refer to dis- turbances which are expected in the vicinity of the signal station dis- playing the signal, but in some cases, notably on the coasts of China, the signals indicate the position and track of a disturbance. 253 Art. 211. The majority of European countries use the same code, called the international code, which is given below. Information relating to the code of signals used at any place will be found in the Sailing Directions for that place. International code. The signal consists of the display of one or two cones, and the signification of each signal is as follow- ; — single cone, point upwards. Gale commencing with wind in the North-West quadrant . Single cone, point downwards. — Gale commencing with wind in the South-West quadrant. Two cones, one above the other, both points upwards. — Gale commencing with wind in the North-East quadrant. Two cones, one above the other, both points downwards. -Gale commencing with wind in the South-East quadrant. Two cones with their bases together. — Hurricane. (Wind force 12 Beaufort's -rile.) The above code is about to be adopted (1914 to 1915) for use in the British Islands, but until any signal station is equipped with the necessary appliances, the code shown below, which has been in use in the British Islands for many years, will continue to be used. One cone, point upwards (North cone). — Strong wind or gale-; from North or Bast, backing through North. One cone, point downwards {South one). — Strong winds or gales from South or East, veering through South to South-West. 211. Forecasting by a' solitary observer. When attempting to fore- cast the weather in a ship at sea, the observer has at his disposal : — (1) The daily weather notice, from which he can probably find the position, at some previous time, of the centres of the principal areas of high and low pressures in the vicinity. (2) Eis knowledge of the present state of the weather and the information recorded in the log during the preceding few days. (3) The movements of the barometer as recorded in the log, or by the trace drawn by a barograph. (4) Wireless reports as to the weather and movements of the baro- meter, which may lie received from other ship-. With this information available the principles set forth in this chapter should be followed as closely as possible, that is. the movement of any disturbance mentioned in the daily weather notice should be estimated from the knowledge of it- probable track and from (2), (.'5) and (4); this, however, is rendered difficult by the movement of the ship, for if a -hip is steaming directly toward- the centre of a depression the barometric gradient appears to be much steeper than i- really the ■ -. and if -he L£ -t ea mile.' awa\ from and being Overtaken b\ a depression the gradient appears slighter. Ml that we can safely deduce from the movements of the barometer is that, if the rati- at which the barometer is falling increa e the gale will probably become worse; and it the rate oi fall deci [ale will probably moderate. In tins connection we see the value of the instrument called a b iph, which draws a trace of the reading! of the barometer Fig. H»i shows pecimen trace, it will be seen that when the barometer is rising or Art. 211. 54 CO C5 M 255 Art. 211. falling uniformly, the trace becomes a straight line; if, however, the rate of rise or fall changes, the trace becomes either convex or concave to the direction of the base line according as the rate increases or decreases. Therefore the shape of the trace, whether straight, convex, or concave is independent of whether the barometer is rising or falling, but simply depends on the rate of change of the rate of rise or fall. Now, as explained in § 188, the velocity of the wind is proportional to the slope of the barometric gradient; therefore, if the trace is concave we may infer that the wind is likely to decrease in Btrength, and if convex to increase in strength. It should be remembered t hat . although a rapid rate of fall, in a general way. indicates worse weather than a moderate one, the inferences drawn from a trace depend en the variation of the rate and not on the rate itself. If no barograph is available very fair results can be obtained by plotting the hourly readings of the barometer on squared paper, and drawing a curve through the points thus plotted, but of course the minor fluctuations of the barometer do not appeal-. On board a ship a difficulty may arise as to what time the barograph should be set to, for obviously the instrument cannot lie adjusted in the same manner as the ship's clocks without breaking the continuity of the trace: for this reason it is customary to set the barograph to some standard time, and to note, by a mark, noon S.M.T. of each day, as shown in the Figure. Arts. 212, 213. 256 CHAPTER XXI. OCEAN CURRENTS, WAVES, &c. 212. Currents. — Having briefly explained the motion of the atmo- sphere and how to forecast the weather, we have now to give a correspond- ing explanation with regard to the ocean. The great disturbing influence in the case of the atmosphere is the sun ; as regards the ocean, the sun affects it indirectly by first causing the winds, which by friction produce surface movements of the ocean called currents, and in addition, the sun and moon directly produce a special kind of movement known as the tides, which will be dealt with in Chapters XXII. and XXIII. As the wind blows over the ocean the surface of the water is dragged onwards and, if the wind continues to blow in the same direction for a considerable time, internal friction causes this onward movement to extend to a considerable depth ; such a movement of the ocean, caused solely by the wind, is called a drift current. In Fig. 165 the various currents of the earth are shown, and we find by comparing this figure with Figs. 151 and 152 that the directions of the main drift currents correspond very closely with the directions of the permanent and periodic winds, the Trades, Westerlies, and Monsoons; the currents which correspond to the Trades are called the N.E. and S.E. Trade drifts, those correspond- ing to the Westerlies are called the Easterly drift currents, and those corresponding to the Monsoons the N.E. and S.W. Monsoon drifts. When a drift current comes in contact with a shoal, or coast, or with another current, it is deflected, and is then called a stream current; the details of the principal stream currents will now be given, and the reader should bear in mind that the direction of a mass of moving water is not only affected by land, which it may approach but, as in the case of the atmosphere, by the Easterly or Westerly movement which it acquires in consequence of the earth's rotation (§ 188). The sets and drifts of the various currents are shown on the current charts supplied to H.M. Ships and are described in the Sailing Directions. 213. Atlantic Ocean stream currents. The Equatorial Currents. — The North-East and South-East Trade drifts, on approaching the equator, turn to a Westerly direction and flow across the Atlantic Ocean, nearly as far as the coast of America. The South equatorial current divides at Cape San Roque ; each portion follows the coast — one, running South, forms the Brazil current, and the other, running North, combines with the North equatorial current and forms the Gulf Stream. The Gulf Stream. — The portion of the South equatorial current combined with the North equatorial current consists of relatively warm water, and flows North along the coast of South America, passing through the West Indies and the Caribbean Sea; it then flows round the Gulf of Mexico and finds an outlet through the Straits of Florida, which, being narrow and shallow, causes the velocity of the stream to increase. I 257 Art. 214. On leaving the Strait- the stream consists of relatively warm and salt water, and is 50 miles wide, 350 fathoms deep, with a speed of about 5 knots. From the Straits of Florida it sweeps North ward growing broader and shallower, until at Bermuda it is about '2m\ miles wide. At about midway across the Atlantic the stream divides: one portion flows towards the British Islands and the ether strikes the coast of Europe about the Bay of Biscay, whence it flows along the coast of Portugal into the Mediterranean Sea and causes an Easterly current on the North coast of Africa. A portion of the latter current occasionally curves Northward through the Bay of Biscay and causes a North-Westerly current across the entrance to the English Channel, called the Renne] current. The area in the North Atlantic Ocean, which is enclosed by the Gulf Stream and the Xorth-East Trade drift, corresponds very closely to the normal high pressure area. Enormous quantities of weed, called Sargasso, or Gulf weed, collect in this area, which is about 1,000 miles in diameter and is known as the Sargasso Sea. The Brazil Current. — The portion of the South equatorial current, which turns South along the coast of Brazil, flows as far as the Rio de la Plata, where, on account of the earth's rotation (in accordance with § 188) and assisted by the Easterly motion of the river water, it turns Eastward to mingle with the general Easterly drift of the Southern ocean. The Davis Strait, Labrador, or Arctic Current. — This current, produced by the prevailing Northerly winds, flows Southward from Davis Strait; it is a cold current and its volume is considerably augmented in summer by the melting of ice. The current hugs the coast of North America. passing along the North side of the Gulf Stream, and sometimes flows as far South as Florida. The demarcation between this cold current and the warm Gulf Stream is called the cold wall, and this can be easily detected by the difference in the colours of the water; the Davis Strait current being largely composed of fresh water from melted ice is green, while the Gulf Stream being very salt is a deep blue. In calm weather the cold wall may often be detected by a ripple ; t he difference in the tem- peratures of the surface water, which may sometimes be as much as .'*<• . also indicates the demarcation between the two streams. The meeting of these hot and cold streams is the cause of frequent off the banks of Newfoundland. (§ l!>.">.) Th< Guinea Current. The Guinea current , caused by the genera] Ulic circulation in the North Atlantic, flows along the West coast of Africa as far ae latitude 3° N. and has a maximum velocity of •"> knots. Thi Equatorial Counter ( 'um nt. As the amount of water in the ooean U invariable, and as there Lb b large volume of water continually moving from the equatorial regions to higher latitude-, it is supposed that a sub surface ourrenl from the higher latitudes rises to the surface between the North and South equatorial currents, and flows Eastward, combining with the Guinea current off the ooasl of Africa. This current is called the equatorial counter ourrenl and runs between the months of July and I December. 214. Pacific Ocean stream currents. Cn Big. 165 it will be seen thai the current* of the Pacific Ocean differ very little from those of the Atlantio, the principal difference being the periodica] ohange oi direction of the drift current in the China Sea due to the change of direction of the Art. 215. 258 Monsoons. The drift currents of the China Sea are called the N.E. and S.W. Monsoon drifts respectively, and correspond in strength to the winds which cause them. Fig. 165 shows the directions of the currents during the S.W. Monsoon, the directions during the N.E. Monsoon being shown in the inset. The Equatorial Currents. — The South equatorial current, caused, like that of the Atlantic Ocean, by the S.E. Trade drift, flows to the Westward, and on reaching the numerous islands situated between 160° and 170° E. divides into two parts ; one runs to the South- West towards Australia, where it skirts the coast until it meets the general Easterly drift of the Southern Ocean, and the other passes among the islands North of Australia. The North equatorial current flows Westward until it meets the Philippine Islands, where it curves to the North and North-East and becomes the Japan stream. The Japan Stream. — The Japan stream, often called the Kuro Siwo (Black Stream) on account of its black appearance, is a warm stream, and corresponds to the Gulf Stream in the Atlantic, but is less clearly defined on account of the numerous islands which it encounters. The stream flows along the East coasts of the Philippine Islands, China, and Japan, after which it curves to the Eastward and follows the general Easterly drift of the North Pacific. When off Formosa the stream is about 200 miles wide and has a maximum speed of about 4 knots. The Oya Siwo. — This is a cold current of pale green water which flows from the Bering Sea to the Southward of the Kuril Islands, and then between the coast of Japan and the Kuro Siwo. Here again the meeting of the hot and cold streams is a cause of frequent fogs. The Mexican Current. — This is a cold current which corresponds to the Guinea current in the Atlantic and is caused in a similar way. The Peruvian Current. — This flows in a Northerly direction along the West coast of South America and is due to the general Westerly set being deflected by land. 215. Indian Ocean stream currents. — The currents in this ocean greatly depend on the Monsoons, and in the Northern part chiefly consist of N.E. and S.W. Monsoon drifts. The Equatorial Current. — This current, caused by the South-East Trade drift, flows to the West and strikes the African coast about Cape Delgado, where it divides ; the part which runs to the North follows the coast of Africa, and, during the South-West Monsoon, combines with the South-West Monsoon drift ; the part which flows to the South forms the Agulhas current. The Agullias Current. — The Agulhas current is a warm current ; it passes through the Mozambique channel and runs Southward along the East coast of Africa until it is deflected by the Agulhas bank, when it curves to the Eastward and mingles with the general Easterly drift of the Southern Ocean. It is a strong current and sometimes attains a speed of 4| knots. The Equatorial Counter Current. — This current, which is that portion of the equatorial current which is deflected to the East on meeting the North-East Monsoon drift, runs during the North-East Monsoon. 259 Arts. 216, 217. 216. Ocean waves. — Ocean waves are due to the wind blowing obliquely on the surface of the water. When first formed they are short and steep, but if the wind continues to blow in the same direction for a considerable time, their length, that is the distance between suc- dve crests, increases, as also does their height, which is the vertical measurement between their crests and troughs; at the same time the period of the waves, which is the interval between the passages of two successive wave crests over the same spot, decreases, until a time arrives when a balance of forces is reached. When waves have once been formed the wind has its greatest effect on their crests, which it tends to drive faster than the main body of the waves and so causes the waves to break. In deep water, waves have no motion of translation, but on ap- proaching shallow water their troughs are retarded, with the result that they break and rush forward with considerable violence ; such waves breaking in shallow waters are called breakers. The dimensions of waves varv in different localities, and with different velocities and directions of the wind. The longest wave recorded is one ( if 2,600 feet length and 23 seconds period. The longest waves are encoun- tered in the South Pacific, where their lengths vary from 600 to 1,000 feet, and their periods from 11 to 14 seconds. Waves of from 500 to 600 feet in length are occasionally met with in the Atlantic, but more com- monly the lengths are from 160 to 320 feet and the periods from 6 to 8 seconds. The relation between the length of a wave and the velocity and direc- tion of the wind is not yet fully understood. 217. To find the di- mensions and period of a wave. — Let O x and 2 (Fig. 166) be two obser- vers on the weather side of a ship, their distance apart being I feet. Let AT, be a wave crest at the instant of passing O v and A l B 1 the same wave crest at the instant of passing 0*, and let the interval occupied in passing from 0, to 2 l„. /. L,.t CD be the position of the same wave crest when the next following oresi arrives a1 V and let the interval occupied in passing from Oj to the position ( 'D be i v Lei the length of the wave be L, and the observed angle between the fore and afl line of the ship and the direction in which the waves are advancing be 0. g moe the creel pa -■■- over the distant e I ec 6 in tunc /, at the same U pa , over the distance / in time i. we have /, sec ') I Fig. 166. /. "■ Again, 1«< V and ybe the i- d o\ the ship and wave re pectively, and Id T be the period of the wravi Art. 218. 260 The velocity of the wave relative to the ship in the direction of the fore-and-aft line is V + v sec 6, and this is equal to -. Therefore V - -u- ~ v ) cos e. L V It) , COS e T - t (l- Vt) cos t * • .T = lt x TT » * l-Vt' The height of a wave is generally found by noting the positions of the trough and the crest on the side of the ship. 218. The specific gravity and colour of sea water. — The specific gravity of sea water is found to vary between 1-021 and 1 • 028, according to its temperature, and to the percentage of salt contained in it. In the tropics the amount of salt contained in the surface water is above the average, on account of the excessive evaporation which takes place in low latitudes ; conversely, in high latitudes the amount of salt is below the average on account of the large amount of fresh water which mixes with it, and which is due to the melting of ice. On the average 77-8 per cent, of the solids contained in sea water consists of common salt ; the following is the average percentage of salt which is contained in sea water in different parts of the world : — Atlantic Ocean - - - . - -3-6 Caribbean Sea - - - - -3-6 Mediterranean Sea - - - -3-8 Red Sea - - 4-1 Indian Ocean - - - - -3-6 Near large rivers the fresh water running ^jea ward lowers the specific gravity for a considerable distance ; for example, the effect of the fresh water of the Rio de la Plata has been detected at a distance of 1,000 miles from the mouth of the river. The specific gravity of sea water is obtained by means of an instrument called a hydrometer, full directions for the use of which will be found in the Barometer Manual. It has been found that there is a distinct relation between the colour of sea water and the percentage of salt contained in it ; the more salt that is held in solution the more intensely blue the colour, and the less salt the more green is its colour. In landlocked seas such as the Mediterranean and Red Seas, where there is little circulation of the water with that of the neighbouring oceans and where the evaporation is great, the colour of the water is very blue ; this is also the colour of the surface water of currents which come from the tropical regions, such as the Gulf Stream. The currents which come from polar regions, such as the Davis Strait current, are distinctly green in colour. Off the estuaries of large rivers the sea water is often discoloured for a great distance by the sediment brought down by the river. 261 Arts. 219-221. 219. Change of draught on passing from sea to river water. -The difference between the specific gravities of sea and river water is of considerable importance in navigation, particularly when a ship has to proceed to a dock which opens into a river, because the draught of the ship varies inversely as the specific gravity "f the water in which she floats. The weight <>f a cubic foot of river water may he taken as 63 lb?, and of sea water as 64 lbs. The increase of the mean draught of a ship when passing from sea to river water is found as follows : — Let W he the weight of the ship in tons (displacement tonnage), then H \ 2240 the volume of water displaced when she floats in river water is — 03 eubic feet, and when she floats in sea water the volume displaced is W ■ 2240 cubic feet. Therefore, it .! is the waterplane area in square , . . 224(t H' I l\ |n 20 W ■ the increase of draught is 12 inches or ., . .1 \ 63 64 / 3.1 inches. Now let 7' he the number of tons required to sink the ship 1 inch when floating in sea water (tons per inch immersion), then T X 22oU -,'V. 1 m .-. A l2ii T. 20 W M Therefore the increase oi draught is or ,., inohes. ExampU . Lei us suppose that B.M.S. " Agamemnon " (16,500 tons displacement and 61 tons per ineh immersion) is proceeding from sea Chatham dockyard, then her increase of draught on arrival at Chatham will he , inches, or about 4i inches. 63 < 6J 220. Temperature of the sea.— The surface temperature of the sea varies considerably in different parts of the world, and chiefly depends on the temperature of the prevailing currents. Owing to the low con ductivity of water a warm current communicates verj little of its heat to the water through w Inch it passes. The temperature of the sea varies t hroughoul the year but the diurnal ..uiation i- very .- r 1 1 . 1 1 1 . the temperature being practically the same by night as by da\ . In the tropics the average temperature oi the sea is aboul 80 K . the highest readings of about '• ,,, F. being found in i be Red Sea The lowest temperature of the sea if found in the polar regions. The temperature .it which sea water fre./. I.oiit 28 F. The norma] temperature of the variou ocean* are hown on charts supplied to H.M. ship-, when- all po m t-. at which the temperatures are the are joined by hue- called isothern 221. Ice. The sea if completely frozen during the winter months m high latitude • oept wh< temperature] raised bj warm ourrei Atlantic coast of North Ameri I ; bj ice to a latitude con siderably South of that of the English Channel, when on the VV< Europe the Gulf Stream prevent the watei from being frozen. j 81< s Art. 221. 262 In the spring and summer the ice fields of the polar regions are to a great extent broken up by the winds and tides ; the pieces of ice become pressed and frozen together, and the large masses thus formed, called icefloes, are carried by currents into lower latitudes. Icebergs, which are generally masses of frozen and compressed snow detached from glaciers, are also carried into lower latitudes and, with the icefloes, constitute a serious danger to navigation. In the Atlantic Ocean, icefloes and icebergs have been carried by the Davis Strait current as far South as latitude 39° N. The majority of the Antarctic icebergs consist of portions broken away from the ice barrier. These are of tabular form, and much larger than those of Greenland. In either the Arctic or Antarctic oceans an iceberg rising to 300 feet above sea level is rare, although bergs of 1,000 feet in height and 20 miles in diameter have occasionally been observed. Icebergs can seldom be submerged to less than -£ths of their whole volume, so that an iceberg 300 feet high probably draws about 350 fathoms of water, and' we conclude that the reason for the absence of icebergs, in the North Pacific Ocean, is probably the comparative shallow- ness of the Bering Sea. The proximity of ice is indicated by the following signs, and, should any of them be observed, caution should be used : — ■ Both by day and night the ice blink is almost always visible on the sky towards the ice. Ice blink is a bright yellowish white fight near the horizon, reflected from the snow-covered ice, and seen before the ice itself is visible. The absence of a swell or motion in a fresh breeze is a sign that there is land or ice on the weather side. The temperature of the air may fall as ice is approached if the ice be to windward, but not otherwise, and only at an inconsiderable distance from it. The appearance of herds of seal or flocks of birds far from land is another sign of ice. The ice cracking, or pieces of it falling into the sea, makes a noise like breakers or a distant discharge of guns, which may often be heard from a long distance. , Recent experiments have shown that the temperature of the sea sometimes rises and sometimes falls in the vicinity of ice ; it is therefore unsafe to assume that the proximity of ice will be indicated by a change in the temperature of the sea. Icebergs and icefloes should not be passed at a close distance owing to the possibility of there being projecting ledges below water, and it should be borne in mind that there may be smaller masses of drift ice in the vicinity of the bergs. No definite rule can be laid down as to whether to pass to windward or to leeward of icebergs ; their out-of -water mass would suggest that they drifted faster to leeward than the hard small invisible pieces which are often found near them, but an iceberg is found frequently setting to wind- ward, due to a strong undercurrent. In the case of the huge bergs calved from the ice barriers of the Antarctic, the air spaces are so great that as a general rule not more than three-fourths of the berg are submerged and sometimes only half. 263 Art/ 221. The average Limit- within which ice may be expected arc shown on the Pilot Charts and Ice Charts, and are also given in the Sailing Direction-. \> the limits of the area, in which ice is liable to be met with, vary at different times of the year, the best tracks to follow when crossing the North Atlantic, between January and August, and between Augusl and January, are given in the Sailing Directions tor Westward and for East ward bound Ships. Occasionally the ice extends over a larger area than usual, and when this occurs the tracks are temporarily modified, notice of such alteration being given in the Notices to Mariners. Art. 222. 264 CHAPTER XXII. THEORETICAL TIDES. 222. The tide generating forces. — The movements of the water of the ocean called currents, which have been considered in the previous chapter are horizontal; in addition to them there is a rhythmical rising and falling of the water caused by the attraction of the sun and moon — called tides. Several theories have been advanced to account for the tides, no one of which entirely explains the actual movement of the water. The theory which most closely agrees with observation is that known as the equilibrium theory, a brief account of which will be given in this chapter. We have first to specify the causes by which the tides are generated. In order to simplify the explanation we shall first consider the tide gene- rating force due to the moon alone, and for this purpose we shall commence by supposing that the earth and moon are the only bodies in existence, that the moon is over the earth's equator, and that the earth has no rotation about its axis. On this supposition the earth and the moon revolve in circular orbits about their common centre of gravity G (Fig. 167), distant 3,000 miles from the earth's centre, the centripetal force on either body being supplied by universal gravitation. Since the earth is supposed to be deprived of rotation about its axis it always faces in the same direction in space; therefore its centre describes a circle of 3,000 miles radius about G, and any particular face of it is always in the same direction in space. Moon Fig. 167. In Fig. 168 let C x and M x be the centres of the earth and moon re- spectively at a particular instant, and let A x and B x be the extremities of any diameter of the earth ; then, when the moon has moved from M ^ to M z , C x will have moved to C 2 and A x B x to A 2 B 2 , and it will be seen that every point on the diameter A x B x will have turned on a circle whose centre is on a parallel line through G and whose radius is 3,000 miles. It follows that, at any instant, the centripetal forces on all the particles situated on the line A x B x are equal, and their directions are 265 Art. 222. parallel to the line joining the centres of the earth and moon, as shown by the equal and parallel arrows in the figure. Therefore the centripetal forces at any instant on every particle of the earth are equal and their directions are parallel to the line joining the centres of the earth and moon at thai instant. M* Fig. 168. .Vow the centripetal forces on the various particles of the earth are supplied by the attraction of the moon, and the mi attract- every particle of the earth towards itself with a force which varies inversely as the square of the distance. In Fig. L69 the arrows represent the magnitudes and directions of the attraction- of the moon on the various Fig 169 particli I the < nth. In Fig 170 the arro^ represent the centri- petal! m the same particle and these fora < explained above are all e<|iul and parallel. No* the attraction! have to provide the Art. 223. 266 centripetal forces, so that if we subtract the forces shown in Fig. 170 from the corresponding forces shbwn in Fig. 169, we shall have a system of residual forces as shown in Fig. 171 ; these forces are the tide generating forces due to the moon. Fig. 170. Let R be the earth's radius and D the distance CM (Fig. 169) so that the attraction at C is ~ 2 where k is the constant of gravitation, then, if U is the geographical position of the moon and U' the point diametrically opposite, the tide generating forces at U and U' are i> 2 " ' (D + R)* \D - Rf " & respectively, and if we neglect squares and higher powers of each of 2 h 7? these forces is equal to " '^ 3 . Thus the tide generating forces at U and U' are very nearly equal, and the tide generating force at any point whatever may be shown to be inversely proportional to the cube of the distance of the point from the centre of the moon. It can also be shown Fig. 171. that the tide generating forces at 54° 44' from U and U' are tangential to the surface of the earth. We shall now consider how the tide generating forces tend to affect the ocean. 223. The horizontal tide generating force. — In Fig. 172 let T represent the tide generating force at any point D, and let V and H be its horizontal and vertical components respectively, then the forces acting on a particle at D are gravity + V to the centre of the earth, and H horizontally. 267 Art. 224. Therefore the effect of the tide generating force is to increase or de- crease gravity by an insignificant amount, and to leave an unbalanced horizontal force // which is called the horizontal tide generating force. 224. The lunar and anti-lunar tides. In Fig. 173, the horizontal tide generating forces towards the points U and U' are shown by arrows. J t we assume thai the earth is entirely surrounded by water of an uniform depth, we see thai the water as a whole is subjected to a horizontal Q Fig. it:;. pressure towards the points U and I ' and away from the meridian QPQ' '. The result is thai the surface of the water lakes an ellipsoidal form as shown in Fig. 174. the level of the water being Blightlj raised above tin- mean level over the areas AUB and .!'/"/>", while over the remainder :/\ FlO. 171. of tin urface "I the earth il is dightrj depre ed beloM thai level The t»- i elevation "t t he wat< i above the mean level oci m a1 the points I and U', while th( b depression occui along the meridian QPQ along the two small circlet! AB&ndA'B' the level of the watei if unaltered. Art. 225. 268 If the annular ring of water surrounding the earth at the equator (Fig. 174) be supposed to be cut in two at Q' and unfolded, so that the line which represents the mean level of the sea is a straight line, then the line which represents the level of the sea, when subjected to the tide generating forces, will assume the wave form shown in Fig. 175. u 1 u a ■ \ Mean Level /A' b\ /B aV c - ~~D~~ Bottom of Sea Fig. 175. The right-hand wave, which corresponds to the elevation of the water immediately under the moon, is called the lunar tide, and the left-hand wave the anti-lunar tide ; the points ?7and U' are the crests of the waves, and the points C and D the troughs. 225. The effect of the earth's rotation.— In Fig. 176, which represents the earth's surface on a Mercator's chart, the crests of the lunar and anti- lunar waves are shown on the prime meridian and the meridian of 180° respectively, the troughs being situated on the meridians of 90° E. and 90° W. At any place on the meridians of 0° and 180° it is said to be high water, and low water on the meridians of 90° E. and 90° W. Let us now take account of the rotation of the earth on its axis ; tins will introduce a force which will have no effect on the tide generating force. As the earth rotates on its axis the points U and U' move over the earth to the Westward and the horizontal tide generating forces move 30°W 90°™ 90"E Fig. 176. 90'W. with them, causing high water at successive meridians. It will be seen from the Nautical Almanac that, on the average, the moon crosses the meridian of any place at an interval of 24 1 ' 50 m , and therefore high water occurs on the meridians of 90° E. and 90° W. about 6 hours 12 minutes after it occurred on the prime meridian and that of 180°. Thus, due to the moon alone, high water occurs at any place at the same time as the moon's meridian passage at that place or at the time of the meridian passage of the moon below pole ; subsequently the level of the water gradually falls and low water occurs approximately when the moon is setting or rising, after which the level gradually rises again until the 269 Arts. 226, 227 next high water. The tide at any place, therefore, alternates between high and low, at interval- of 6 hours 12 minutes approximately. 226. The effect of declination. So far, we have supposed the moon to be over the equator, and consequently its declination to be zero. Now let us consider the change in the tides at any place due to the declination not being zero. In Fig. 177, let U be the geographical position of the moon when it North declination, and let UB be a parallel of latitude, U'B' being the corresponding parallel of South latitude. The crests of the lunar and anti-lunar wave- are at I' and U', and as the points U, U', B and />' are on opposite meridians the moon causes high water to occur at them simultaneously; but, as the moon's horizontal tide generating force heaps up the water more at U and U' than at an)' other point, the height of the tide i< greater at V and U' than at B and />''. When the earth ha- turned on it- axis through 180 B becomes the geographical position K^ Fig. 177. of the moon and B' the opposite point, and it will be seen that the greatest heights of the tide now occur at B and B'. We conclude that. as t he moon's declination has a period of one month, the tides at any place due to the upper meridian passage are higher than those due to the lower meridian passage for a fortnight; during the next fortnight the converse occurs. The difference between the Levels <>f high water of Successive tides e called the diurnal inequality of heights. \~ the moon moves away from the equator, the tide generating forces experienced a1 any place deviate more and more from those expe rienced w hen the body is over Jhe equator ; for tin- reason a tide produced he moon, Bay, the lunar tide, is regarded as the result of two tides one. the ordinary lunar tide due to the moon being mi the equator, and called tin- Lunar jemi diurnal tide because its period is hali .i Lunar daj . the other, due to the declination <>f the moon, is called the lunar diurnal i ide I" it period i^ a lunar day. 227. The effect of parallax. It has hitherto been supposed that the moon revolves at a fixed distance from tin earth, hut a- the m actual path round tl ui ellipse it di tance is continually changing when the moon ie m rth it i said to be in perigee and when furthest awaj in apogee. No^i the tide generating forces he cube ot t he distant i I hat i hej mu I also vai Arts. 228, 229. 270 as the cube of the horizontal parallax. 'The moon's horizontal parallax has a period of one month, so that for a fortnight the height of the tide exceeds the average and for a fortnight it falls below the average. Taking 57' as the moon's average horizontal parallax and 61' as the maximum, the variation from the mean value is ( — ] - 1 = - nearly. 228. The solar and anti-solar tides. — So far the moon has been sup- posed to exist alone, but the sun acts on the ocean in a similar manner, although, on account of its great distance, with less effect. The mean ratio of the tide generating force of the moon to that of the sun is 7 to 3, so that we conclude that if the sun and earth alone existed there would be tides, similar to those produced by the moon, and of ^ths their height ; the interval between high and low water would, be 6 hours. The change in the solar tide at any place due to the sun's declination not being zero is similar to the corresponding change in the lunar tides, and the solar tide may be regarded as a combination of a solar semi- diurnal tide and a solar diurnal tide. Again, if we consider the change in the distance between the earth and sun due to the earth's orbit being an ellipse, the tide generating forces due to the sun must vary as the cube of the sun's horizontal parallax ; as the sun's parallax has a period of one year the height of the solar tide exceeds the average for half a year, and for the next half year it falls below the average. Taking 8" -8 as the sun's average horizontal parallax and 8" -95 as the maximum, the variation from the mean , . /8-95\ 3 _ 1 . value is ( ) — 1 = — nearly. \8-8/ 20 J 229. The composition of the lunar and solar tides. — So far we have supposed that only one body, the moon or the sun, is in existence with the earth. Let us now consider the combined effects of the sun and moon, assuming their declinations to be zero. Two separate effects, the lunar tide and the solar tide, do not appear separately on the ocean, but there is a simgle tide which is the resultant, so to speak, of the lunar and solar tides. Let us suppose that the moon is on the meridian of a particular place at noon, that is at new moon or at change of the moon, M 8 in Fig. 178, then the crests of the lunar and anti-lunar tides are at C 8 and C 4 respect- ively, and the troughs at C 2 and C 6 . Similarly the crests of the solar and anti-solar tides are C 8 and C 4 , and the troughs at C 2 and C 6 . The result is that the tides, when combined, produce a higher high- water at C 8 and C 4 and a lower low-water at C 2 and C 6 . The same result will be seen to occur when the moon is on the meridian at midnight, that is, at full moon, M A in Fig. 178. Thus, at full or change of the moon, tides are caused which are about f ths greater than the lunar or anti-lunar tides, and such tides are called Spring tides from the Saxon springan, to bulge. When the moon is in quadrature M 2 or M 6 (Fig. 178) the crests of the lunar or anti-lunar tides are at C 2 and C 6 , while their troughs are at C 8 and 4 ; the crests of the solar and anti-solar tides are at C 8 and C 4 , and their troughs are at C 2 and C G . The result is that the crests of the lunar and anti-lunar tides combine with the troughs of the solar and anti-solar tides, and the troughs of the lunar and anti-lunar with the crests of the solar and anti-solar. In this case high water occurs at C 2 and C 6 , and low water at C 8 and C 4 , the high water being about f ths the size of the lunar or anti-lunar tide. Such tides are called Neap tides, from the Saxon neafte, scarcity. 271 Art. 230. It follows thai twice in a Lunar month, or a lunation 3 at the time of full or change of the moon, that Ls 3 when the moon crosses the meridian at 12 h or •» . spring tides occur; that twice in a lunation, when the moon is in quadrature, thai is, when the meridian passage of the moon is at 6 h or 18 h , neap tides occur: that the interval from spring tides to neap tides or from neaps to springs is about seven days. When the moon is over the equator and at an\ position between full and change and quadrature, its angular distance from the sun (the differ ence of R.A.'s) being 0. it can be shown thai the heighl of the composite tide is N 'L- - N- - 2/.S cos 20 where L and S are the heights of the lunar and solar tides respectively above the mean level of the sea. From this expression it will be seen M>: ffifflffl fa New Moo n. ffl Change To Sun thai the maximum heighl of the composite tide is L 8 and occurs when I - oi . thai is, a1 lull and change of the moon (Spring tides); that the minimum heighl is L 8 and occurs when 6 6 or 18 h /thatis, when th<- moon i- in quadrature (Neap tides); at any intermediate position th<- heighl of the composite tide is, therefore, greater than the neap tide and less than the spring tide. When we take into account tin- changes in the declination of the sun and moon. v.. & thai the composite tide, actually experienced al anj place, i j i ; i \ be regarded ■> the combination ol four tides, two semi diurnal and t wo diurnal. 230. Priming and lagging of the tide. The cr< I of the composite tide obviouslj lief between the crest I th< lunar and solar tides and per to the formei thi fact make* it convenient to refei the time of Art. 230. 272 high water at any place to the time that the lunar or anti-lunar tide would have been experienced, had the sun not been in existence, that is, to the time of the upper or lower meridian passage of the moon. The interval between the time of the moon's meridian passage at a place and the time of the arrival of high water, caused by that passage, varies from day to day, and as explained above (§ 229) this interval vanishes at full and change of the moon and at quadrature. When the moon is in the first quarter, M x in Fig. 178, we see that as the earth rotates in the direction shown by the arrow, an observer will experience high water on arrival at C x , whereas the moon will cross his meridian some time later at M\; this interval is called the priming of the tide. >The same thing occurs when the moon is in the third quarter. When the moon is in the second or fourth quarter, M 3 or Ml, we see that it crosses the meridian of an observer before the occurrence of high water caused by that meridian passage, and in these cases there is said to be a lagging of the tide. Thus, when the moon is in the first or third quarter the tides prime, and in the second and fourth they lag. The symbols L, S and 6 having the same significance as in § 229, it can be shown that the angle x between the crest of the composite tide and that of the lunar tide is given by x 1 tan - l ( Ss ™ 26 \ 2 tan \L + 8 cos 2d) Therefore the priming or lagging of the tide, on account of the moon's 149a; motion, § 225, is -tt^ , which when plotted for various values of 6 gives a curve such as ABGD in Fig. 179, the maximum ordinates occurring when the time of the moon's meridian passage is about 4 or 8 hours. A Time of Moon's O Meridian passage As the daily change in the priming and lagging is not great, the interval between two successive arrivals of the same tide crest at any place, sometimes called a tide day, differs very little from the lunar day, the average length of which is 24 h 50 m ; consequently high water occurs at any place at intervals of about 12 h 25 m , and the interval between high and low water is about 6 h 12 m . The theory of the tides which has been briefly sketched above is known as the .Equilibrium theory, because it assumes that the tide generating forces have sufficient time to bring the ocean to such a state that all its particles are in equilibrium. Observation appears to indicate that the actual tides of the world conform fairly closely to this theory, but theory only tells us the kinds of phenomena to expect ; the amount to be expected, and the time of its arrival at any place, can only be ascertained from the analysis of a large number of observations taken at that place. 273 Arts. 231, 232, i 'H AFTER XXIII. OBSERVED TIDES AND USE OF TIDE TABLES. TIDAL STREAMS 231. Disagreement between theory and observation. -When we reflect on the previous chapter, and remember that the time and place of the tide's crest, on an ideal earth completely surrounded by water, depend on the positions of the sun and moon in right-ascension, on the declina- tions of the bodies and on their parallaxes, we ran see thai the theory is extremely complicated; if we take into consideration the large and irregular continents, and the varying depths of the oceans, the theorj becomes even more complicated, and we can hardly expect complete agreement between it and observation. Observation agrees fairly closely with the theory: for example, we find that spring tides occur at about Full and < 'hange of the moon, and neap tides al about when the moon is in quadrature; moreover the magnitude of the tide al springs is somewhere about twice that at neaps. The occurrence of maximum and no diurnal inequality corresponds very closely with the moon having maximum declination and no declination respectively, and the magnitude of the tide is found to vary between the times of Perigee and Apogee. In spite of these points of approximate agreement with theory there are a number of points in absolute disagreement, and for this reason the prediction of the tides at any place has to be for the most part based on observation. We shall now explain the meanings of various terms which are made use of in observing the tides. 232. Rise and range of a tide. — To measure any particular tide a datum must be selected from the level of which measurements can be made. In order that the Admiralty charts may show the least depth of water under ordinary condition-, the level selected < rally thai of the mean low water of spring tides, so that, it' al any [dace the height of the tide above this lev< I can be calculated for any particular time, it baa only to be added to the depth of water a1 thai place, as shown on the chart, to give the depth a1 I hat t ime. The gj ■ beighl to m hich any pari icular tide rises abo\ e I be l<-\ el oi the datum is called the rise of thai tide, and its beighl al any other time (whether the tide is rising or falling) is the height of the level of the water al thai time above thai of the datum. The rising and falling of the tide are often called the flood and ebb respectively, and the condition oi the tide al any time is sometimes expressed in the form, halt Hood, quarter ebb, &c, by which is meanl thai the time is half wa\ between the timet oi low and high water, or a quarter of the way from the time of h rard the time of low water respecth elj . The mean l< vel oi the ea al anj place i the a level of th< obtained froi erj long erie oi observation The mean tide level i- the mean between the level oi high and low water obtained from a of ol ition oid diffei \ erj In i le from i he mean level of 1 1 Art. 232. 274 The mean tide level of any tide is the mean between the levels of high and low water of that tide, and may differ very considerably from the mean level of the sea and from the mean tide level. The range of a tide is the difference between the heights of high and low water of that tide. A particular tide wave may be represented by a curve such as that shown in Fig. 180, A being the crest and B the trough, and the figure shows graphically the meanings of the terms — rise and range of tide and mean tide level, for a particular tide. Level of High Water Mean Tide Level Ljevel of Low Water L,evel of Datum Fig. 180. The ratio of the rise of the tide at neaps (neap rise) to that at springs (spring rise) is by no means the same for every port, but generally neap rise is .? to §■ spring rise and neap range § spring range. In the tide tables the spring rise is given for nearly all ports, and neap rise is given for a large number. Fig. 181 shows graphically the meanings of the terms neap range, neap rise, spring range, and spring rise; it will be seen that half the spring rise gives the approximate height of the mean level of the sea above the level of datum (§ 246). Mean High Water Springs High Water Neaps H.W.N. Mean Level of Sea (approx.) M.L> Low Water Neaps L.W.N. Mean Low Water Springs Level of Datum Fig. 181. From the formula in § 229 we see that the height of any tide depends on the relative positions of the sun and moon in right ascension; in addition to this the height depends on the declinations of the two bodies and on their parallaxes, and consequently the heights of successive spring tides vary. Similarly the heights of successive neap tides vary. When the various causes combine, spring tides occur higher than the mean. When the various causes are in opposition, the spring tides will be lower than the mean. High spring, and low neap, high waters occur at about the equinoxes ; low spring, and high neap, high waters at about the solstices. These tides (commonly called ' extraordinary spring tides ") are called equinoctial and solstitial tides. 276 Art. 233. The water is not seen to rise bo its greatest height and then immediately fall, hut it apparently remains at the high level for an appreciable interval; this interval is called the stand of the tide. The time of high water is the mean between the time at which the water apparently ceases to rise and the time at which it apparently begins to fall : the time of low water % defined in a similar way. 233. The primary and derived tide waves. -Owing to the presence of the land which lie- across the path »>f the theoretical tide crest, if is impossible tor such a crest to he formed and to travel round the earth. bul in the Southern ocean there is a complete belt of water along which it is possible tor the two tide waves to travel; the tide waves which travel round the Southern ocean are called primary waves. As a primary wave -weep- pound the Southern ocean, passing in succession the Southern coasts of Australia. Africa, and South America, it gives off waves which travel freely up the various oceans in a more or Northerly direction, and which are there unaffected by the sun and moon; these waves are called derived waves, and from them arise the tide- along the various coasts which they pass. The primary wave which gives birth to a particular derived wave is sometime- referred to the mother tide of that derived wave. - If we consider the derived wave which travels up the Atlantic Ocean, we find that ii causes high water to occur at the various places which it ses "ti the West coasts of Africa and Europe: somewhere to the South d the British Islands the derived wave .-end- an offshoot up the English Channel causing high water at the various places on the South coast of England in succession, and a second offshoot up the Irish Channel. The derived wave en passing the North of Scotland -ends a third offshoot down the North Sea, and this causes high water at the various places on the East coasts of Scotland and England in succession. The offshoots which travel up the Irish Sea aud the English Channel arrive simultaneously at Liverpool and Dover respectively; the offshoot at Liverpool combines with the main derived wave, while that at Dover combines with the offshoot which has travelled down the North Sea from tin' previous derived wave. In ih'' open ocean where the depth is great the height of the derived wave i- -null and probably less than 3 feet, but on reaching the submarine hank Which extends from the British Islands in a South-Westerly direction it- height begins to increase, till, on arriving at the coast, it is at some places as much a- 2~> feet , Although successive high and low waters on the coasts of the British Islands rased by the progress of the waves as roughly sketched above, in some oases the tide- appear in he caused by tun waves; thus, vein Portland and Selsea Hill, four tide- are experienced in the l'I hour-, two ot these being probably due to the offshoot which travels tward up the English Channel, and the other- to a reflected wave moving in the opposite direction. The combination | PC. Arts. 234-236. 276 The progress of the tide wave may be traced by means of a chart on which all places where the crest of the tide wave arrives at the same time are joined by lines, called co-tidal lines, and such charts are called co-tidal charts. A co-tidal chart for the British Islands and the North Sea will be found in a book (entitled " Tides and tidal streams of the British Islands ") which is supplied to H.M. Ships, and which should be studied in connection with this article. 234. The age Of the tide. — From the above we see that, in general, a considerable time must elapse, after the birth of a derived wave, before high water is caused at any place by the arrival of that wave ; the interval between the times of high water at any place and of that meridian passage of the moon which corresponds to the mother tide is called the age of the tide at that place. The age of the tide is expressed in days to the nearest quarter of a day and may be as much as three days. The age of the tide is not known for every port of the world. On the West coasts of France, Portugal, and the British Islands the age of the tide is about 1| days, while in the vicinity of the mouth of the Thames it is 2| days. At places where little is known about the tides, the age may be estimated from the foregoing, and, in general, at places adjacent to the various oceans it may be assumed to be 1| days. The age of the tide may be found from the mean of a large number of observations of the interval between the time of the moon's meridian passage at full or change and the time of the next following highest tide. It should be observed that the age of the tide thus found is the interval between the crest of the mother tide crossing the meridian and the arrival of the derived wave, because, at full or change, the crest of the mother tide is immediately under the moon and there is no priming or lagging (§ 230). 235. The amount of the priming and lagging. — The times represented by the ordinates of the curve for priming and lagging, shown in § 230, depend on the ratio of the height of the lunar tide to that of the solar tide. By taking this ratio as 2-73, the greatest priming or lagging is 44 m , which agrees with observation at London and Liverpool; at Plymouth and Portsmouth observation gives 48 m and 40 m respectively. With 2-73 as the value of the ratio the priming and lagging for various times of the moon's meridian passage are those given in the following table, which also appears in the Tide Tables under the heading " Correc- tion of Mean Establishment " ; the negative and positive values corre- spond to the priming and lagging of the tide respectively. h. h. h. h. h. h. h. h. h h. h. h. h. Hours of moon's meri- dian passage 1 2 3 4 5 G 7 8 9 10 11 12 m. m. m. m. m. m. m. m. m. m. m. m. m. Priming and lagging -16 -31 -41 -44 -31 + 31 +44 + 41 +31 + 16 236. The mean establishment of a port. — The age of the tide roughly refers the time of high water to the time of that meridian passage of the moon which corresponds to the mother tide, and this may be called the meridian passage of the mother moon. Since the age of the tide cannot be found exactly, it is necessary, in order to predict the time of high water on any day, to refer the time of high water to the immediately preceding meridian passage of the moon. The interval between the 277 Art 237. tinier <»f the moon's meridian passage on any day and the next following high water is called the lunitidal interval on that day. hi Fig. L82 In the curve ABGD represent the priming and Lagging of the primary wave in the Southern ocean, the zero line being AD; then the time represented by any ordinate of this curve, when subtracted from, or added to, the time of meridian passage of the mother moon, give- the time of the arrival of the crest of the mother tide on the meridian of an}- place. Let AE represent the age of the tide (in this case I] days) a1 a particular place ; let EFGB be the curve ABGD transferred parallel to itself through a distance AE; then the ordinates of the curve EFGB measured from the zero line AD, represent the intervals between the times of the meridian passage of the mother moon and high water at G Aqc cf T.ae _t A L 2 Hows of Mother H ~ A Moons passage Mean Establishment , Z Hours of Mother q Moons passage. Fig. 182. the place; we see that these intervals depend on the amount of priming and lagging of i he mother lide. The interval represented by AE (the age of the tide) consists of a number, or a fractional number, of days, during which the moon maj have crossed the meridian of the place several times (in this case twice): m is therefore convenient to measure the ordinates of the curve EFGB from a zero line XI which i- such that the distance I A represents a certain number oi Lunar days. The times represented bj the ordinates oi the curv< EFGB, measured Erom the line XY, are the lunitidal intervals, and their mean value during a lemi Lunation, represented l>\ XE or ) //. i the mean lunitidal interval at the place or the mean kblishment of t\\<- port. It will be -ecu that the Lunitidal interval on any particular da} differ* from the mean Lunitidal interval by the corre sponding priming and lagging of the mother tide, and that the mean • bablishment oi no pla approximately the time . it high water on the day ol spring tide becau e there wtu no priming or lagging of the mother tide w bich i au ed i hem. ■ I'M. To find tl <• of bigfa water 00 any (lay from the mean estahlisllinent. In order to find the time of high water on an\ day we have to ipply ^\\'- lunitidal interval for that particular high water to the x 610 l Arts. 238, 239. 278 time of the preceding moon's meridian passage. If the mean establish- ment of the port is known we can find the lunitidal interval by applying to this mean establishment the priming or lagging of the mother tide. To find the latter necessitates the age of the tide being known or assumed. Example. — It is required to find the time of high water on the after- noon of March 3rd, 1914, at a particular place on the meridian of Greenwich where the mean establishment is 2 h ll m and the age of the tide is 11- days. From the Nautical Almanac the time of the moon's meridian passage is 4 h 44 m p.m. Since the moon lags behind the sun 48 m in 24 h , at the birth of the tide, 1| : days earlier, the moon crossed the meridian at which the derived wave was given off 1| X 48 m or 1 hour earlier, that is at 3h 44 m P M n ow from the table (§ 235), or from the Tide Tables, we find that for a time of meridian passage 3 h 44 m the priming of the mother tide was 43 m ; therefore the lunitidal interval required is 43 m less than the mean lunitidal interval or mean establishment. The time of high water may now be found as follows : — Mean establishment - - - - - - - 2 h ll m Priming of mother tide - - - - - - ■ — 43 Lunitidal interval - - - - - - - 1 28 Time of moon's meridian passage - - - - 4 44 p.m. Time of high water - - - - - - 6 12 p.m. 238. The vulgar establishment of a port, or the H. W.F. & C. — Owing to the difficulty of finding the mean establishment another interval is employed, called the vulgar establishment, which is the lunitidal interval on the days of full or change of the moon. The vulgar establishment is therefore approximately the time of high water on those days, and is shown on the charts in the abbreviated form H.W.F. & C. (high water full and change) * Now the high water on the days of Full and Change of the moon is due to a mother tide which occurred some days previously, while the moon was still in the second or fourth quarter, when the tides were lagging; therefore this particular lunitidal interval (H.W.F. & C.) is greater than the mean lunitidal interval; in other words, the vulgar establishment of a port, which is the lunitidal interval for a particular tide, is greater than the mean establishment by the lagging of the mother tide at the birth of that tide. 239. To find the time of high water on any day from the H.W.F. & C. — When finding the time of high water, having given the H.W T .F. & C, we may proceed as in the previous example, the mean establishment having first been obtained. Example. — It is required to find the time of high water on the after- noon of March 3rd, 1914, at a particular place on the meridian of Greenwich where the H.W.F. & C. is 2 h 27 m and the age of the tide is \\ days. The H.W.F. & C, being the lunitidal interval on the day of full and change, is greater than the mean establishment by the lagging of the mother tide which took place when the moon's meridian passage was \\ X 48 ln or 1 hour earlier, that is at ll h . From the table in § 235 or from the Tide Tables the lagging for a time of moon's meridian passage ll 1 ' is found to be 16 m , so that the mean establishment is 279 Art. 239. 2 i*; 1 " - I6 m or -2 1 I : the time of high water will now be found to 6 li' ■ p.m. as in ^ 237. In order to simplify the work, the two corrections, namely the Lagging of the mother tide on the day of Full and Change, and the priming or ging of the mother tide a; the birth of the tide in question, may be combined a- follow-. InFi-. L83 the curve EFGH and the lines EH and A F being the same a- those shown in Pig. 182 (§ 236), we have the mean establishment of the I by A'/., and the lunitidal interval for any tide by the ordinate of the curve measured from the base line XT, at the point corresponding to the time of the meridian passage of the mother moon. Lei US suppose that the age of the tide is 1 ', days, then the ELW.F. & C. is represented by the ordinate YK, because the meridian passage of the mother moon, 1-j- days before the days of Full or Change, occurred at 11 hours. Through A" draw a line KL parallel to EH or A'}', then, in order to find the lunitidal interval on any day, we have to subtract from the H.W.F. & ('.. or add to it. the time represented by the ordinate of the curve measured from the line LK at that point which corresponds to the time of the meridian passage of the mother moon. Now . ae the meridian passage of the mother moon for any particular tide occurred one hour earlier (4S m x 1 J) than the meridian passage of v>k 'tours c r Moon's Mean ^,/W.ysoW. Estob.'ish-ngnt l['__NP., .'/--.''J of Mother /boons pessvj 1 : Fig. 183. the moon on the day in question, it is convenient to graduate the line LK bo thai the divisions represent the hours of the preceding moon's ridian passage, and this is done by moving each graduation one place to the left, thai it A' becoming . and so on. In th< example just given, where the age of the tide was I J days, the 2 of tin' mother tide, corresponding to the day of Full and Change, 16 represented l>\ MX. t he priming of t he mother tide on the day when the ii crossed t lie meridian at I W* 1 p.m. (the meridian passage oi the mother moon being •'; ii p.m.) was 43 ra , represented bj ML. The total correction to the II.W'.F. & < '. is 59 m , represented l>\ the ordinate A7'. The lunitidal interval Is therefore represented by ZF H.W.P. .V ' . AW 2 27 59 I 21 In a similar manner a line such a- LK may be drawn for an\ other of t he tide. In the [ntroduction io the Tide Table Table I give the age of the tide m different Localities and Table [I. givee the times represented by the o|'.; ,,f 1 he e U | A ,■ . foj I |.|, ,,| ,| ELW.l ' iven m tin Tide 'F.. Id. for nearly all port* »nd anchoragi A- it i- the approximate time oi high water mi the da ot Full and Change, it i given I M I. a well a M.T.F. This i a convene yhen the ahip - clock ar< i I to G.M.T. or an} Btandard tim '•,. i Arts. 240, 241. 280 240. Examples of finding the time of high water. — The G.M.T. of the moon's upper meridian passage at Greenwich is given for every day of each month in a table at the beginning of the Tide Tables, immediately before the tide predictions. The age of the moon, in days, is also given. Example (1). — Find the approximate time of high water on the morning of March 19th, 1914, at Port Natal. The following information is given in the Tide Tables : — Port Natal. Longitude 31° 04' E. H.W.F. & C. (M.T.P.) 4 h 30" 1 . Moon's meridian passage 6 h 31 m . Moon's mer. pass. - 8 !l 31 m a.m. H.W.F. & C. - - - - 4 h 30 m Cor. for Long. - — 5 Mean from tables (1) and (2) - — 51 M.T.P. of moon's mer. pass. - - - . Lunitidal interval - M.T.P. of high water - Lunitidal interval 3 39 6 26 3 39 10 05 A.M. Example (2). — Find the approximate time of high water on the afternoon of March 3rd, 1914, at Richmond Island (U.S.). The following information is given in the Tide Tables :— Richmond Island. Longitude, 70° 14' W. H.W.F. & C. (M.T.P.), ll h 03 m . Moon's meridian passage, 4 h 44 m p.m. Moon's mer. pass. 4 h 44™ p.m. Mar. 3rd. H.W.F. & C. - - - IP 03 m Cor. for long. - +10 Mean from tables (1) and (2) — 1 05 M.T.P. of moon's mer. pass. - 4 54 p.m. Lunitidal interval 9 58 Lunitidal interval 9 58 M.T.P. of high water - 2 52 a.m. Mar. 4th. Duration of one tide- - - 12 25 M.T.P. of high water 2 27 p.m. Mar. 3rd. If it is required to find the time of low water, 6 h 12 m should be added to, or subtracted from, the time of high water. As will be explained in §§ 241, 242, this method of finding the time of high water gives results which are approximate only, and therefore should only be employed when neither of the methods which are explained hereafter are available. 241. Diurnal inequality. — In the preceding article examples of finding the time of high water were given but no account was taken of the effect of declination or, in other words, of diurnal inequality (§ 226). In many parts of the world the diurnal inequality is so great that we cannot find the time of high water from the H.W.F. & C. There is diurnal inequality of the times as well as of the heights of the tides, but no practical rule can be given for calculating the amount of either ; therefore, at a place where diurnal inequality is pronounced, it is only possible to predict the tides from an analysis of a large number of observations at that place. The general conclusion as regards diurnal inequality appears to be that the day tides are highest in summer and the night tides highest in winter ; diurnal inequality is revealed in the times of high water and in the heights of low water. At some places the diurnal inequality of 281 Arts. 242, 243. ^- Level of High Water heights occasionally becomes so great that the difference in heights of high and low water of one of the tides is inappreciable, and in such a case the tide rises for 12 hours and falls for 12 hours; such tides are called single day tides The tides of British Columbia, and of the majority of the ports of India and China, are affected in a marked degree by diurnal inequality. 242. Tide prediction. Standard ports. -Owing to the fad that changes in the time of high water, due to tin- changes in the declination ami parallax of the -un and moon, are net allowed for in the method of finding the time of high water by the B.W.F. & ('.. it is impossible u> irately predict tin- time of high water by this method. 'The spring and neap rise, although known for \ ships which are likely to visit 1 hose port s. 243. To find the height of the tide at any lime, &c. Let />. Fig. 184, he the level of the datum .ind 8 the level "t the water at an interval / hours after high water. Let .1 .md /.' be the levels of high and low water pectivelj . so i hat I B if I In- range "I' t he t ide and it - middle point ( ' t he mean t ide level of t he tide. Lit 7' In- the time occupied by tin water in falling from I t<> l>. that i- the interval between the timet of high and low wat The heighl <>f the tide, / hours after high water, is DS, which is equal to /" DC i- the height of the mean tide l< ve\ and ie the mean of the heights of high and low water. heighl of the tide above or below mean tide level. Now the tide maj be b timed to ri e and fall with imple harmonic motion, im L to 2? in uofa a w aj i hat it is t he project ion on AH "i a point /' which travels uniformly in the semicircle de cribed on Tide Level. Fio. 184, Art. 244. 282 the range AB as diameter. Therefore the position of the point P, t hours after high water, is given by AGP t 180° " T and hence CS can be found. At those places where the height of low water is not given in the Tide Tables, the mean tide level of any tide must be assumed to be the same as that of an ordinary spring tide, and therefore the half range of any tide must be assumed to be the difference between the rise of that tide and half the spring rise. Conversely, if it is required to find the time after high water at which the tide will be at a given height, the position of the point P is found by first plotting the given level of S ; the angle AGP may then be measured, and the time obtained from the relation given above. The method just described should not be used for places where the tides are known to be irregular, such as in the Solent and where single day tides occur. 244. Examples of finding the height of the tide at any time, &c. :— Example (1).— On March 9th, 1914, at ll h 30 ra a.m., Dublin time, it is required to find the height of the tide at Kingstown. The following information is given in the Tide Tables :— M.T.P.j Height. Preceding high water Succeeding low water Height of tide at H.W. Height of tide at L.W. ft. ins. 10 03 2 04 12 07 DA DB ft. ins. - 9 h 06 m a.m. 10 03 - 2 53 p.m. 2 04 ft. ins. Height of tide at H.W. - 10 03 = DA Height of tide at L.W. 2 04 = DB Range 7 11 = AB Half range 4 00 = BC Height of mean tide level 6 03 = DC Draw a line DF, Fig. 185, to represent the level of the datum, and at any point D erect a perpendicular DC to represent the height of mean tide level on any convenient scale. With centre C and radius 4 ft. (on the same scale), describe a semicircle, cutting DG produced in A and B. M.T.P. of L.W. .M.T.P. of H.W. 2 h 53 m p.m. 9 06 a.m. Time tide takes to fall (T) - 5 47 M.T.P. of H.W. - Longitude Dublin time of H.W. Time at which height is required Interval after H.W. (t) 9 h 0G'° 1 A A. M 9 05 M 11 30 A. M 2 25 Fig. 185. t Tn the Tide Tables, the predicted times are usually given for Standard time; vide the note at the foot of each page of the predictions, 283 Art. 244. The angle A( /' is, therefore, 180 2- i 5-8 71 Lay off the angle ACP 74 , and draw PS perpendicular bo .1/.'. then S is the level of the water at the time required. Now OS represents l ft. 1 in., and. therefore, the height of the tide (LH < s is 6 ft. 3 ins. I ft. 1 in. = 7 ft. I ins. ExampU (2). On March inh. L914, at L0 1 00 lm., G.M.T., it is required bo find the least depth of water on Sheerness bar, the least depth given on the chart being 23 feet. The following information is given in the Tide Tables : — M.T.P. Height. Pre< <•' ling low water Succeeding high water II- -i. H.W. Heighl of I..W . Heighl iii in. '.in bide level Heighl of II. W. _Mt of L.W. - Half range M.T.P. of H.W. M.T.P. of L.W. Time i ide bakes to rise ( T) M.T.I', ol L.W. Longil tide of Sheerro ■ M.T. of I..U. O.M.T. -e which depth is required L.W. It) ■ ft. ins. p - - s 03 \.\i. (IJlii ter •> 12 P.M. |s"(l(. ft. ins. A is 6 DA 8 DB DC C ~k~ 18 ii 9 (i ' f~ T~ ft. ins. is 8 DA DB AB S D B *S$N ^\p/ i i 1 > 6 09 'i i i • 1 8 03 \.M. i : 3 (E.) i : g Mil A.M. • 1 1 1 1 in mi \.M. E • y 1 • 1 2 mi Fig. 186. The angle BCP is, therefore, 1 Ml »;• \5 58 J . !;• laying ofl CP a in Pig. i s,; . if is found that 08 represents id. 11 ii therefore, the depth of water is given by / D DC l it. 1 ti. II in 27 ft. 1 in. / ampU (8) On March 19th, 1914, ii ii required to find the G.M.T. in the forenoon ai which the depth "l the water at Hull will be W feeti position where the depth given 00 the chart 1 I '• fathoms, Art. 244. 284 The following information is given in the Tide Tables : — M.T.P. Height. High water - - ll h 15 m a.m. - Tide rises in 5 h 40 m approximately. Mean tide level 10 ft. 5 ins. The level of the datum is that of mean L.W. springs. ■ Level of H.W Mar. id 16 ft. 8 ins. S C 8 th £ Level required Meat i Tide Level -1 ^--r — Level of L.W. Mar. 19™. t • Hi — Level of Datum ■-t — Bottom of Sea Fig. 187. Height of tide at H.W. Height of mean tide level I range of tide - Depth charted - Height of mean tide level Depth of water when at mean tide level Depth required - Height above mean tide level - ft. ins. 16 8 = DA 10 5 = DC 6 3 = CA 27 10 5 = ED -DC 37 40 5 = EC r=ES 2 7 = cs Draw the horizontal line PS so that CS represents 2 ft. 7 ins., tlicn the angle AGP will be found to be 65°. 285 Art. 244. 65 Therefore the depth of the water will be 40 ft. at x 5 h 40 m . or loO 2 h 3" before high water. M.T.P. of H.W. Long, of Hull U.M.T. of H.W. Time before H.W. G.M.T. required ll 1 ' 15™ A.M. 1 (W.) 11 10 A.M. 2 03 9 13 A.M. Example (4). — During daylight on March 13th, 1914, between what 6.M.T.S will the depth of water be greater than 28 feet over a 3-fathom bank at Harwich J A A S \p • Let "in tsc Dspth required S 1 \P' Least Depth required , *2y' Mean Tide Level C 1 i^"*" \— t— -f- - 1 - Mean Ji de-Lev el c ) * i / * i / N ; - > i Level of Datum _i ! Level of Datum i i • tvi 1 ■ 1 1 1 1 1 1 1 I 1 1 1 1 1 1 1 t 1 1 Y Bottom 1 1 1 1 1 1 f 1 Y Bottom Fig. 188. The following information is given in the Tide Tables : — M.T.P. Height. Low water 1 ligli water Low water Iti-iinc tide. 6 h 18"' A.M. 35 p.m. 17 P.M. Falli Height of ll.W. Heigh! of L.W. ft. ins. 3 13 4 1 ng tide. ft . iti^. Height of ll.W. - - 13 4 Heigh! of L.W. - - <» 3 - ft. ins 13 4 1 13 7 1 1 I Heigh! of mean tide level ti 9 I [eight of mean i ide level ft. i ft. in^. Heigh! of ll.W. - - 13 i Heigh! of u.w. - . 1 3 i Heigh! of L.W. 3 Heigh! of I..W. - l ti Range - - 1 3 l Range « - I ■_' i - 6 7 l I l.iif range - - 8 I ("A' Art. 245. 280 Rising tide. Least depth required Depth charted - ft. 28 IS ins. cs Falling tide. Least depth required - Depth charted - Least height of tide required Mean tide level Least height required above mean tide level ft. 28 18 ins Least height of tide required Mean tide level - 10 6 9 10 7 2 Least height required above mean tide level 3 3 = 2 10 C'S' It will be found that the angles SOP and S'C'P' are 60° and 63° respectively. Rising tide. Falling tide. M.T.P. of H.W. - M.T.P. of L.W. - 0" 6 35" 18 P.M. A.M. (T) (t) P.M. (E) P.M. A.M. M.T.P. of L.W. M.T.P. of H.W. Time tide takes to fall Interval from H.W. 63 180 X 5-7 = M.T.P. of H.W. Longitude G.M.T. of H.W. - Time after H.W. - G.M.T. required - - 6 h - 17 m P.M. 35 p.m Time tide takes to rise 6 2 h - 0" 17 35'" 5 5 42 (7") Interval from H.W. 60 v a. q _ 180 X ° a ~ M.T.P. of H.W. - Longitude Oh - 0" 0"' (O 35 m p.m. 5 (E.) G.M.T. of H.W. - Time before H.W. - 2 - 10 30 06 24 - . 2 30 p.m. 00 G.M.T. required - - 2 30 p.m. Therefore the depth of water over the bank will be greater than 28 ft. between 10 !l 24™ a.m. and 2 h 30 m p.m. G.M.T. To avoid the necessity of drawing a diagram for every problem, diagrams are given in the Tide Tables in which the radius of the circle is represented as varying from 1 to 11 feet, and the line CP is laid off for every half hour from the time of high water. Diagrams are given for tides which take 5, 5|-, 6, 6|, and 7 hours to rise or fall. For a tide which does not rise or fall in an exact number of half hours, the height above mean tide level may be found by interpolating between the results obtained from two diagrams. 245. Comparison between the tides at two places. Tidal constants. — On the days of Full and Change of the moon the difference between the local times of high water at two places is the difference between their Vulgar Establishments, but this is not true on any other day of the lunation unless the age of the tide is the same at both places. For this reason the Mean Establishment, being unaffected by the age of the tide, should be used when comparing the times of high and low water at two places, or when tracing the progress of a tide wave along a coast. The times and heights of high water, at a certain number of ports, can be found by applying corrections to the times and heights of high water at those standard ports which have the same age of the tide ; these corrections are called tidal constants, and are given in the Tide Tables for a large number of ports and anchorages in the United Kingdom and its dominions, as well as for certain foreign ports. To illustrate the use of tidal constants let us consider the following. _>sT Art. 246. Example.— On March 17th. 1914, at what G.M.T. (about midday) will there be 35 feet of water over a 5-fathom hank at Port Patrick \ The following information is given in the Tide Tables : — Pert Patrick I rreenock Standard port, Greenock. Time constant - h 58 m . Heighl constants, Springs, 5 ft. + 3 ft, !> ins. Springs rise I 5 feet . Longitude in time, 20" 1 (W.). M.T.P. Heiglit. H.W. 3 h 34 m p.m. 9 ft. :> ins. Neaps, Tide rises in 6 h 30'" approximately. March 17th is three days after spring tides. Mean tide level at Port Patrick is 7 ft. 6 ins. - DC, Fig. 189. The height constants are 5 ft. and 3 ft. 9 ins. at springs and neaps respectively ; therefore, since the date is three days after springs, the constant for March 17th is + 4 ft, 6 ins. ft, ins I [eight of H.W". ( rreenock Height constant - Beight of H.W. at Port Patrick - Mean tide level at Porl Tat rick - \ range of tide at Port Patrick - I >eptb required - I >epth charted Height of tide required Mean tide i<-\ el - Depth below mean i ide level The angle ACP is found to I-- 1 13 , therefore ili<- i i 1 1 j ♦ • before high water is 113 6- •< hours M.T.P. of H.W. Greenock - Time constant M.T.P. of H.w . Port Patrick Long, of Porl Pal i ick G.M.T.of H.w . Port Patrick Time before H.W . 9 :» + 46 13 11 7 fi G 5 = CA ft. in-. 35 30 f, (i 7 G 2 6 = IS c s I 06 I r.M ,T. required • » :; t cm. - 2 :!•; p.m. 20 (W.) •> 1 56 p.m. or, in 5] A.M ■J- f — Mesn T/'a'o Love/ 1 z'.e" -j — * Given Leva/ -^ Datum ; i I i i : I : i i i i i ■ i i Botcom I'l.:. 189 24G. Effect of meteorological conditions. The mean tide leve] of any tide ifi affected by the wind and by change oi atmospheric pressure. The wind producef 8 considerable effect on the tide- and. generally, an onshore wind raise* the level "I the water while an offshore wind lower Arts. 247, 248. 288 it ; for example, at Liverpool, South-Westerly winds raise the level while Easterly winds lower it. In ports with narrow entrances the wind may alter the times of low and high water, for example, at Portsmouth, a Northerly wind may delay the flood as much as three-quarters of an hour. As regards the effect of change in atmospheric pressure, the mean level of the sea rises or falls as the barometer falls or rises, the change in the level being 1 inch for about .^th of an inch of mercury. The effect of change in atmospheric pressure, as well as the possible effect of wind, should be taken into consideration when great accuracy is required ; the mean level of the sea at any place should be assumed to be correct when the barometer is at its average height for that place. 247. The cause Of tidal streams. — The direct effect of the sun and moon is to produce the vertical movements of the water which have been discussed above under the name of tides. So long as we consider the tides in the ocean, where the depth is great, there is practically no horizontal movement of the water, the height of the wave being only two or three feet while its length is some hundreds of miles ; when, however, a tide wave meets a submarine plateau, its height increases considerably, its length diminishes, and its speed decreases ; the con- sequence of this is that the gradient from crest to trough becomes sufficiently great to allow the water to flow from the higher to the lower level, and such a flow of water is called a tidal stream. In Fig. 190 let ABCDE be a tide wave moving in the direction shown by the arrow, A and E being crests, and C a trough. As the crests and trough pass an observer there is no gradient, while at the points B and D there is a tendency of the water to move in the directions shown by the small arrows. When the crest of a tide wave approaches an inlet, it is preceded by a stream running in the same direction, and when the crest recedes from the inlet it is also preceded by a stream ; such tidal streams, when their directions change within an hour of high or low water, are called the flood tidal stream and the ebb tidal stream respectively, and are indicated on the chart as shown in § 160. When a tidal stream first begins, there is a flow of the surface water only, but as the tide wave arises in shallower water the horizontal movement extends to a considerable depth, and finally, if the depth is sufficiently small the whole mass is in motion. 248. Tidal streams in a channel. — As the tide wave, Fig. 190, passes an observer, the crest, trough, and intermediate points pass in succession, moving in the direction shown by the large arrow which we will suppose to be East. While the wave form extending from B to C is passing there is a Westerly stream, and this continues to flow, after the trough C has passed, till its momentum has been checked by the gradient between C and E, when an Easterly stream begins to flow. Similarly there is an Easterly stream at E which continues to flow till checked by the gradient between E and F, when the stream is again AVesterly. 289 Arts. 249, 250. 249. Times of turning oi tidal streams. — From the above it will be seen that, in general, the tidal streams at any place will not turn at the times of high and low water at that place. The time of the turn of a tidal Btream is generally referred to the time of high or low water of some adjacent port or anchorage, but in some places the time at which a particular stream begins to How is given on the chart for the days of Pull or Change of the moon; for example, "North-Easterly stream begins at IX V. & ('.'* indicates that on the days when the moon crosses the meridian of the place at 12 h or O h , a stream begins to flow to the North- •••.? Eastward at !> o'clock. This is analo- .-'3 gous to the use of the vulgar establish- '•••§ A *uu, mem of the port with respect to tides, •*:!§ i v and the beginning of the stream on any •.£ da v may, therefore, be found in a similar Sltoal ;;;^ ^^ I way to that of finding the time of high ?}% 3 a h r °£* ~~^J t h e r U Hw water from the H.YY.F. & C. (§ 239). :•$ L.w. \ In a few places the time of the turn of :'f ^ the tidal stream is referred to the age :.';.& s At L.W. of the moon. :"$•' The time at which a tidal stream FlQ. 191. turns is often different at different dis- tances from the shore, being generally rather later in the offing than inshore. In the vicinity of shoals which dry at low water the direction of the tidal stream is affected by the water flowing on and off the .shoal, and is different at different stages of the tide ; such a stream is called a n»tary stream, and is illustrated in Fig. 191. 250. The rates ot tidal streams. — As a general rule the rate of a tidal stream at any place varies throughout a lunation, being least and greatest at the times of neap and spring tides respectively. The rates shown on the chart are the average rates at those times; for example, the tidal stream at a certain position in the English Channel is shown on the chart as 233° (S. (57 W. Mag.), average rate, \ to H knots. As was explained in § 247, tidal streams are caused by the tide wave meeting a submarine plateau, and, naturally, when it reaches compara tively shoal water, the presence of rocks or irregularities in the bottom bring about local changes in the directions and rates of the tidal streams : thus it is found that the rate of a tidal stream is greater in the close proximity of salienl points than in the offing. Where a submarine ridge of rocks rises abruptly the tidal stream flows over it at ;i greal rate, and the Burface of the water is very disturbed ; ■it such a place the tidal stream lg called a race, many examples of which are found round the British Islands, the mosl familiar being that nth oi Portland Bill. Where sudden changes of depth occur the tidal stream presents the appearance of ha\ e been made, and t hat in 1 he process of manufacture a corresponds t'- I and b t<> B; then it is found that, if the magnet n/> be freely suspended, the pole .1 will repel the pole (i and attract the pole //. This property of two magnets is generally stated in the form of a law Like j, i,i, repel, unlike poles attract <"" another. \ pole "i ,i magnet is said to be of unit strength if, when placed in .or ;it ;i distance of one centimetre from a similar pole, it is repelled with a force of one dyne. It is found by experiment that, if the strengths ■ •t two pole- are 8 and 8 . and l> is the distance between them, the force exerted by either pole on 1 he ot her i 8 . s' />■ ' and tin force i an attraction or a repulsion according a the poles are unlike or lil Art. 252. 292 It is impossible to separate the two poles of a magnet, but for convenience we may suppose that the magnet AB, Fig. 192, is acting on a solitary pole a. This pole is under the action of two forces — a force of attraction in the direction aB, and a force of repulsion in the direction Aa ; the resultant of these forces is in some direction aC, and this direction is called the direction of the line of force of the magnet AB at the point a. Similarly, if a large number of points, such as a, are considered, the directions of the lines of force of the magnet AB will be as shown in Fig. 193; the area over which the influence of the magnet is felt is called the field of the magnet. If a small magnet ab, whose influence on a large magnet Fig. 192, A i i i ■ *.». -r \^ \ \ I 1 t ■ 1 1 Fig. 193. AB is inappreciable, be freely suspended in the field of the magnet AB it will take up a position along a line of force as shown in Fig. 194. CL | CL' \ J a b\ b. I / CL\ CL/ S AJ- B Fig. 194. If the magnet ab be freely suspend- ed at any place on the earth's surface, it will take up a definite position at that place ; in North latitude one pole, a say, will point downwards and roughly in the direction of the North pole of the earth (Fig. 195) ; at the equator the magnet will be nearly horizontal, and in South latitude the pole b will point downwards and roughly in the direction of the South pole of the earth. From this and the law stated above we conclude! that the eartli is a natural magnet, and that its poles, called the North and South magnetic poles, are situated in. the vicinity of 293 Art. 253. the geographical poles. Thus we see that the magnetism of the pole b, which is at the South-seeking end of the magnet ab, is of the same nature as the magnetism at the North magnetic pole; so, in order to avoid confusion when using the terms North and South, the magnet- ism of the earth at the North magnetic pole is called blue magnetism and that at the South magnetic pole red magnetism. The magnetism of the pole a is, therefore, red and that of b blue. It will be convenient to consider that the lines of force of a magnet always proceed from the red pole to the blue, so that the direction of the lines of force of a magnet at any point in its field may be defined as being the direction in which a solitary red pole would travel under the influence of the magnet. 253. The effect of a magnet on an isolated pole.— Lei AB (Fig. 196) be a small magnet of length 2/ and pole strength 8, and let be an Fig. 196. isolated red pole of unit strength, distant r from the centre of the magnet, r l>ein'_ r f may be neglected. Let Ox and Oy be two rectangular axes, the former being parallel to the magnet. Lei COy and each of the angles AOC, COB (which are approximately equal) dd. 8 The pull of Bon The push of A on , along 10. ..... along OB. 8 (/■ / sin Oy Therefore 1 1 » « - force on along Ox is 8 > s . . . . . sin(d , sin(tf -I )- (/' / in 0) x a 6 d6 oofl 6 S tin 6 d6 <■■ (1 / sin 6)* x BlOfl I Art. 253. 294 S T . I 2Z l 21 "1 = 2 (sintf - -cos 2 0) (1 + —sin 6) - (sin0 + - cos 2 0) (1 - - sin 6) ?- 2 L »• cos 2 = -3(1 -3 cos 25). sin 2 # 4#Z When = 90°, this expression becomes -*-, and when = 0° it becomes 2SI ; therefore the force due to the magnet in the direction Ox when " end on " is twice that due to the magnet when " broadside on," and in the opposite direction, as shown in Fig. 197. Again, the force on along Oy is — • 8 S IZ 7T 1 — n\z cos (. cos (0 + dd) (r — I sin 8) 2 v ' (?• -f / sin 0) 2 x ' _ 8 cos 5 + dd sin <9 £ cos — dd sin 5 - *.2 • I (1 -- ~sin0) 2 (l + J T sin0) 2 ffcostfH r[_V I cos d sin d\f, , 2/ . a \ ( )(!+ -sin*)- (cos cos d I cos 5 sin 6 _ S F61 sin d cos 5-l , ' ' / 1 1 ' ' I ■',"» '» / f i ' v 1 S \ v, , M » ,".v ,''//' B e?---- - - - - ftty>'///l -\\ .' / ' Fig. 198. is placid in the field of the magnet I />' so thai the lines of force pass directly through it and cause it to be magnetised as Bhown. When in the position a' >>'. the Lines of force arc deflected from their normal paths and pass through it producing magnetism as shown. It will be noticed that, since the lines of force are supposed to proceed from tli<- red pole to the l>lu<- the end of the iron rod at which the lines enter becomes a blue pole, and thai at which thej leave becomes a red pole, ft will also be noticed that the lin*'- ol force tend to crowd together through the iron bar because iron i- a better conductor of magnetism than air, and that in the immediate vicinitj of the iron rod the lines ol force, which d<> not enter it, are further apart than elsewhere. If the iron bar i- placed in th<- position a" b* so that its length is normal to r Art. 256. 296 the lines of force no magnetism is induced if its diameter is small compared with its length. If, instead of the iron rod a b, a soft iron ring, Fig. 199, were placed in the field of the magnet, the lines of force, following the path of least ill ft /s I 'I 'i '/"•■' — ■ A — -«. —'~-~T 2. ™" ^ *fc. *»« N \ «|l f' ' ll B V&J. Fig. 199. resistance, would travel round the ring and emerge on the opposite side. Thus the effect of the ring would be to screen off the area within it from the effect of the magnet AB, and the ring would be magnetised as shown. If the ring were made to revolve, the poles a, b, would remain in the same places relative to the magnet AB, and therefore would apparently travel round the ring. If, however, we suppose the metal of the ring to be intermediate between hard and soft iron, two poles a', b', Fig. 200, would be formed * tf ** s *• ** - * ^_— S s ^ t/' "III! i /A'* "lit hi/ '',',? Fig. 200. on the inside of the ring and lines of force would flow from a' to b' within the ring. If this ring were made to revolve, the four poles a, b, a', b' would not exactly retain their positions relative to the magnet AB but would move slightly in the direction of rotation, and thus the direction of the lines of force within the ring would be slightly altered ; this effect is of considerable importance, as will be explained in § 304. 256. Artificial magnets. — We have now to explain how artificial magnets are made, and in order that they may be of a permanent nature, a special alloy, consisting of steel with the addition of 5 per cent, of tungsten, is used, because the most poAverful magnets can lie produced from this on account of its great coercive force. (a) By percussion. — In Fig. 198 if the bar a'b' is of hard iron and is held in the direction of the lines of force of the powerful magnet AB it will not become magnetised, on account of its coercive force ; a succession of blows from a hammer, however, assists the molecules, which are very small magnets, to take up a position parallel to one another, and the bar as a whole becomes a magnet. This method is not empWed in the manufacture of artificial magnets, but advantage is 297 Art. 256. Fx<;. 201 taken of the property of magnetic induction mentioned above, various processes being employed, the most important of which are : — (6) By single touch. — In Fig. 201 let ab be a bar of hard iron which it is desired to magnetise. The bar ab is stroked with a powerful permanent magnet AB as shown in the Figure, the direction of movement being always the same; ab becomes magnet- ised as shown, the end 6, where the rubbing magnet leaves, acquiring oppo- -itc magnetism to the rubbing pole A. (c) By separate or divided touch. — The bar of hard iron ab is, in this ease, stroked from its centre to its ends with two powerful permanent magnets AB and A 'll as shown in Fig. 202. The bar becomes magnetised as shown, each end acquiring opposite magnetism to that of the rubbing pole. Magnets of small power are fre- quently made by this or the preceding method. (d) By electric current. — Around a wire through which an electric current flows there is a magnetic field, the lines of force being concentric circles whose planes are perpendicular to the wire. Thus, if an electric current is flowing from the positive to the negative pole in the direction shown by the arrow in Fig. 20l>, and if CD is a plane perpendicular to the wire, the lines of force in the plane CD are the dotted circles shown, and their direction — thai is. the direction in which a solitary 'n-d pole 202. t / / f * . - \ * \\ N » D Fig. 204. would move in the plai ■ ' i-^ that shown by the curved arrow, rule for finding tin direction "I the line- of force due t" an electric inn -wnn with the current and face the solitarj red pole, then youi hand indicates I h< direcl ion. If the wire is benl mi" the form <>l a Loop, ae shown in Fig. 204, il be seen that the directions "t all the lines "I \<<\>'- within the !<><>]> i lie cut . left will ire Arts. 257, 258. 298 the same; consequently, if a bar of hard iron is placed within the loop so that the lines of force flow through it, the bar will become magnetised as shown. When an artificial magnet is made in this manner, an insulated wire which carries the current is wound round the iron bar several times so as to strengthen the field. This method is employed for making powerful magnets such as those used for the correction of compasses, and needles for compasses of recent date. 257. Effects of temperature on magnets. — Magnets constructed of the alloy mentioned in § 256 retain their magnetic properties permanently, unless they are brought into an opposite magnetic field of great power or subjected to very high temperatures. If a permanent magnet is heated to a temperature between 1300° and 1500° F., it loses its magnetic properties, and the temperature at which this occurs is called the critical temperature for the particular metal of which the magnet is composed. Ordinary changes of atmospheric temperature have little or no effect- on magnets. Raising the temperature of soft iron has the effect of greatly increasing its capacity for induction; thus, at a temperature of 1427° F. the capacity of soft iron is many times greater than at ordinaiy temperatures, but after further heating there is a rapid decrease until, at 1445° F., the iron is non-magnetic. 258. Terrestrial magnetism. — As stated in § 252, the earth is a huge natural magnet whose poles, as is found to be the case in all natural magnets, are unsymmetrically placed. The North (blue) magnetic pole is situated N.W. of Hudson Bay, and the South (red) magnetic pole in the Northern part of South Victoria Land. These magnetic poles are not fixed points on the earth but are constantly moving onward in unknown paths, and apparently complete a cycle in a period of many hundreds of years. Besides this onward movement of a few miles per annum, the poles have a small daily oscillation. The lines of force of the earth vary in direction from the vertical at the magnetic poles to the horizontal in the vicinity of the equator. A line drawn on the surface of the earth through all points where the lines of force are horizontal is called the magnetic equator, and this line may be assumed to be the line of division between the red and blue magnetism of the earth. If a magnetic needle were freely suspended at any place under the influence of the earth's magnetism only, it would lie in the direction of the line of force at that place, and that great circle of the earth in the plane of which the needle would lie is called the magnetic meridian of that place ; the angle between the meridian and the magnetic meridian of the place is the magnetic variation (§ 14). The earth's magnetic force on a solitary red pole of unit strength at any place, called the total force at that place, acts along the line of force at that place, and this, as stated in § 252, is inclined at various angles to the earth's surface. The angle which the line of force at any place makes with the horizontal plane is called the dip at that place and will be denoted by 6. It is convenient to resolve the total force at any place into its hori- zontal and vertical components, denoted by H and Z respectively, so that tan — „ • H 299 Arts. 259, 260. The earth's horizontal and vertical forces at any place are shown on charts, called charts of equal horizontal force and charts of equal vertical force respectively, by means of lines drawn through all points where the forces, expressed in c.g.s. units (dynes), are the same. The dip at any place is shown on a chart called the chart of equal magnetic dip, by means of hues drawn through all points where the dip is the same: these lines are sometimes called lines of equal magnetic latitude. The magnetic equator is the line of no dip, and the pecked lines on the chart, .South of the magnetic equator, indicate that the .South (blue) end of Hu- needle is depressed. Charts of equal horizontal and vertical force and of equal magnetic dip will be found in the Admiralty Manual for the Deviations of the < lompass. 259. Changes in the variation. — The variation at any place is liable to regular and irregular changes, the regular changes being secular, annual, and diurnal. 1'ln secular change. — The secular change of the variation is that which take- place over long periods, and from which the regular yearly change, given on the variation chart, is obtained. '/'A, annual change. — From April to July, Westerly variation decrease- and Easterly variation increases: the converse occurs during the remainder of the year. In May and October the variation, apart from its secular change, is about the same. During the winter months the channel are small. '/'//■ diurnal change. — From early morning till l 1 ' or 2' 1 p.m. in the Northern hemisphere the mean movement of the North (red) end of the needle i^ from Easl to West : from 2 h p.m. to 10 h P.M. it is from West to East, and during the night it is practically nil. In the Southern hemisphere the mean movements during the same intervals take place in the opposite directions. In the Northern hemisphere Westerly variation is greatest during the hottest part of the day. The diurnal change i- smallest near the equator, where, in some places, it does not exceed .V or !'. and it increases with the Latitude. In England the diurnal change varies from 25' in summer to 5' in winter. The irregular changes are said to be due to magnetic storms, which ur with great rapidity and cause deflections of the needle to the right and left. It is found that magnetic storms are nearly always accom- panied by tin- exhibition of the auroral in high latitudes (§ l ( .»0°. ( a ■ -'. Object >l will have the in.dlc i eifcct mi the h« i ir/ < a 1 1 a I angle OZX'. .Mi:.'. Example or finding variation on shore. <>n Julj 25th, 1914, at about? l.m. M.T.P. a1 Wei-hai-wei, in latitude 37 30' 10' NT., longitude \ii 9' !•">' B., the following observations were taken to determine the variation. The index error "I fche sextants with winch the altitude- Art. 262. 302 and the angular distances were observed were respectively + 1' 00" and — 1' 30". ©45° 00' 30" Beacon (on horizon) 95° 56' 10" |0 045 17 00 „ 96 33' 10" |© Horizontal Angles. Beacon 69° 00' 40" Centurion Flagstaff 72° 15' 00" Earthwork. Earthwork 121° 37' 50" Lighthouse 64° 03' 00" Flagstaff. Compass Bearings. Beacon - N. 10° 10' W. Centurion Flagstaff N. 58° 45' E. Earthwork - S. 49 00 E. Lighthouse - - S. 72 30 W. Flagstaff N. 43° 30' W. To find the azimuth of the sun. M.T.P. Long. - G.D. - I.E. App. alt. S.D. App. alt Kef-Px True alt. - 19'' 00'" July 8 08 (E.). 24th 24th Dec. 20° 00' 5 °3" 37 •3N. •2 lar nee 31-02 10-87 - 10 52 July 19 90 54 00 46 00 N. 21714 24816 2 / L.L. 45° 00' 30" + 1 00 10055 33514 $2906 36674 3102 70 05 14 Po: dista I.E. - App. alt. S.D. - App. alt. Ref-Px True alt. L.L O i 45° 17' + 1 60/337-1874 5' 37" -2 00* 00 45 01 30 1/4:5 18 00 22 30 45 + 15 46 22 + 39 15 00 46 22 46 31 - 2 11 22 54 _ 9 46 10 22 44 20 22 52 36 Lat. Alt. 37° 22 30' 10" 44 20 L sec • L sec 0-1 Jihav4-J *ihav4.( Lat, Alt. Pol. dist, Azinuil 37° 22 30' 52 10" 36 J J i L I L vr a , sec 0-10055 , sec 0-03558 Pol. 14 dist, 70 45 50 05 14 14 70 37 05 34 14 * 84 55 51 04 19 24 84 55 42 27 48 40 hav4-82848 hav4-66774 Azimuth 9-63149 ± X. 81° - 9-63235 N. 81° 43' 30" E. 10" E. I.E. - - 1 30 S.D. - 95 54 + 15 40 46 96 10 26 To find the true bearing of the beacon. 95° 56' 10* 96° 33' 10" I.E. - - - 1 30 96 31 40 S.D. - - - - 15 46 96 15 54 303 Art. 262. Aug. dist. 96° In' 26 App. alt. 22 4G 31 7. cos 9-03162 L sec 0-03526 7, cos 9-00688 Ang. dist. 96 15' 54" A|>p. alt. 22 54 4(i Lcos 9 03790 /. aec 0-03575 /.cos 9-07365 Hor. Angle - 96 41' 55 r Sun's Azimuth X. 81 43 30 E. True bearing of beacon - X. 14 58 25 \V Her. Angle - 96° 48' 15" Sun's Azimuth X. 81 49 30 E. True bearing of beacon - X. 14 58 45 W To find the true bearings of the various objects. Mean true bearing of Beacon - Beacon ------ True bearing of Centurion Flagstaff ( 'Tituiion Flagstaff True bearing of Earthwork Karthwork True bearing of Lighthouse Lighthouse , - Ti in bearing of Flagstaff N. 14° 58' 35" W. 68 59 10 Centurion Flagstaff. X. 54 00 35 E. 72 13 30 Earthwork, S. S: L26 14 05 180 00 00 53 45 55 E. 121 36 20 Lighthouse. 67 50 25 W. 64 00 30 Flagstaff. 131 51 r t r, 180 00 00 X. is os 05 \V. Arts. 263, 264. 304 To find the mean variation. Beacon. True bearing - N. 14° 58' 35" W. Compass bearing N. 10 10 00 W. Variation 4 48 35 W. Centurion Flagstaff. N. 54° 00' 35" E. N. 58 45 00 E. 4 44 25 W. Earthwork. S. 53° 45' 55" E. S. 49 00 00 E. 4 45 55 W. True bearing - Compass bearing Variation Lighthouse. S. 67° 50' 25" W. S. 72 30 00 E. 4 39 35 W. Flagstaff. N. 48° 08' 05" W. N. 43 30 00 W. 4 38 35 \Y. 4° 48' 35" W. 4 44 25 W. 4 45 55 W. 4 39 35 W. 4 38 35 W. 5/23 37 05 [ean Variation - 4 43 25 W. 283. Local attraction. — In a few places, where magnetic ore exists the lines of force of the earth deviate considerably from their otherwise natural directions ; therefore, in the immediate vicinity of such ore, the variation suddenly differs from that in the neighbourhood, and the attraction which causes the difference is called local attraction. The effect of a mass of magnetic ore can only be felt when very close to it, because the effect of one magnet on another varies inversely as the cube of the distance between them (§ 253), and we infer that no effect is likely to be felt on board a ship unless she happens to be in shallow water. It has been calculated that to produce an appreciable effect when a ship is in 30 fathoms of water a magnet of enormous power would be required. Thus it is obviously impossible for magnetic sub- stances on shore to produce any effect on board a ship, unless she is extremely close to them. Information is given in the various Sailing Directions as to the places where local attraction has been found to exist. The most remarkable of these places is near Cossack in Western Australia, where, in nine fathoms of water, the variation has been observed to vary from 56° E. to 26° W. in a distance of 200 yards. 264. The compass. — We have seen that at any place a freely sus- pended magnetised needle lies in the direction of the line of force at that place and, in general, is inclined to the horizontal plane. Since direction on the earth's surface is measured by a horizontal angle we require the compass card to he horizontally ; therefore the card with its needle (or system of needles) is suspended in such a way that its centre of gravity is vertically below the point of suspension. Now the forces acting on the compass needle (or needles) at any place are the earth's vertical force Z and the earth's horizontal force H ; the effect of Z is counteracted by the particular method in which the compass card is suspended; the force H causes the needle to point in the direction of magnetic North at the place, and may therefore be termed the directive force of the earth at that place. Line of Dip. Ship built head East in England Dip 67. Section looking from Aft forward. c Ship built head South West in England . Starboard side- Port side. Starboard side. Port side. 6 Ship built head North in England. Line of dip Ship built head North On the Magnetic Equator No dip Ship built head North at Sydney (N.S.W.) Line of dip. Fig- 207. 305 Arts. 265, 266. 265. To compare the earth's horizontal force at two places. — The time of oscillation (T) of a compass needle when displaced in the horizontal plane from its mean position is given by T - 2 Vro M where / is the moment of inertia of the needle about its axis. M is the magnetic moment of the magnet, and H is the earth's horizontal force at the place. If the compass needle is removed to a place where the earth's horizontal force is H', the time of oscillation (T") is given by therefore *"Jsri T 2 ^ H ' Thus, it the times of oscillation of a compass needle are noted at two places, we see that the horizontal forces at the two places may be compared by means of this formula. . 266. The permanent magnetism of a ship. — If a compass needle is brought into the field of a magnet, the directive force will be increased or decreased according as the lines of force of the magnet act with or unst those of the earth. Xow a ship, on account of the large amount of iron used in her construction, assumes the character of a large magnet, and therefore a compass on board a ship indicates direction under the action of two systems of linos of force — the system due to the earth which tend- to make the needle lie in the magnetic meridian, and thai to y being to starboard and considered Let ON be the magnetic meri dian, and let the angle NOa which i- the magnetic com e measured from the magnetic meridian in an Ea terlj direction from to 360 be denoted^by £. Pio. 210 Art. 267. 308 With these conventions as regards signs, it will be seen that the components of the earth's horizontal force, in the fore-and-aft and athwartship directions, are H cos £ and — H sin £ respectively. There- fore the components "of the earth's total force, in the three perpendicular directions mentioned above, are shown in Fig. 211. From the above we see that the soft iron of the ship is magnetised by three forces : — H cos £ fore-and-aft, — H sin £ athwartships, Z vertical ; and in order to study the magnetism of the soft iron we shall deal with the effects of each of these forces separately. Let us first consider the effect of the fore-and-aft force H cos £ on the soft iron of the ship. As explained in § 255, when a bar of soft iron is placed in a magnetic field the directions of the lines of force due to the magnetic field are modified in the vicinity of the soft iron, and the lines of force due to the magnetism induced in the bar are in the opposite direction to that of the inducing force. We may therefore consider that a similar result will occur when the fore-and-aft component of the earth's magnetism (H cos £) enters the soft iron of the ship, and we may conclude that the direction of the force at the compass, due to the induced magnetism, will not be in the fore-and-aft horizontal fine but in some other direction. From the assumption (2) above the magnitude of the force at the compass will be IH cos £, where lis a constant depending on the soft iron of the ship. In order to analyse the effect of this force at the compass we must resolve it into the three directions above mentioned. Let us suppose that 309 Art. 267. the cosines of the angles which its direction makes with Ox, 0// and Qz (Fig. 212) are ~ .and - respectively, then the resolved parts are aH cos £ dH cos £ qH cos £ along Ox, along Oy, along Ox. Fig. 212. In a similar way it may be shown that the athwartship force — H sin £ gives rise to three forces — bH sin £ along Ox, — e// sin £ along 0//, //// sin £ along Oz, and lli;M the vertical force Z gives rise to three forces cZ along 0#, /Z along Oy, kZ along Oz. 'I hue the effect of the induced magnetism in the »of1 iron of the ship hae been resolved into nine forces, as shown below : \ ■ \tt. \tl liips. I Ml. // cos C // sin £ - eZ in the fore-and-aft line. ell sin £ -\-fZ athwartships. /># sin £ + kZ to keel. In the last three expressions P, Q, and /2 are constants -generally called constant parameters — which depend on the amount, arrangement, and permanent magnetism of the hard iron of the ship; similarly. a. I>. <•. d. e, /. ;/. h. and k are constant parameters which depend on the amount, arrangement, and capacity for induction of the soft iron of the ship. When considering the various forces due to the hard and soft iron of the ship, it is often convenient to represent them by permanent magnets and soft iron rods, the effects of which are the same as the forces which they represent. Fig. 213 shows the arrangement of the soft iron rods which correspond to the forces + all, + bH, + cZ, &c. ; the rod which has the same effect as —aH, for example, being named a - a rod as in the Figure. < >n examining the Figure it will be noticed that there is a great similarity between pairs: for example, the rods a and e are similarly situated with regard to the compass except that a is fore-and-aft and thwart-hips. Similarly b and d may be taken together as well as C and /'. and g and h. 258. The horizontal forces at the compass when the ship heels. When a ship heels the hard and soft iron are differently situated with . ird to the compass, and the soft iron is differently situated with regard to the earth's lines of force, so that the horizontal forces which act at the compass change when the ship is heeled. Let / lie the angle of heel of the ship, and let it be considered - - or - according as the ship heels to starboard or port respectively. I'm;. 2 Wh nen t he hip heele i he fore and aft line ■ hange, hut i he ;ii hwart ihip line, Oy, and t he new po ition* < >>, >> i in l'i 'i i line Fiji to l ■ 211, •I. " does not take up \ ■ Art. 269. 312 It was seen in the preceding article that the components of the earth's force along Ox, Oy and Oz are H cos £, — H sin £ and Z ; when the ship heels, — H sin £ has a component H sin £ sin i to keel and a component — H sin £ cos i along Oy' ; Z has a component Z sin i along Oy' and a component Z cos i to keel. Therefore, the total force to starboard along Oy' is — H sin £ cos i -f Z sin *", and the total force to keel along Oz' Z cos i -f H sin £ sin i. Therefore the inducing forces are, along Ox H cos £, along Oy' —H sin £ cos i -\- Z sin i and along Oz' Z cos i 4- H sin £ sin t. Therefore the components of the forces which act on the North end of the compass needle in these three directions may be found by sub- stituting — H sin £ cos i -\~ Z sin i, for — H sin £ ; and Z cos i -\- H sin £ sin i, for ^, in the expressions given in the preceding article where the ship was supposed to be upright. The components are as shown in Fig. 215, where it has* been assumed that b = d = f — h = Q and that the angle of heel i is so small that we may put sin i = i, and cos i = 1. Now, since the compass needle is constrained to move in the horizontal plane, we have to resolve the forces which act along Oy' and Oz' into their components along the horizontal line Oy and we find that the force along Oy is the original force — i.g.H cos £ + i(eZ — kZ — R). The force along Ox is the original force + i.c.H sin £. 289. The sub-permanent magnetism of a ship.— In the expressions given above it has been assumed that the iron of the ship is either hard 313 Art. 269. or soft. Now there is a certain amount of iron, used in the construction of a ship, which is neither hard nor soft but of a character intermediate between the two. .Such iron, after lying for some time in the direction of the lines of force of the earth, and after being subjected to the vibra- tions of the engines and the tiring of heavy guns, becomes magnet i by percussion. When the direction of the ship's head is changed the magnetism does not immediately disappear as in the case of soft iron, but Buffers a gradual diminution which depends on the coercive force of the metal in question. Such magnetism is called sub-permanent magnetism and is generally small in amount. Thin iron superstruct- ures, particularly when near heavy guns, are very liable to be magnet ised sub-permanently. Owing to the transient nature of this kind of magnetism, its amount cannot be calculated and its effect cannot In- allowed for. Art. 270. 314 CHAPTER XXV. THE MAGNETIC COMPASS— {continued). THE ANALYSIS AND CORRECTION OF THE DEVIATION. 270. The deviation of the compass. — In addition to the earth's magnetism the compass needle is subjected to the influence of the permanent and induced magnetism of the ship; the effect is that the compass needle does not always lie in the magnetic meridian but generally to one or other side of it, and we have what is called deviation. 'Let us first examine the effect on a compass of a fore-and-aft permanent magnetic force -f P. Effect of+ P Head North. No dev? Gain of Dir" Force. HeadN.W. Dev n M Head West Dev?W HeadN.E. DevPE Semicircular Curve s^bl due to + P Head East Dev?E W Head St. Dev n E Head South. No DevP • LosscfDir v ? Force. Fig. 216. In Fig. 21 (i it will be seen thai when the ship's head is North, the force P is acting with the earth's force, and we have what is called a gain of directive force. When the ship is on an Easterly course the compass needle is defleeted to the Eastward, and we have Easterly deviation. When the ship's head is South there is a loss of directive force, and when she is on a Westerly course there is Westerly deviation. 31f» Art. 270. + r rod North Mag c LaLitL A Head North. Corr.yiSc o'Mpg c / \ Nc C<*,:;t,on.Gmnof Deforce / Thus the deviation, due to this permanent magnetic force • /', changes with changes in the direction of the ship's head, and changes its name when the ship's head is directed in opposite semi-circles. Such deviation is called semi-circular, and may he represented by the abscissae of the curve shown at the side of the Figure. Jn Fig. 217 is shown the effect of a -- c rod in the Northern hemisphere, where the induction in such a rod is to cause a Hue pole before the compass. It will be seen that the effect is exactlv similar to Head wett b y Con- >*« . . , J . .. y,**?W. Cretin,' that of the permanent magnetic /y oe f*c.' b) /. and dividing through by XIL we have — Sm8 =H [^Kh) C ° B8 + { XI, J*"'' ; I A// J 00 "' + A ( a 2x V) sin (V + «) + H | '[ 2xJ ^ cos (2f + 8). Denoting the coefficients on the righl l>\ A', /.". C", D' and A-', we i — Bin I 'cos 8 B'sinf + C'cosf' + 7)'sin(2C' + 8) + #'cos(2f +8). The right-hand side of this equation gives the sine of the deviation expressed uearly, though uol wholly in terms of the coefficients I B sailed th< exacl coefficients) and the compass cours In the Admiralty -Manual for the Deviations of the Compass the « • x . i < • i • denoted by old English letters. 273. The meaning of /. We shall now explain the meaning of the tbol /.. an lie force /.// appears in each <>f the exact coefficients I he symbol is of considerable importance. Lei //' be th<- directive for< □ the compass needle in the direction of com] North then the force acting on the compass needle in the direction of magnetic North is II cos 8. Since the directive force to magnetic North is given bj resolving the i in Pig. 219 along the magnetic meridian, we h ivi //' ooe 8 - H (/' off cob t /-//sin r . / . - Q H( > H »in I j fZ . // [P cZ) co* ( a( + all .-...<: i II in [d b) U sm ( « // [P Q //)-.,,,; I ("±- e )tf ■I "(\, ? )< •' "f', ~) '"-■ = a//m /;' ■ ' • " m 2( B Bin Arts. 274, 275. 318 Now this equation is true whatever the value of £, so that, if we suppose the ship to be headed successively in every direction from 0° to 360°, and remember that the mean values of the trigonometrical ratios on the right are all zero, XH is the mean value of H' cos 8 ; that is, XH is the mean directive force to magnetic North at the place in question. Therefore X is the ratio which the mean directive force to magnetic North at the compass needle bears to the earth's horizontal force at the place in question. Since each of the exact coefficients varies inversely as XH we see that 8 roughly varies inversely as XH. For this reason the position selected for the compass should be such that the value of X is as large as possible. It is found that on board ship the forces all and eH are always such as to reduce the directive force, and consequently X is always less than unity. The value of X at a well placed compass often exceeds ■ 8, but at a badly placed compass it may be as small as '2. The value of X does not alter appreciably in different parts of the Avorld, but time and high temperature tend to slightly increase it. 274. The approximate expression for the deviation. — The form of the exact expression for the deviation, given in § 272, suggests that the deviation, when of only moderate amount, may be expressed in the simple and convenient form — 8 = - A + B sin £' + C cos £' -f D sin 2 £' + E cos 2 £', where A, B, C, D and E are angles in degrees, and arc called the approximate coefficients. If 8 is observed for various positions of the ship's head, the approxi- mate coefficients may be found more easily from the equation above than can the exact coefficients from the exact expression for the deviation. Therefore, if we find the approximate coefficients from observation, it is necessary to find the connection between the approximate and exact coefficients before we can ascertain the values of the various forces involved in the exact coefficients ; but, before doing so, we shall consider the component parts of the deviation as given by the approximate expression . 275. The component parts of the deviation. — The deviation of the compass, as given by the approximate expression, consists of five terms, as follows : — -i-B -B A, which is independent of the compass course and is called the constant deviation. H sin £', which is a maximum, + or — , when the ship's head is East or West, and vanishes when the ship's head is North or South. This part of the deviation is given by the abscissae of the curves shown in Fig. 220. and, as it changes its name in opposite semicircles, it is called semicircular. Fig. 220. 319 Art. 276. Fig. 221. NE ;r 5W ( cos £', which is a maximum, -j- or — , when the ship's head is North or South, and vanishes when the 1 ship's head is »r West . This part of the deviation is given bj the abscissae of the curves shown in Fig. 221, and Ls also called semicircular. Tin' two parts B sin £' and C cos £' constitute the semicircular deviation of the compass, and the combination of the curves (Figs. 220 and 221 | gives the curve for the semicircular deviation; this curve is of similar form, but its maximum and mini iiium abscissae do not, in general. occur at the cardinal points. 1) sin 2£', which is a maximum when the ship's head is on either of the inter-cardinal points, and vanishes <>n the cardinal point - This part of the deviation is given by the abscissae of the curves shown in Fig. 222. and as it changes its name in adjacent quadrants, is called quadrantal. E i os :.'l . which i-^ a maximum when the ship's head is "ii either of the cardinal points, and vanishes on the inter cardinal points. This part of the deviation is given by the abscissae of the curves shown in Fig. 223, and is also called quadrantal. The two parts l> sin 2£' and E cos 2£' i j — t ii ute t he quadrantal deviation ' he compass, and t he combinat ion of the two curves (Figs. 222 and 223) givi irve for the quadrantal de\ iation « hah is of a similar form. The total quadrantal deviation D Bin 2j| E Fig 223 2( m.tv be d in the form s 7 /'" I Mr] -V 23/), when 2.1/ '. Thorefore the maximum value ot Fig. 222. + E -E ' he quadranti I d--\ ial ion i- >//'■' E J 276. Relations between the exact and the approximate coefficients. i< mi fi »r t he 1 le\ is I i< »n, we put sin ft in the exact 1 /;' b D in 2f]. I /. 1 1 h ii / 1 ■ 1 ml 1 ■ ' Art. 277. 320 As will be understood later, the coefficients A' and E' are always small compared with B', C and D' , so that we may consider B', C", D' to be small quantities of the first order and A', E' to be small quantities of the second order. Retaining small quantities of the second order only, we have — S = A' + B' sin C + 6" cos f + D' sin 2f + W cos 2f + B JL (sin 3 f _ S i n f ) + ^ (cos 3f + cos f) - ^ sin 4f + etc. On comparing the coefficients in this equation with those of the approximate expression, we have — ■*A . . A =180 = sm ^' _, B'D' -rvB . „ B - -T^ = T80 =smjB ' ° +-2- = 180 =SmC ' W = J^ = sin 2S. . 180 From which it follows that— 4' = sin 4, D' --= sin Z), JE' = sin E, B' = s ^, = «rin B (1 + * sin £>), 1 ~¥ C" = ^-^, = 3in c (1 - |- sin D). More exact relations can be found, but these are sufficiently accurate in practice when the approximate coefficients do not exceed 10°. 277. To find the approximate coefficients from observation.— If the deviation of the compass is observed with the ship's head in various directions the approximate coefficients may be found from a short analysis of the deviation table. Let S N , Sn.e.> £e.> be the deviations observed with the ship's head successively on the eight-compass courses N., N.E., E., . . . ., then from the approximate expression for the deviation, namely— 8 = A + B sin £' + C cos £' + D sin 2 £' + E cos 2£' we have Course £' [ 8 = ^4 + 5 sin £' + C cos £ -f £> sin 2f -f -E cos 2f N. 0° »K. = A + c N.E. 45 C + a/2" E. 90 **. = ^+ s S.E. 135 8 s. E . ~ A + V2- ' ^2" S. s.w. 180 225 S =-4 s. B 8 s.w. " T - G c V2 w. N.W. 270 315 8 -^ ~ B w. 8 = 4 7s N.W. V2 C + 7i + D D + D - D + E - E + E - # 321 Art. 278. By addition 8 I 8 V + S x .e. + + S N . W ., t A is the moan of the deviations for the eight compass courses. By subtracting th< ition for West from that for Bast, we have 25 = 8 Ki - 8 W . Tn a similar manner = On. — Ss.- By adding the deviations on the four intercardinal points, the signs of the deviations on S.E. and N.W. being chanced, we have ^•' : Sn.E. 8s.E. " Ssay. — Sn.W. Similarly by adding the deviations on the four cardinal points, the 1 i deviations on Kasi and \V sing changed, we have W 8x. Se i.. -+- >w. •.l«l be remembered that we have named Easterly deviation • and Westerly deviation—: therefore, when using these algebraical signs, - of the coefficients are given by the equations. method of obtaining the approximate coefficients just given illed a rough analysis ; a more exact method i< •_ in the Admiralty he Deviations of the Compass. As an example, let us find the approximate coefficients from the following observed deviations : — Sliij 1 >eviation. Ship's head. I Vviat ion. X. 2° E. NT.E. :; E. E. Nil. S.E. • :; .lO' \\ s. s.w. w. N.W. ■2 \Y. :i E. 4 E. 1 50' E. We have from above : — 3 :: .->()' - 2° ■'■ :; i° + 1° 50' i i; — _ •> — o % 2 :: 50' :* L°60 l> i 2 i ■2 I 2 Therefore the deviation for an} compass course i given approxi- mately by l 2 sin f 2 cos £' 2 sin 2£' l cos 2£'. 278. To fini thi exact coefficients. When the approximate ooeffi cienta have b i found by tin- method ol rough anal} .a- otherwi e, Art. 279. 322 the exact coefficients may be found from the relations given in § 27G. In the example above, we have A' = sin^l = sin 1° = + -017. B' = sin B (1 + J sin D) = sin ( - 2°) (1 + \ sin 2°). = - -035 (1 + -0175) = - -036. C = sin C (1 - \ sin Z>) = sin 2° (1 - J sin 2°). = -035 (1 - -0175) = + -034. D' = sin D = sin 2° = + • 035. E' = sin E = sin ( - 1°) = - -017. 279. The correction of coefficient 5'. iff ' m^ ih' From this formula we see that that part of the deviation, which is represented by the second term of the exact expression, arises from the fore-and-aft forces, P, due to the fore and aft component of the ship's permanent magnetism, and cZ, due to the fore-and-aft component of the induced magnetism due to Z, and represented by a c rod. In order to counteract the effects of these two forces it is necessary to correct like with like, and to place at the compass a fore-and-aft permanent magnet which has an equal and opposite effect to P, and to place before or abaft the compass a rod of vertical soft iron the induction in which has an equal and opposite effect to cZ. To do this we must find P and cZ. Let B x ' and B 2 be the exact coefficients at two places where the earth's horizontal and vertical forces are H 1} Z x and H 2 , Z 2 respectively, then from above we have — P + cZ x = XH X B\ P + cZ 2 --= XH 2 B' 2 provided that nothing has been done between the two observations, such as moving the magnets, to alter the value of P. From these equations P and c may be easily found. Screwed on to the binnacle is a brass case, in which can be placed a rod of soft iron, three inches in diameter and of the necessary length, to correct the effect of cZ. This rod is, in effect, a c rod of opposite sign to the c rod which represents the component of the induced magnetism under consideration. This soft iron corrector is called a Flinders bar, and is supplied in the following lengths — 12, 6, 3, l£ ins. and two lengths of f in., so that the greatest length that can be used is 24 ins. In the Admiralty Manual for the Deviations of the Compass, Table V. gives the lengths of Flinders bar for values of c from -01 to -16, and also the amount of the deviation caused by these lengths at a compass TT on shore in the South of England, where the value of _ is 2-33. The Z length of Flinders bar used should be placed in the tube in such a manner that the longest portion is uppermost, and the upper pole, which is about one-twelfth of the length of the bar from the extremity, is on a level with the compass needles ; the latter is effected by placing pieces of wood of requisite length at the bottom of the tube. It is obvious that if cZ has been counteracted by a correct length of Flinders bar it will always remain so whatever part of the world the ship may be in, because the force which induces magnetism in the ship 323 Art. 279. is also that which induces magnetism in fche Flinders bar. We see from this the importance of correctly placing the Flinders bar. The rinding of c requires two values of B' which correspond to different magnetic latitudes; when it is impossible for a ship to change her magnetic latitude, the value of c is estimated by comparison with the values obtained in other ships of the same class. A suitable length of Flinders bar is then inserted, and the remainder of the deviation, with the ship's head East or West, is corrected by permanent magnets placed in the fore-and-aft direction. If U is obtained by observation when the ship is on the magnetic P equator the whole of B' is due to . because Z is zero; in this case the whole of the deviation, with the ship's head East or West, should be corrected by permanent magnets. If a change of deviation subse- quently occurs on change of magnetic latitude it is due to the Flinders bar being incorrect . Example :— In 11*12, the value of />" for the standard compass of a ship was found by observation at Plymouth and Zanzibar to be -]-■ 141 and • 193 respectively. The value of X for the compass was -9 and there was a 12-inch Flinders bar in place on the fore side of the binnacle. Required to correct the coefficient B' . From the charts of equal horizontal and vertical force, we find that— at Plymouth, H x = • 190 dynes, Z x — -425 dynes, at Zanzibar. //. -290 „ Z 2 = — -210 „ From the equations above we have — P 4- • 125c = -9 X -190 X • 141 = -0241 P - -210c = -9 X -290 X -193 = -0504. By subtraction, -635c = — -0263 • 0263 A., • C= - -635 -=--°41. Now this value of c ( - -041) consists of the C due to the ship, and that du<- to 1 he I 2-inch Flinders bar which is already in place. From Table Y. of the Admiralty Manual we see that a 12-inch Flinders bar, on the fore side of the binnacle, corrects a c which is -05, so that this length of Flinders bar i- equivalent to a c rod of + '05. Therefore C of ship 05 = -041 : .-. r of ship = -091. From Table V. we find that, corresponding to '091, a length hi-:; inches of Flinders bar is required on the fore side of the binnacle. Length of Flinderc bar required 16*3 inch ,, .. already in pku e 12*0 to be added I • .'! The nearest length to this, whioh can be made up from the lengths supplied, Lb \\ inch In practioe the yalue oi P i not found, but the remainder of the deviation, when the Bhip head i Bast or We I i corrected i>\ fore and aft permanent magnet How to place these magneti in the binnacle Arts. 280, 281. 324 is easily determined by noting in which direction, whether forward or aft, the North point of the needle should move, and by placing one (or more) of the corrector magnets (all of which are coloured red and blue) with its blue end in that direction, till the deviation vanishes. 280. The correction of coefficient C". c> Q +f z = -2- 4- /? From this formula we see that that part of the deviation, which is represented by the third term of the exact expression, arises from the athwartship forces, Q, due to the athwartship component of the ship's permanent magnetism, and fZ, due to the athwartship component of the induced magnetism due to Z and represented by an / rod. At a well-placed compass in the midship line / is generally zero, and therefore C is generally due to Q alone, and may be counteracted by placing an athwartship permanent magnet (or magnets) beneath the compass. Q has its maximum effect when the ship's head is North or South, and therefore if the deviation is corrected by athwartship permanent magnets, when the ship's head is in either of these directions, the effect of Q is counteracted. How to place the magnets in the binnacle is easily determined by noting in which direction, starboard or port, the North point of the compass needle should move, and by placing one (or more) of the corrector magnets, as necessary, with its blue end in that direction, till the deviation vanishes. To summarise the rules given for counteracting the effects of P and Q, assuming that the Flinders bar has been correctly placed : — with the ship's head on any cardinal point, insert permanent magnets, as necessary, at right angles to the compass needle, and with their blue ends in that direction in which the North end of the compass needle should move; repeat the operation on an adjacent cardinal point. 281. The correction of coefficient D'. 2XH J 2X ' From this formula we see that the deviation, represented by the fourth term of the exact expression, is due to the difference between the component in a fore-and-aft direction of the induced magnetism (repre- sented by an a rod), and the component in an athwartship direction of the induced magnetism (represented by an e rod). On board ship it is invariably found that these components are represented by — a and — e rods, and that the numerical value of e is considerably greater than that of a ; we therefore see that D' is always positive. To counteract the effects of - - ell and — aH, soft iron spheres, called quadrantal correctors, are placed one on either side of the compass in the athwartship line, their centres being in the plane of the compass needles (§ 283). The spheres are hollow and their thickness is about one inch. Fig. 224 shows how the effect of the spheres counteracts the combined effects of the — e and — a rods. From the formula, we see that D', or sin D, is the same in every -part of the world, and therefore, if the soft iron spheres are so placed as to exactly counteract the effects of the - - e and - a rods, this coefficient will be correct in all parts of the world. 325 Art. 281. Table^IV. of the Admiralty Manual gives the sizes and positions of spheres required to correct various values of D in different types of compasses. To correct coefficient D' at a particular compass, enter the table for that compass with the value of D, found by observations of the deviations on the intercardinal points (§ '111), and rind the size of the spheres and the distance from the side of the binnacle at which they should be placed. When D' has once been corrected, it will remain so in all parts of the world, but this is only true if the compass needles are so short, and their magnetism so weak, that the} - produce no sensible induction in the spheres (§ 284). It will be seen from the formula that D' is closely connected with ?., and therefore if D' is found to change from any cause, a change in ?. y be expected. As the deviation due to D' is quadrantal — that is to say, changes its ■ _ in adjacent quadrants — the total deviation, if D is uncorrected, must vary considerablv for small alterations of course, and thus we see the great ssity for the spheres being placed in position as accurately Curve of Dev nr Cu" dijeUi5phc?-e5 cucto-.- sw SE sv. Pig. 224. a possible, in the i a e of a new ship an estimation must be made of the value of D, and spheres placed accordingly. If, when observations >■ been takes on the intercardinal points, D is found to be zero, it Lb obvious that the estimation has been correctly made; but if an appreci- able value of l> i obtained the spheres require readjustment, as will be understood from the following example. ExampU : Spheres, 8^ inches in diameter, have been placed on a Chetwynd comp Patt. 22), the distance between the surface of either and the oentre oi the compae being ,( inche , The following deviation been found i.\ ob bion tip head >> >> x 6108 \ 1 Deviation 2 15' \\ . 3 l. 30 W - w o ie w . N w w 80 E. Arts. 282, 283. 326 Required to correct coefficient D' . From (§ 276) — 2° 15' + 0° 30' — 0° 45' — 3° 30' 4 .-. D = - 1° 30'. From Table IV. of the Admiralty Manual we find that the spheres, as placed, correct a D of 6° 30', or cause a — D of 6° 30'. Thus we have D obtained by observation — 1° 30' D introduced by spheres - - — 6 30 Original D of the ship - - + 5 00 By reference to Table IV. we find that 8^-inch spheres at a distance of 10 inches from the compass, or 7-inch spheres at a distance of 9 inches, correct this value of D. Consequently, either the, spheres at present in place must be moved outwards one inch, or they must be replaced by 7 -inch spheres at a distance of 9 inches. 282. The correction of coefficient E'. From the formula we see that the deviation, represented by the fifth term of the exact expression, is due to the sum of the component in a fore-and-aft direction of the induced magnetism (represented by a d rod), and the component in an athwartship direction of the induced magnetism (represented by a b rod). It is very unusual for d or 6 to have any appreciable value at a well-placed compass, but if E' is found to exist, it should be corrected, in] conjunction with D' , as explained in § 283, by placing the spheres at an angle] if to the athwartship line, the angle being- determined by tan 2M = ? When E is + the port sphere should be forward, and when — the starboard sphere should be forward. In order to determine the size of the spheres required and the distance of either from the compass, Table IV. of the Admiralty Manual should be entered with the maximum quadrantal deviation, namely Jd* + # a: (§ 275). 283. The correction of the total quadrantal deviation.— In Fig. 225, let Ox and Oy be the fore-and-aft and athwartship lines of a ship, and let us consider the forces acting at a compass at O, due to the induction in a soft iron sphere of radius p, at a distance r from the compass, and at an angle M before the port beam. The inducing forces on the sphere are H cos £ and H sin £ parallel to Ox and Oy respectively, and these cause the sphere to be equivalent to two magnets of pole strengths ap 2 H cos £ and — ap 2 H sin £, where a 327 Art. 283. i- a constant depending on the nature of the soft iron of the sphere. By § 253 the forces acting at the compass due to these two magnets arc as follows : — Due 1 1 > ap-H cos £ - " -in. f Force along Force along Oy. ap>H co* C {{ 3o082M) ap 3 H cos C 3 sin 2M ap 3 II Sin f _ . „_. ' , :; sin -.1/ ,.3 ■ap*H sm( h3 cos2M). Fig. 225. [f thereare two spheres as in the Figure, the forces along Ox and Oy are twice those just given, and the total force along Ox is lnpl\ (I :; cos -.1/) cob £ 3 sin 2JM Bin £ ] and 1 he total force along i ' :; in _'.!/ oob £ i 3 co 2 '/ 1 in £ lomparing these force alo "- and 0# wrtth those due to the induced i i n the jofl iron ol the ship (8 207), we have, if a', 6', d in igneti , » 2 Art. 283. 328 arc the parameters for the spheres corresponding to a, b, d, e for the ship, a' = 2ap 3 (1—3 cos 2M), = '~jf (! + 3 cos 2M )> V = d! = - ^ 3 sin 2if . r 3 Also, if a' corresponds to X, we have r i .i- a ' + e ' i 2a ^ 3 A - 1 + —2— = 1 + -j- . Now the quadrantal terms due to the spheres are a' — e' . a9 , . b' + d' oyl and, substituting from above, these become 6ap 3 cos 2itf sin 2£' + sin 2M cos 2£' Therefore, if the spheres correct the quadrantal terms due to the ship, namely D' sin 2£' + E' cos 2£', 6a» 3 we have -^L cos 2M = — D' and - ^ sin 2if = - E' . Air From these two equations we can find at what angle with the athwart- ship line the spheres should be placed, and the distance of either from the compass. By division, we have tan 2M = ~ = sinj; = £2? sin D D x — A 180 E - B' If E = then i¥ — 0, and the spheres should be placed athwart- ships. If E is negative the port sphere should be placed abaft the beam. Again, by squaring and adding, we have 320 Art. 284. Therefore! substituting for /.'. we have JW* - B'* '*-2a[ . * _. -l] ? " Ly/D' 2 E'- r P 180 and when E = r v ! -i ISO The equation shows that for a given maximum quadrantal deviation ( s / /> 2 r E 2 ), and a given kind of soft iron (a), the ratio of the distance of either sphere to its radius can be calculated. This, however, is not- done in practice on account of the induction in the spheres by the compass needles, and Table TV. of the Admiralty .Manual has been constructed from the result- of experiments with various types of lompasses. We may here notice the effect of induction in the Flinders bar by the earth's horizontal force. Tins bar. having an appreciable diameter (3 inches), may be considered to behave in the same way as a soft iron sphere, and, M being 90° or 270° in this ease, the quadrantal terms, due i" the equivalent sphere, reduce to j& sm 2f which corresponds to a -f &• For this reason, as well as for others (§§ 284 and 296), the coefficient I) should be re-determined and the spheres moved, as necessary, whenever the length of the Flinders bar i- altered. 284. The induction in the soft iron correctors due to the compass needles. \- stated in §281, the quadrantal deviation, if properly corrected by the spheres, remains correct in all magnetic latitude-. provided thai no appreciable magnetism U induced m the spheres l»\ the compass needli if F be the force al the compass, due to the magnetism induced m the Bpheres by the needles, when the compass cow e i - and if the spheres are in the athwartship line, the quadrantal terms of the deviation due to the spheres reduce to •_•;.// '" ' '"'■"' K ii r the Becond term of which change i the hip changes her magnetic latitude. For this tea on, when long and powerful compase needles are Arts. 285, 286. 330 employed, a change in the quadrantal deviation may be expected on change of magnetic latitude. The effect of tins induction can be seen by examining Table IV. If the needles of the Thomson compass (in binnacle Patt. 48a) are so short and weak as to have no effect on the spheres, the table for this compass only gives the effect of the induction of the earth in the spheres ; for example, 12-inch spheres at a distance 14-5 inches (from centre of compass to centre of sphere) cause or correct 10° 36' of quadrantal deviation, whereas in the Chetwynd compass (Patt. 22a) the same spheres, at the same distance, cause or correct 12° 15' ; thus the effect of the induction by the needles in England, where H — -184 dynes, is to cause or correct 1° 39'. In a similar manner the compass needles induce magnetism in the Flinders bar, the effect being to accentuate the value of D and cause it to change with change of magnetic latitude. This effect, combined with that due to the earth's horizontal force (§ 283), was found to introduce a D of + 1° 40' when 11 J inches of Flinders bar was placed before a compass, the D of which had previously been exactly corrected. 285. The coefficient A'.— The coefficient A' represents the constant deviation and, since cl and b are seldom found to have any value at a well placed compass, it is unusual at such a compass for A' to have any value. It is impracticable to counter- act A', but when it exists at a steering compass, it may be allowed for, as far as the course alone is concerned, by altering the lubber's point. 286. To obtain I by observation. — In order to obtain the value of a at a particular compass, the value of H' (the directive force to compass North) must be observed for a particular direction of the ship's head, and this is done by timing the oscillations 'of a horizontal needle as explained in § 265. The instrument employed consists of a flat highly magnetised needle, three inches long, mounted in a circular box with a glass lid. The method of taking the observations is as follows : — take the instrument on shore and set it up in a place free from local attraction and sufficiently far removed from possible magnetic influences. Deflect the needle from the magnetic meridian by means of a magnet and allow it to oscillate. When the whole arc described by the needle is about 40°, note the instant when the North-seeking end (marked) has reached the extreme deflection on the right, and subsequently note the instant of every tenth oscillation, till the needle has nearly come to rest. The mean of the intervals occupied in ten oscillations is T (§ 265). Take the instrument on board and, having obtained the exact coefficients from the observed deviations, unship the compass bowl and place the instru- ment in the binnacle, so that its centre is in the position originally occu- pied by the centre of the system of compass needles ; repeat the observation as on shore, and thus obtain the value of T' for the particular direction in which the ship's head happens to be. Then from § 265 we have //' T 2 H = T' 2 ' and "k may be obtained from the formula (§ 273) — ■ ; H'[ cos 8 \ H \1 + B' cos £ - C sin £ + D' cos 2£ - E' sin £/ 331 Art. 287. It is advisable to repeat the operation for three or tour different directions of the ship's, head, and to take the mean of the results. should observations be taken on four equi^istanl points, /. is the ... . ,. //' COS 8 mean of the tour values ot Example : — It is required to tiud the value of /. for the compass, the deviation table for which is given in § 15, and the exact coefficients for which have been found in § 278. The time of ten "-'illations of the needle on shore is 18/2 second.-, and the time of ten oscillations of the needle on hoard, with the ship's head X. 673 K. (compass), is 20*2 seconds. Here T = 18-2 seconds and T = 20-2 seconds. From the table (§ 15) the deviation (8) is 2 E. and therefore the magnetic course (£) is N. <">n.l K. T 2 1 cos a Xow ,\ T' 2 \l + B: <*>£ C - C* sin ( + D' cos 2f - A" sin 2£/ L8-2*j cos 2 \ 20-2«\l 036cos69$ • «•:;{ siu » • (#5cosl39 017sinl^ 331-24 cos 2° IO8-04 (I - -OILT, - -0318 - -0204 + -Oil I) 331-24 ooa 2° 4US 0t -9403 = -863. Therefore the required value of /. is -863. 287. The effect oi spheres on / and the formula for A 2 — In Fig. 224. it will be seen that the effect of the spheres i- to increase the directive force on the compass when the ship's head is East or West, and to decrease it when the ship's head is North or South, and therefore placing the spheres on the compass has almost always the effect of altering the mean directive force, or of altering X. The new value of ?. is denoted by A 2 , the formula for which will now be obtained. Let a' and e' he the values of a and e due to the spheres alone. Let a,. < ., and /._, he the values of a, a and ). after the spheres have been placed. The fore and aft forces which induce magnetism in the sphere-' are // ppg £ due to the earth's magnetism. nH COS £ due to the ma u i let i-lil induced in the hip. Therefore the Eore-and-aft force which induces magnetism in the sph< // eqe i oil cos £. 'rh.- fore ,,nd af1 force at ill'- compai . due to the magnetism induced in the -phep | hi force i £ nil I Put, due to the inducing force // eof £ on the hip and Bpheres, the ion- and itt [orce Art. 288. 332 Therefore a 2 H cos £ = aH cos £ + a' (H cos £ + aH co s£), or a 2 = a + a' (1 -f &)• Similarly e 2 = e + e' (1 + e). Now by § 283 _*' 1 — 3 cos 2M e' ~ 1 + 3 cos 2ifef' therefore g 2 -a (1—3 cos 2Jf ) (1 + a ) H - e ~~ (1 + 3 cos 21T) (1 + e) Again, since D' has been corrected, a z = e 2 and therefore l t = 1 + a 2 or 1 + e 2 . Therefore A 2 — (1 + a) (1—3 cos 2J f ) (1 + a) A 2 - (1 + e) "~ (1 + 3 cos 2Jf) (1 + e)' Now i+?L+i. = A and a -J J -= m ' Therefore, by addition and subtraction, we have l+a = 2(l+D') and 1 + e = X (1 - D')- Therefore A 2 -A(l -f D') (1-3 cos 2if ) (1 + D' ) A 2 - 1 (1 - D') ~ (1 + 3 cos 2ilf) (1 —D') .'. A 2 [(l + 3 cos 2M) (1 - D') - (1 - 3 cos 2M) (1 + D')] = A[(l + 3 cos 2M) (1 - D' 2 ) - (1 - 3 cos 2M) (1 - D' 2 )] 3A cos 2Jf (1 - J>' 2 ) *'• 2 ~ 3 cos 2 if -D' When M = 0, we have 3 3A(1 -i>' 2 ) ^ - 3 _ jy • From this formula it may be seen that A 2 is greater than X provided D' is less than \, which is generally the case. 288. The effect of sub-permanent magnetism. — The most marked effect of sub-permanent magnetism is experienced when the ship, having been on one course for a considerable time, particularly in rough weather, alters to a direction at right angles to her original course ; for example, if a ship has been steaming East, the athwartship iron, the character of which is intermediate between hard and soft, becomes magnetised as shown in Fig. 226. When the ship has altered course to North it will be seen that the sub -permanent magnetism remaining in this iron causes an Easterly deviation, which gradually disappears. If we were to consider other cases it would be found that the effect of sub -permanent magnetism is 333 Arts. 289, 290. to attract the North end of the needle in the direction of the old course, and the possibility of this effect should be carefully guarded against by taking frequent observations for deviation. Suppose a ship were bound from England to Gibraltar: whilst crossing the Bay of Biscay and Fig. 226. proceeding down the coast of Portugal the course would be more or less Southerly; but on altering course to the Eastward, to round Cape St. Vincent, an Easterly deviation would be caused, due to sub- permanent magnetism, and, if unallowed for, might result in the ship steering more to the Southward than desired. 289. The effect of lightning. — When a ship is struck by lightning, large changes take place in her magnetism, in some cases of sufficient magnitude to completely reverse the original magnetism. The change experienced in the deviation is generally a maximum when the ship's head is North or South, and consequently the most common effect of lightning is an alteration of the coefficient C. The magnetism thus -uperimposed is generally sub-permanent; it gradually disappears, and the ship regains her original magnetic condition in a few months. 290. The expression for the deviation when the ship heels. —When the ship heels the horizontal forces (§ 268) which act on the North point of the compass needle — to magnetic North, to head and to Btarboard beam — are shown in Fig. 227. and the needle lies in the direction of compa i iZ I 1 R \ y> + A -sin\ - ^-cos t -h )jj\e ~ « ~ "# J cos £ • Again, if 8 is the deviation for a given compass course £' when the ship is upright, we have, by putting i = 8 = B' sin C -f C" cos f + £>' sin (2f + §)• Therefore vc , *cr „ iZl , iA A — b x " w b ' XH^ ■ Z If we assume that the Flinders bar has been correctly placed the expression — sin 2 £' vanishes, and the change in the deviation (8' — 8)° A for an angle of heel i° is ie - 1c -~) cos C — ^cosV V Z' X AH degrees. Fig. 227. £ Therefore, denoting k - - -=hy p — \, the change in the deviation due to an angle of heel of 1° is \jh ( e ~~ ^ + T) cos £' " I cos2 £' de S ree,s< 33"> Arts. 291 293. The coefficient of cos C is called the heeling coefficient, and is denoted by •/ : therefore the change in the deviation due to an angle of heel of f iv J cos £' . cos 2 £' degrees 291. The meaning of \x. — From § 2)17, if Z' is the total vertical force acting at the compass when the ship is upright, we have on the assumption that h = 0, Z' = Z -f R + kZ \-(jH cos C and this is true whatever be the value of £. Therefore, if we suppose the ship to be headed successively in every direction from 0° to 3t><» , we have, since the mean value of the trigonometrical ratio on the right is zero mean value of Z' Z - R -j- kZ = *(!+*+§) = fxZ. Therefore \l is the ratio of the mean vertical force at the compass at any place to the vertical force of the earth at thai place, that is mean value of Z' ^ = z • 292. The correction of the heeling coefficient J. The expression, which has been found in § 290 for the change in the deviation due to an angle of heel of 1°,* contains two coefficients, J and '.. It is impracticable feo counteract the force — gH, so that the correction of the deviation due to the heel is reduced to making J 0. Now •/ ', (•—/* + 1) and from § 287 I e = X{\ />'). Therefore z r J -m L A(1 Therefore ./ d V) H 1 t hat i it mean value of Z* Z /( )- Therefore the mean vertical ion 9 at the. compai must be so altei that it- value I pie /. (1 h • Z It the phexe j^ave been placed, and the altered value of 4, and D are Aj and D . n pectively, the mean vertical force at the compai must be altered to X t (1 l> ,\Z. 293. The heeling error instrument. In ordei ko determine the Dumber and positions of the vertical magnet required for the correction Ait. 293. 33C of the heeling error — that is, the amount of vertical permanent magnetism that must be added at the compass so that the mean vertical force may be A 2 (l — D' 2 )Z — an instrument called the heeling error instrument is employed, and one of these is supplied to each of H.M. Ships. The heeling error instrument, Fig. 228, consists of a circular flat-sided brass case aa, provided with a stand b, and a chain c for susjoending it when necessary. One of the sides is of glass and hinged at the bottom so as to form the door of the instrument, and on this glass door a horizontal diameter dd is marked. Inside the case are brass bearers, capable of being raised or lowered by means of a lifter e, worked by a milled head at the back of the case. Above the bearers are agate planes, on which the knife-edges of the needle NS rest when the instrument is in use. A level / is provided, and so arranged that when the bubble is central the line dd is horizontal. The needle is round and graduated from the centre in a scale of equal parts, the North-seeking (red) end being denoted by a mark. The axis by which the needle is sup- ported passes through its centre of gravity. Small aluminium rings or weights w, which fit closely on the needle, are supplied. The needle is kept in a special tin box when not in use. The needle, when mounted, should be kept raised above the agate planes by means of the lifter, except when actually observing, and the greatest care should be taken to keep it free from rust and moisture. If the instrument is set up at a place free from local attraction, the needle, being placed in the plane of the magnetic meridian, will he in the direction of the earth's total force at that place, so that the angle which it makes with horizontal line dd is the dip at that place. Let one of the rings, of weight w, be placed on the upper end of the needle (the unmarked end in the Northern hemisphere), and so adjusted that the needle takes up a horizontal position, as indicated by parallelism to the line dd ; then, if n be the number on the scale at which the inner edge of the ring is set, and Z the vertical force of the earth at the place, we have'from Fig. 229 . nw = IZ. Fig. 228. 2 k < M-4HH--r H--lH-4-H--~rBEEE3 *-- n — -> I V Fig, 229, 337 Art. 294. Similarly, it we take an observation at another place, where the earth's vertical force is Z', we have n'w = IZ'. Therefore « / ' 294. The correction of heeling error in harbour. -The correction of the heeling error necessitates observations being taken on shore as well as on board. Observations on shore. The heeling error instrument should he taken on shore to a place free from local attraction and removed from possible magnetic influences. It should be set up on a -land or support so as to be at least 3 feet from the ground, and in such a position that the needle lies in the magnetic meridian. The needle should be levelled by means of one of the rings, and the value of n noted. Should one ring not be found sufficient, two rings in contact with one another must be used, and the value of n read off from the inner edge of the inner ring; the reason for always reading from the inner edge of the ring i> to ensure uniformity of observation. Observations on board. As stated above, it is impracticable to correct . oos 2 £', and therefore, when correcting coefficient J, the ship's head should be East or West, because cos (['vanishes at these positions. Since C k V, ' 1- .V small when the course is within 10° of East or West, an\ position of the ship's head within these linitfi is suitable, provided that the value of a is not very large. Having removed the compass bowl place a wooden rod, of semi- circular section, acroe the binnacle, in the direction of the magnetic meridian and with its Hat side downwards. Pass the chain of the heeling error instrument over the rod. and raise or lower the instrument until the needle is in the same position as that lately occupied by the compass needles, and then secure the chain. Should the line dd not be exactly horizontal, it ma\ be made so by moving the spare length of the chain to one side or the other as necessary. From above it is required to satisfy the equation / 2 (1 -D' 2 ); Z Z thai n or "' iAt(l D't). The factor /.j I />'., u called the heeling erroi oon tant, and n value, for each position al which a oompa placed in a particular ship, i- given on a paper to be found in the boa containin heeling error instrument The value oi '/■.. which is the heeling erroi con tant if D'j i- assumed to be zero, ifi given in a pamphlet entitled " Sphe i Blinders Bai Therefore, the inner i if the ring hould be set at a scale division n', at found by multiplying a by the heeling error Arts. 295, 296. 338 constant, and the needle should be placed in the instrument with its marked end towards the North. If the North end of the needle dips, vertical magnets should be placed in a specially constructed bucket below the compass, red ends uppermost, and raised or lowered as necessary till the needle is horizontal. If the South end dips, the magnets should be placed with their blue ends upper- most. The distance between the top of the magnets and the compass needles may be read off on the marked chain which supports them. On account of the possibility of magnetism being induced in the Flinders bar by these magnets it is advisable that they should be as low as possible, and therefore several magnets at a distance should be used in preference to a smaller number near to the compass. In a Thomson compass (§ 300) another error, called the error of translation, exists, and this is due to the translation of the compass bowl arising from its mode of suspension It has been found by experi- ment that this error is allowed for by lowering the bucket 2 inches after the correction has been made. 295. The correction of heeling error at sea. — It is obvious that, when correcting heeling error at sea, the value of n for the position of the ship cannot be obtained by observation. Now the value of n varies according to the vertical force of the earth, and therefore, if its value has been obtained at some place on shore, its value at the position of the ship may be deduced by aid of the chart of equal vertical force. Example : — It is required to find the scale reading at which to set the ring of the heeling error instrument in a ship in Lat. 30° S., Long. 0°, n having been observed at Portsmouth to be 30-0, and the heeling error constant for the compass being • 9. From the chart of equal vertical force we have — At Portsmouth - - - - - Z = • 425 dynes. At the position of the ship - - - Z % — — • 250 „ Then, if n 2 is the value of n at the position of the ship n 2 __ Z 2 n" Z n % = 30 X — •250 •425 n' = • 9n 2 = - --30X-- — 15-9. The negative sign indicates that the ring should be placed on the North or marked end of the needle. The ring should, therefore, be placed on the marked end with its inner edge at the scale division 15-9. At first sight the necessity for the correction of the heeling error may not be apparent, because a ship, unless she be a sailing vessel, does not heel to one side or the other for more than a few seconds ; but, as a ship rolls, the vertical force which causes heeling error is applied alternately to starboard and port of the compass, and this periodic force on the compass needle causes the compass card to swing and become unsteady. Thus we see the necessity for the close correction of the heeling error, in order that the compass card may be steady under all circumstances. 296. The change of the heeling error due to change of magnetic latitude. — The heeling error, when corrected, will remain correct provided 339 Art. 296. that the ship does not change her magnetic latitude, and this is so because, in the correction oi this error, practical difficulties necessitate a departure from the main principle of compass adjustment that is, of correcting like with like — and we correct the induction in soft iron, represented 1') - i and + k rod-, by permanent magnets. Taking, as an example, the ease of the compass of a ship built in England, we should probably have a • U, - k and e. These would all act in the same direction to cause heeling error, and permanent magnet-, red ends uppermost, would have to be placed under the compass to counteract their effects. If the ship -team- South, on arrival at the magnetic equator where Z = 0, jfc and ' will have no effect, and fewer magnets will be required because li alone will be acting. When the ship arrives in the Southern hemisphere I: and — e will, after a ume. counteract ■ R, and no magnets whatever will lie required. Further South the effects of k and — e may exceed the effect of + R, and magnets with their blue ends upper- most will be required. Thus, after any considerable change of magnetic latitude, the heeling error should be re-corrected: but as, on each occasion of so doing, the vertical magnets are moved and possibly the magnetism induced in the Flinders bar or spheres altered thereby, it is necessary, whenever the heeling error i- corrected, to obtain a new deviation table by observation. From the formula it will lie seen that the heeling error is a maximum when the -hip- head is North or South; therefore, should the ship not be perfectly upright and the heeling error not exactly corrected, a change in the deviation for those directions of the ship':- head may be expected. Art. 297. 340 CHAPTER XXVI. THE MAGNETIC COMPASS— continued. THE DESCRIPTION AND PRACTICAL CORRECTION OF THE COMPASS. 297. The bowl of the Chetwynd compass. — Magnetic compasses are of two kinds, according as the compass card lies in liquid or air. The two types of compasses in use in H.M. Ships are the Chetwynd compass and the Thomson compass, and as the former is in use in the majority of modem ships we shall describe it first. A compass may be regarded as consisting of two parts, the bowl and the binnacle, each of which consists of a number of minor parts. The upper part of the compass bowl, Fig. 230, consists of a brass cylinder ABB' A', closed at the top and bottom by two flat glass discs E E' * w/*v/;>s/////;;////;//A//s;/w////s///////;/A t £7 B|Z5 &////><','///>/ /< -VU^l &ZZZZZ L J y/ZAw//////,-^ 1 - \ Fig, 230. A A' and BB' ; in the centre of the latter is situated the pivot I). The cylinder is filled with pure distilled water in which there is 50 per cent, of alcohol to prevent freezing. The card NS is of mica, and is secured to a copper float F, in order to reduce the friction on the pivot D, and to a system of two magnets ry, each 3*75 inches long. The lubber's point I consists of a horizontal pointer projecting inwards from the brass cylinder, its extremity, reduced to a fine point, being close to the edge of the card. In order to allow for the expansion and contraction of the liquid and metal due to change of temperature, two small corrugated chambers g, g, Fig. 231, called expansion chambers, are fitted, one on either side of the bowl. These chambers are in communication, by means of a small hole h, with the interior of the bowl, and are consequently full of liquid. The corrugated sides of these chambers jdeld Fig. 231. 341 Arts. 298, 299. to the expansion and contraction of the liquid and bowl. On the side of the bowl is a hole for adding to the liquid in the bowl as necessary; it is called the filling hole and is fitted with a screw plug and leather washer. Attached to the lower portion of the bowl is a glass chamber BOB', Fig. 2:>n. which is partially filled with castor oil or glycerine; this gives stability to the bowl in a seaway, and at night diffuses the light placed beneath the bowl. In the latest pattern the glass chamber BCB' is absent and a ring is fitted to give stability to the bowl. The bowl is supported by gimbals on roller bearings, the outer gimbal ring being pivoted in roller brackets on the side of the binnacle. The metal ring EE\ called the verge ring, which secures the upper glass of the bowl in place, is, in the standard compass, graduated in degrees from 0° to 180° to starboard and port, the graduation corresponding to the ship's head. This is useful because when a bearing of an object is taken, a small pointer on the azimuth mirror indicates the angle on the bow. In steeling compasses the verge ring i^ fitted with an adjustable magnifying prism over the lubber's point, to enable the steersman to more clearly see the direction of the ship's head; counterpoise weights are fitted on the opposite side of the verge ring, 298. To remove a bubble from the compass. — If air enters t he compass bowl a bubble is formed which lies between the upper glass and the compass card. This not only makes the reading of the graduations of the card difficult, but reduces the sensitiveness of the card and causes it to hang. To remove a bubble, the bowl should be unshipped from the binnacle i nd laid on its side with the rilling hole uppermost. The screw plug should first be removed from the filling hole, and then the expansion chambers distended to their maximum extent; this is done by aid of small milled nuts which screw on to the screw j (Fig. 231), they will be found in the box in which the compass is supplied. Care should be taken not to strain the expansion chambers when distending them. This action of distending the expansion chamber causes the level of the liquid to fall. Recently distilled water should then be poured into the filling hoi'-, the bowl being gently moved from side to side in order to facilitate the escape of the air. When it is considered that all the air hae escaped, the milled nuts on the expansion chambers should be cased back one or two turns, so as to allow the expansion chambers to slightly close; the extra pressure thus brought on the liquid will cause a slighl overflow al the filling hole, and should tend t<» drive oul any air that remains. The plug of tin- filling hole should then be screwed in, care being taken that the leather washer i> in place: the milled nuts may now bi ea ed up aojd removed, should there -till be an air-bubble the operation should be repeated. 299. The binnacle. The binnacle, Fig. 232, oon ist of a hollow wooden -tand it t In- top of which are fittings for carrying t he bowl, while outside .nid inside it an- various arrangements for carrvinfl and securing the different correctoi Screwed to the out ide of the binnacle i the for the Hindi* bai and on either side are bra - braokt '• c to which the *ph< ecured. On the opposite tide to the brass x 810f / Art. 299. 342 case are situated doors by which the inside of the binnacle can be reached. Inside are brass tubes for carrying and securing the fore-and-aft "and Fig. 232. athwartship permanent magnets. There are two sets of tubes, a and a, for carrying the fore-and-aft magnets, but only one set, a', for the 343 Art. 300 athwartship magnets, and this is situated on the side of the binnacle opposite to the brass case. The brass tubes are attached to en Hess chains, b, 6, and so arranged that. by turning a handle, their distances from the compass needles can be varied at will. The mechanism is securely locked by two studs, 'I, (I. when the safety door g is closed. Along the centre line of tin- binnacle is a brass tube, c e, in which is a bucket, /. foi carrying the vertical magnets. The bucket is supported by a chain It. each link of which measures half-an-inch, in order that it may be lowered or raised as required; the number printed on that link of the chain, which is at the securing position, indicates the distance in inches between the upper ends of the magnets and the compass needles. At the upper pari of the binnacle are two brass doors which open into a space immediately below the compass bowl: in this space there is an electric lamp and a contrivance for regulating the illumination of the compass. If necessary the doors may be removed and oil lamps substituted. On the top of the binnacle is fitted a removable brass helmet which completely covers the compass bowl, and is conveniently fitted with sliding shutters and windows through which observations can lie made, The binnacle i< secured to the deck by four bolts, and care should he taken that it is so secured that the line joining the centre of the compass card to the lubber's point is parallel to the fore-and-aft line of the -hip. To ascertain if this is so two plumb lines should be sus- pended, one before and one abaft the compass, from points whose positions in the fore-and-aft line have been found by measurement. A straight-edge laid on the compass in the plane of the two plumb lines should pass vertically over the centre of the compass card and the lubber's point . All material nsed in the construction of the binnacle is non- magnetic. The doors of the binnacle which when shut, secure the magnets in the tubes, should always be kept locked, in order that unauthorised persona may not be able to tamper with the magnets. 300. The Thomson compass.— This compass is in use in many of the older of II. .M. -hip-: the card, which is \cry light, is pivoted in the lire of the howl, ami consists f an aluminium ring joined to an iminium centre by thirty two silk threads; a ring of paper on which ■ printed the graduations is cemented t<> the aluminium ring. The which an irery weakly magnetised, oe suspended under the id by -ilk threads. The card is pivoted on a small brass rod having : ii idiiim poin' . This type of compass is very sensitive, but as the retarding influence of the liquid i- absent, oscillation are liable to ho se1 up by shooks, and t he mot ion of t he ship. The binnacle Consists of a wooden stand with holes drilled in it to receive the magnets; it is fitted with brackets for the spheres, and a hi e for the Flinders bar a - in the Chel wynd com pas-,. In a Thomson standard compass the verge-plat< raduated in a -i mil it m inner to t hit of a Chel wynd -l.nid.u I COmpaSS. In a Thomson beering compass no prism is fitted, but .i nrrjuilying <_da-s placed on the verge glass if desired, may be used instead. Z j Arts. 301, 302. 344 301. The azimuth mirror. — The azimuth mirror, Fig. 233, is an instrument which may be placed on the top of the compass bowl for the purpose of taking bearings. It consists of a stand, on which is mounted a pedestal which carries a prism, magnifying glass, pointer, &c. The stand has three arms, the extremity of each of which is fitted with a clip, which engages over the projection of the verge ring of the compass, in order to guard against displacement by shock. From the centre of the bottom of the stand projects a small pin which enters a hole in the centre of the upper glass of the compass bowl. Above the stand is a pedestal at the lower extremity of which is a pointer a a' which lies, one end, a, over the graduation of the compass card and the other, a' ', over the graduation of the verge-plate. On the pedestal is carried a magnifying ^iisfeFJSS- Fig. 233. glass, 6, and a prism, c. The prism may be revolved about a horizontal axis by means of a milled head d, on which is engraved an arrow. Two coloured shades, e, e, are provided for use when taking bearings of the sun, as well as a small level /. In the centre of the instrument is a socket, in which may be stood a vertical pin g g, called a shadow pin. The vertical plane which passes through the shadow pin g g and the pointer a a' cuts the prism at right angles ; but, should it not do so, small clips are provided by means of which the jDrism may be adjusted. 302. How to take bearings. — As stated above, the milled head for rotating the prism of the azimuth mirror has an arrow head engraved on it, and the direction of this arrow, whether pointing up or down, 345 Art. 302. indicates the position of the prism according to which method of taking bearings is employed. Arrow up. — This method is generally used when taking hearings of elevated objects, such as heavenly bodies, but, if desired, i1 may be used for objects mi the horizon. Fig. 234 shows the position of the prism, the ray from the object being reflected upwards to the observer's eye, which is in such a position that the graduation of the compass card i- seen directly through the lens. A small movement of the prism will enable the object and the graduations of the compass card to be seen together with the small pointer at the base of the instrument, and the graduation which is coincident with the object may be read off. ('are should be taken that the reflection of the object is coincident with the pointer; when this is so the azimuth mirror is pointing directly at the object. The error in the bearing observed, due to lack of this ex ** >» ^ / v £ / / Compass Card 'Arrow up Fig. 234. precaution, is not very great provided thai the altitude of the object is not greater than 38 degrees, but above thai altitude the error increases v 5> T:UU ,, ,, ,, 70 — 200 K.W., 220 volt, 6 pole - 45 70 Fan, small high speed (Blackman) .... 4 4 ,, motor, 80 volt (Verity) - 15 20 . „ 100 volt, \ ampere ------ 4 4 ,, 220 volt, 1 ampere ------ 6 9 „ 1\ inch, 220 volt, 2 amperes (Siemens) 6 9 ,, 12J inch, two speeds ------ 6 9 „ ,, (Westinghouse) ----- 9 13 ,, 20 inch, 220 volt, 2 amperes (Verity)- 8 12 Fan, 35 inch (British, Thompson Houston) 16 23 Fire control, range receiver (Barr and Stroud) - 5 8 ,, ,, ,, for 4-inch guns 4 4 ,, ,, ,, screened (Vickers) 7 9 ,, ,, ,, unscreened (Vickers) 12 15 ,, ,, transmitter (Barr and Stroud) 5 8 Forbes speed indicator, receiver - 4 6 Gong, Captain's, Indicating shutter for 4 4 ,, ,, Iron case for ----- 4 4 ,, Reply (Siemen) ------ 6 9 ,, other patterns ------ 6 9 Gyro-compass, " Anschvitz," Motor Generators for 18 25 „ „ „ receivers 2 2 ,, ,, ,, Reversible motor for 4 4 ,, ,, " Sperry " Motor generator for - 10 14 ,, ,, ,, ■ receivers 2 2 Hummer, Transformer box for - - - - - 4 4 Indicator, Helm (Elliott Bros.) - 4 6 ,, ,, (Eversheds) - 4 4 ,, Revolution (Elliott Bros. ) - - - - 4 4 „ „ (Two) (Everett Edgcombe) 4 4 „ (Elliott Bros.) - 4 4 Isolator, 60 volt, 8 amps. (Evershed and Vignolles) - 10 14 Junction box, 220 volt, Patt. 586 11 15 349 Art. 305. [nstrumenl . From Standard ( lompass Position. From Lower ( > 22<> volt, 150 c.p. (No effect i n position as fitted.) Inches. >> 16 c.p. - ....... 7 Feet. Feet. Motor , Ammunition hoist for 6-inch guns - 12 — »> Bakery. 220 volt (Lawrence Scott )- 4 4 » Reversible, for gyro-compass (Elliott Bros.) - 4 4 > Brine pump ------- 7 10 > Capstan, Multipolar, 50 h.p. - - - - 30 — J Coal hoist, 220 volt, 17 h.p. (Siemen) - 10 14 9 Compressor, CO., ...... 12 16 > Dotter, 220 volt" 8 11 J Dredger ammunition hoist (Armstrong Whit- worth). 10 14 > Flue cleaning, 80 volt, 20 amperes - 9 12 J generator : — » Fire control ...... 10 14 > (" Hibernia " class) ..... 12 16 > Navyphone ...... 12 20 J Searchlight (.Mat Iter and Piatt) - 14 20 > ,, 220 volt (Lawrence Scott) 24 36 » „ ,, (Westinghouse) - 13 17 >> Telephone (Lawrence Scott) 22 30 » lift (Lawrence Scott) - 8 12 >> Oil pump ....... 9 13 J pump, 10-ton (Verity) - 11 16 > ,, 50 ,, (Lawrence Scott) 13 19 J saw bench, 80 volt - 13 18 > sounding machine, 220 volt (Kelvin) 4 4 ► , Torpedo bar, 220 volt, 39 amperes (Verity) 28 42 »> Training searchlight (Crompton) 5 7 1 > Turbine turning, 220 volt (Allen) - 24 36 >» Workshop, 220 volt, 7 J h.p. (Newton) - 10 14 nlator, Sin int — For telephone motor generator 1 4 Resistance potentiometer, 100 Vol1 (I\«'lvin) 1 6 200 „ (Kelvin) 4 6 Searchlight, single projector 12 — „ t win projector (< tompton) 12 — Section box, Patt. s 12 Starter, Automatic For searchlight generator ■ 10 i i i» COj compressor motor ■ 10 1 i »» irchlighl motor gi aerator- 24 36 »» (Westinghouse) ) i »» Shunt For brine pump (Lawrence Scott) L2 it; »» 1 1 lephone mot »r g< aerator • l ( IS Workshop mob »r ( New ton) « 1 1 Telephone, Box, \im <■■ til 5 8 »» Patt. 2461 N.o. j phone .... i i 1 1 2462 .... i i Voltmet* r, Patt. 2381 i i M ■■>) - ■ i i w ire, Main conducting ...... 8 Art. 305. 350 From From Lower Instrument. Standard Compass Conning Tower Position. Position. Feet. Feet. Wireless instruments : — Alternator, 100 volt, 24 h.p. (Crompton) - 13 20 Type 9, 100 volt ... - - 4 6 „ io ... .- - 5 7 Auto transformer, converter for - 6 9 Blower (Crompton) - - ■ - - 6 9 Coil Impedance, Type 2, 80 volt - 4 6 Combined starter and regulator, converter for 6 9 (Crompton). Induction coil ...... - 30 — Key, Magnetic, Patt. 461 - 6 9 Rotary converter, Type 2, 100 volt - 4 6 Rotary converter (Crompton) for T.B.D.s. and small 6 9 ships. Rotary converter, old type — For T.B.D.s. - 20 30 Fan, circulating ------ - 4 4 Set, battleship, auxiliary .... - 4 6 ,, cruiser, auxiliary, Type. 9 - 6 9 ,, Mark II. (for big ships) - - - - - 12 18 ,, submarine ...... - — 6 Starter and regulator (Crompton) - - 18 24 Switch, operating, Type 1, Patt. 1066 - - 6 8 Relay, Type 1, Patt. 441 - - 4 o Transformer— For T.B.D.s .... ■ 4 4 These distances have been obtained by experiment for a standard compass position where X = -86, and for a lower conning tower position where 1 = • 65. In the construction of a ship-, the following points, in addition to the distances given above, should be adhered to. No iron or steel of any kind should be placed within 10 feet of the standard compass. The extremities of elongated masses of iron, or steel, should be placed as far as possible from the compasses. The nearest great funnel should not be nearer than 32 feet, and other iron or steel fittings of considerable dimensions, such as conning towers or turrets, should not be less than 20 feet from the compass. No iron subject to occasional movement (such as revolving cowls, hatches, doors, &c.) should be fitted so near the compass as to disturb it. Any cowl which exceeds 6 feet in diameter, the nearest part of which, when turned in any direction, comes within 18 feet of the compass, should be made of non-magnetic material. In no case should iron or steel, subject to occasional movement, be fitted within 12 feet of a compass. As regards the compass in the lower conning tower, no moveable iron or steel should be within 12 feet of the compass, and no fixed iron or steel, other than decks or bulkheads, within 10 feet. Bulkheads which are_situated within 4 feet of the compass should be made of non- magnetic material, to a distance of 10 feet in the horizontal plane and 4 feet in the vertical plane from the compass, and doors, hatches, &c. within 12 feet of the compass, should be made of non-magnetic material. 351 Art. 306. In some vessels the davits, when turned in, have the efifecl of altering the deviation. The King's Regulations and Admiralty [instructions lay down that if the davits, when turned in. approach within 1-4 feet of the compass, the deviations are to be obtained by swinging the ship both with the davits turned in and out. 306. To obtain the deviation by observation. — The principle under- lying the correction of the compass is to ascertain from analysis the forces which cause deviation — whether from the permanent magnetism of hard iron or induced magnetism in soft iron or from both, and then to apply correctors which produce equal forces in opposite directions. As we have -ecu in the previous chapter, the forces which cause deviation are involved in the coefficients, and to find these it is necessary to know the deviations tor various directions of the ship's head (§§ 277. 278). The difference between the magnetic and compass bearings of an object is the deviation, so that, to obtain the deviation of the compass for any particular' direction of the ship's head, it is necessary to take the compass bearing of some object whose magnetic bearing is known or can be obtained. There are three methods in use for obtaining the deviation, namely : — (a) By reciprocal bearings. (/>) By bearings of a distant object. (c) By bearings of a heavenly body. (<7) By bearings of marks when in transit. (a) By reciprocal bearings. — If the bearing of the standard compass is observed with a compass on shore which is unaffected by local attraction, the hearing so obtained is t he magnetic hearing of the standard compass from the shore compass, and if reversed is the magnetic bearing of the shore compass from the standard compass, or what is called the reciprocal bearing. If. at the same instant, the bearing of the shore compass, as indicated by the standard compass, is observed, the devia- tion, for the direction of the ship's head at the instant, can be obtained. Tin- method has certain advantages over the methods (6) and (c) : (1) The magnetic bearing and thus the deviation is immediatelj obtained. (2) The Bhip ni;i\ lie under way, and may. if required, be actually Steaming ahead while the observations are being taken. This .itl\ facilitates keeping the ship's head in any required direct ion. (3) Tin- ship maj be comparatively close to the shore compass, while the method (6) necessitates the ship being at a considerable distance. Con equentlj this method can frequently be employed in thick or cloud} weather when the other two met hod w ould be impract icable. At many important port* a bearing plate, fitted with sight vanes, is ii up. so that it zero line \i in the magnetic meridian of the place, and con equently bearing taken bj it are magnetic. Sued bore Btatio are provided with the means oi tignalling the re ults ol ob ervations to a ship, and ar< frequently made use of when adjusting com] or swinging ship for deviation, [fit is desired to employ thi method at ;t p| ; , re where no in h provision i .hi improvised I,.. i. i .1 1 1. hi may be Bet ap bj aid oi the landing com] i.re being taken, when -electing Art. 306. 352 the position, that no local attraction or other magnetic influence is present. In order that the observations, from the shore station and from the standard compass, may be simultaneous, it is necessary to have some prearranged code ; the following signals are generally employed : — A pennant at the mast-head " close up " signifies " Stand by." The " dipping " of the pennant signifies " Observe." A large flag should be suspended immediately above the standard compass in order to assist the observer on shore in taking the bearings. When the observer at the standard compass is satisfied with his bearing he orders " dip," which signal is repeated at the shore station and bearings are taken from both positions, that from the shore station being immediately signalled to the ship in order that the deviation may be noted at once. (b) By bearings of a distant object. — With this method the compass bearing is taken of a well-defined object whose magnetic bearing is known ; the difference between the two bearings is the deviation. The magnetic bearing is found — (1) From the chart, as explained in § 307, provided it is seen that the survey was made in considerable detail (§ 169). On some charts of harbours there are lines which show the true bearing of a certain distant object, from which the magnetic bearing may be found. When making use of such lines, the position of the ship should be fixed, and the true bearing for the particular position of the ship can then be seen. (2) By obtaining the horizontal angle between the sun and the object and at the same time noting the time by the deck watch ; the true bearing of the sun may now be obtained, and the horizontal angle applied to this gives the true bearing of the object from which the magnetic bearing can be obtained. (3) Approximately, from the mean of standard compass bearings on eight or sixteen equidistant points, provided that the circle, described by the standard compass, as the ship turns round, is small, and the object sufficiently distant. In all cases when method (b) is employed the ship should be turned round in as small a circle as possible and it should be remembered that, provided the distance of the object is 350 times the radius of the circle, the magnetic bearing of the object will not differ by more than 10' from the mean. If the distance of the object observed is less than the distance just stated, the magnetic bearing for each observation should be noted. (c) By bearings of a heavenly body. — In this method the compass bearing of a heavenly body, the altitude of which is not greater than 38°, is observed; at the same instant the time by the deck watch is noted, in order that the true bearing may be obtained (§ 101) or taken from the Azimuth Tables or Azimuth Diagram; the difference between the true and compass bearings gives the compass error. This method is most commonly employed when the ship is at sea, and, as will be explained in § 313, the mean of the compass errors on eight or sixteen equidistant points gives the variation at the place. The azimuth of the heavenly body which is selected should not be changing very rapidly, for, if it is doing so, a small error in the time produces a 353 Art. 307. considerable error in the azimuth. The rate at which the azimuth is changing may be seen by inspection of the Azimuth Tables. The azimuth of the sun at sunset or sunrise is given in the Azimuth Tallies, so that if the bearing of the sun is taken when its lower limb appears to be about a semi-diameter above the sea horizon, the operation of finding the azimuth is simplified, because there is no necessity to find the hour angle. This does not apply to the moon, because, as explained in ^j 136, when the upper limb disappears, or appears, the true altitude of it- centre is about 3'. and, therefore, when the true altitude of the moon's centre is zero, that is at moonrise or moonset, the moon is invisible. ( follows : Steady the ship on some cardinal point, say North, observe and note the deviation, and then insert the athwartship magnets as explained in § 280. It will now be found that the ship's head is not exactly North by compass, so again steady the ship on North, repeat the observation and. if necessary, alter the magnets: and so on until the deviation on North is zero. The ship's head should now be placed on an adjacent cardinal point. East or West, and an adjustmenl with the fore-and-aft magnets made in a similar manner. The ship should now be turned round and the deviations noted on the four* cardinal and four intereardinal points, when a rough analysis will show whether coefficient D is correel and whether the other coefficients have any appreciable value. Should it be found that coefficient /> has any value, the spheres should be moved as explained in § 281. and any small adjustment of the horizontal magnets that may be necessary should be made, the ship being steadied on the cardinal points as required. When adjusting compasses the correctors should be placed so as to satisfy I he follow ing condition-, : — (a) The athwartship vertical plane which passes through the centre of the compass needles should always pass through the centres of every fore-and-aft magnet. (h) The fore-and-aft vertical plane which passes through the centre of the compass should always pass through the centre of every athwartship magnet. (r) The line of intersection of the vertical, fore-and aft. and athwart ship plane- should coincide with the centre line of the vertical magnets or sj stem of magnets. ('/) The horizontal plane which passes through the centre of the COmpase needles should also pass through the centre of the >tt iron Bphere The horizontal plane which passes through the centre of the compass needle- should also pass through a point on the Blinders bar which is distant about one twelfth of the length of the bar from it- upper end. (f) Horizontal magnets should not be brought oloser to the compass needles than t w ice the length of the magn< 309. To obtain the deviation of and to adjust a between-deck compass. I M ii H . (.;,.,. ,,f ;i between-decb compact from which direct observation for deviation cannot hcni.Kle.it becomes neo< arj bo obtain the devia ti,, n by comparing the direction of the ship's head as mown bj such a compa with that ihown bj the tandard compass which ha- pn riouslj been corrected. In order to determine whether the phere at uch a Art. 310. 35G compass have been correctly placed, it is necessary to determine what the deviation is when the ship's head is on the inter-cardinal points as indicated by that particular compass. For this reason an observer is stationed at each between-deck compass ; at the instant the ship's head is on a particular point by the standard compass, a signal is made by means of a syren or whistle, and the observer notes the direction of the ship's head as shown by the between-deck compass. By comparing the direction of the ship's head with that shown by the standard compass, the deviation of any between-deck compass can be obtained for the direction of the ship's head as shown by that compass. To find the deviation on the cardinal and intercardinal points, it is necessary to plot the deviations for the observed directions of the ship's head, and to take from the curve the deviations required. While it is desirable to keep the deviation of each compass a minimum, it is inadvisable to frequently change the positions of the correctors ; the correctors should only be moved when it is certain that a permanent change in the ship's magnetism has taken place, and, on all occasions of so doing, the ship should be swung and a new deviation table deduced as follows. 310. Swinging ship tor deviation. — Swinging ship for deviation consists in turning her slowly round, steadying her on various courses and observing the deviation on each course. When the deviations are large the ship should be steadied on every point of the compass in succession, but when they are small it is sufficient to steady her on every other point. When she is steady on a point of the compass, as indicated by the lubber's point, the deviation is observed for that direction of the ship's head by any one of the methods given in § 306 ; at the same instant the signal mentioned in the preceding article is given, and the observers stationed at the other compasses note the directions of the ship's head as shown by those compasses respectively. A ship while being swung should be steadied, on each point on which the deviation is observed, for a sufficient time to allow the sub-permanent magnetism, due to the last direction in which she was heading,- to dis- appear. As a general rule a ship should be steadied for at least a minute before an observation is taken, and a neglect of this precaution will result in there being an apparent A on analysis of the deviation table, an error which is sometimes referred to as Gaussin error. In a steering compass, the deviation of which is obtained by comparison with the standard compass, an apparent A may sometimes be caused by a misplacement of the lubber's point. When swinging ship and observing a heavenly body, it is advisable, in order to avoid delay, previously to tabulate, for intervals of about four minutes, the magnetic bearings and corresponding deck watch times for the period during which it is likely that the observations will be taken. It may happen that, after an action, a ship's magnetism may become so altered as to necessitate a new deviation table being made out. In the event of it being impossible to employ either of the foregoing methods, the following procedure may be adopted. Let us suppose that a ship X has been in action, and that soon afterwards she meets with a ship Y which has not been in action, and the deviations of whose standard compass are known. The method of reciprocal bearings can be employed, the bearings signalled from Y to X being magnetic. 357 Art. 310. A somewhat similar procedure may l>e followed in the vase of two ships, for neither of which is the deviations known. Let X and )" be two ships which have been in action, with the result that the deviations of their compasses have been changed and are unknown. The senior ship X directs Y to steer a steady course, S. 40 IT. by eompass. say: X then heads North by compass and reciprocal bearings are taken as shown in Fig. 237. If 8 is the Easterly deviation of Y on S. 40 \\ '.. we have Magnetic bearing of Y from X - - N. (23 c 8) W. Compass „ Deviation of X on North X 31 W ( 8° + S) E. Y s*o'w Bearing ofX,S23E North Bearing of Y,N 3 1'W In;. 237. A now heads South by compass and reciprocal bearings are again taken •!-■ shown in Pig. 238. In i hi- case we ha 1 ! e Magnetic bearing "I > from .V - X. (68 8) \V. Compe ,, ., - X. 56 W. Deviation of .V on South (12 8)W. Xou from § 277. coefficient C i"i X i 8 N . 8s. - 8) (12 8) 2 - In x 6108 \ Arts. 311, 312. 358 Therefore, assuming that for X the coefficients A and E are zero, the deviation of X on North is 10° E. Therefore (8° + S) E. = 10° E. .-. 8 = 2°E. Beanng ofX,S.68'E. Bearing of Y,N 56 W South Fig. 238. Having found the deviation of Y on 8. 40° W., X may swing using the method of reciprocal bearings, and find the deviation on every point, care being taken that 2° E. is applied to each of the bearings signalled by 7. 311. Necessity for frequent observations for deviations. — When we reflect on the numerous forces mentioned in the previous chapters which tend to cause deviation, and that their effects vary in different ways as the course and the magnetic latitude vary, and if, further, we consider possible effects of the firing of guns, electric currents, movable stanchions, &c, it is clear that a deviation table is unlikely to remain correct for very long. Therefore the only safeguard against the ship being set out of her reckoning, due to an unknown error in the course steered, lies in frequent observation of the heavenly bodies, transit marks, &c, with which to check the deviation. Observations should be taken, when possible, on every change of course, or at least once a day, and the ship swung when necessary. It is often possible to obtain the deviation for a few directions of the ship's head, when time or opportunity is lacking for obtaining a complete swing, and no opportunity of so doing should ever be allowed to pass. 312. The criteria of a good deviation table. — To test the deviation table at a glance, the deviation on North should equal the deviation on South (with the sign changed), and the deviation on East should equal the deviation on West (with the sign changed), while the mean of the deviations on N.E. and S.W. should be equal to the mean of the deviations on S.E. and N.W. (with the sign changed). ft should not be expected that the deviation table for a badly placed compass will satisfy these conditions, for it will be seen from § 277 that they are only strictly true when the coefficients A and E arc zero. A curve of the deviations shows whether any of the observations, from which the deviation table was constructed, were at fault. 359 Art. 313. 313. Obtaining the variation by observation at sea, Besides finding the variation from observations on shore, the variation may be found, and the chart kepi up to date, from the analysis oi the observations taken when the ship is swung for deviation, using the bearings of a heavenly body. Now variation = compass error + deviation, and if the deviations on eight or sixteen equidistant points are meaned (§ 277) the resuU Lb coefficient .4. Thereto:, mean variation = mean of compass errors .1. Thus, if coefficient A for the compass is known, the variation at the place ran be found. As explained in vj 310, when a ship is swung too rapidlj . an error due to hysteresis, called Gaussin error, is introduced ; this causes an apparent J which vitiates the variation, and its effect is felt to a small extent even when the swing w carried out quite slowly. For this reason, when swinging to obtain the variation, tin- ship should be swung in both directions, care being taken that the time occupied in swinging from point to point is about the same on both occasions; by this means the apparent A will probably hi- eliminated in the mean of the results. This apparent .1 is generally found to he when -winging to port and when swinging to starboard. When forwarding results of swings to the Compass department of the Admiralty, care should be taken to give all necessary information as to the observations. The direction of each swing (starboard or port) should always be stated, for in the event of a swing having only been made in one direction, the observations ma\ still be yi40. continue t<> precess as long as the couple is appled. The effect ^\ a couple is, therefore, to make the axle of the rotor precess in the plane Which Contains the axle and the axis Of the couple. 316. The effect oi the earth's rotation on a gyroscope. At a particular instant let on.- end of tin- axle of the rotor shown in Fig. 240 be pointed to tin- North point of the horizon. We may imagine that the North point of the horizon at this instant coincides with a star X. Since the axle maintains the same direction in space, it always points to X notwithstanding the movement in -pace .,t the whole gyroscope due to the rotation of t he cart h. Now. if we regard the earth a- fixed, the star A appears to trace .i circle Oil the celestial concave and it- altitude and azimuth continually change throughout the have been magnified four times. Had the North end of the axle been directed to au\ other point of the heaven-, it would have traced out a similar ellipse, larger or -mallei', w hose centre would have been coincident with )'. the centre of the ellipse described a lx.ve. Had the North end of £ the axle been originally directed to Y. the ellipse would have — reduced to a point, and there would have been no motion of y u , 243. t he axle whatever. The time of a complete oscillation of the North end of the axle depends on the distance, between the centre of gravity of the gyroscope and the point of suspension, and on the velocity of the rotor. These are so arranged in the two type- of gyro-compasses which are described in this chapter, that the time of oscillation i.^ about s ~> minutes, which i- the same as the period of a simple pendulum, the length of which is equal to the radius of the earth. Tin- North end of the axle of any rotor may 1>" easily distinguished, a- it i- thai from which the rotor i< -ecu to (urn in an anli clockwise direction. 318. The damping of the oscillations of a gyroscope. It has been explained that the North end of the axle, except when directed to ). must be in continual motion. Now the motion in azimuth would render such a gyroscope useless as a compass, and therefore it is necessary to introduce some means of damping the oscillations. In order to reduce the amplitude of the oscillations, a couple must be applied to the rotor, in such a manner as to tend to make the axle point nearer to )'. or to make it precess towards the centre of the elliptic orbit. This ffected by one of two methods, the first to be described being thai adopted in the " Sperry gyro-compass. If a couple in the horizontal plane Is applied to the rotor, a precession in t lie vertical plane is 3et up; if this couple is applied so thai the vertical precession is upward- while the North end oi the axle is tracing ou1 the arc A'.V.l/ (Fig. 243), and downwards while it is tracing ou1 the arc MLK, the resull is that the North end of the axle move in a spiral curve, and finally comes to rest directed to a point which i nol on the meridian, bul hae a very slight Easterly azimuth and a slight altitude. Tin- point is called the resting position of the axle. If t he North endoi the axle had originally been directed to the North point of the horizon, and if a and/3 are plotted as in the previous articles, the result is a 9piral curv< hown in Fig. 244, where '/' is the resting position. It the North end ot the axle had been due. ted to anj other point ,,t the heavens, the result would be a curve oi imilar Form, but in everj .- t he rest inu posit ion T would be t be lan The mechanical arrangement for the provision ot thn couple will be described in g 322 Art. 319. 304 The second method by which the oscillations may be damped is that employed in the " Anschiitz " (three gyro) gyro-compass. If a couple in a vertical plane is applied to the rotor, a precession in the horizontal plane is set up; if this couple is applied, so that the Horizontal Fig. 245. (X - — N >CC Horizontal. Fig. 244. precession of the North end of the axle is to the Westward while the end of the axle is tracing out the arc LKN (Fig. 243), and to the Eastward while it is tracing out the arc NML, the result is that the North end of the axle moves in a spiral curve, and finally comes to rest directed to a point on the meridian which is not the North point of the hori- zon. This point is the resting position of the axle. If the North end of the axle had originally been directed to the North point of the horizon, and if a and d are plotted as in the pre- vious articles, the result is as shown in Fig. 245, where F is the resting position. If the North end of the axle had been directed to any other point of the heavens, the result would be a curve of similar form, but in every case the resting position F would be the same. The mechanical arrangements for the provision of this couple will be described in § 325. 319. The effect on a gyroscope when carried on board ship.— In the j3revious articles, the movement of the gyroscope in space was assumed to be due to the rotation of the earth alone, and therefore its direc- tion of movement to be East. When the ship is steaming on any course, other than East or West, the direc- tion of movement of the gyroscope in space is not East, but slightly to the North or South of it, according as the course is Northerly or South- erly. The ship's course and speed may be resolved into the speed in latitude ( V cos course), and the speed in departure (V sin course), where V is the speed of the ship in knots. In Fig. 246, let AC represent the speed of the ship in the direction 900 cos L t V sin course Fig. 24G. >-B 365 Art. 320. North or South, then AC represents the speed of the ship in latitude V cos course. Let AB represent the speed of the ship in an Easterly direction, then AB represents the speed of the ship in space due to the rotation of the earth + the speed of the ship relative to the earth; therefore. .1/? represents (900 cos L V sin course) knots, where L is the latitude of the ship. The resultant direction of movement of the gyroscope in space is along the line AD, and therefore the axle lies along the line AE, which is perpendicular to AD. Let the deflection (CAE) of the North end of the axle be denoted by S. Now nD T . .. J)B I cos course tan o All 900 cos L + V sin course I ' cos course . . , r .,»„„„/. ( " ri,H - v) . J' cos course or o tan ' , . 900 COS L From this formula the deflection may be calculated for any given latitude, course and speed. It will be seen that the North end of the axle lies to the Westward of the meridian when the course is Northerly, and to the Eastward of the meridian when the course is Southerly. This deflection 8 is mechanically, and semi-automatically, allowed for in the '* Sperry " gyro-compass. In the " Anschutz " gyro-compass, 8 has to be applied to any course steered, or bearing taken, in the same way as the deviation of the magnetic compass. 320. The effects of the rolling and pitching of the ship on a gyroscope. A' gyroscope has great inertia in the vertical plane of the axle, which we may call the North South vertical plane and cannot oscillate as a pendulum in this plane without simultaneous oscillation taking place in the horizontal plain- due to precession: the period of oscillation in the North South vertical plane is, therefore, about 85 minutes (§317). In the East West vertical plane there is no gyroscopic effect, and the gyroscope may therefore oscillate in that plane as a simple pendulum. When a ship rolls and pitches, the gyroscope on board will oscillate in the East West vertical plane, due to the periodic impulses imparted to il l>\ the motion of the ship, and the more nearly the periods of the ship and of the gyroscope in the East West vertical plant- synchronise, the greater will be the amplitude of the oscillation-. Winn the ship's course is along <>r perpendicular to a meridian, the impulses due to rolling and pitching should have n<» effect on the gyroscope, because everything is symmetrical, and the impulses arc alternating in direction. When a ship is steering on anj other course, the impulses act onsymmetrically with regard to the Easl West vertical plane, and a horizontal couple i- introduced, which increases or decreases the tilt of the axle, and consequently causes the North end of the axle to be deflected slightly from its resting position. The direction of this deflection varies with the course, and the effect of pitching is opposite to that of rolling. The direction of the deflection under \ arious condit ion it a follow - ! Course .V Wly.orS. Ely. Rolling. Deflection Westward. ,, Pitching .. Eastward. V Ely. or - Wly. Rollin M Pitching. .. Westward. Art. 321. 36G This deflection is not very great in the two types of gyro-compass described in this chapter, because they are so constructed, that the period of oscillation of the compass in the East West vertical plane does not synchronise with the average period of rolling or pitching of a ship. The possibility of the existence of this deflection must be borne in mind when the ship is in a sea way, as under certain circumstances it has been found to be as much as 5°. Experiments are now being carried out, with the object of determining a method for the elimination of this error. 321. Description of the " Sperry " gyro-compass. — The " Sperry " gyro-compass consists of a stand or binnacle which supports a frame, which in turn supports the sensitive element and card. The frame J, Fig. 247, is pivoted in a gimbal ring K, by suitable bearings L v L 2 . The ring K is pivoted in bearings L 3 in another ring, which is suspended by a large number of spiral springs from the upper edge of the binnacle. The rotor, driven by a three-phase stator, at about 8,600 revolutions per minute, rotates on a horizontal shaft A, within an airtight case B, from which the air has been partially exhausted by means of a small hand pump. The case B is pivoted on a horizontal axis C, which passes through its centre of gravity, and is supported in a vertical ring D. The ring D is supported by a torsionless wire E, and mounted in bearings F, F v which allow a free oscillation, of limited amount, about the vertical axis within an outer ring G, called the phantom. The phantom has a hollow stem H, to which the strand E is attached at 367 Art. 322. it- upper end. The rotor and phantom are capable of turning in azimuth, with reference to the frame •/. aboul the stem //. Within the frame is mounted a follow-up motor M. which drives a -ear wheel .V; the gear wheel A" is rigidly connected to the phantom (•. and the motor J/ is driven through electric contacts en the ring D, in such a manner that every motion of the ring D in azimuth is immediately followed by an exactly similar motion of the phantom G. Thus we see. that any twist introduced in the wire strand h\ by the motion of the rotor in azimuth, is instantaneously removed by the phantom G, which supports the upper end of the wire strand, making an exactly similar movement; tin- system provides an almost frictionless suspension. Gravitational stability is imparted to the rotor casing />'. bj ;i 'nail- weight " /,'. which is pivoted on the phantom at C, and connected to II by mean- of a small pivot S. The compass card 0, the graduations of which are the same as those of the magnetic compass, except that the degrees are marked from 0° to :;.v.i clockwise from North, is secured to the phantom in such a manner that the North South line of the card is parallel to the axle . I . 322. Damping of the oscillations of, and the automatic collection of the ''Sperry-' gyro-compass. In order to introduce the horizontal couple necessary to provide the damping described in § 318, the pivol S Fig. 247), connecting the heavy hail R to the rotor casing />'. i- placed slightly eccentrically, its distance from the vertical axis of the rotor being aboul | inch. A- the bail is pivoted at points which are above its centre of gravity, its natural tendency is to hang vertically down- wards; when the axle is tilled, the pin S raises the bail from it- normal isition, and the eccentricity of the pin 8 causes the gravity couple on /; to have a horizontal component, which provides the necessary vertical precession to reduce, or increase, the tilt; the instrument comes to resl with the North end of the axle directed to the point T of tin- celestial concave as described in § 318. This point T is slightly to the East of North and has ;i slight altitude, except when the instrument is on the equator; the deflection of the North point of the compass varies as the tangent of the latitude. We have now to -how how this deflection and t hat due to the ship's motion (§ 319) are allowed for. On the frame are two dial-, one marked •• Latitude " and the other " Knots," which should he sel to the latitude and speed of the ship respectively. The setting of the latitude dial places 'he lubber's point at an angle r tan Lai. to the fore and alt line, where /• i< the number of degrees in the angle F r \s. Attached to the phantom ;- a lilted grooved ring /' an arm. which is in connection wdii the mechanisms controlled i>\ the two dial-, works in the ■jkx.x,- When the -hip alters course, the tilted ring rotates relative to the arm. which therefore moves up or down in the groove of t he ring ; the tilt oi the Hi u'-li thai the vertical movement of the arm varies a- the .,,,. ,,f it,.- .miii <■ The aim communicate it* movement through the latitude and speed mechani m to 'he lubber - point, and sets it at ,,,, angle 8 to its normal position for the latitude. Thus the combined ,.f., • thai 'he lubber 1 point i et at an an l< 8_. to the fore and aft line, 8 - tair . md Sj ' tan I - it Arts. 323, 324. 368 In order that the axle may be horizontal when no precession is taking place, an arrangement is provided for altering the centre of gravity of the bail, the centre of gravity being moved to the North when in North latitude and to the South when in South latitude. A level which is parallel to North South line of the card, is provided, and the position of the bubble indicates the angle of tilt of the axle ; with experience the amount and direction of the deflection of the North point of the card from the meridian may be estimated from the position of the bubble. This is of considerable value, because after the rotor is first started, and has been precessing freely for a short time, the indication of the level may be taken as an approximate measure of the deflection, and the compass may be set by hand approximately on the meridian. 323. The "Sperry " receivers. — The alteration of the lubber's point, described above, would appear at first sight to only correct the compass for the course steered. Now the compass described above, called the master compass, is placed at some well protected position in the ship, in general in the lower conning tower, and in this position it is only used for observing the direction of the ship's head. The movements of the master compass are conveyed electrically to instruments, called receivers, or repeating compasses, which are placed as convenient at different steermg positions, and on the manoeuvring platform. A ' Sperry ' receiver is illustrated in Fig. 248. The card is driven through gearing by an electric motor, and the instrument may be mounted in any position, but it is generally mounted vertically on a bulkhead, or horizontally in gimbals in a pedestal. When mounted on a manoeuvring platform, it is supported in gimbals, and is fitted with an azimuth mirror, very similar to that described in § 301. The graduation of the card, opposite to the lubber's point of the receiver, is always the same as that opposite to the lubber's point of the master compass ; as the necessary correc- tions are applied by moving the lubber's point of the master compass, the direction of the ship's head, as indicated by the receiver, is true. If the receiver is mounted in gimbals, so that it is horizontal, and if its lubber's point is in the fore-and-aft line, directions shown by it will be true. When laying off courses, or lines of bearing, obtained from observa- tions with this compass, it is convenient to lay them off from the outer graduated circle of the compass rose engraved on the chart, because this is graduated in the same manner as the compass card. 324. Description oi the Anschiitz (three gyro) gyro-compass.- The Anschiitz (three gyro) gyro-compass consists of a metal stand or binnacle which supports a framework, inside of which is a bowl and card. The framework A (Fig. 249), is pivoted in a gimbal ring B ; this ring is pivoted in another C, which is suspended by a large number of spiral springs D from the upper edge of the binnacle. Inside the framework is the bowl E, the axis F of which can turn in ball bearings in the lower part of the framework. The rotation of the bowl relative to the framework is recmired in connection with the trans- mission system to the compass receivers, and is effected by means of an electrical apparatus G at the bottom of the framework. A stem H, supported by three arms ./, is for the purpose of conveying the electrical current to the gyrostats, and for keeping the card central. A section of a portion of the card is shown in Fig. 250. Attached to the float K, which is immersed in mercury contained in the bowl, is Fk;. 248. , 369 Art. 325. a conical tube L: at the bottom of this tube is the bearing surface M for the projection of the stem //. as shown in Pig. 251. At the top of FlG. 241). i In- lube L jv secured a triangular shaped casting N, which carries three gyro-casings X, Y, Z, in ball bearings. The graduations of the card are marked on the horizontal ring 0, the graduations being the same as those of a magnetic compass, except that the degrees are marked from 0° to 359°. The South point of the card (180°) is on that radius of the card which intersects the stem of the gyro casing A, the stems of )' and Z being 12<> from that of A". The axle of the gyro A' is maintained parallel to the North and South line of the card by means of two spiral springs, ami the axles of }' and Z make angles of 30 with uif North South line of t he card when in t heir < entral positions. In Fig. 252 are mown the three gyro-casing A )'. and X. as viewed bom In-low tin- compass card. Tin- casings F and Z air connected by mean- of ;i system of three levera P, which only allows the casinge to turn abort their vertical stems in opposite directions. The position of the axles of tin bate are norm. illy maintained ;it an angle of 30 on either side of the North .Hid South One of the compase card, bj meant of two spiral springs Q, The gyrostat* are driven at 20,000 revolution* per minute, by meant of thrc<- phase induction motors, the directive force of the \ bem being due t«» the action of \ and the n altanl effeote of > and Z. 325. Damping of the oscillations of, and applying the corrections to the , 'Anschutz 1, (three gyro; gyro-compass. In order to introduce the vertical couple nece wary to provide the damping di cribed in § 318 the three gyro i a ing A ) /. are enolo ed in a i a ing R carried by the. Art. 325. 370 floating system (Fig. 250), at the bottom of which is a circular trough S ; this trough is partially filled with oil, and is divided into small compart- ments by means of diaphragms which have orifices in them. When the Fig. 2511 compass is not pointing true North, the card is tilted, and the oil Hows slowly to the lower side of the trough. On the North point of the card passing the meridian, the card commences to tilt the other way, the oil in the trough comes into play, and acts against the tendency to tilt, and so retards the rate of precession. The oil slowly crosses the trough, and the flow is so restricted by means of the diaphragms, that the oil always just reaches that side of the trough which is about to rise owing to the continual alteration in the tilt of the card. The result is that the North point of the card traces a spiral (§ 3 IS) and comes to rest in the direction of true North in about 21 to 3 hours. The oil in the trough is also made use of to provide lubricant to the bearings of the three rotors by means of the' wicks T. Let us now consider the effect of a ship's motion in a sea way on the indications of the gyro-compass, and let us first consider the effect of the North or South point of the compass card being depressed. It will be seen from Fig. 252 that all three gyrostats will precess in the same direction, and since the two gyrostats Y and Z are connected together by a system of levers as shown, the angle between their axles and the North South line of the compass card will not change, but the card will revolve to the right or left due to the precession of all three gyrostats. The card will subsequently regain its horizontal position after one or two oscillations, the period of which is about 90 minutes. If the East or West point of the card is depressed, X is merely turned in its plane of rotation, and therefore docs not precess : Y and Z have opposite ends of their axles depressed, and consequently process equally in opposite directions, causing a disturbance of the equilibrium of the two springs Q, which tend to maintain these gyrostats in their normal Fig. 252 I compas s Rec G)^ Kio. 37] Art. 326. positions relative to the compass card. The springs reassert themselves and the card regains its horizontal position after a few swings, the period of which i- about one minute. This equal and opposite precession of the gyrostats ¥ and Z does not deflect the compass card, but its effect is to greatly increase the period of oscillation of the compass in the East West vertical plane, and thus avoid any possibility of synchronism between the periods of the ship and compass (§ 320). Two levels are fitted on the card: that which lie- North and South indicate- when the compass has finally settled down in the direction of the meridian, by its bubble then remaining stationary; that which lie- East and Wot merely indicates the horizontality, or otherwise) of t In' card in that direction. The angle 8. which depends on the latitude, course and speed, should be applied in the same manner as the deviation of a magnetic compass, a- follow- : — Given the compass direction, to lind the true - Apply 8 or according as the course i> South or North. Given the true direction, to lind the compass — Apply 8 + Or - according as the course i> North or South. I lie values of 8 lor various latitudes, courses, and speeds are calculated from the formula in >; 319, and tabulated <>n card- which are supplied wit h each compass. To test the accuracy of the gyro-compass, its deflection from the meridian should he found in the .same way as the deviation of the magnetic compass (§ 306); this deflection, if the instrument is correct, should agree with the tabulated value of 8- The Anschiitz master compass, which has been briefly described above, is usually mounted in a well-protected position, generally in the lower conning tower, and receiver- or repeating compasses are provided similarly to the Sperry gyro-compass. 326. The " Anschutz '' receivers. An "Anschutz' 1 receiver is illustrated in Fig. 2~>:'> : it- card is graduated in a similar manner to that of the master compass, and concentric with it i- a smaller card which makes one revolution lor every alteration of course of ten degrees. The whole circumference of the latter i- graduated from o to 10, and each space i- ..died a degree; each space which represents a degree is sub- divided into tenth-'. The card i- driven through gearing i>\ an electric motor, and ma \ be mounted in an\ position, bul it i- generally mounted vertically on a bulkhead, or horizontally on a pedestal. Ae Ear as the course is concerned the direction of the lubber's point i- immaterial, but, if the receiver is to be used for taking bearings, the lubber line should be fore and aft, in order that the North South line ot the receiver card maj be parallel to that of the master compass. For thi- rea on, when mounted on a manoeuvring platform, the receiver is supported in gimbals, and is fitted with an azimuth mirror, very similar to that described in $ •"{ (| I . The inner com pa— card enables the direction of the ship's head to be read off with great accuracy, and when the ship under w a v the cud i- almo i continuously moving a the hip yav to the right or lefl "l hei cour e it i al o ot i on iderable value when conning the hip, altering can i ,\> because the instant al which i he ship ha ed to tan be readilj determined. Art. 326. 372 As the deflection due to the course and speed of the ship is not allowed for in the master compass, it must be applied to all courses steered, or bearings taken, with the receivers, in the manner explained in the previous article. When laying off courses, or lines of bearing obtained from observa- tions with this compass, it is convenient to lay them off from the outer graduated circle of the compass rose engraved on the chart, because this is graduated in the same manner as the card of the gyro-compass (§ 23). 373 Art. 327. CHAPTER XXVIII. THE SEXTANT. 327. The principle of the sextant. — The sextant is an instrument designed for the measurement of angles, particularly at sea, • where the motion of the ship precludes the use of fixed instruments. As will be understood from Part I., the sextant is a most important navigational instrument, since it is used in nearly all observations for determining the ship's position. The optical principle embodied in the sextant is that if a ray of light suffers two successive reflections in the same plane by two plane mirrors, the angle between the first and last directions of the ray is twice the angle between the mirrors. This may be shown as follows. Fig. 254. Lei a ray of lighl from the poinl X, Pig, ~.~>\, suffer reflection at the points / and // of two plane mirrors whose planes are perpendicular to the plane of the paper, the angles to the normals a1 / and // being a and v respectively. 1-et the ray XI intersect the last ray in A, bo that [AH is the angle between the first and last rays. Let the normals to the mirror intersect at B, so thai /////is the same as the angle between the mirroi , In the trian<_'lr-i I Ml and IHII W< I Ml i 20— - and //;// - <, . Therefore IAH 2 IBH\ that is to say, the angle between the Qi I and la I directions of the raj i twice the angle betwei n the mirrors. t 01! Bb Art. 327. 374 Now, suppose that a ray of light from another point Y, Fig. 255, coincides with the ray HA : then the angle subtended at A by the arc XY is the angle XAY, or twice the angle between the mirrors. Again, suppose that the mirror I can revolve about a fixed axis, perpendicular to the paper, then if X' is another point in the plane of X Y, the ray from X', after reflection at H, can be made to coincide with YA by suitably revolving the mirror /, and the angle X'A'Y is twice the new angle between the mirrors. Thus, with the aid of the two mirrors, Fig. 255. we can find the angle subtended by the arcs YX, YX', &c, at various points along YH produced. Now XIY = XAY + AYI and sin AVT ~ IH Sin 2( P so that, if we measure angles at the fixed point / by means of the two mirrors, and denote the angle A YI by p, we have XIY = 2 (angle between mirrors) + p, where IH sin 2 smp= IY Y . From the following descrij)tion of the sextant it will be seen how the optical principle is embodied, and it should be observed that the angle p, called the sextant parallax, may generally be neglected, since IH is very small compared with the distance between the points / and Y. 375 Arts. 328, 329. 328. Description of the sextant. — The sextant. Fig. 256, consists of a metal frame A, one edge of which is a circular arc CD ; an arm B, called the index bar, can rotate about the centre of the arc. Standing perpen- dicular to the frame is a small frame //, in which is fitted a glass mirror called the horizon glass, the upper part of which is usually unsilvered, small screws being provided for adjusting the position of the mirror. Standing on the index bar over the centre of the arc is another small frame /, which carries a mirror called the index glass. The arc ( 'D is graduated, and the graduations are so arranged that. when the index glass is parallel to the horizon glass, an index on the index bar points to the zero of the scale. The graduations are continued over a small are on the other side of 0, which is called the arc of excess. The index bar may be secured in any position on the arc Cl> by means of a damping screw beneath it, and. when clamped, it may be given a .-low motion to one-side or the other by means of a screw E, called the tangent screw. The setting of the index on the scale may be accurately determine* I by means of a vernier, winch will be explained in § 32i> : a small micro- scope F, carried on an arm pivoted on the index bar, is provided to facili- tate the reading of the graduations. The telescope G i- carried in a collar ./, which can be raised or lowered at will by means of a milled head A' beneath the frame; the telescope is so arranged that its axis makes the same angle with the plane of the horizon glass, as the line joining the centres of the index glass and horizon glass. Two sets of coloured shades L and 31, are provided for use when taking observations of bright objects. On the opposite side of the frame to that shown are three legs and a wooden handle N. When measuring an angle subtended by two objects, the observer, looking through the telescope, sees one object through the unsilvered part of the horizon glass, and the image of the other object after reflection at the index and horizon glasses ; the relative amount seen of each object iverned by the height of the collar. Therefore, from the previous article we see that the angle subtended by two objects at the index glass i- twice the angle between the index and horizon glasses -\- the sextant parallax. Now the angle through which the index has moved, from the zero of t he scale, is the same as t be angle between the mirrors ; therefore, in order that the reading of the index on the graduated arc may repre- twice the angle between the mirrors, each degree of the arc is graduated int.) two equal parts called degrees. These arc again subdivided into -i.\ equal part-, each of which is called ten minutes. 329. The vernier. When it is required to read a small graduated arc, such as that of a sextant, to a close degree of accuracy, a supplementary graduated arc, called a vernier, is employed. The vernier tit- oloselj to tin- graduated arc of the instrument under consideration, and the method of ascertaining the correct reading will he understood from the following. bet the value represented l>\ the distance between two adjacent graduatione of the instrument be a and suppose that it i- required etting of the index to a degree "I accuracy d, and that \ four should give the semi diameter of the sun, and should therefore i e with the semi diameter tabulated in the Nautical Almanac tor the day in question. When taking observatione of the sun in an artificial horizon, the index error may he found in .i similar manner, by making use of the reflected image "t t he mi a < < n in the artificial horizon. I he nidc .. . nor. being ■> correction which is the same for everj angle observed, need not be eliminated, but, being verj liable to ohai should he determined when ever observation are taken. Should ii he Fig. 264. 3S5 Arts. 342, 343. plane part of the star wheel 8' and checks further winding. At the other end of the fusee axle is a pinion, which, on the fusee being turned, drives a wheel which indicates, by means of a hand on a small dial on the face of the chronometer, the number of hours which have elapsed since the last winding. This contrivance is called the up and down indicator, but is not shown in the Figures. The toothed wheel D'", called the great wheel, drives the train, and in order that the action of winding may not affect the great wheel, and that the power transmitted by this wheel to the tram may remain constant during winding, the great wheel is con- nected to the fusee by a special mechanism at the base of the fusee, called the main- taining mechanism, Fig. 264. The ratchet wheel a is screwed to the base of the fasee; the ratchet wheel D', which is con- centric with the fusee, Figs. 262 and 263, carries two pawls, b, b, which engage with the ratchet wheel a. The ratchet wheel D' is comiected by means of a spring xy to the great wheel D'" , x being the point of attachment to the ratchet wheel and y to the great wheel. A pawl D" engages with the ratchet wheel D' . Let us now consider the action of this mechanism under ordinary circumstances and during the winding of the chronometer. \\ liile the chronometer is going, the fusee revolves in a clockwise direction, carrying with it the ratchet wheel a, which turns the ratchet wheel D' in the same direction by means of the pawls b, b. The turning of D' causes the spring xy to drive the great wheel D'" and, in so doing, puts the spring xy in a state of tension. When the chronometer is being wound, the ratchet wheel a is turned in an anti-clockwise direction, and its teeth slip under the pawls b, b. The ratchet wheel D' is prevented from following this movement by the pawl D" . The tension of the spring xy now asserts itself, and causes the greal wheel D'" to continue its movement. 342. The train. — Under this heading is included, with the exception of the escapement, the remainder of the mechanism which lies between the pillar and top plates. The great wheel D'", Pig. 261, engages with the pinion E, on the axle of which is fixed the wheel E'\ this wheel and axle revolve once an hour. The wheel E' engages with a pinion 0, on tin- axle of which La fixed a wheel 0' \ the wheel <•' engages with a pinion //, on the axle of which is fixed a wheel //'. called the seconds or fourth wheel, which revolves once a minute, and on the axle of which i- mounted the seconds hand tp". The wheel II' engages with the pinion K, called the escape pinion, on the axle of which is fixed the escape wheel A.". 343. The motion work. The motion work is the name given to the incrii.iiii.il, which i the hour and minute hands to revolve ooi oentricalrv at their correot relative peed , The axle »— Fig. 265. roller i is a small projection r called the discharging pallet, and on the impulse roller i' is a projection s called the impulse pallet; these pallets are of ruby or sapphire. • Let us suppose that the escape wheel K' is at rest with one of its teeth in contact with the locking pallet o, and that this tooth is just about to be released by the impact of the discharging pallet r on the tip of the gold spring p, due to the oscillation of the balance in the direction of the arrow ; at the instant of impact the balance spring is in its position of equilibrium and the balance has its maximum velocity. 387 Arts. 345, 346. When the tooth has been released, the spring j causes the locking pallet to catch the next tooth. Immediately after the release of a tooth the main sjmng set- the escape wheel in motion, and a tooth impinges on the impulse pallet s, thus supplying energy to the balance to make up for what has been lost in friction. The balance swings to its extreme position in the direction of the arrow, till the compression of the balance spring starts it in the reverse direction; on its return, the discharging pallet /■ passes the tip of the gold spring without affecting the locking of the next tooth, and the balance swings to its extreme limit and returns to repeat the cylce of operations. Thus for each complete oscillation of the balance, the escape wheel moves through an angle which is subtended by the arc between two teeth. As a general ride. tlfe complete oscillation of a chronometer balance is performed in half a second; thus a chronometer beats half seconds, and each movement of the second hand corresponds to half a second of time. 345. The balance. — The balance consists of the balance wheel /. and the balance spring M, Tigs. 2<>2 and 203. The axle of the balance wheel fits perpendicularly into an arm lc. Attached to each extremity of the arm is a circular arc or rim L, which is formed of two strips of metal, the interior being of steel and the exterior of brass, and the latter being abut twice the thickness of the former and melted on to it. A mass /', called a compensating mass, is carried on each rim, and can be secured in any position by means of a screw. At each end of the ami is a screw /" called a regulating screw. A supplementary screw I" is fitted on each rim as shown in Fig. 263. On the lower part of the axle are the discharging roller i and the impulse roller i' . The balance spring is a long and delicate helical -ted Bpring, one en, 1 of which i- attached to a stud on the bridge .1'. , Pig. 202. and the other to a piece of metal called a collet, /? "X on the axle of the balance. To ensure isochronism, as far // \ as possible, the end- of the spring are formed in sym- r V v : -J metrical curves, as shown in Fig. 200, in order thai the \\-J whole spring may open and close symmetrically with \^n^^ regard to it- axis, and that no stresses may be set up at «_. _, (; , ; t he point.- of attachment . 346. Time oi oscillation of the balance. Let / be the moment of inertia of the balance about it- axis of rotation, and .1/ the restoring torque due to the elasticity of the spring when the balance wheel has turned through an angle from its position of equilibrium, then, it /' U the time of oscillat ion. we have IT i to 17 \ o Now, if r, is the natural radiui of the balance pring and r s the radius when the torque U M, we have from the theorj oi bending .1/ /. / where i is the moment of inertia oi a < • tion of the balance spring about n - neutral axis, and E \ the modulu ot ela ticitj . Art. 347. 388 But if L is the length of the balance spring, we have e = L — k Therefore M Ed i 1 » T = 2 V 111 Ei eVinch. 10f. 3 X 10 As a numerical example, the time of oscillation of the balance of a chronometer may be found from the following details : — ■ Mass of balance - - - - - 147 grains. Radius of gyration of balance - - -65765 inch. Diameter of balance spring - - - - | inch. Thickness - - - - - - fo inch. Width - Number of coils - lbs. Modulus of elasticity - - - - 3 X 10 . — ~. By substituting these values in the expression given above, the time of oscillation of the balance will be found to be approximately half a second. As a chronometer balance, whose time of oscillation is uniformly and exactly half a second, oscillates 24 X 60 X 60 X 2 = 172,800 times in 24 hours, it will be seen that an extremely minute error in the time of oscillation causes the chronometer to have a considerable daily rate. 347. The thermal compensation of the chronometer. — Let the time of oscillation when the temperature is x be 2jt\/-^ so that / is the moment of inertia of the balance wheel and S the elastic moment of the (Ei\ spring per unit angle of displacement of the balance ( y )• Let m be the mass of the balance wheel and k its radius of gyration at temperature x . Let a be the coefficient of expansion of the metal of the balance wheel, which we shall first suppose to be homogeneous. Then at temperature x , I = mk 2 , at temperature x, I = mk 2 [1 -\- a (x — x ) 2 ]. Therefore when the temperature rises, / is increased by a constant quantity (mk 2 a) multiplied by the square \ cx^. of the increase of temperature. Conse- quently if we plot / to a temperature base the resulting graph will be as shown in Fig. 267. Again, it is found by experience that, for a rise of temperature (x — x ), the elastic moment S becomes S[l — ft (x — x )], where ft is a constant, so that x zc S is diminished by a constant quantity Fig. 267. 389 Art. 347. Sfi multiplied by the change of temperature. Therefore, if we plot S to a temperature base, the resulting graph will be a straight line as shown in Fig. 267, and it will be seen that the ratio of I to S, and consequently the time of oscillation, is different at every temperature. Now let us consider a balance wheel in which the rims are bimetallic as described in § 345. The coefficient of expansion of the outer metal (brass) is greater than that of the inner (steel), so that, when the tempera- ture rises, the rims approach the centre of the wheel, and when it falls they recede from the centre. The result is that the moment of inertia of the balance increases or decreases according as the temperature falls or rises, which is the converse of what happens with the homogeneous balance. Let x be the temperature at which the rims are circular, and have their common centre in the axle of the wheel; then at temperatures above ,r the rims curve inwards, while at temperatures below .r they curve outwards. At temperature u- , / will be the same wherever the compensating masses may be on the rims, but at an\ temperature other than x , I will depend on the position of the compensating masses on the rims as well as on the temperature. It follows that there will be an / curve for every position of the compensating masses. If we consider six positions of the compensating masses, say, close up, :in . 60°, 90°, 120°, and 150°, reckoned from the fixed ends of the rims, the corresponding / curves will be as shown in Fig. 268, the curvature of each being opposite to that in Fig. 267. From Fig. 268 it mil be seen that, by placing the eompensating masses at a particular angle (120° in this case), the ratios of / to 8 at FlO. 268 temperatures .'•, ami x % will !><• tin- same, ami therefore the times of oscillation at those temperatures will i>«- id.- him Between these limit tin -re will be a Blight increase, ami outside of them ■' decrease in t In' time ol oscillation. That which ha- been laid above should !'«■ regarded a a i"UL r h explanation only, ami it should 1m- observed that, since / ami 8 are not .if tin- same nature, h u nof strictlj accurate to speak of the ratio ..f / to x. The fait that the times "f Oscillation 'an be made the samr at an\ two temperatures, by suitably placing the compensating masses, is the principle of the thermal compensation <>f the ohronometer. The two temperature* tfi K. and 90 I' . are elected a- the limits likely t" •»<• experienced, and the compensating m adju >'-.| bj trial o 'hat the time* "I oscillation at these two U-mpcratui the ame, tin- time nf oscillation ■>' tin- mean tempei bavin been found tilUS Arts. 348, 349. 390 For example, suppose that the daily rate of a chronometer when subjected to a temperature of 67|° F. ' was 4 seconds gaining, and that when subjected to a temperature of 45° F. and 90° F., the rates were 2 seconds and 7 seconds gaining respectively ; then it is clear that the compensating masses are too close to the free ends of the rims, and must be moved towards the fixed ends, and so on, till the rates at the two temperatures are found to be the same. When the compensating masses have been adjusted, it may be necessary to reduce the rate at the two limiting temperatures, and this is done by means of the screws I" . It will be seen from Fig. 268 that, if the rate at the extreme tempera- tures is zero, the chronometer will lose slightly at intermediate tempera- tures, the maximum losing rate occurring at the middle temperature. The rate at the middle temperature is called the middle temperature error, and in a good chronometer should not exceed 2 seconds. Various forms of auxiliary compensation are applied to chronometer balances in order to reduce the middle temperature error, and the principles on which most of them are constructed are (1) to check the opening of the rims at low temperatures, (2) to cause an auxiliary weight to move inwards at high temperatures. During the past few years it has been found that the middle temperature error may be very much reduced, by replacing the steel of the balance by an alloy of iron and nickel, which belongs to the same series of alloys as invar. This alloy is almost non- magnetic. Up to the present time this alloy has been very little used in the construction of the chronometers which are supplied to H.M. Ships. 348. Testing of chronometers at the Royal Observatory. — Chrono- meters, before being purchased for use in the Royal Navy, are subjected to very severe tests at the Royal Observatory at Greenwich, in order to determine their performances at various temperatures. These tests extend over twenty-nine weeks and comprise observations of the rate at temperatures up to 98° F. A considerable number of chronometers are tested together and, after the test, are tabulated in order of merit as shown by the formula a -f- 26, where a is the difference between the greatest and least weekly rates, and b is the greatest difference between two consecutive weekly rates. For a considerable number of chronometers, the formula gives a result below 30, while for a few it is as small as 10, from which we see the high pitch of perfection to which the thermal compensation has been brought. The limits, within which the daily rate of a chronometer should lie, before the chronometer is supplied to one of H.M. Ships, is given in the preface to the chronometer journal, which should be studied in this connection. 349. The formula for the rate. — With the compensation described in § 347, it is found that R = R x + K (x — x ± )* in which R is the daily rate; x is the mean temperature during the day : R 1 is the daily rate when the temperature is x x and K is a constant. In the application of this formula x may be taken as the mean of the. readings of the maximum and minimum thermometers (§§ 367, 368). 391 Arts. 350, 351. Experience shows that K and x t remain constant for a long period, but fij is liable to change, and should, therefore, be frequently verified. Example. — A chronometer was found by observation to have a losing rate as follows : — Rate 2-29 sees. Temperature 50° F. •04 „ ., 65° F. •97 „ .. 80° F. Required the formula for the rate, and the rate when the readings of the maximum and minimum thermometers (for the day) are 70° and 70° respectively. r>\ substitution in the equation above we have 2-29 = R X + Kxf - 100 Kx x + 50- K. •64 == R x + Kx* - 130 Kx 1 + 65 a K. • 97 = R 1 + AX 2 - 100 Kx x + 80- K. Subtracting the second of these equations from the first and third we have 1-65 = 30^ — 15 X 115 K, ■33 = - 30 Kx 1 -4- 15 X 145 K. adding 1-98 = 15 x 30 K; .-. K = -0044. With this value of K it is easily found that x x = 70° F. and 7? x = -53 sees. Therefore the formula for the rate is R = -53 sees. 4- -0044 (x - 70°) 2 sees., and when the temperature is 73 ', which is the mean of the thermometer readings, we have R = .53 sees. 4- -0044 x 9 Bees. = «57 sec-'. 350. Variation of. the rate due to age. —The effect of age on a chrono- meter is i" produce a change in the viscosity <>f the oil, a deposit of dirt on the various parts of the mechanism, and a slight wear between the moving parts. These tend to produce a slighl acceleration. To avoid the possibility <>t the <>il evaporating, a deck watch should never !><• left exposed to the sun. Chronometers should be senl to their makers at least every foui yean forrepairs. The date of 1 1 1 « - last repair is given on a paper pasted on tin- lid of the wooden case. A ohronometer, when four years have elapsed since the last repair, Bhould be sent to the nearest chronometer depdt and another procured. Should it be necessary t" send a chrono meter bj rail, the [ "«• should be taken to guard against dam in friii it. Full printed instructions as to the method ot packing, &c lied to each hip in the chart et, and should be carefully followed 351. Abnormal variations in the dailv rate, fn pite of the compensation of a chronometer for temperatun variations in t h< * rate, iluc to ol her cause occur. Tl 1 n due to 1 ] ) At mosphei ic condition Motion "i the hip. 1 Damp. 1 • Art. 351. 392 Atmospheric Conditions. — It is found that dampness of the atmosphere causes a retardation, which may be accounted for by the increase of the moment of inertia of the balance due to a deposit of microscopic sediment. Magnetism. — At the Royal Observatory at Greenwich, trials have recently been carried out, to determine the effect of a magnetic field on the rate of a chronometer, and it has been found, that a field in which the lines of force are parallel to the plane of the balance has the greatest effect, while a field in which the fines of force are vertical has practically no effect. It has also been found that the effect of the former field varies with the direction of the lines of force, as regards the XII. to VI. line of the dial ; it was concluded that the variation of the rate was due to the magnetisation of the steel of the balance wheel, and that the magnetisation of the balance spring had no appreciable effect. Let us neglect the magnetisation of the steel of the rim of the balance wheel, and only consider that of the arm, which will first be supposed to lie along the lines of force when the wheel is in the position of equilibrium ; it will be obvious that the arm, when displaced from this position, will be acted on by an additional couple which acts with the balance spring, and consequently lessens the time of oscillation. Now, suppose that the arm is at right angles to the lines of force when the wheel is in its position of equilibrium ; in this position the arm is not magnetised, but, as soon as it deviates from this position, the field produces a couple, which acts against the balance spring and consequently lengthens the time of oscillation. Therefore, between these two positions, there must be one at which the time of oscillation of the balance is unaffected by the field. The above was borne out at the trials, when it was found that the rate was unaffected if the arm of the balance wheel, when in equilibrium, was at 45° to the lines of force. The position selected for the chronometers on board ship, should be so far removed from magnetic influences, that the rate of the chrono- meter is unaffected. From the experiments mentioned above, it appears that a magnetic field of strength F dynes may change the daily rate of a chronometer by an amount, not exceeding 1 • 35 F 2 seconds. Now it may be assumed that the strength of the magnetic field of each of the various instruments mentioned in § 305, when at the distance tabulated under the heading " From Standard Compass Position," does not exceed half the earth's field, that is 0*09 dynes. As the strength of a magnetic field varies inversely as the cube of the distance, at a fraction K of the tabulated distance the strength of the field is 0-09 , -JP d y nes - Therefore, due to this field the maximum change in the daily rate of a chronometer is /°'09\ o 1 • 35 I — Tr% J seconds. If we equate this ex|)ression to one second, we find that K == 0-47 Therefore no instrument mentioned in § 305 should be brought withm one-half the distance tabulated under the heading " From 393 Art. 352. Standard Compass Position"; tins rule being followed, the change in the daily rate, due to any one of these instruments, should be less than one second. The correcting magnets and heeling error instrument should be as far away as possible, and the chronometer box should not be placed against an armoured bulkhead. The effect of magnetism on the deck watch, which may have to be carried from one position in the ship to another, may be considerable, and experiments are now being carried out with a view to finding to what extent the deck watch is shielded from magnet ie influences, by being kept in a soft iron box. Motion of the shij). — It has been found that the rolling and pitching of the ship causes a very slight acceleration of the chronometer, and that shocks due to waves striking the ship, &c, cause a retardation. It has also been found that, as a rule, the rate is different according as the ship is under way or in harbour, the rate in the former ease being called the sea or travelling rate and in the latter the harbour rate. Care should be taken that each chronometer is properly suspended in its gimbals, for if there is a small amount of play in the bearings the chronometer will experience shocks as the ship rolls or pitch) Damp.— One of the greatest dangers to which a chronometer is liable on board ship is rust, which acts on the balance spring and alters its elasticity. Conditions, leading to a deposit of moisture on the chrono- meter, or "Sweating.'' should be care-fully avoided, and any material. such as cotton waste, used to pack the chronometers in the box, should be perfectly dry. The danger is to a great extent avoided in the con- struction of the chronometer boxes which are supplied to modern ships; in these, as will be explained in § 35.'}, Bprings are substituted for packing. 352. To wind and start a chronometer. As will be understood from the above, in order that the daily rate of the chronometer may be as constant as possible, it is important that the interval, during which the motive power is transferred from the mainspring to the spring xy liould be of the same duration each day; for this reason, chronometers should always be wound in the same manner and by the same person, and, although a particular chronometer may have been constructed to run for two or more days, it should be wound daily. Again, in order that the same portion of the mainspring, chain and fusee may be in action on each day, the chronometer should be wound at the same hour. A chronometer i- wound by turning the key from right to left, the died a tipsy key, being instructed thai no couple is com municated to the fusee if it i turned in the wrong direction. When about to wind, the chronometer should be gently turned over in its gimbal ring until its i downwards; it -I Id then be held firmly the left hand and the shutter moved to one ide th< ould then be u h md ud the winding performed g< ntlj and evenly till the mechani m is fell to butt, the instant '•• nticipated by counting the number oi half turn ol the hey which is known to be required. ould then be withdrawn, and the ohronoraetei gently turned i >ri inal position, note being taken that the up and down indicator poii ' wound." It ia convenient to note the number oi balf tu [uired on a piew oi papei and to pa <•■ it Art. 353. 394 in the lid of the box. The number of half-turns required daily for different chronometers are approximately as follows : — One-day chronometer, 10 half -turns. Two-day „ 1\ Eight-day „ 4 A one-day chronometer runs for about 30 hours, and a two-day for about 54 hours. A deck watch, when being wound, should be held steadily in one hand, with the face downwards. It should not be oscillated in sympathy with the winding of the other hand. It is advisable that the comparisons should be made at the same time as the chronometers are wound, and, to avoid forgetting any details, a regular system should be adopted; for example — wind the chrono- meters in turn, commencing from the left ; then wind the deck watch or watches; note the readings of and reset the maximum and minimum thermometers; compare all chronometers and watches with the A chronometer as explained in § 140; work up the error of each chrono- meter from that of the previous day and deduce the error of the deck watch; note the error of the deck watch on a piece of paper placed inside the lid of its box. In order to start a chronometer, the gimbals should be locked and the instrument held by the hands with its dial horizontal ; it should then be given a quick turn in azimuth through about 90°, without any shake. This movement, on account of the inertia of the balance, will give a slight compression or tension to the balance spring, which should be sufficient to cause the balance to unlock the escape wheel and allow the mechanism to start. If it is desired that the chronometer should show G.M.T., the instrument should be started at the correct time, rather than the hands should be moved ; for example, suppose that the C chronometer has stopped, showing 4 h 10 m 27 8 '5, and that the error of the A chronometer on G.M.T. is 2 h 19 m ll a slow. G.M.T. - 4 1 ' 10 m 27 s -5 A - - 2 19 11 -0 slow on G.M.T. A shows - 1 51 16-5 In this case the G chronometer should be started when A shows ih 51m 16s- 5 an( i this may be done by giving the turn to C about half a second before the above time is indicated by A. On account of the possibility of straining the mechanism or bending the hands, it is inadvisable to set a chronometer to time by moving the hands. 353. The stowage and care of chronometers on board ship. — A special room, called the chronometer room, is selected for the stowage of chrono- meters, and is as far as possible removed from magnetic fields and not exposed to large variations of temperature. In the chronometer room is a box, called the chronometer box, in which the chronometers are kept. Specially prepared blocks of well-seasoned wood, about 2 feet high, are bolted to the deck ; on the top of these is a sheet of india rubber, and on this sheet is a tray, divided into compartments for the reception of the chronometers. The interior of each compartment, at the sides 395 Art. 353. and bottom, is provided with springs for holding the chronometer ctwes firmly in place. Fitting over the. whole of the above, but not touching it. is a wooden casing, the lower edge of which is secured to the deck; tliis casing is fitted with two lids, each of whirl) is provided with a lock, the inner being of glass and the outer of wood. Before the instruments are placed in the compartments the top lids of their cases are removed. The glass lid of the outer casing of the chronometer box is so arranged that, when it is closed, the glass lids of the chronometer cases are very close to it, so that the indications of the chronometers may be read without opening the glass lids or touching the instruments. When it is necessary to move a chronometer, the greatest care should be taken to avoid disturbing its rate and possibly damaging its delicate mechanisms. In such a case the gimbals should always be locked and the instrument carried in both hands, great care being taken not to turn it in azimuth, for, should a turn happen to coincide with the direction of movement of the balance, the instrument may stop; should the turn coincide with the opposite direction to that of movement of the balance, the spring may be strained. If the chronometer is to be carried for some distance, it is advisable to place it in the padded guard case which is supplied with each instrument. In armoured ships, in which the chronometer room is not situated behind the armour, a protected position is selected to which the chrono- meter box should be moved in time of war. It is usual to place the A chronometer in the middle compartment of the chronometer box and the others on either side of it, because this facilitates comparison. Art. 354. 396 CHAPTER XXX. VARIOUS INSTRUMENTS. 354. The patent log. — A patent log is an instrument for recording the distance run through the water. The principle embodied is that a small screw propeller (called the rotator), when towed through the water, makes a certain number of revolutions in a given distance and hence, by being attached to a mechanism (called the registering apparatus), registers the distance run through the water in a given time. Various kinds of patent logs are in use in the Royal Navy, and that which will be here described is called the Trident Electric Log. The registering apparatus, two views of which are shown in Fig. 269, is fixed Fig. 269. to the stern of the ship, while the rotator is in the water and connected by means of a long line to one extremity of the axle of a wheel, called the governor; the other extremity of the axle of the governor is con- nected by a short length of line to the registering apparatus. . The rotator communicates its motion to the eye M, at the end of the axle of the registering apparatus, which, in turn, by means of a reducing mechanism contained in the case A, communicates its motion to three pointers on the face. The case A is attached to the body of the instru- ment by four screws B. The body is supported by trunnions in a fork G, and this can revolve in the foot D, which fits into a shoe E, secured to the ship. The pull of the rotator and line is taken, through ball- bearings, by a cap F screwed on to the end of the instrument. The ball-bearings are covered by a tube G, which may be revolved to allow the bearings to be oiled through a hole in it. Fig. 270 shows the ball-bearings, axle and eye, which together can be detached from the instrument by unscrewing the cap. The bearings consist of two necklaces of balls which roll in V-grooves ; the outer necklace receives the pull of the rotator and line, and the inner is for the purpose of adjustment and for keeping the axle steady. The balls SO- Art. 355. Pig. 270. and grooves are enclosed in a skeleton cage A", which can be unscrewed from the cap for cleaning or renewal. The adjustment of the bearings is effected by screwing up the cage rap &, which may be Locked 1>\ a specially -formed washer and the two screws a, a. Should the outer grooves become worn the whole cage and bearings may be reversed, and the pull of the line thus trans ferred to what was previously the inner and practically unused balls and groove. The electrical portion of the instrument consists of a make and break mechanism in the registering appar- atus, and a receiver; the dial of the receiver is arranged in a similar manner to that of the registering apparatus, Pig. 269. The receiver is placed in the chart lu m-.- and is connected by a permanent circuit to terminals at the stern of the ship; a watertight flexible lead from the terminals is connected to the registering apparatus at the watertight connection //. The make and break mechanism completes the circuit at every tenth of a mile as indicated by the instrument, and thus every movement of the hands of the registering apparatus are repeated on the receiver. Care should be taken when handling the rotator that the blades are not damaged, for a blow may impair the accuracy of the instrument. When the log is to be used, the governor wheel should be attached to the registering apparatus by means of the eye M and the rotator put overboard, the hook on the inner end of the line being placed in the eye of the governor and the hands set to zero. The accuracy of a patent log depends largely on its being used with a suitable length of line, and as this varies in different vessels, it is necessary to make some experiments at sea, when steaming over a known distance, 30 as to ascertain the best length for a particular vessel. The following length of line have been found to be suitable for normal ••1- : — Maximum speed 10 knots. Length of line lo fathoms. 15 ,, ,, ,, 50 to 55 fathoms. >> >> 1° >> >> )» 00 ,, DO ,, ,, 20 ., ,, ,, 70 ,, 80 ,, „ 26 „ .. „ LOO ., L20 ., Should the above nof accurate results, Lengthening the line will generally be found to increase the Log registration, and via versd. For BmaU high speed vessels, such as Torpedo Boat Destroyers, shorter lines may \><- u ed th) □ tho e given above. The Length <>f line, when found t<> be correct, should be adhered t<>. and new lines, whioh stretch con- siderably, should In- shortened as measurements may Indicate. It Ls better to use a Line which i too long than one too short, because with ;i longei line the rotator i deeper in the water ;md the log ia li - affeoted by rough weal her. 355. The speed by steaming over B measured distance. I ,< peed hip i- found by {teaming over a mea ured di tanoe, and for thj purpose b« I apal various places along the coa I in Fig 271, I r and /< B' are two pain of beacon uch thai I I i parallel i" Ship's Course 8'* Art. 356. 398 BB' , and the distance between these lines is exactly known. The ship whose speed is to be ascertained steams at right angles to these lines j and notes the time when A' and B' »*>— { are in transit with A and B respect- ively, the speed of the engines being kept uniform. The distance and ] «— Measured Distance -A time being known, the speed may ^ Tl ^stream or current ^f^^mmm^. exists, the ship should steam over , the measured distance in both direc- tions, and her speeds with and against the stream should be ascer- A tained ; her speed through the water is then the mean of these speeds. * IG - 271. 356. The error of a patent log. — Patent logs do not always correctly register the distance run through the water. The error of a patent log should be recorded as a percentage of the distance which the log actually shows, and not as a percentage of the distance run. This error may be found in either of the two following ways, the second of which is to be preferred, as being the more accurate : — (1) By noting the readings of the patent log on two occasions of fixing the ship's position. The distance run over the ground may be taken from the chart and, due allowance having been made for the effect of the tidal stream or current, the distance run through the water may be obtained and compared with the distance shown by the log. (2) From runs over a measured distance, with and against the tidal stream. Example of (2) : — A ship steamed at a uniform speed between the transit lines (8,678 feet apart) given by the beacons in West Bay, Port- land, and the following observations were taken : — D.W. Patent log. JA<}>A' - 4 h 34 m 18 s 39 -5 miles \BftB', - 4 40 47 41-2 „ Against the tidal stream With the tidal stream /B0B' 4 56 27 42-9 miles \A(pA' - 5 02 04 44-2 „ The run against the tidal stream gives a speed of 8,678 feet in 389 seconds; that is, 13*2 knots. The run with the tidal stream gives a speed of 8,678 feet in 337 seconds; that is, 15-24 knots. The mean of these speeds is 14*22 knots, which is the speed of the ship over the ground. Now the patent log gives a speed of 3 miles (1*7 + 1*3) in 726 seconds ; that is, 14* 88 knots. Therefore the speed of the ship as found by the patent log is too great by -66 knots in 14*88; the error of the patent log is, therefore, 4*44 per cent, overlogging. When finding the error of a patent log from the indications of a chart house receiver, it should be borne in mind that the pointer of this instrument only indicates every tenth of a mile. In order to find what the patent Log showed al the instant of the transit coming on, it is 309 Arts. 357, 358. necessary to note the times at which the electric impulses, immediately preceding and succeeding the transit, were received as well as that of the transit ; the trading of the patent log at the time of the transit may then be found by interpolation. 357. The speed by the revolutions oi the engines. The number of revolutions per minute at which the engines are working provides a ready and. under ordinary circumstances, an accurate nut hod of obtaining the speed of the ship. A tabular statement showing the speed of the ship in smooth water, when at her normal draught and with a clean bottom, corresponding to various speeds of the engines, is made out for each -hip from actual trials; from this statement the -peed of the ship may be estimated. It must not be expected that this method will give correel results when the ship's bottom has become foul, and therefore an allowance should be made, obtained from experience, depending on the interval which has elapsed since the ship was docked. Again, when steaming against a head sea, the speed developed will be less than thai. tabulated, and therefore under such circumstances it is difficult to estimate the speed of the ship from the revolutions of the engines. 358. The sounding machine. — A sounding machine is an instrument with which to ascertain the depth of water at any place. The type of sounding machine in general use in the Royal Navy is that known as the Kelvin Mark IV., which may be worked either by hand or by electric motor. Pig. 272 -hows the Mark IV. hand machine, which consist- of a framework supporting a drum on a horizontal axle, the drum being wound with 300 fathoms of 7 -st rand flexible steel wire. The drum is free to revolve on its axle or may be gripped to the sprocket wheel by means of wooden brake cheeks actuated by the handles. Thus, the sprocket wheel having been fixed to the frame b\ mean- of the brake catch-pin, a turn of the handles in the direction in which the wire runs out will free the drum; a turn of the handle.- in the opposite direction will grip the drum to 1 he Sprocket wheel, and. if the brake catch-pin be w ithdiaw n. the dram and sprocket wheel may lie revolved by turning the handle On the left face of the drum i- a V-shaped groove, in which rests the automatic brake cord, on t he inner end of w Inch is a (i lb. weight working in ;i vertical tube, and on the outer end a L-lb. weight. The objeel of the automatic brake is to ensure that, when the wire is running out. the drum revolves at a uniform speed, and to prevent the drum over running when t he lead n aches the bottom. On the top <»i t he frame is a pointer, which i- connected by gearing \<> the drum, and indicates on a horizontal dial the number Oi fathoms "I wire that have run out. When the -hip i- steaming above 13 knot it i sometimes found that the 8-lb. weight i- liable to jumb out of it- tube, and lor tin reason four I lb. weights, Bhaped i ictlj tit over the former are provided >r more ol which may be added ry. < )n the end of the wire wivel, to which i attached 9 feet of plaited hemp, called the tray line, at the extremitj of which ie secured the lead which weigh 24 Ibe \ti iched to the traj line about 6 feet above the bottom oi the lead. U ■ > bra tube, called a guard tube, the upper end of which ie fitted w it h a cap with a bayonet joint, the lowei end having holes in it to fre.K udmif th< The u <■ of thi guard i ii he will be undei ' I latoi . Art. 358. 400 The sounding machine is usually mounted in the fore part of the ship, and generally in such a position that it is visible from the bridge. The wire is led from the machine through a special swivel block carried on a traveller at the end of a spar, 30 to 40 feet long, which projects horizontally from the ship's side. The wire of the sounding machine having been snatched in the block, and the latter on its traveller having been hauled to the end of the spar by means of an out haul, the lead should be lowered until it is just clear GUARD PLATES WIRE DRUM. SPROCKET WHEEL. GUARD DISTANCE PIECE. GUARD BRACKET, i .REAR STRUT CASTING. AUTOMATIC BRAKE CORD. 6 LBS. AUTO. BRAKE WEIGHT REAR WEIGHT-TUBE BRKT REAR WEIGHT-TUBE. DIAL. TOP. BRAKE CATCH BRACKET. BRAKE CATCH PIN. SHAFT BUSH. COTTER PIN AND NUT. ♦-HANDLE SOCKET. RIGHT SIDE OF FRAME. HANDLE. DECK BOLT. -DECK PLATE. 1 BASE OF MACHINE. Fig. 272. of the water, and this may be done by withdrawing the brake catch-pin and revolving the drum by means of the handles. When the lead is at the required position, the brake catch-pin should be re-inserted and the pointer set to the zero of the scale. If the ship is at rest, the depth may be easily obtained by allowing the wire to run out, and noting the reading of the pointer when the lead strikes the bottom, the instant being easily detected by means of a feeler pressed on the wire. When the ship is under way it is impossible to obtain an up and down cast of the lead, and hence the dejjth by direct measurement; for this reason, one of two indirect methods are employed, which will be now described. 401 Art. 359. 359. The depth by chemical tube. — A glass tube, the inside of which is lined with chloride of silver (coloured red), one end being open and the other sealed, is inserted in the guard tube with its open end downwards ; then, as the r=~ -— 1~ lead descends, the water is forced up the tube, and the air within the tube compressed. ~.~ The salt water, as far as it rises, turns the chloride of silver white ; therefore the height to which the water rose in the tube at the greatest depth is known ; from this height the depth may be found as follows. Let h (Fig. 273) be the length of the inside of the tube and x the height the water rises in the tube. Let p be the atmospheric pres- [ sure, and p the pressure of the air in the — r=^:r. tube when at a depth d, then from Boyle's law, we have v h x Now p' wd - p, where w is the weight of sea-water per unit volume. I - p h "' h — a Therefore V d px w(h — x)' Now the weight of a cubic inch of mercury is -49 lb., so that, if // is i In- height of the barometer in inch' The specific gravity of Bea water is 1-025, and as a cubic fool of fresh water weighs 02A lbs., I lb^ 27 inch 8 ' Therefore substituting these values for p and w, we have d 13-23 // ( j inch ■1837 // I , ) fathom I i<. in tin- we • ■<■ that the depth depends "ii the height of the rometer and that it increases 7ery fast as x approaches h. To avoid tin- necessity (if ca Iculat on, a boXWOOd icale IB graduated tn difT. The boxwood scale u fitted with a bra projection al one end, and when curing it the t u t »« should be in contact with tic- oale and with ii sealed end again I the bra projection, The oal< i o adju ted that no appreciable erroi Is introdui ed when the heighl of thi barometei i between Art. 360. 402 28| and 29£ inches, but when it is above this height a correction must be applied as follows : — Barometer 29 • 75. Add one fathom in 40. 30-00. „ „ 30. 30-50. „ „ 20. 31-00. „ „ 15. The temperature of the tube, at the instant it is immersed, should be the same as that of the sea water, because a change in the temperature of the tube will change the pressure of the air inside the tube and vitiate the reading. In order to ensure that the temperature of the tube is the same as that of the sea water, the tube should, for a few minutes before being used, be partially immersed, sealed end downwards, in a bucket of freshly drawn sea water. When a tube has been brought to the proper temperature before being used, the whole volume of water forced into the tube, when at its lowest depth, will be expelled by the compressed air on the tube being brought to the surface. If, however, due to the above precaution having been omitted, the tube was warmer than the water, a small quantity of water will be found inside the tube after it has been removed from the brass guard tube. In order to ensure that the mark in the tube which indicates the height to which the water rose, usually referred to as the cut, may be regular and definite, the following points should be attended to : — (1) The wire should not be allowed to over-run after the sinker has touched the bottom. Should a considerable amount of over- run be permitted, the tube may he horizontally on the sea bed and the water tend to flow up the tube and cause a bad cut. (2) The brakes of the sounding machine should not be applied too suddenly. Should the running out of the wire be stopped with a violent jerk, the sinker, being at the end of a long line of steel wire, will oscillate and cause the water inside the tube to jump and make a bad cut. (3) The guard tube and chemical tube must be held vertically until the depth has been read off on the scale. If, from any cause, the cut is found to be irregular, the reading should be taken to be the lowest part of the cut. The tubes are supplied in hermetically sealed tins, 10 in a tin and 10 tins in a wooden box. It is important that the tubes should be kept free from damp and not exposed to the light, in order to preserve the chloride of silver from deterioration. For this reason a tube, when it has been used, should not be replaced in a tin in which there may be new tubes. Should a tube have deteriorated through age or neglect of the above precautions, it will usually appear of rather darker colour and more opaque. 360. Change of depth by the number of fathoms of wire run out. — On account of the regular rate at which the wire runs out, due to the action of the automatic brake, any large change in the depth of water at succes- sive soundings is immediately apparent, on the lead reaching the bottom, if the reading of the dial is noted on each occasion. This method of noting a change in the depth of water is particularly valuable, because it gives an earlier indication that the ship is approaching shallower water than is obtained by the subsequent measurement of the chemical tube. For this reason, the men who work the sounding machine should be 403 Art. 361. instructed to immediately report ajiy large decrease in the number of fathoms of wire run out between successive soundings. It is found, when the precautions, which are enumerated below, are complied with, that for a particular speed of the ship, the depth of water bears a more or less constant relation to t he number of fathoms of wire run out. and therefore it is possible to construct a table for a particular sounding machine, which shows the amount of wire required for the lead to reach the bottom, corresponding to various depths and speeds of the ship. Such tables, constructed for sounding machines in perfect adjustment, arc supplied to 11. M. ships. As it is unlikely that all machines are identical, the tabic should be checked before being used by comparing the amount of wire run out with the depths obtained with chemical tubes at various depths and for various speeds. The depth of water should not, in general, be obtained by means of these tables, but a chemical tube should be used at each sounding, except as explained in the following article. In order to ensure that the proportion between the depth and the num- ber of fathoms of wire run out should be as constanl as possible for any given speed of the ship, the following points should be attended to— (a) When releasing the main brake, which should have been pre viously eased, at the order " Lei go " the handle is given one complete turn in the contrary direction to heaving in; ihis should be done smartly. (6) Sinkers of the same shape and of exactly the same weight should always be used. (c) The same length and size of stray line should always be used, the swivels should be identical and the guard tube seized on in the same place. [d) The same brake weight should be in use, because at a given speed a heavier weight would not allow the wire to run out as fasl as a 6-lb. weight . 361. How to take soundings. The wire having been snatched in the block, insert the chemical lube in the guard tube, with its sealed end uppermost. Ann the lead, thai is. fill a small cavity in its base with soap. in order thai a -ample of the bottom may be obtained. Haul the traveller to the end of the -par. .ind lower the lead to the water's cdue. easing off the wire by mean- of the handles while doing SO, then the brake Catch pin should be rein-cited and the pointer se1 to zero. Base up the main brake until the wire is jusl aboul to run out. Holding one of t h<- handles in one hand and the bra - feeler in the other, gently pre - the leel.i on the wire. and. having noted th( I position of the hand e it exactly one turn in the direction of running "lit. The wire will now- run out. and .1 man should be stationed to note the exact reading of the dial at the infant the lead I'eache- f h« ■ I ,. .tt . .111 , w h ich is dctceted h\ the slackening of the wire under the preHsure ol the feel< r ; the handle -hould now be turned in the direction of heaving in, and this will apply the brake and stop the wire. Tin application of the bral >uld be made gradu ally and evenly and nol violently 159). The brake catch-pin maj now be withdrawn and the wire hove in being guided on to the drum through a piece oi oiled canva When the lead is oleai ol the water the outhaul i when the continued reeling in of the wire will bring the eller into the hip ide and the chemical tube ma} be removed and Art. 362. 404 compared with the scale. The base of the lead should now be examined in order to determine the nature of the bottom. A book, called the sounding book, is provided, and all information relating to soundings taken should be entered in it. As one of the data entered in the book is the speed of the ship, an inspection will show whether the table for sounding without the tubes is correct. When sounding at frequent intervals it is unnecessary to use a chemical tube on each occa- sion if the depths are regular, but if one is used at about every sixth cast of the lead, the depth at the intermediate casts may be inferred from the amount of wire run out. The spars, or sounding booms, should always be rigged in place when under way, and soundings should be taken continually when in pilotage waters. It is advisable that the sounding party should be instructed to sound at certain regular intervals as indicated by the clock, for, should it be necessary to estimate the ship's position by plotting the soundings on tracing-paper (§ 67), the work is much simplified. Sounding machines are generally placed on either side of the ship and, when it is necessary to obtain soundings with great rapidity, it is advisable to have two sounding parties, and to work the machines alter- nately. When steaming in 20 fathoms at a speed of 10 knots, soundings can be continuously taken with one machine at the rate of one a minute. When the machine is not in use the main brake should never be left set up. The iDiinciple of the action and the method of working the sounding machine which is driven by an electric motor, are similar to what has been described above, with the following exception : — On the left of the machine is a skeleton wheel, keyed to the shaft, and, when taking a sounding, this wheel is turned through one revolution to release the drum in the same way, as the handle of the hand-worked machine. On the lead striking the bottom the switch of the motor is put over about half-way, when the motor puts on the main brake and com- mences to heave in the wire. The switch should now be gradually put over to the " on " position, when the wire will be hauled in at full speed. While heaving in, a careful watch should be kept on the indications of the dial ; the motor switch should be eased up gradually when the pointer shows 10 fathoms, in order that it may be possible to stop heaving in the wire at the correct time. Should the motor be out of order, handles may be shipped and the machine used as a hand machine. 382. The station pointer. — The station pointer, Fig. 274, consists of a graduated circle and three arms, the chamfered edges of the latter radiating from the centre of the circle. One leg OA is fixed and its chamfered edge corresponds to the zero of the graduations of the circle, which are marked at every half degree from 0° to 180° on either side of the zero. The two legs OB and OC, called the left and right legs, may be revolved about the centre O and clamped in any position. The settings of their indices on the graduations indicate their respective inclinations to the centre leg. The centre of the circle is indicated by a small nick in the chamfered edge of the fixed leg, and, when using the instrument, a very sharp pencil point should be used, in order that the mark made on the chart may exactly correspond with the centre of the instrument which is on the continuation of the edge of the fixed leg. 405 Art. 363. The chamfered ed_ the right leg cannot be brought very close to that of the centre leg : for this reason when the righl hand angle is verj small, and consequently the right leg cannot be set to it. the left leg should be set to the small angle; the right leg should be moved round and set to the sum ot the right and left angles measured from the fixed leg to the left. Under these circumstances the lived leg should hi- directed 10 the right-hand object. To check the accuracy of the instrument radiating lines should !>«• ruled on a sheet of paper, the angle between adjacent lines being i<» . and laid off by the method of chords. The Instrument should be placed Fig. 274. on the paper with the nick exactly at the centre of the radiating lines, and with the chamfered edge of the fixed leg coincident with one of them. Weights mould be placed on the instrument to prevenl il from being identally moved, and the right and left legs should then be raccessivelj ;,, coincide with the lines, and the readings of the scale ascer tained. The errors corresponding to the various angles, marked or i hey ghould !»• applied to an observed angle, should be tabu ■ ! m the li-l of the box. While testing the Instrument i1 ,!d be noted whether the chamfered edge of each leg coincides through out it length w if h one of the straight lin< 363. The marine barometer. The barometers used on board ship ,,i three kinds the marine barometer the aneroid and the raph. The marine baromeU ial t\ pe of mercurial barometer, which lattei in it form, i merelj a gla tube closed at one end and ailed with mercury, the tube and mercurj having been boiled in or de r to extracl anj minute parfi< lee of air which ma$ adh< re to the .;,!,.. of th< the ml"' i- inverted and its open end placed below the I ,,| the surfa e ol the mercurj contained in a mall i istern I he mercur no* de cend in the tube until the weighl of the colunu balanced bj the pr< ssun of bh< atmosphere on the mcrcurj in the ci tern cale ,,i inch< i ro level with the lurface ol the mercury in the lh ' column maj b< ded (( . ,.,,,,, thi read bown bj luch B ;, i ter In ord< i thai i be made with other " d Art. 363. 406 barometrical observations. The necessities for these corrections are as follows : — (1) Capacity. — When the barometer scale is fixed, its zero is level with the surface of the mercury in the cistern at one particular pressure only. When the pressure decreases, the mercury in the tube drops and flows into the cistern, where it raises the level; the reading is now too high, since the zero of the scale is below the surface of the mercury in the cistern ; the converse occurs when the pressure increases. (2) Capillarity. — This correction is made necessary by the affinity of the mercury for the interior surface of the tube, which lowers the level at the edge and gives a curved form to the top of the mercury column. (3) Temperature. — As the temperature rises or falls, so does the volume of mercury increase or diminish, so that to make comparison possible a certain fixed temperature, to which all readings may be reduced, must be selected. (4) Height. — The pressure of the atmosphere is a maximum at the sea-level and decreases with the height therefrom, so that to make comparison possible a certain level has to be selected. (5) Latitude. — The weight of a column of mercury increases from the equator to either pole, so that it is necessary for some latitude to be agreed upon as the standard latitude at which weight is measured. The marine barometer, Fig. 275, consists of a glass tube mounted in a metal case, at the bottom of which is a cistern ; the mercury tube is exposed to view at the top in order that the level of the mercury may be read off by means of a brass scale and vernier, the latter being constructed to read to -01 of an inch and in some cases to -005 of an inch, and being- adjusted by means of the milled head D. Between the cistern and the scale an air-trap A is fitted, so as to catch any particles of air which may creep up the inside of the glass tube. There is a small hole H in the top of the cistern, which allows the atmo- sphere free access to the surface of the mercury. When the instrument is laid down or inverted, the mercury is prevented from escaping through this hole by means of a leather valve. The bore of the tube is contracted for the greater part of its length for the purpose of giving the tube greater strength and reducing the weight, and it is further contracted, as shown at C, in order to prevent an up and down motion of the mercury (called pumping), due to the rolling and pitching of the ship ; this contraction increases the friction of the mercury in the tube and consequently the marine barometer is somewhat slow in recording changes of pressure. The instrument is supported in gimbals carried on a spring bracket, which is secured to a bulkhead. The instrument should be placed in a carefully selected position, which should be, if possible, near the centre of gravity of the ship, away from traffic and in a uniform temperature. When it is necessary to remove the barometer from* the bulkhead, as, for example, when it has to be packed or when guns are being fired, the instrument should be inclined in order that the mercury may fill the space which is ordinarily a vacuum, and so be unable to impinge on 407 Ait. 363. tin' top of the tube. Che process should be carried oul very slowlj i,use, as the instrument is inclined, the pressure of the atmosphere drives the mercury up the tube, and the impact on the top of the tube may cause breakage. The instrument, when removed from the bulkhead, should be kept with the cistern end above the level of the top of the tube. The handle of the barometer box is so fitted that, when the instrument is being carried in the box, the cistern end is slightlj elevated. 7\\ ^ B to 3 00 Fig. -'::.. Tin- various errore enumerated above are eliminated or allowed for in i he marine barometer as follow - : i i 'n parity. Thin i- eliminated in the graduation "I the scale by mean of what are known a ' equivalent inches," tl><- inch i. , ling being made morter than true inches; for example, it the area of the cistern it 24 times the area of the upper part the tube where the variation in level take- place for a change ol barometric pr< sure oi I inch the column rise* oi I, ill- i ii of .in inch while the m fa< e in thi bei u fall or tli .,| an iimIi. ami a- the /< i<> < >t tin- < ale - amid be h Arts. 364, 365. 408 altered, the divisions marked on the scale as inches must be really yth inch. (2) Capillarity. — A correction for this error is permanently made by cutting off a small amount from the bottom of the scale. In this connection it may^be remarked that, when reading the instrument, the zero of the vernier should always be made to coincide with the highest part of the curved surface of the mercury column. (3) Temperature. — The temperature selected is that of the freezing point of distilled water, namely, 32° F. Attached to the side of the marine barometer is a thermometer B, Fig. 275, and in order that all readings of the barometer may be of value to the Meteorological Office in the construction and correction of isobaric charts, the reading of this attached thermometer should be taken and noted at each observation. A table for the correction is given in the Barometer Manual, reference to which shows that the correction is zero when the temperature is 28° F. ; this is so because a correction for the expansion or contraction of the brass scale is included in the table. (A) Height.— -The level of the sea has been selected as the standard level, so that when comparing the readings of two barometers, the corrections due to their respective heights should be added to each. The decrease of atmospheric pressure is -001 of an inch of 'mercury for every foot above sea-level. The height, at which the barometer is placed on board, should be entered on the first page of the ship's log for the information of the Meteorological Office. (5) Latitude. — The latitude of 45° has been selected as the standard, and a table for reduction to this latitude is sfiven in the Barometer Manual. The heights of the barometer and attached thermometer should be observed and recorded in the ship's log every four hours ; in unsettled weather additional observations should be taken. 364. The aneroid barometer. — The aneroid barometer depends for its indications on the movement of the top of a thin corrugated metal drum, which is partially exhausted of air so as to make it very susceptible to slight changes of external pressure. The top is connected to a pointer by means of a delicate mechanism which greatly magnifies its movement. The pointer can be set to indicate any particular pressure by means of a screw at the back of the instrument, and as the mechanism is liable to derangement, the reading of the instrument should frequently be com- pared with that of the mercurial barometer. If any difference is found, the aneroid should be adjusted to correspond with the mercurial barometer. The great advantages of the aneroid barometer are its convenient size, and the rapidity with which it shows any change of atmospheric pressure. 365. The barograph. — A barograph is an aneroid barometer provided with a lever which records variation of pressure on a revolving drum. It is in some respects a more valuable supplement to the marine barometer than the aneroid of the ordinary form. It is not only useful in enabling an observer to detect casual errors in the readings of the marine barometer, but also gives* a continuous record of barometric pressure for reference. Barographs, moreover, register minor fluctuations of atmospheric pressure which are seldom noticeable in the action of the mercurial barometer. 4<><) Aits. 366, 367. The instrument should be secured, or suspended, in a position where it is least likely to be affected by concussion, vibration or the movements of the ship. The drum is driven by clockwork and makes ohe revolution in seven • lay-. The paper forms, which lit on the drum, are graduated so as to show the day and time of day. as well as the height of the barometer in inches; a part of a specimen is shown in Pig. 104. Means are provided for adjusting the pen point so that it corresponds with the reading of the marine barometer, and a Lever enables the pen to he withdrawn from the paper while the instrument is being moved, or during the tiring of guns. 3G6. Thermometers. Besides the thermometer used for taking the temperature of the sea-water, which should be observed every four hours when the ship is under way. two thermometer- are kept mounted side by side in a wooden screen. One of these is lined with a single thickness of fine muslin or cambric, fastened tightly round the bulb, and this coating is kept damp by means of a few strands of cotton wick. These strands are passed round the glass stem, close to the bulb, so a- to touch the muslin and ha\ e their lower ends in a how I of water placed close to the thermometer. Tin- thermometer usually shows a lower tempera- ture than the other, and the difference, commonly called the depression of the wet hulh. depends on the degree of dryness of the air. Such a combination is called a hygrometer, and a thermometer titted a- above i< called a wet hulh thermometer, to distinguish it from the ordinary thermometer, which has its hull) uncovered and i< known as the dry hulh t hermometer. The depression of the wet bulb thermometer is caused by t he evapora tion fr^m the moistened covering of the hulh. When the humidity "1 the atmosphere is very great, during or just before ram. or when fog is prevalent or dew i- forming, then- is little «.i- no evaporation, and the dings of the two themometers are very nearly the same; at other lime- the wet bulb thermometer gives a Lower leading than the dry, kUSe the water evaporates from the muslin, and in the process of in- into t he atate <>f invisible vapour, it ab-<>il>- Ictt from I he mercurj in the bulb with the result that a lower temperature is indicated. \- i he air becomes Less humid, the evaporation is greater, and the fall of temperature of the wet bulb is also greater ; accordingly the difference of reading bet ween the dry and wet bulbs is then also greater. The differ ence ometimes amounts to 15 or 20 l\ in England, and more in some other pan- of the world ; but at -.a the difference seldom exceeds LO , The accuracy oi the record of the humiditj of the air depends greatly on the precautions taken to ensure cleanliness, and on the provision of a propel supply of fresh water. It should be remembered that the observatioi rendered faulty by the presence ol -alt water or dirt on the uvu tin or in the water. During frost, when the muslin hi m.i\ -nil be taken, because evaporation takes place from ic< from watei The reading of the hygrometer hould be observed and recorded in the -hip log everj fouj I. ours. 807. The maximum thermometer. Tin in trument i provided for the maximum temperature ol the air in the chi meter box durii h day, I' diffei bom an ordinarj thermometer in that the zero ' the end ol the tube furthi loan the bulb .n\>\ n ha small contraction in the bore just above the bulb, the effect ol which ii to ii e the friction set up bet n i he merourj and 1 1 and re to prei enl anj p ol m< unl< undei i on Art. 368. 410 siderable pressure. Its action depends on the difference between the frictional resistance offered by the contraction of the bore and the combined forces of gravity and expansion of the mercury due to increase of temperature, the two last named being largely in excess of the first. When the instrument is suspended vertically, its bulb uppermost, the mercury in the bulb remains there if the temperature remains uniform, because the force of gravity is not sufficient to overcome the friction at the contraction. If the temperature decreases, the mercury still does not move, but a small space is formed in the bulb due to the contraction of the mercury. On the other hand if the temperature increases, the mercury expands and the surplus portion is forced through the contraction and falls to the bottom of the bore, which it fills by an amount which depends on the rise in temperature. Thus the height of the mercury in the bore of the tube gives a record of the maximum temperature reached since the instrument was last set, and may be read off on the scale. The mercury which has been forced through the contraction may not fall to the bottom of the tube, but may adhere to the side. In this case the thermometer should be inverted and the two portions of mercury allowed to join and move together to the bottom of the tube. To reset, swing the instrument with the bulb downwards ; the mercury at the bottom of the bore, under the influence of centrifugal force and gravity, is then able to overcome the resistance of the contraction and to refill the bulb. After being reset and suspended, bulb uppermost, the instrument should indicate the temperature at the time. The maximum thermometer should be read and reset every day when the chronometers are wound and compared, and the reading should be entered in the chronometer journal. 388. The minimum thermometer. — This instrument is provided for recording the minimum temperature of the air in the chronometer box during each day. It differs from an ordinary thermometer in that alcohol, on account of its transparency and low freezing point, is sub- stituted for mercury. A small black glass index, shaped like a dumbbell, is inserted in the column of liquid in the bore of the tube, and the action of the instrument depends on the movement of this index, which results from its being unable to break through the surface of the liquid. The tube is kept in a horizontal position, and when the temperature rises the index remains stationary, and the liquid flows past it along the bore ; but if the temperature falls, the index is carried towards the bulb as soon as the surface of the liquid touches it, and this move- ment continues until the temperature ceases to fall. Thus the position of the index gives a record of the minimum temperature reached since the instrument was last set, and may be read off on the scale. Sometimes a division occurs in the spirit due to a fall or shake ; to clear this the thermometer should be held, bulb downwards, and shaken vigorously. To reset, the instrument should be held with the bulb uppermost; the index will then slide down till one end encounters the surface of the liquid, through which it will be unable to break. The minimum thermometer should be read and reset every day when the chronometers are wound and compared, and the reading should be entered in the chronometer journal. 41 APPENDIX A. EXTRACTS FROM ABRIDGED WUTK'AL ALMANAC, 1014. 412 MARCH, 1 914. I. AT GREENWICH MEA1T NOON. Date. THE SUN. Equation Right Var. Semi- Hi tn/^^*"»*» of Time Var. Ascension Declination. in Add to in of the Add for hours. 1 hour. 'J let III Apparent Time. 1 hour. Mean Sun {Sidereal Time). O / / / /' m ■ 1 h m « m s h Sun. 1 s. 7 477 °'9S 16 10 12 38-5 0-48 22 33 47-0 99 I Mori. 2 7 24-9 °'95 16 10 12 26-8 0*50 22 37 43-6 197 2 Tues. 3 7 2*0 0*96 16 9 12 14-5 0*52 22 41 40*1 29-6 394 3 4 Wed. 4 s. 6 3 9 -0 0*96 16 9 12 1*8 o'S4 22 45 367 49*3 5 Thur. 5 6 I5-9 0*96 16 9 II 48-6 0*56 22 49 33*3 59-1 6 Frid. 6 5 527 0-97 16 9 11 34"9 0*58 22 53 298 1 ♦ 1 9'° 18-9 7 8 Sat. 7 s. 5 29-5 0-97 16 8 I I 20*8 o'6o 22 57 26-4 1 287 9 Sun. 8 5 6-2 0-97 16 8 I I 6'2 o"6i 23 I 22'9 1 38-6 10 Mon. 9 4 42-8 0-98 16 8 10 51-3 0-63 23 5 19-5 1 1 48-4 58-3 1 1 12 Tues. 10 s. 4 *9'3 0-98 16 8 10 36*0 0*65 23 9 16-0 2 8-i '3 Wed. 11 3 55-8 0*98 16 7 IO 20'3 o-66 23 13 12-6 2 18-0 14 Thur. 12 3. 32-3 0*98 16 7 10 4-3 0*67 23 17 9-1 2 2 27-8 377 \\ Frid. 1 3 s. 3 87 0-98 16 7 9 48 'o 0*69 23 21 57 2 47-6 17 Sat. 1 4 2 45'i 0*98 16 7 9 31-4 070 23 25 2*2 2 57-4 18 Sun. 15 2 2 1 -j. 1 0-99 16 6 9 H"5 071 23 28 58-8 3 3 7'3 17-1 19 20 Mon. 16 s. 1 57-8 0-99 16 6 8 57-5 072 23 32 55-4 3 27*0 21 Tues. 17 1 34" 1 0-99 16 6 8 40*2 o* 72 23 36 51-9 3 36-8 22 Wed. 18 1 10-3 0-99 16 5 8 227 073 23 40 48-5 3 3 467 56-6 23 24 Thur. 19 s. 46-6 2 2 9 °'99 0*99 16 5 5 8 5-0 7 47*3 074 074 23 44 45'° 23 48 41 *6 Frid. 20 s. 16 Sat. 21 Sun. 22 N. N. o-8 24-5 0-99 °*99 16 16 5 4 7 2 9'3 7 "*3 075 075 23 52 38-1 23 56 347 Add for min utes. a o**> m 1 Mon. 23 48-2 °'99 16 4 6 53*2 076 31*2 0-3 0-5 1 Tues. 24 1 u-8 0-99 16 4 6 35-0 076 4 27-8 3 Wed. 25 N. 1 35'5 0-98 16 4 6 167 076 8 24-3 07 o"8 4 5 6 Thur. 26 1 59-1 o-gS 16 3 5 53-5 076 12 20-9 I 'd Frid. 27 2 22-6 o"93 16 3 5 4 " 2 076 16 17-4 1 "*J 11 7 Sat. 28 N. 2 4.6*I o* 9 S 16 3 5 21-8 076 20 14*0 1 "3 i*5 t-6 8 Sun. 29 3 9 -6 0*98 16 2 5 3'5 076 24 10-5 (J 7 IO 1 /■"*» Mon. 30 3 32-9 0-97 16 2 4 45*3 076 28 7*i Tues. 31 3 56-2 o--97 16 2 4 2 7"i o" 76 32 37 3 3 4'9 ZU 3° Wed. 32 N. 4 195 0-97 16 2 4 8-9 °'75 O 36 0*2 6-6 8'2 40 5° n. MARCH, 1 9 14. ■ 1 3 MEAN TIME. Date. Sun. 1 Mou. 2 Tues. 3 Wed. 4 'Ihur. 5 Frid. 6 Sat Sun. Moa 7 8 9 lues. 10 Wed. 11 Transit of the First Point of Aries. Tliur. 12 Frid. 13 14 Sun. 15 Mon. 16 Tue . 17 18 Thur. 19 Frid. 20 21 Sun. 22 Mod. 23 24 Wed. 25 ir 26 I. 27 28 Sun. 29 Mon. 30 Tii'-.. 31 W 32 h 1U 8 I 25 58-8 I 22 2 - 9 i 18 --o I II I 1 + I IO i 6 15-2 1 o 2 23-4 58 27-5 o 54 31-6 o 5° 357 o 46 39-8 o 42 43-9 o 38 47-9 |2'0 ;6-i CT2 4*3 84 o 34 o 30 o 27 023 o 19 '5 I I 7 l'3 J9 23 ; 3 55 1 ■ ? I'. ' 20-7 » * ■ 81 » « • 9/ 33 -0 37*' 23 47 411 23 43 45' 2 -3 39 • 23 • 23 (1 23 28 1 6 *3 2 4 57 23 20 9'8 THE MOON. S.mi- liameter, Noon. Var. in 1 hour Hori- zontal Parallax. No n. Var. in 1 hour, +6 49 55 5 +4 6 o 6 15 6 43 6 37 6 27 •5 1 47 5 33 5 81 f, 1 1 5 r 5 ! 1 M 43 4 5° O" I 4 '5 29 ' 06 o 4 °"5 °"7 °'7 06 6 28 : o-s 6 38 0-3 6 43 01 o - 1 °"3 °"5 o-6 o-6 °"5 °'S 0-4 o"3 O* 2 O' 2 O' I O* I o'o O' I O' 2 °'3 o'4 54 >"4 54 4° 3 18 55 »* 55 53 56 42 57 3^ 58 36 59 32 60 21 60 56 61 1 ; 61 60 60 '3 53 is 59 32 58 41 57 49 57 o 56 15 55 37 55 51 6 41 22 54 « 53 5« 54. 6 51 20 5+41 1 1 10 o 4 o"7 1 " 1 '"5 "'9 ^'4 2'4 2" 2 i-8 I ' I °'4 Meridian Passage. Upper. 3 '4 3 57 4 44 5 6 8 9 10 1 1 12 1 2 34 28 25 22 20 '5 9 o 52 Diff. °"5 '3 44 1 ' 1 •4 38 «*7 '5 34 2'0 16 33 2" I '7 32 2 ' 1 lS 32 2 '0 19 2S '"7 20 20 ' 'i 2 1 9 1 ' 2 2 1 53 °'9 2 2 °'7 23 " °'S »3 53! °'3 * + o'o ' 1 1 1 2 05 1 55 0*7 40 1 '0 1 ' 4 1 2" , Lower. 43 47 54 57 57 58 55 54 5' 5 2 5 1 54 5" 59 59 60 56 5* 49 44 4- 39 4° 4i 4S 4 V 5* 15 35 16 20 17 8 18 I 18 56 19 54 20 5 1 21 48 2242 23 3 5 * * 26 1 iS 2 10 3 5 4 3 5 2 6 2 7 7 o 55 8 4; 9 3' 10 14 10 55 1 1 1 2 1 • 13 1 1 IS 34. 1 ! 17 4 54 16 4.8 Diff. 45 48 53 55 58 57 57 54 53 5' I * 5* 55 58 59 60 {I 55 5° 4 43 4' 19 39 39 4' 44 47 5° 54 Age. Noon. 4'5 5'5 6-5 7-5 8-5 9-5 10-5 115 12-5 •3-5 >4'5 1 55 i6- 5 17-5 .8-5 195 20-5 2i-; 22'5 23-5 2>5 17-5 295 07 • 7 17 37 47 57 414 MARCH, 1 9 14. in. G.M.T THE SUN. 1 Sunday 1 Equation of Thursday 5 Equation of R.A.M.S. Dec. Time. R.A.M.S. Dec Time. h h m s / fri a h m s o / m 8 22 33 47-0 s. 7 477 + 12 38-5 22 49 333 s. 6 1 5- 9 + 11 4 8-6 2 22 34 67 7 45-8 12 37'5 22 49 53-0 6 14-0 11 47*5 4 22 34 26*4 7 43 "9 12 36*6 22 50 127 6 120 11 463 6 22 34 46M 7 42-0 12 35-6 22 50 32-4 6 io-i 11 452 8 22 35 5*9 7 4 '" 12 34-6 22 50 52'2 6 8-2 11 4+*i 10 22 35 25-6 7 38-2 12 337 2 2 51 I I "9 6 62 n 42-9 12 22 35 45-3 7 36-3 12 327 2 2 51 31-6 6 4'3 11 418 14 22 36 5*0 7 34+ 12 317 22 51 513 6 2-4 n 407 16 22 36 247 7 32'5 12 30-8 22 52 II'O 6 o+ 11 39*5 18 22 36 44-5 7 3° - 6 12 29'S 22 52 307 5 58-5 11 38 + 20 22 37 4-2 7 287 12 28-S 22 )2 50*4 5 56-6 11 57-2 22 22 37 23-9 7 26-8 12 27*8 22 53 IOI 5 54'6 11 36*1 Monday 2 Friday 6 O 22 37 43-6 s. 7 24-9 + 12 26-8 22 53 29-8 8. 5 527 + 11 349 2 22 3 8 3'3 7 23-0 12 25-8 22 53 49*5 5 5°" 8 11 337 4 2 2 38 2 3'0 7 2 i-i 12 24-8 22 54 9-2 5 48-8 11 32-6 6 22 38 427 7 19-2 12 23-8 22 54 28*9 5 46-9 11 314 8 22 39 2'5 7 '7'3 12 22-8 22 54 487 5 45"° 11 30-2 10 22 39 22'2 7 '5-4 12 217 22 55 8-4 5 43-o 11 29* 1 12 22 39 41-9 7 I3-5 12 207 22 55 28-1 5 4 1 "' 11 279 14 22 40 1*6 7 1 1-6 12 I97 22 55 47-8 5 39'2 11 267 16 22 40 2I - 3 7 97 12 18-6 22 56 7-5 5 37-2 11 256 18 2 2 40 4 TO 7 7-8 12 17-6 22 56 27-3 5 35*3 n 24-4 20 22 41 07 7 5-9 12 i6'6 22 56 47 "O 5 33 + II 23 - 2 22 22 41 20"4 7 3*9 12 1 55 22 57 67 5 3i + II 2 2"0 Tuesday 3 Saturday 7 22 41 40-1 s. 7 2'0 + 12 14-5 22 57 26-4 S. 5 29*5 + 11 20-8 2 22 41 59-8 7 o'i 12 13-5 22 57 46*1 5 27-6 II 196 4 22 42 19*5 6 58-2 12 1 2 -4 22 58 5-8 5 25*6 11 1 8+ 6 22 42 39*2 6 56-3 12 1 1 -4 22 58 25*5 5 237 11 17*2 8 22 42 59-0 6 54-4 12 10-3 22 58 45-3 5 21*8 n i6 # o 10 22 43 187 6 52-4 12 9-3 22 59 5*0 5 "9" 8 11 147 12 22 43 38-4 6 50-5 12 8-2 22 59 247 5 17*9 11 13-5 14 22 43 58-1 6 48-6 12 7*1 22 59 44-4 5 1 6-o II I2"3 16 22 44 17-8 6 467 12 6'I 23 4-1 5 H'° II 1 1*1 18 22 44 37-6 6 44-8 12 5*0 23 23 - 8 5 I2'I II 9-9 20 22 44 57'3 6 42-9 12 3'9 23 43*5 5 101 II 87 22 22 45 17-0 6 40*9 12 2*9 23 1 3-2 5 8'2 11 7-4 Wednesday 4 Sunday 8 O 22 45 367 s. 6 39-0 + 12 1-8 23 I 22'9 s. 5 6-2 + 11 62 2 22 45 56-4 6 37-1 12 07 23 I 42*6 5 4*3 11 50 4 22 46 1 6- 1 6 35-2 II 597 23 2 2'3 5 2-3 11 37 6 22 46 3 5-8 6 33*3 II 58-6 23 2 2 2 "O 5 °+ 11 2-5 8 22 46 55'6 631 + 11 57-5 23 2 41*8 4 58+ n 1-3 10 22 47 1 5*3 6 29*4 II 56-4 23 3 *5 4 5 6- 5 II o*o 12 22 47 35-0 6 27-5 11 5 5*3 23 3 21*2 4 54*5 10 58-8 14 22 47 547 6 25*6 n 54-2 23 3 4°"9 4 52-6 10 57-6 16 22 48 14*4 6 23*6 11 531 23 4 .0-6 4 5°'6 10 56-3 18 22 48 34-2 6 217 11 52-0 23 4 20-4 4 487 10 551 20 22 48 53-9 6 19-8 11 509 23 4 4 0>I 4 467 10 53-8 22 22 49 13-6 s. 6 17-8 + 11 497 23 4 59"8 s. 4 44*8 + 10 52'6 TheB ..A. of Mer. (local Sidereal Time) is foun signs ± under Equation of Time denot d by adding the E ight Ascension of the Mean Sun to the 1 ical Mean Time. The j additive or tubtt active to Apparent Time and vice versa to Mean Time. • 11. IV. MARCH, 1 9 14. G.M.I i THE SUN. Monday 9 Equation of Friday 13 Equation of R.A.M.S. Dec. Time. R.A.M.S. Dee. Time. h hin 8 / m s h ni s o / m ■ 23 5 >9"5 s. 4 428 4-IO 51-3 23 21 57 s. 3 87 + 9 4 8< o 2 2 3 5 39* 4 4°"9 IO 50-0 23 21 25-4 3 67 9 466 4 2 3 5 5*9 4 38-9 10 4S-S 23 21 45-1 3 4-8 9 45*3 6 23 6 iS-6 4 37-o 10 47-5 23 22 4-8 3 2-8 9 43 9 8 23 6 38-4 4 35"° 10 46*2 23 22 24-6 3 o-8 9 42-5 10 23 6 581 4 33i 10 45-0 23 22 44-3 2 58-9 9 4*> 12 23 7 17-8 4 jfl 10 437 23 23 40 2 5 6 '9 9 397 14 2 3 7 37'5 4 29-1 10 42-4 23 23 237 2 54*9 9 3S'3 16 23 7 57*2 4 27-2 10 41*2 23 23 43-4 2 53'° 9 37'° 18 23 8 16-9 4 2 5'2 10 399 -* 24 3-1 2 51-0 9 35' 6 20 23 8 36-6 4 23-2 10 3S-6 23 24 2 2 - 8 2 49° 9 34'2 22 23 8 56-3 4 21-3 10 37-3 23 24 42-5 2 47'" 9 32-8 Tuesday 10 Saturday 14 o 23 9 16*0 s. 4 19*3 4- 10 36-0 23 25 2'2 s. 2 45"* + 9 3''4 2 23 9 3 57 4 17*4 10 347 23 25 21-9 2 43' 1 9 3°'° 4 23 9 55*4 4 I5-4 10 33-4 23 2; 41-6 2 41 "2 9 286 6 23 10 15-1 4 '3-5 10 32*1 23 26 1*3 2 39*2 9 27*2 8 23 10 349 4 •"•5 10 30-8 23 26 211 2 37-2 9 25-8 10 23 10 5 + -6 4 9' 6 10 29^ 23 26 40*8 2 3 5*3 9 2 4"4 12 23 »i '+'3 4 7'6 IO 28'2 23 27 o'S 2 33*3 9 230 14 23 11 34-0 4 5' 6 10 26-9 23 27 20 - 2 2 3' '3 9 2 1'6 16 23 11 537 4 37 10 25"6 23 27 39-9 2 29-4 9 20 - 2 18 23 12 1 55 4 17 10 24-3 23 27 597 2 27-4 9 1S-8 20 23 "2 33'2 3 597 10 23-0 23 28 19-4 2 254 9 *7'4 22 23 12 52-9 3 57-8 10 2 I "6 23 28 29*1 2 23-4 9 '5'9 Wednesday 11 Sunday 15 O 23 13 12-6 s. 3 55'8 + 10 20-3 23 28 58-8 s. 2 2 1*4 + 9 "4"5 2 23 '3 32-3 3 53*9 10 19*0 23 29 1*8 ■ 5 2 *9'4 9 "3"i 4 23 '3 520 3 5**9 10 17-6 23 29 382 t 1 75 9 117 6 23 14 117 3 5°"° 10 163 23 29 579 »> «5'5 9 103 8 23 H J"*5 3 48*0 10 i5 - o 23 3° '77 £ 13-5 9 89 10 23 '4 5''2 3 4 6 '" 10 1 3 -6 23 3° 37'4 2 I 1*6 9 7'4 12 23 15 10-9 3 4 4 * 10 123 23 30 57-1 2 96 9 6*o 14 23 15 30-6 3 4* ' 10 110 23 31 1 6-8 2 7-6 9 4'6 16 23 15 50-3 3 4°*2 10 9-6 23 31 365 2 57 9 3* 18 23 16 io-o 3 38-2 10 S 3 23 3' 5 6 '3 2 37 9 i-8 20 23 16 297 3 3^2 10 70 z ^ 32 160 2 17 9 °'4 22 23 16 41/4 3 34 '3 10 5-6 " 32 J57 1 59-8 8 58-9 Thursday 12 Monday 16 23 17 91 s. 3 323 + 10 43 23 32 5 5 + s. 1 + 8 57 5 2 23 17 28-8 3 3°'3 10 30 23 3 3 "5*1 . 558 8 561 4 23 17 485 3 28-4 10 16 "3 33 34 8 1 s 8 54.6 6 23 18 8'2 3 • 10 0-3 1 54"5 1 51 8 53-2 8 23 18 28-0 3 2 Ci 23 H '43 ' 4 B qr8 io 23 18 477 j ig*5 9 ; 23 34 34*o 1 1 8 503 12 23 19 3 20-5 23 H 537 1 .\>>o 8 48-9 14 23 1 . J ' ■ 35 " 3 4 1 ., 8 4 16 2; I'y \*>% 3 166 9 '35 2\ is ' 4- > 8 460 18 23 20 6*6 3 »4' 6 ;i-i 23 35 52-8 1 40* 1 8 446 20 23 20 26-3 3 1 9 507 ■**5 « ; . 8 4V 22 232'. • 107 + 9 49'4 23 36 32*2 s. r ,6 , 4- 8 417 Xka i. _.\ of Mer. (!■•• tl -', !*rtOl tml r\f* Trril 1 Slr»n rim*. 416 MARCH, 1 9 14. G.M.T 1 THE SUN. Tuesday 17 Equation of Saturday 21 Equation of RA.M.S. Deo. Time. R.A.& Dec. Time. b h m 8 / m 8 h m 8 / m ■ 23 36 519 S. 1 34' > 4- 8 40-2 23 52 38-1 N. o-8 + 7 29'3 2 23 37 "'6 1 321 8 38-8 23 52 57-8 2-8 7 27-8 4 23 37 3 r 3 1 30-2 8 37*3 23 53 i7'5 4-8 7 26-3 6 23 37 51-0 1 28-2 8 35'9 23 53 37*2 6-8 7 24-8 8 23 38 io-8 1 26*2 8 34*4 23 53 57"° 8-8 7 23-3 10 23 38 30-5 1 24*2 8 33'° 23 54 167 107 7 21-8 12 23 38 50-2 I 22'2 8 3i-5 23 54 36-4 127 7 20-3 14 23 39 9*9 I 20*2 8 30-0 23 54 56-i H7 7 18-8 16 23 39 2 9" 6 I 183 8 28-6 23 55 15-8 166 7 »7'3 18 23 39 49"4 I l6'3 8 27-1 23 55 35* 6 18-6 7 158 20 23 4° 9-1 * H"3 8 25-6 2 3 55 55*3 20*6 7 14*3 22 23 40 28*8 1 12-3 8 24-2 2 3 56 15-0 22 - 5 7 12-8 Wednesday 18 Sunday 22 23 4° 4 8 '5 S. 1 1 0-3 + 8 227 23 5 6 347 JN. 24-5 + 7 "*3 2 23 41 8'2 1 8-3 8 2 P2 2 3 5 6 54'4 26-5 7 9-8 4 23 41 27-9 1 6-4 8 19-8 23 57 H' 1 28-5 7 8-3 6 23 41 47-6 1 44 8 18-3 23 57 33'8 3°"5 7 6-8 8 23 42 7-4 1 2-4 8 16-8 2 3 57 53'6 32-5 7 5"3 10 23 42 27-1 1 0-5 8 15-4 23 58 I3-3 34"4 7 3-8 12 23 42 46*8 58-5 8 13-9 23 58 33'o 3 6 "4 7 2-3 14 23 43 6-5 56-5 8 1 2*4 23 58 527 38-4 7 o-8 16 23 43 26-2 54-6 8 no 23 59 12 "4 4°'3 6 59-3 18 23 43 45*9 52*6 8 9-5 23 59 32-i 42-3 6 57-8 20 23 44 5 6 50*6 8 80 23 59 5^-8 44"3 6 56-3 22 23 44 2 5"3 48-6 8 65 1 1*5 462 6 547 Thursday 19 Monday 23 23 44 45*° y. 46-6 + 8 5-0 31-2 N. 48-2 + 6 53-2 2 23 45 47 44'6 8 3-5 50-9 50*2 6 517 4 23 45 24-4 427 8 2-1 1 io-6 52-1 6 50*2 6 23 45 44" 1 407 8 o-6 1 3°'3 54-i 6 487 8 23 46 3-9 387 7 59 1 1 50-1 56-1 6 47-2 10 23 46 23-6 36-8 7 577 2 9-8 58-0 6 45 6 12 23 4 6 43'3 34-8 7 5 6-2 2 29-5 O'O 6 44-1 14 23 47 3"° 32-8 7 547 2 49*2 2'0 6 42*6 16 23 47 227 30-9 7 53'3 3 8-9 3*9 6 41*1 18 23 47 42-5 28*9 7 5i-8 3 287 59 6 39-6 20 23 48 2'2 26-9 7 5°"3 3 48-4 7'9 6 38-1 22 23 48 2I"9 24*9 7 48-8 4 8-i 98 6 36-5 Friday 20 Tuesday 24 23 48 41-6 S. O 22 - 9 + 7 47"3 4 27-8 K 1 1 18 4- 6 35-0 2 23 49 r 3 O 20'9 7 45-8 4 47-5 13-8 6 335 4 23 49 21-0 19*0 7 44'3 5 7'2 15-8 6 32*0 6 23 49 407 i7'o 7 4 2 '8 5 26-9 17-8 6 30-5 8 23 50 0-5 i5 # o 7 4i-3 5 467 19-8 6 29*0 10 23 50 20*2 13-1 7 39' 8 6 6-4 217 6 274 12 23 50 39-9 1 pi 7 38-3 6 26*1 237 6 25-9 14 23 50 596 9*i 7 36-8 6 45-8 257 6 24 4 16 23 5 1 ! 9*5 7*2 7 353 7 5'5 27-6 6 22-8 18 23 5 1 39"° 5-2 7 33'8 7 25-2 29-6 6 2i*3 20 23 5 1 587 3-2 7 323 7 44"9 31-6 6 198 22 23 52 18-4 S. 1 2 + 7 30-8 8 4-6 N. 1 33*5 + 6 18-2 The! l. A. of Mer. (local Sidereal Time) is foun d by adding the P ,ight Ascension of the Mean Sun to the 1 ocal Mean Time. Th 3 signs ± under Equation of Time denot i additive or tubti ■active to Apparent Time and i ace versa to Mean Time. II MARCH, 1 914. G.M.T. " '"" THE SUN. Wednesday 25 Equation of Sunday 29 Equation of R.A.M.S. Dec. Time. R.A.M.S. Dec. Time. h h in • / m • h in • / Ill s 8 247 N. 1 35'5 + 6 167 O 24 107 N. 3 9*6 + 5 3"5 2 8 440 1 37'5 6 l 5 -2 24 30-2 3 1 1 - 6 5 2-0 4 9 37 1 394 6 '37 O 24 49-9 3 »3'5 5 0'5 6 ° 9 2 3"4 1 41-4 6 I 2"2 O 25 96 3 '5*5 4 59'° 8 9 43-2 1 43'4 6 I07 O 25 29-4 3 '77 4 575 10 10 2 - 9 1 453 6 91 O 25 49M 3 '9'4 4 559 12 10 22 - 6 I 473 6 7-6 26 8-8 3 217 4 547 14 10 42 - 3 1 49"3 6 61 26 287 3 232 4 52 7 16 Oil 2*0 1 5 12 6 4-6 26 48*2 3 2 5* 2 4 5'7 18 II 21"8 1 53-2 6 3-1 27 8-o 3 2 7'' 4 49'9 20 II 41-5 1 55-2 6 16 27 277 3 290 4 4 s- 4 22 OI2 I "2 1 571 6 00 27 47-4 3 31-0 4 468 Thursday 26 Monday 30 12 209 X. 1 591 + 5 587 28 7-1 N. 3 32-9 + 4 +5*3 2 12 40-6 2 11 57-0 28 26-8 3 349 4 ' 4 13 0-3 2 3-0 5 55 28 467 3 36-8 4 I 6 13 20'0 2 5-0 54-0 29 6"2 3 38-8 4 4°'8 8 O 13 398 2 7 - o 5 2 '5 29 260 3 4°7 4 393 10 ° »3 595 2 89 50-9 29 457 3 4 2 7 4 3 12 14 192 2 10-9 49'4 30 5-4 3 44 6 4 362 14 14 38-9 2 129 47*9 30 25*1 3 467 4 347 16 14 58-6 2 14-8 467 30 44*8 3 487 4 33' 2 18 15 18-3 2 16-8 448 3 1 4 - 6 3 5°-4 4 3»7 20 15 38-0 2 1S7 437 31 247 3 5 2 '3 4 }0-i 22 '5 577 2 207 4' 7 31 440 3 54'3 4 286 Friday 27 Tuesday 31 16 174 X. 2 22'6 + 5 40'2 32 37 N. 3 56-2 4- 4 2 7"' 2 16 37 1 2 246 387 32 237 3 58-2 4 *5"6 4 16 56-8 2 267 3/-i 32 431 4 o - i 4 2 4' 6 17 165 2 287 35-6 33 2-8 4 2-1 4 22 6 8 1- 36-3 2 307 341 O 33 22'6 4 4'° 4 2 1 • 1 10 17 560 2 327 327 33 427 4 6-o 4 " 12 18 157 2 347 3 1 34 20 4 4 1 So 14 18 35-4 2 7 297 34 217 4 4 167 16 18 55-1 2 7 27-9 34 4 1 -4 .( u-8 4. 15-0 18 19 147 2 |0 3 264 35 11 1 '37 4 '35 20 19 346 2 422 »4"9 35 20'8 4 '5 6 4 1 20 22 19 54'3 2 4^2 233 35 407 4 176 \ 10-4 ' 24 Saturday 20 140 «. 28 2 4 4- 5 21-- O 36 0'2 N. 4 197 + 4 8-9 2 20 337 2 .fl 20 7 4 20 534 2 '-> 6 021 131 . 2-0 r '77 8 021 329 2 54O 1 ■ 10 21 526 2 142 12 22 1 23 2 5 , 127 14 22 32 2 • 1 12 16 022 517 18 23 hi 3 ■ 1 20 13 |i*i 1 66 22 3 4- 5 1 Th'- 1 . v ' ■ II. 1 tlgnt t nnoei I n aditi ir vein* 418 MARCH, 1 9 14. MOON'S EIGHT ASCENSION AND DECLINATION. G.M.T. R.A. Sunday 1 Dec. G.M.T. R.A. Thursday 5 Dec. b h m ■ / h b m ■ 2 4 6 8 10 I I I I I 2 42 45 49 53 57 "4 56 2 " 39 " 3 2 3 ■" 224 7 226 53 227 N. 14 '4 '5 *5 16 16 33-1 579 2 2*4 46-8 i erg 347 248 2 4S 244 241 238 2 37 2 4 6 8 10 3 7 12 •7 22 26 5 286 37 286 23 2 88 11 288 59 289 N. 28 28 28 28 28 28 7-6 "3*2 182 22 - 6 26-4 29-5 56 5° 44 38 3' 26 12 14 16 18 20 2 2 2 2 2 4 8 12 16 19 4° c Is 22S 2-JO 7 232 59 ,„ 16 17 17 18 18 58-4 217 44"9 77 3°'3 2 33 232 228 226 12 14 16 18 20 3i 36 4 1 46 Si 48 T 201 39 •^ 201 30 y J 202 22 * IS 293 28 28 28 28 28 32M 34'° 35*2 35-8 3S"8 '9 12 6 22 2 23 2 72 5' 234 N. 18 52-6 223 220 22 56 8 293 2 95 N. 28 '35'i 7 14 Monday 2 Friday 6 2 4 6 8 10 2 2 2 2 2 2 27 3' 35 39 43 47 45 2 35 4° \ 36 236 3 237 239 32 J * J 240 3 2 J 241 N. 19 '9 '.9 20 20 21 1 46 36-3 577 18-8 39-6 o-o 217 214 21 1 208 204 202 2 4 6 8 10 6 6 6 6 6 6 1 5 10 '5 20 25 58 295 295 53 29 6 4 9 29 6 45 2 97 42 y/ 297 N. 28 28 28 28 28 28 337 317 29-0 25-6 21-6 16S 20 2 7 34 40 48 54 12 14 16 18 20 22 2 2 2 3 3 3 5i 55 59 3 7 12 33 245 36 243 244 40 2 45 45 247 52 „ 3 248 249 21 21 21 22 22 N. 22 20*2 40*0 59"4 iS-5 37'2 55'5 .98 194 191 .87 183 180 12 14 16 18 20 22 6 6 6 6 6 6 3° 35 40 45 5° 55 39 29 8 37 2 8 3 5 2 8 ' 29S 28 28 27 27 27 N. 27 1 1-4 5-3 58-5 51-1 42-9 34"° 61 68 74 82 89 95 Tuesday 3 Satu rday 7 2 4 6 8 10 3 3 3 3 3 3 16 20 24 28 33 37 9 *5" 20 * 2 53 33 *, 2 S4 47 a* 255 2 " 2 57 '9 4s ■N. 23 23 23 24 24 24 *3'5 3'i 48-2 5-0 21-3 37*3 176 i7' 168 .63 160 ■55 2 4 6 8 10 7 7 7 7 7 7 5 10 15 20 25 5 298 23 298 2 1 % 29b '9 2 8 17 v 297 N. 27 27 27 26 26 26 2 4'5 I4'2 3*3 517 39'4 26*4 103 109 116 123 130 136 12 14 16 18 20 22 3 3 3 3 3 4 41 45 50 54 59 3 37 26o s t 262 4° * T 264 4 266 3° c J 267 24 25 25 25 25 N. 26 52-8 7-8 2 2'4 36-5 50*2 3H 150 .46 141 »37 >3 2 127 12 14 16 18 20 22 7 7 7 7 7 7 3° 35 40 45 5° 54 "4 II 297 8 297 296 ^ 296 v 29? 55 295 26 25 25 25 25 N. 24 12-8 58-4 43H 277 1 1-4 54*4 144 ,50 •57 163 170 177 Wednesday < i Sunday 8 2 4 6 4 4 4 4 7 1 2 16 21 57 26 8 2 5 J 270 5 £*' 26 ' N. 26 26 26 26 l6l 28-3 40"o 51-2 122 117 1 12 2 4 6 7 8 8 8 59 4 9 H 5° 44 294 37 293 2 93 30 y * N.24 24 23 23 367 18-4 595 39'9 .83 .89 .96 8 10 4 4 25 3" 273 59 2 74 33 27s 27 27 '9 I2-I 107 102 96 8 10 8 8 '9 24 293 23 y * 291 '4 291 23 22 19-6 58-8 203 208 215 12 14 16 18 20 22 4 4 4 4 4 4 35 39 44 49 53 53 8 277 +5 2 s 23 * 2 79 2 281 +3 a8l 24 e 27 27 27 27 27 28 2 17 307 39" 2 47-2 54-6 *'3 90 ss 80 74 67 12 14 16 18 20 22 8 8 8 8 8 8 29 33 38 43 48 53 ? 291 5 6 289 +5 289 34 2 88 " 2 *7 56 * 87 22 22 21 21 21 20 37*3 I5-3 52-6 29-4 5*5 41-2 220 227 232 2 39 M3 24 5 3 I 283 N. 28 7-6 63 24 8 57 N. 20 l6'2 'H no MARCH, 19 14. MOON'S EIGHT ASCENSION AND DECLINATION. G.M.T. R.A. Monday 9 Dec. G.M.T. R.A. Friday 13 Deo. h h ru ■ / h b in • / 2 4 6 8 10 8 9 9 9 9 9 57 2 7 12 16 2 1 i6 -H ♦*.» 294 IO „ 283 53 ,., 36 J 3 281 N. 20 »9 '9 lS 18 18 16-2 507 24"6 5 8-l 3 10 3"4 25S 261 265 27' 276 z8l 2 4 6 8 10 12 12 12 12 I 2 12 35 40 44 49 54 58 56 271 27 57 272 29 1 ' 27 2 33 273 S. 6 6 7 8 8 9 234 5S9 34" 2 93 44-1 188 355 353 35" 34S 347 344 12 14 16 18 20 22 9 9 9 9 9 9 26 30 35 40 4+ 49 1 7 . 281 279 17 /y ^ 277 17 17 16 16 "5 X. 15 35*3 67 377 8-2 38-2 7-8 290 2 95 300 304 3°7 12 14 16 18 20 22 '3 13 13 •3 13 13 3 7 12 16 2 1 26 6 40 274 *4 xi \ t 276 276 2 ' 178 9 10 1 1 1 1 12 S. 12 53'2 27'3 1 1 34-7 7'9 40-8 34' 338 336 332 329 , 326 Tuesday 10 Saturday 14 2 4 9 9 10 3 1 1 4" ;: 1 z N.14 '4 "3 37-i 5'9 34'3 312 3 1 6 2 4 13 13 13 30 35 39 4° c .s 278 279 57 ,8, S. 13 '3 »4 "34 45-6 ■7 + 322 ' 318 3'4 3" 306 302 6 8 10 10 10 10 7 1 2 17 -- • 5 & 13 1 2 1 1 2-3 30-0 57-3 320 3 : 3 3*7 33° 6 8 10 13 "3 13 44 49 54 38 . 3 281 •9 282 1 2S2 '4 15 15 4 8-S 19-9 50-5 12 14 10 10 21 26 IO 1 1 10 24"3 51-0 333 12 14 '3 "4 58 3 + 3 284 27 4 16 16 207 5°'4 297 16 18 20 22 10 10 10 10 3° 35 39 44 272 4 2 2 7' '4 : 10 9 9 X. 8 '73 43 4 9-2 34"8 337 339 342 344 347 16 18 20 22 '4 "4 "4 '4 8 1 2 >7 22 285 ;; * > 286 ++ 288 ' 289 17 •7 18 S. 18 197 48-5 16-8 446 293 288 1 283 1 278 ! 273 ' Wednesday Sunday 15 2 4 6 10 10 10 1 1 48 53 5 . 2 ♦4 ;70 ' + 269 1 ' „ X. 8 7 6 6 O'l 25-2 1 47 35- JS3 2 4 6 ■4 «4 •4 14 27 32 37 4' 21 289 10 I *»' 53 „„, >. 19 '9 20 20 1 1 -9 38-6 4'9 3° - 5 267 263 256 8 10 1 1 1 1 6 1 1 20Q 40 267 5 5 39'- 3*5 355 357 358 8 IO '4 "■4 46 5' 2 U 2 45 294 39 3 ' 2 94 20 2 1 556 20*2 2;i 146 23') 12 14 16 1 1 1 1 1 1 '5 20 *4 35 268 3 267 3 o ^68 4 3 3 277 5 r8 •57 359 36, 362 362 12 14 16 '4 15 "5 56 1 6 ^ 296 2 5 2 8 2 1 22 22 41' 7*5 3°' 2 234 227 ; 18 20 22 1 1 1 1 1 1 33 57 58 " 8 5 " 1 2 2 N. 1 395 n 27-0 18 20 22 '5 "5 '5 ! I 16 2 I 28 2 1 v 299 20 ^ 300 2 2 *3 S. •; 2'5 208 202 Thursday 12 Monday 16 2 4 6 8 10 1 1 1 1 1 1 1 1 1 2 , 1 2 4- 4' 5' 55 4 5 N. N. 1 2 50*6 11-3 J64 2 4 6 8 IO 1 5 15 1 5 ■s 1 5 1 5 $1 I' 5 1 20 300 20 302 3°4 1 8. M •1 1 fl J 3 '3 182 16a 12 14 16 18 20 22 24 12 1 2 la 1 ' 2 1 2 1 1 2 1 ' 2 1 ■ 22 3' 35 3 3' ,6, 28 tea T s. 6 47-6 239 00 36*0 120 234 36. 360 360 35" 12 14 1G 18 20 22 24 1 5 16 16 16 1 1 1 16 22 1 , ' ,06 M •7 '■ 1 j 1 r 1 1 140 IJ3 119 420 MARCH, 1 9 14. MOON'S EIGH1 ' ASCENSION AND DECLINATION. G.M.T. R.A. Tuesday 17 Dec G.M.T. R.A. Saturday 21 Dec. h h m s / b b m 8 / 2 4 6 8 l6 16 16 16 l6 27 32 37 42 47 1 1 18 3 ° 7 25 3 ° 7 * 308 33 08 4 1 S. 27 27 27 27 27 4-0 15-2 25-6 353 44" 3 1 12 104 97 90 82 75 2 4 6 8 20 20 20 20 20 20 24 28 33 37 21 2 CO 40 5 * 2 . 209 3 209 3+ 20 3 2,! 2 3 3 4 4 47-3 1 5 5 437 1 1-8 39-8 282 282 281 280 279 2 4 6 8 10 3 7 ' 2 2 7 3 " '9 28 3 '5 27 ^ 249 3 *9 3° 3 2 3 47 J ' T# 252 22 22 23 23 23 310 49*3 7-2 247 41-8 .83 179 '75 171 167 12 14 16 18 20 22 26 30 33 37 4° 44 33 2I0 3 2,0 33 1I0 3 2,, 3+ ,„ 5 2,2 X. 5 5 6 6 6 7 77 35-6 3 4- 311 587 26*2 279 2 7 8 277 276 275 274 12 14 16 18 20 22 3 27 59 3 32 13 ; * 3 36 27 6 3 +° +3 2 8 3 49 '9 j 23 24 24 »4 25 N. 25 58-5 14-8 3°7 46 1 11 156 163 '59 '54 150 '45 141 Friday 27 Tuesday 31 2 4 6 8 47 5' 54 1 37 ■" 212 9 ' 212 4 1 21 3 •4 214 48 4 214 X. 7 8 8 9 9 53"6 20-9 48-0 150 419 273 27' 270 269 268 2 4 6 8 3 53 39 26l 3 58 4 2 23 5 /: £ 26 3 4 46 ' ■ 26c + " " J X.25 25 2 5 26 26 297 433 56-5 9-1 213 .36 '3* 126 122 1 17 10 5 22 * 2'5 10 87 a 66 10 4 »5 37 26S 26 33° 1 1 1 12 14 16 18 20 22 ' 8 1 2 16 '9 23 -7 57 2.5 32 8 2 ' 6 + 5 2.7 22 ' 218 119 Satui 1 N. 'day 10 1 1 1 1 1 1 1 2 1 2 28 35'3 1-8 28-1 54*2 20"2 460 265 263 261 260 258 256 12 14 16 18 20 22 24 4 20 5 269 4 2 4 34 26 4 29 3 4 33 34 ,; 4 3* 7 71 2 73 4 42 40 274 4 47 14 26 26 27 27 27 27 N. 17 44"i 54-8 5-0 1 ^ "6 237 3 : "2 402 107 102 96 9' 85 80 3° 39 J ' 220 N. »3 1 r6 '•">4 2 34 •9 '3 37*o J ' 4 37 4' x 220 59 222 *' 222 '4 2'2 2 5 2 I'll. ASKS OF THE MOO 6 '4 27'2 250 248 1. in 8 10 1 45 4 ) 23 ,.23 '4 J 5 52 r 1 Mar. 4 on. R, A. Sim. 1 Mon. 2 Tues. 3 Wed. 4 Thur. 5 Frid. 6 Sat. 7 Sun. 8 Mon. 9 Tues. 10 Wed. 11 Thur. 12 h m a 2 3 4 + 2 27 8 23 9 2 ° 27 s 2 3 '3 58 23 '8' 35 23 23 11 2 3 2 7 47 Frid. I 13 Sat. 14 Sun. 15 Mon. 16 Tues. 17 Wed. 18 Thur. 19 Frid. 20 Sat. 21 Sun. 22 Mon. 23 Tues. 24 Wed. 25 Thur. 26 Frid. 27 Sat. 28 Sun. 29 Mon. 30 Tues. 31 Wed. 32 276 276 2 75 23 32 22 23 36 57 '-\ 274 23 41 31 '*! 2741 23 46 2 38' 23 55 »» 273 273! 23 59 44 27 , o 4 17 "' 5 o 272 8 49 ', o 13 21 273 o 17 54 26 272 272 O 22 o 26 58 03I 30 2 o 36 272 273 ° 4° 3 5 ° 45 7 o 49 40 272 2 73 2 73 54 »3 58 46 " 273 1 3 IQ /J 7 274 7 53 274 12 27 '* 2 75 *75 / 21 37 26 13 276 s. Dec. Meridini: Passage. S. 7 28-6 6 59-4 6 30-0 : 9 2 : u 6 5 3°"7 297 o-8 2 " 300 S 4 3° - 8 o7 3 30-4' ' 3 o-i 2 297 1 59-2 3°4 3°5| 306 28-6 58-0 2 7"4 306 306 3°7 K o 3 -3 306 33 9 c 3°7 1 4-6 J ' 307 35-3 6 P u 3 6 '5 o6 3 7* 1 , nc 3 37-6 4 8-o 3 ° 4 303 4 38-3 5 8-6 3 ° 3 5 387 3QI J 300 6 87 6 386 2 " 7 8-3 2 97 7 37-8 2? 294 N. 8 7-2 h m o 31 o 32 o o o o o o o o o o o o 33 34 34 35 36 36 37 o 38 o 38 o 39 39 o 40 4 1 4 1 4 2 4 2 43 43 o 44 o 45 o 45 o 46 o 46 o 47 o 48 o 48 o 49 o 50 o $0 MARS. At Greenwich Mean Noon. 6 6 6 7 7 7 7 it. A. Dec. b in 6 32 6 3 3 6 33 18 8 5 ° 5' 59 55 6 3+ 5+ -6 6 35 50 > 6 36 49 ^ 51 5< 6 38 53 6 39 58 4i 4 2 43 6 44 6 45 6 47 5 '4 2 5 38 5 3 10 63 65 67 69 7' 73 6 48 28 6 49 4S 6 5. 10 6 5 2 33 6 53 58 6 55 24 6 56 52 6 58 21 6 59 52 7 1 7 2 7 4 2 + 33 °5 86 88 89 9 1 92 94 95 96 6 9 7 46 97 9 2 5 99 1 1 5 10 7 12 46 X.26 26-8 C 21 20 2J.7 £ 22 20 22'5 22 26 20'3 26 ISO * 3 26 157 *3 24 26 13-3 10-9 ; 26 26 26 26 26 24 8-i 26 5 9 3 '4 o-8 25 26 27 3 5 8-i 2 5 5 53 2 5 5 2 '5 28 28 2 5 +97 25 4 6-8 ~ 9 2 5 43-8 3 ° 25 407 2> 37-6 2 2 5 34H3 25 31-1 25 27-8 33 - 34 25 24-4 ^ 35 25 20-9 25 17-3 25 13-6 j/ 37 39 2 5 2 5 25 2'2 o 4° 24 58*2 * 41 K.24 54*1 Meridian Passage. 7 7 7 7 6 6 6 6 6 6 6 58 54 5 1 7 48 7 45 7 4 2 7 40 7 37 7 34 7 3» 7 28 7 2 3 7 20 7 17 »5 12 10 7 7 7 5 7 2 57 55 5 2 5° 48 6 45 6 43 4' 38 6 36 XII. MARCH, 19 14. t23 MEAN TIME. Sun. Mon. Tues. Wed. Tlmr. Frid. Sat Sun. Mon. Tues. Wed. Sun. Mon. ! Wed. Thur. Frid. 1 2 3 4 5 6 7 8 9 Thur. 12 Frid. 13 Sat. 1 4 Sun. 15 Mon. 16 Tues. 1 7 Wed. 18 Thur. 19 i 20 21 JUPITER. At Greenwich Mean Noon. K. A. Dec 20 +6 3 2 ° 4 6 57 \\ 20 47 50 bi 53 20 48 43 20 49 36 - 20 28 5 1 5* 20 51 20 20 \z l 2 20 53 4 52 5« 10 20 53 55 11 ! 20 54 46 5 20 55 37 5 1 5° 20 20 20 20 20 21 56 27 57 58 17 5 8 57 59 46 49 35 21 123 2 1 2 11 21 2 59 22 23 24 25 26 27 Siit. 28 Sun. 29 Mon. 30 i 31 W...I 32 21 2 I 2 I 2 I 21 21 21 2 I 2 I 21 3 4 6 4 34 5 20 6 6 7 5° 5° 5° 7 53 3« 49 48 48 47 48 46 47 46 45 45 8 23 8 45 45 9 9 53 t 10 36 4 M 21 t 1 20 8 24-6 33 8 21-2 34 33 8 »7"9 , 8 14-6 J 8 ir* 3 7 4 8 "° 7 447 7 4' "4 187 "55 12 3 2-K 6 5S"5 6 505 s 16 47 4 8 7-9 8 4-6 " 8 1-2 34 33 57'9 „ 54-6 ! 5 ' 1 33 J3 33 ja 7 3 8 ' 7 34'9 , 7 3'-6 " 33 7 28-3 7 25*> 7 21-9 J» 3* 3 2 3* 7 9 ' 7 fro 3 3* 3' 6 597 6 3 ' 3" V V Meridian Passage. h 22 22 22 22 2 2 2 2 2 2 2 2 2 2 2 2 20 O 57 54 5' + S 45 42 39 36 33 29 26 23 20 17 14 1 1 8 4 1 5 8 20 55 20 52 20 49 20 45 20 42 20 39 20 36 20 33 SATURN. At Greenwich Mean Noon. R.A. Dec. 4 4° 43 4 4° 5' 4 41 o 4 41 9 4 4i '9 4 4' 2 9 4 41 40 4 4 1 5' 4 42 3 4 42 15 4 42 27 4 42 4° 4 42 54 4 43 7 4 43 22 4 43 36 4 43 5' 4 44 7 4 44 4 44 4 44 22 39 55 1 2 4 45 4 45 3° 4 45 47 4 4 6 5 4 4 6 24 4 4 6 43 22 4 47 4 47 4 47 4 2 4 4« 2 20 : 1 4 4* 2 3 N.20 44-5 20 45-0 20 45-5 20 460 20 466 20 47 - 2 20 477 20 48-3 20 48^9 20 49-5 20 50*2 20 50-8 20 51-4 20 52*1 20 52-8 20 q3"4 20 54-1 20 54-8 20 20 20 55 > 563 >' 'O 20 577 20 584 20 592 2 I 2 I 2 I OO 07 5 21 2 1 2 1 2 1 2 3 ! 38 4'» ff.ti 5*4 Meridian Passage. h m 6 6 6 2 5 5 8 5 55 5 5i 5 47 5 43 5 4° 5 36 5 32 5 28 5 25 5 21 5 »7 5 H 5 10 5 6 5 3 4 59 4 55 4 52 4 4 8 4 44 4 4' 4 37 4 33 4 30 4 26 4 23 4 «9 4 '5 4 '* K e 2 424 APRIL, 1 9 14. 1. AT GREENWICH MEAN NOON. THE SUN. Equation Date. of Time Right Declination. Var. in Semi- diameter. A dd to Var. in Ascension of the Add for hours. Subtract 1 hour. from 1 hour. Mean Sun Apparent Time. (Sidereal Time). 1 / 1 it Ill 8 a h in s m ■ h Wed. 1 N. 4 19-5 0-97 l6 2 4 8-9 075 O 36 0*2 O 99 I Thur. 2 4 42-6 0*96 16 I 3 50-8 0-75 O 39 568 O 197 2 Frid. 3 5 57 0' 96 l6 I 3 3 2 "9 075 43 533 O O 29-6 39"4 3 4 Sat. 4 N. 5 287 0*96 l6 I 3 150 0-74 47 49-9 O 49'3 5 Sun. 5 5 5i' 6 0-95 16 I 2 57"3 0*74 51 46-4 O 59-1 6 Mon. 6 6 14-3 °'95 16 O 2 39-8 0-73 55 43"° I I 9*° 18-9 7 8 Tues. 7 N. 6 37-0 0*94 l6 O 2 22*4 072 59 39'5 I 287 9 Wed. 8 . 6 59-5 0-94 16 O 2 5*2 0*71 1 3 36-1 I 38-6 10 Thur. 9 7 22'0 o- 93 15 59 I 48*2 0*70 1 7 32-6 I I 48-4 58-3 1 1 12 Frid. 10 N. 7 44-3 093 15 59 I 31*5 0*69 1 1 1 29*2 2 8-i 13 Sat. 1 1 8 6-5 0*92 15 59 I 15-0 o-68 1 15 257 2 18-0 14 Sun. 12 8 28-5 0*92 15 59 O 58-8 o'6j 1 19 22-3 2 27-8 15 1 2 377 16 Mon. 1 3 N. 8 50-4 0*91 15 58 O 42-9 o-66 1 23 18-9 2 47 '6 17 Tues. 14 9 I2'2 0*90 15 58 O 27-4 0*64 1 27 154 2 57'4 18 Wed. 15 9 33*8 0*90 15 58 O I2'I C63 I 31 I2'0 3 3 7'3 171 19 20 Thur. 16 N. 9 55-2 0-89 15 58 O 27 o-6i 1 35 8-5 3 27*0 21 Frid. 1 7 10 16-5 o-88 15 57 O 17*2 o'6o 1 39 5"i 3 36-8 22 Sat. 1 8 10 37-6 o-88 15 57 O 31-3 0-58 1 43 i-6 3 3 467 56-6 23 24 Sun. 1 9 N.io 58-6 11 19-3 0*87 o-86 15 57 15 56 45-0 ° 5 8 '3 o" 56 °'54 1 46 58*2 1 50 547 Mon. 20 Tues. 21 Wed. 22 11 39*9 N.i 2 0*3 0*85 0-85 15 56 15 56 1 1 1*1 1 2 3'5 o*53 0-51 1 54 5i'3 1 58 47-9 Add for min utes. 8 0'2 m I Thur. 23 12 20-5 0-84 15 56 1 3 5*4 0-49 2 2 44-4 0-3 0-5 2 Frid. 24 12 40-5 0-83 15 55 1 4 6 '9 0-47 2 6 4 1 - o 3 Sat. 25 N.i 3 0-3 0-82 15 55 1 579 o*45 2 10 37-5 07 o-8 4 5 6 Sun. 26 13 19-9 o*8i 15 55 2 8-5 0-43 2 14 34"i i*o Mon. 27 13 39' 2 o'So 15 55 2 18-5 0*41 2 18 30-6 11 7 Tues. 28 1 N.i 3 58-4 0-79 15 54 2 28*1 0-39 2 22 27'2 1 "3 16 8 9 10 Wed. 29 14 '7"2 0-78 15 5 + 2 37-1 0-37 2 26 237 Thur. 30 1+ 35"9 0-77 15 5+ 2 457 o - 35 2 30 20*3 3'3 20 Frid. 31 N.14 54-3 0*76 15 5+ 2 537 072 2 34 16*8 4'9 6-6 30 40 %mm — 1 8-2 5o 425 n. APRIL, 1 9 14. MEAN TIME. Transit of the First PoiDt of Aries. THE MOON Date. Senii- diameter. j Var. in 1 hour. Hori- zontal Parallax. Var. in 1 hour. Meridian Passage. Age. Upper. Biff. Lower. Diff. Noon. Noon,. Noon. Wed. Thur. Frid. 1 2 3 b 23 23 23 m s 20 0/S l6 I 39 12 1 8*o t // '5 4 15 14 15 26 ON °"5 •'5 55 IO 5 5 47 56 32 «"4 »"7 2"0 h 4 5 6 m 21 '5 I I m 54 56 56 h m l6 48 "7 43 •8 39 m 55 56 55 d 57 67 77 Sat. Sun. Mou. 4 5 6 23 2 3 23 8 22-1 4 262 3°'3 15 40 '5 55 16 10 o-6 o-6 57 23 58 19 59 l6 2'2 2-4 *"3 T / 8 8 7 1 54 >4 53 5 1 19 34 20 28 2 1 19 54 5' 5' 87 97 107 Tues. Wed. Thur. 7 8 9 22 22 22 5 6 34"3 5 2 3 8 "4 48 42-5 16 25 16 36 16 44 0"2 60 8 60 5 1 61 iS 2"0 o'7 9 10 1 1 45 36 27 5 1 5 1 54 22 10 23 1 23 54 5' 53 54 117 127 i37 I Frid, - ■ Sun. 10 11 12 22 22 22 44 466 40 507 $6 54-8 16 46 16 43 «6 35 O'O O" 2 0'4 61 26 61 14 60 44 0" I °'9 i-6 12 13 >4 21 17 18 56 6r 61 * * 48 1 47 59 61 147 "57 167 .Mon. I Wed. 13 14 15 22 22 22 32 58-9 29 3-0 25 7-1 16 22 16 7 15 52 o-6 o-6 '°'7 59 58 59 4 58 6 2" I 2'3 2"4 »5 16 »7 '9 21 20 62 59 55 2 48 3 5° 4 5i 62 61 57 177 1S7 '97 Thur. Frid. it 16 17 18 22 2 2 22 21 1 1*2 ■7 J 5*3 13 194 15 36 15 22 15 10 o-6 °'5 °'S 57 10 56 19 55 35 2 - 2 2 "O <"7 18 '9 '9 15 6 52 51 46 42 5 48 6 41 7 29 53 48 44 1 207 217 1 227 Sun. Mi T 19 20 21 22 22 22 9 23-4 5 *7'5 1 3 1 .■ 15 '4 53 14 48 o- 4 °'3 0' 2 54 59 54 32 54 '3 '"3 1 '0 o*6 20 2 1 2 1 34 '4 53 40 39 39 8 13 8 54 9 34 4' 40 38 237, 247 257! Tl ur. Frid. 22 23 24 2 1 2 1 2 1 57 3 53 +9 43*9 "4 45 '4 14 44 0* i O'O O' 1 54 ' 5 3 57 53 °'3 o - 1 o' 2 2Z 2 3 3 2 1 2 5 3 40 4' 4^ 10 12 10 52 1 1 32 40 40 43 267, 277. 287 Sat. Sun. Moil. 25 26 27 ? 1 2 1 2 1 IS ; 41 521 37 ■ 14 46 1 1 1 1 SI 0' 1 O* 2 O - 2 54 5 51 1 5 1 3 1 0-4 o*6 o-S * O I * 5' 12 15 1 ^ 1 ■3 5" 46 5° 5* o - o ro 20 Tue . Wed. Thur. 28 29 30 2 1 2 1 2 1 34 °'3 30 n 26 7 15 .6 °'3 0-4 54 5'' 55 55 ' 1 "o ' ' ; 1 2 1 1 10 5 5 5 ss '1 1 1 IS '" 33 55 55 54 3-0 40 5-0 Frid. 31 ' 1 22 1 2 • 5 ' °"5 34 • "? 5 17 27 60 426 APRIL, 1914. VL G.M.T. THE SUN, Saturday 25 Equation of Tuesday 28 Equation of R.A.M.S. Dec. Time. R.A.M.S. Dec. Time. h m s / in s h in s O / m s 2 10 37-5 1ST. 13 •3 - 1 57-9 2 22 27-2 N. 13 58 •4 - 2 28-1 2 2 10 57-2 13 1 •9 1 58-8 2 22 46-9 14 •0 2 28-9 4 2 11 16-9 13 3 •6 1 59-7 2 23 6-6 14 1 •5 2 29-6 6 2 11 36-6 13 5 •2 2 0-6 2 23 26-3 14 3 •1 2 30-4 8 2 11 56-4 13 6 •8 2 1-5 2 23 46-1 14 4 •7 2 31-1 10 2 12 16-1 13 8 • 5 2 2-3 2 24 5-8 14 6 • 2 2 31-9 12 2 12 35-8 13 10 •1 2 3-2 2 24 25-5 14 7 •8 2 32-6 14 2 12 55-5 ■ 13 11 •7 2 4-1 2 24 45-2 14 9 •4 2 33-4 16 2 13 15-2 13 13 •4 2 5-0 2 25 4-9 14 10 •9 2 34-1 18 2 13 350 13 15 •0 2 5-9 2 25 24-6 14 12 •5 2 34-9 20 2 13 54-7 13 16 •6 2 6-8 2 25 44-3 14 14 •1 2 35-6 22 2 14 14-4 13 18 •3 2 7-6 2 26 4-0 14 15 •6 2 36-4 Sunday 26 Wednesday 29 2 14 34-1 N. 13 19 •9 - 2 8-5 2 26 23-7 N. 14 17 •2 - 2 37 1 2 2 14 53-8 13 21 •5 2 9-3 2 26 43-4 14 18 •8 2 37-8 4 2 15 13-5 13 23 • 2 2 10-2 2 27 31 14 20 ■3 2 38-6 6 2 15 33-2 13 24 •8 2 11-0 2 27 22-8 14 21 •9 2 39-3 8 2 15 53-0 13 26 •4 2 11-8 2 27 42-6 14 23 ■5 2 40-0 10 2 16 12-7 13 28 •0 2 12-7 2 28 2-3 14 25 •0 2 40-7 12 2 16 32-4 13 29 •6 2 13-5 2 28 22-0 14 26 6 2 41-4 14 2 16 52-1 13 31 •2 2 14-3 2 28 41-7 14 28 2 2 42 1 16 2 17 11-8 13 32 •8 2 15-2 2 29 1-4 14 29 7 2 42-9 18 2 17 31-5 13 34 •4 2 16-0 2 29 21-2 14 31 3 2 43-6 20 2 17 51-2 13 36 •0 2 16-8 2 29 40-9 14 32 8 2 44-3 22 2 18 10-9 13 37 •6 2 17-7 2 30 0-6 14 34 4 2 45-0 Monday 27 Thursday 30 2 18 30-6 X. 13 39 •2 - 2 18-5 2 30 20-3 N. 14 35 9 — 2 45-7 2 2 18 50-3 13 40 •8 2 19-3 2 30 40-0 14 37 4 2 46-4 4 2 19 100 13 42 •4 2 20-1 2 30 59-7 14 39 2 47-0 6 2 19 29-7 13 44 •0 2 20-9 2 31 19-4 14 40 5 2 47-7 8 2 19 49-5 13 45 •6 2 21-7 2 31 39-2 14 42 2 48-4 10 2 20 9-2 13 47 •2 2 22-5 2 31 58-9 14 43 6 2 49-0 12 2 20 28-9 13 48 ■8 2 23-3 2 32 18-6 14 45 1 2 49-7 14 2 20 48-6 13 50 ■4 2 24- 1 2 32 38-3 14 46 6 2 50-4 16 2 21 8-3 13 52 ■0 2 24-9 2 32 58-0 14 48 2 2 51-0 18 2 21 28-1 13 53 ■6 2 25-7 2 33 17-7 14 49 7 2 51-7 20 2 21 47-8 13 55 •2 2 26-5 2 33 37-4 14 51 2 2 52-4 22 2 22 7-5 13 56 8 2 27-3 2 33 57-1 14 52 8 2 53-0 24 2 22 27-2 N. 13 58-4 - 2 28-1 2 34 16-8 N. 14 54-3 2 53-7 The R.A. of Mer. (local Sidereal Time) is four Ld by adding the Right Ascension of the M can Sun to the local Mean 1 'ime. The sij. ras + under Equation of Time denote additive or subtractive to Apparent Tin oe and vice versa to Mean Time. ♦a Aurigse. «0 rionis. nAn ?us. a Can. Min. -a Leonis.' a Ursae Mag. Date. (Capella) ; 2 (Betel ) 1-0-1-4. (Canopu R.A. j s) -1*0. (Procyon) 0'5. URegnlus) VS . (Dubhe) 2-0. R.A. Dec. N. R.A jDec. N. Dec.S. R.A. jDec. N. R.A. Dec. 1 *. R.A. Dec.N. h m li m 1 h in O h rn h in ti 1T1 „ 5 10 45 5 5C I 7 6 22 52 7 34 5 10 3 12 10 58 62 Jai 1. 1 22 1 54' -9 s 32v 5 23'- 6 4-8 38' -8 49-6 26'- 8 48-9 23'-. 2 28-5 12-7 Ap ril 1 20-6 55-0 31- ' J 23-(i 2-7 39 1 49-3 26-7 49-8 23- I 30-7 12-9 Jtu i< 30 20 • 8 54 • 8 31- 1 i' 23-7 1- 1 38-8 48-7 26-8 48-9 23-. 2 28-1 13*1 Sej )t. 28 24-4 54-8 34-( ► 23-8 ::-7 : 38-5 50-4 26-9 49 • 5 23- I 27-8 ]2-6 De 3. 27 26-9 55-0 36-1 23-6 6-3 1 38-8 53-0 26-7 52-2 22- .) 32-2 12-3 427 APPENDIX B. DAILY WEATHER REPORT OF THE METEOROD >( tfCAL OFFICE. CHANGE OF UNITS OF .MEASUREMENTS. Barometric Pressure in Pressure Umits. In their Eighth Report to the Lords Commissioners of His Majesty's Treasury, the Meteorological Committee intimated their intention to use Absolute Units for pressure in the Daily Weather Report of the Meteorological Office from 1st May 1914. The absolute unit of pressure on the Centimetre-Gramme-Second system* is the dyne per square centimetre. As this unit is exceedingly small a practical unit one million times as great has been suggested. This unit, the megadyne per square centimetre, is called a " bar." In the Daily Weather Report the centibar and the millibar, respectively, the hundredth and the thousandth part of the "bar" are adopted as working units. The relation between the millibar and the inch of mercury is given in the tables overleaf. Reasons for the Change. One of tin- principal reasons for this change is that it is a step towards the adoption of a system of units which may become common to all na1 ions. The system was approved by the Meteorological Council in L904 and by tin- Gassiot Committee of the Royal Society in L910. Upon tin initiative of Professor V. Bjerknes, formerly professor at Christiania, and now of t he < reophysica] [nstitul ion at Leipzig, it was used in important publication)- of the Carnegie Institute of Washingtonj and was adopted by the Internationa] Commission for Scientific Aeronautics for the international publication of the results of the investigation of the upper air. Since L907 the system has been used in the Meteorological Office for the upper air, and since I'M l for the data from the Observatories where Centimetre-Gramme-Second units have been used for many in connection with magneti m and electricity. The Weather Bureau of the United States has adopted millibars and absolute tempera tun "ii the Centigrade Scale for the issue of dailj charts of the Northern Hemisphere which began on 1st January, 1914; the Royal Meteorological Society has decided to use millibars for the expression of the series of me normals for the British Me-, which it is now preparing; and • r.irt i • - 1 1 1 .- 1 1 ..i th< < < 1 1 1 ir i .< 1 1, ■ < : im 1 1 , 1 1 ie s. . . .i 1. 1 • .in given in the - ■ Handbook . IU13 i 'In ion. 428 the Meteorological Office has followed the example of the Weather Bureau in using absolute units for the daily maps in the Weekly Weather Report, but its isobars are figured in centibars as they were in the specimen issued with the Eighth Annual Report. The Scientific Appeal. The ground of scientific appeal to all nations to adopt the bar, centibar, and millibar is that these units fall naturally into place as members of the Centimetre-Gramme-Second system of units which has already become universal for Magnetism and Electricity and most branches of Physics. Its principles are therefore well "known. The inch and the millimetre are really units of length, and to estimate the effect of a pressure measured in terms of height of a column of mercury it is necessary to introduce the value of the density of mercury at some particular temperature, and the value of the acceleration due to gravity at a 2>a.rticular place. It is well known that the atmospheric pressure at sea level in Britain varies between 13| and 15^ lbs. weight per square inch. The pound weight per square inch is often used by engineers, but it is not a convenient unit because its value depends upon latitude. The Upper Air. The past fifteen years have witnessed the collection of extensive meteorological observations in the upper air made by means of kites and balloons, from which important results have already been deduced. The absolute system of units is the most convenient for the discussion of the data so collected, and it is being generally adopted for the purpose. . The rapid development of aviation makes it impossible to draw a line between the academic study of the meteorology of the upper air and the practical meteorology of the Daily Weather Report. The use of two systems of units, one for observations made at the surface, and the other for observations taken at higher levels, could only retard progress. Practical Consideration s. It is acknowledged that an accuracy of one thousandth of an inch is not really attainable in practice. For many years the Inspectors of the Meteorological Office have had to be satisfied with agreement within •003 in., and now the National Physical Laboratory has ceased to certify barometers of the Kew pattern to the thousandth of an inch. Conse- quently with an instrument graduated to -001 in., observers are being asked to read to an accuracy which is acknowledged to be unattainable. On the other hand an accuracy of the hundredth of an inch is not good enough for scientific purposes. The practical degree of precision for a mercury barometer of the Kew type is one-tenth of a millibar. Graduation in centibars and millibars, with a simple vernier scale for estimating to tenths of a millibar, thus brings the demand for accuracy made upon the observer into harmony with that actually attainable. The new graduation does away with the complications of the conventional vernier scale in use on barometers graduated in inches, and consequently the risk of errors of observation is reduced. 429 The Percentage Barometer. Another advantage is that the Bar, or Centimetre-Gramme-Second atmosphere, differs but little from the standard atmosphere. The equivalent of the adopted normal value at sea level of 29-92 mercury inches is 101*32 centibars, or 1013-2 millibars. The lowest barometer value ever observed for Bea level in the British Isles is 925-5 millibar-. the equivalent of 27-33 inches. This value was recorded at Ochtertyre on January 26th, 1884. The highest value is 1053-5 millibars, the equivalent of 31 * 11 mercury inches. It was recorded at Aberdeen on January 31st, L902. A reading of 100 centibars, or 1.000 millibars, is equivalent to 29* •">;} mercury inches. It will be remembered that the word " change ' i- placed opposite the sea-level reading 29-5 in the conventional de- scriptions engraved on dial barometers. Thus in a barometer graduated in centibars the reading 100 would occupy the position conventionally marked " change." Practical Cour.se to be pursued. It is evidently impossible at one operation to change all the barometers in use in the various services, and even in the most favourable circum- stances there must be tor many observers a time when the readings are taken on one scale, and the results quoted or published in another. Tables of equivalents arc given herewith for making the necessary conversion. The barometers issued by the Meteorological Office will be graduated in both scales.* Uaim'.m.l Data in Millimetres. A- a fin thci' step in ilic direction of international uniformity all rainfall data will be published in the Daily Weather Report in millimetres instead of inches. The occasion for making the change is that modifies lions are being introduced into the telegraphic code used for t he exchange of meteorological information in Europe. The reading of rainfall in this country has been carried to hundredths) sometimes to thousandths of an inch, but the readings t<» the higher degree of accuracy have seldom anj practical meaning. The readings on the metric system are carried to ni millimetre. 0*004 inch, which represents satisfactorily the highest degree of accuracy. The ramie i- rrom •<»! to ::. t. or even more inches in exceptional circumstances, tor ;i i|,i\ 'g i. mi. The telegraphic code hitherto in use ha- made proi ision for- reporting amounts up to in inches, though the large majority ol the readings are under 2 inches. The code now to be introduced makes provision for reporting amount- up to 100 millimetres or i inches. \ one inch i approximately equivalent to 25 millimetres the con ion from millimetre to inches, or vict versd, may be made with * It should I"- borne in mind thai the inch ncule is graduated !<■ be correct I- , tin- millibar cale ;»t the temperature "t the to ./mi' p. .mi. i'.'J I. When liotl ature \\»- relation between them is that shown in tin- ci.n \ i rsion tabli corrected bj the ubtraction ol 0*3 millibar, tin- graduation 28*0 incl rec with the graduation 048 I or R47-9 millibai 430 sufficient accuracy for most purposes by multiplying or dividing by 4 and appropriately shifting the decimal point. Tables of conversion are given herewith. Wind Velocities in Metres per Second. Wind force will be specified on the Beaufort scale. Occasional reports are received from anemometer stations regarding the extreme wind velocities attained in gales. These data are published on the front page of the report. The unit of wind velocity used in such cases will be the metre per second. Tables for converting velocities from miles per hour to metres per second, or vice versa, are given below. Meteorological Office, London, S.W., W. N. SHAW, April, 1914. Director. 431 CONVERSION TABLES. Pressure Values. Equivalents in Millibars of inches of Mercury at :>2 and Latitude 45°. Mi r eury Inches. 00 01 02 03 04 05 06 07 08 •Millibars. ■09 _ . 27 27 27 28 28 28 28 28 28 28 28 28 28 29 29 29 29 29 29 29 29 30 30 30 30 30 39 :ki 30 30 914- 91 7 • 921- 924- 927- 931-2 934-6 938-0 941-4 944-8 948' 951- 954- 958- 961' 1032 1036 1039 1043 1046 965 968-5 971-9 975-3 978-6 982- 988- 992- 995- . > • I 914' 918' 921- 924- 928- 931-6 935-0 938-3 941-7 945- 1 948- 951 ■ 955- 958- 962- 965-4 968-8 972- _ 975-6 979-0 982-4 ■ 989- I 992-5 995-9 5 899- 6 1002-4 7 1005-1 - 1009- I g 1012 ii In] i 1019-3 •> 1022-7 3 1026- i i 1029- i 999-3 L 002-7 L006- I lull's 1016 KU9 1029- 1033- L036- 1039- 1043- 1046- 915 918 92] 925 928 931 935 938 942 945 948 952 955 959 962 965 969 '.172 '.•7.7 979 982 986 989 992 996 099 1003 L006 1009 L013 1016 1020 1023 1026 1030 L033 1036 1040 1043 1047 915-3 915-7 916- 4 918-7 919-0 919 8 922-1 922-4 922- 1 925-5 925-8 926- 5 928-9 929-2 929- 9 932-3 932-6 932- 3 935-6 H36-0 936- i 939 -0 939-4 939- 1 942-4 942-8 943- 5 945-8 946- 1 946- 8 949-2 949-5 949- o 952-6 9.72 -9 953- ii 956-0 956-3 956- 959-3 959-7 '.u,ii- 4 962-7 9113- 1 963- 8 966-1 966-6 966- •> 969-5 969-8 970- 6 972-9 973-2 973- 9 976-3 976-6 977- 3 979-7 980-0 980- _ lis:;- ii 983-4 983- 1 986- i 986- 8 987- 6 989-8 990-2 990- '■' 993-2 993-5 993 3 996-6 996-9 997- 8 I 000-0 L000- 3 I in in- n li hi:; i 1003- 7 Kim- l L00I L007- 1 1007- 8 loin- I 1010 5 mi" 2 1013 6 1013-9 l"l i ii 1016 g 1017-3 1017- ii 1020-3 1020-6 1021- 3 IU23-7 1024 1024- < 1(127- 1 1027- i 1(127- I 1030-5 1 (Kid- 8 L031- . • In:; 1034 ' 1034' g i" 103 1(137- :i HUH- i, mi i i. Hill / 104 l " In) I :; l"l 1 I 104" i |m| , , l'.| - g 3 7 1 5 9 ■ > ii l I (i (i 3 916-3 919-7 923- 1 926-5 929-9 933-3 936-7 940-0 943-4 946-8 950- 953- 9.77 ■ 960' 963' 967- 970- 973- 977- 997-9 998-3 998 ii 100] -3 1001-7 1002 ii 1004 ■ 7 1005- I L005 4 Kins- I 1008- i 1008 s 1011-5 Mil 1 >8 1012 ■ ) 1014-9 1015-2 1016 li 1018-3 1018-8 1018 9 1021-7 1022-0 1022 :; 1025-0 1025- i 1025 7 1028-8 1029 1 |H31 >8 1032-2 1082 ■ ll 13.7 -2 108 ■ 1035 'i m:;- Q 1038-9 1039 :; [04 ' 1042-3 104 ' H I'M., I mi . 1040 II 1048-7 I'M 1040 1 Milli- bars. 432 Equivalents in Mercury Inches at 32° and Latitude 45 c of Millibars. 910 26-87 920 27-17 930 27-46 940 27-76 950 28-05 960 28-35 970 28-65 980 28-94 990 29-24 1000 29-53 1010 29-83 1020 30-12 1030 30-42 1 040 30-71 1050 31-01 26-90 26-93 27-20 27-23 27-49 27-52 27-79 28-08 28-38 28-67 28-97 29-26 29-56 29-86 30-15 30-45 30-74 31-04 27-82 28-11 28-41 28-70 29-00 29-29 29-59 29-89 30-18 30-48 30-77 31-07 Mercury Inches. 26-96 26-99 27-02 27-26 27-29 27-32 27-55 27-58 27-61 27-85 27-88 27-91 28-14 28-17 28-20 1 28-44 28-47 28-50 28-73 28-76 28-79 ' 1 29-03 29-06 29-09 29-32 29-35 29-38 ; 29-62 29-65 29-68 29-92 29-94 29-97 30-21 30-24 30-27 | ! 30-51 30-53 30-56 : 1 30- SO 30-83 30-86 | 31-10 3113 31-16 , 27-05 27-35 27-64 27-08 27-38- 27-67 27-97 28-26 28- 29- 12 29-15 29-41 29-71 30-00 30-30 30-59 30-89 31-18 29-44 29-74 30-03 30-33 30-62 30-92 31-21 27-11 27-41 27-70 28-00 28-29 28-53 28-56 28-59 28-85 28-88 29-18 29-47 29-77 30-06 30-36 30-65 30-95 3 1 • 24 27-14 27 -44 27-73 28-03 28-32 28-62 28-91 29-21 29-50 29-80 30-09 30-39 30-68 30-98 31-27 Differences for tenths of a millibar nib. 1 •2 •3 •4 •5 •6 •7 •8 •9 in. •003 •006 •009 •012 •015 •018 •021 •024 •027 Rain fall Val u es . Equivalents in Millimetres of Inches. 1 inch = 25*4 Millimetres. •00 •01 •02 03 •04 •05 06 •07 •08 •09 Inches. i Millim stres. 00 0-0 0-3 0-5 0-8 l-ii 1-3 1-5 1-8 2-0 2-3 •10 2-5 2-8 3-1 3-3 3-6 3-8 4-1 4-3 4-6 4-8 •20 5-1 5-3 5-6 5-8 6- 1 6-4 ()•() 6-9 7-1 7-4 • 30 7-6 7-9 8-1 8-4 8 • (i 8-9 9-1 9-4 9-7 9-9 •40 10-2 10-4 10-7 10-9 11-2 11-4 11-7 11-9 12-2 12-5 •50 12-7 13-0 13-2 13-5 13-7 14-0 14-2 11-5 14-7 15-0 •60 15-2 15-5 15-8 16-0 10-3 16-5 16-8 17-0 17-3 17-5 •70 17-8 18-0 18-3 18-5 18-8 19-1 19-3 1 19-6 19-8 20- 1 •80 20-3 20-6 20-8 211 21-3 21-6 21-8 2 2 • | 22-4 22-6 •90 22-9 23-1 23-4 23-6 23-9 24-1 24-4 24-6 24-9 25-2 433 Equivalents in Inches of Millimetres. 1 » . 2 3 4 5 a 7 8 . Milli- metres. Inches. 0-00 0-04 0-08 0-12 0-16 0-20 0-24 0-28 0-32 0-35 10 0-30 0-43 0-47 0-51 0-55 0-59 0-63 0-67 0-71 0-75 20 0-70 0-83 0-87 0-91 0-95 0-98 1-02 1-06 1-10 114 30 1- IS 1 • 2° 1-26 1-30 1-34 1-38 1-42 1-46 1-50 1-54 40 1-58 1-61 1-65 1-69 1-73 1-77 1-81 1-85 1-89 1-93 50 1-97 2-01 2-05 2-09 2-13 2-17 2- 21 2-24 2-28 2-32 60 2-36 2-42 2-44 2-48 2-52 2-56 2-60 2-64 2-68 2-72 70 2-76 2 • 80 2-84 2-87 2-91 2-95 2-99 3-03 3-07 3-11 80 3-15 3-19 3-23 3-27 3-31 3-35 3-39 3-43 3-47 3-50 90 3 • 54 3-58 3-62 3-66 3-70 3-74 3-78 3-82 3-86 3-90 Wind Velocity Equivalents of Miles-per-Hour in Metres-per-Second. Miles per Hour. Metres per Second. 0-0 0-4 „.„ ,.:« 1-8 2-2 2-7 31 3-6 4-0 JO 1 ■ .-. Mi 5< t ;, • S 6-3 6-7 7-2 7-6 8-0 8-5 20 S-'l 9-4 9-8 10-3 10-7 11-2 11-6 12-1 12-5 13-0 3'i 13-4 L3-9 14-3 14-8 I.V2 15*6 16-1 16- 5 17-0 17-4 in 17-9 18-3 18-8 19-2 L9-7 20-1 20- G 21-0 21-5 21-9 .-.(i 22« 1 22-8 23-2 23-7 24-1 24-G 2f>-0 15-5 2.-. -9 2(1-1 60 26- • 27-3 27-7 28-2 28- (i 29-1 29-5 30-0 30-4 30- S 7ii 31-3 31-7 3 2 • 2 32-6 33-1 33-5 34-0 34 ■ 1 34-9 35-3 - ■ ::.-,• 8 36-2 3C.- 7 37-1 37-6 38-0 38-4 38-9 39-3 39- S 90 M)«2 H>-7 411 41 li 42- 42- 5 42-9 43-4 43-8 1 1 ■ 3 Equivalents of .Mrtn-s-per-Secoii'l in Mil<-> p< r-Hour. M< i ■ r rid. I II' .ur. 9 1 I • 2 I:: 1 I.V7 IT-'.! 2(1- 1 33 (i ■ 8 38*0 10-3 1 2 • ;. - 2 60- i 82*6 Ill '1 v,, ' B . I! S7-L' I'M, , 102*9 in.,- I 1(17 1 l(l!li, 434 ■.loqumvj; ^.iojriT?0{j PQ i— i P 0? O i-h 01 10 to 03 0) © O O $ 3 © a o Jr? © ft © +3 co P © -p rd 82 4.-JtlOJJ .I8d S8l}J\[ UT fc» 03 -P oi O * « ft w 03 © a: d 03 © PQ a _o 03 o ?s '© © ft CO S3 p © a © a -p cfi > © . 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It is important that all angles should be observed between Objects situated at the same level, and the angles should be taken iii the horizontal plane. The error due to objects not being at the Bame Level is greatest when the observed angle is small. When making use of B -mall angle and any doubt to the objects being .it the same level, it is advisable to observe the angle from each objecl to a third, the latter being so situated as to make a large angle with each of the other objects. The required angle will he the difference between the two audi observed. For example, an observer at 0, Pig I. -I he- to measure the angle AOB The angles AOC and BOC are measured, C being .i distant bul well . defined mountain peak and t he angle [OB AOC BOC. , 8108 438 When selecting the charted objects to which the angles are to be observed the following points should be considered. The charted object should be as nearly as possible at the same distance from the observer as the object to be fixed. The angle should be a horizontal one and should be as small as possible. Another method is to observe from one point, the position of which is fixed on the chart, the angle between the object to be fixed and the nearest suitable charted object. A round of angles having been observed at the object it is desired to fix and plotted on a piece of tracing paper, the line corresponding to the first angle observed should be laid off, and then the position should be fixed by means of the angles on the tracing paper ; the fix should fall exactly on the fine. Compass bearings should never be used in place of sextant angles for corrections or additions to a chart. In laying off angles, if great accuracy is required, the method of chords should be adopted. 3. To Lay off an Angle by Means of Chords. —It is required to find the length of a chord which subtends an angle 6 at the centre of a circle of radius R. In Fig. 2 let AOB be d, then AB is the chord whose length is required. From drop a perpendicular OC on to AB. Then OC bisects the angle AOB, n and, therefore, the angle AOG = . Now AB = 2AC = 2R sin f . 2 Fig. 2. Referring to Fig. 3. In order to lay off at the point a line at an angle 6 to the fine OD, on OD select a point A such that OA = R, the radius selected. With centre and radius OA describe the arc of a circle. Having calculated the length of the chord from the above Fig. 3. formula, with centre A and the chord as radius, describe the arc of a circle intersecting the previous circle in B. Join OB. Then the angle BOA = 6. The largest radius which can be used should be sleeted, and the operation should be repeated on DO produced as shown in the figure, not necessarily with the same radius. The three points B' , 0, and B should all he in a straight line, which will be a check on the accuracy of the work. 439 4. The Plotting Sheet. — When it is thought t hat the published chart is inaccurate, either in the soundings or in the coast line, and it is determined to re-examine a particular area, the first consideration should be the method to be adopted in plotting the work. When the existing chart is on a sufficiently large scale and the various conspicuous objects on shore are well charted, the operation is very much simplified. In such a case, having examined the chart and noted all the conspicuous objects, a tracing should be made of those portions of the chart which it is assumed are correct, talcing care that all the conspicuous marks are shown. This tracing is then laid on a sheet of paper, and all the conspicuous marks are pricked through. As soon as the tracing paper ha< been removed a circle should be drawn on the paper round each of these points and their names written against them. Consideration must now be given as to whether there are sufficient marks on the paper, and whether their relative positions are such as to enable good fixes (Manual of Navigation, § 65) to be obtained from all ] tarts of the area it is proposed to examine. Should there not be sufficient, other conspicuous objects must be fixed as explained in § 2. If insufficient objects exist, it becomes necessary to erect temporary marks and to fix their positions. When making such temporary marks whitewash will be found most useful. A patch of whitewash on a Mall or on the sloping surface of a rock, or a small whitewashed cairn of stones, make excellent and conspicuous marks. The size such a mark should be made depends on the distance at which it will be used, and it i- better to err on the side of making a mark too large rather than too small. Another type of mark which is frequently useful is a small flagstaff with a particoloured flag, one of the colours being white. When the chart is not on a sufficiently large scale we proceed as follows : — Having noted the conspicuous marks and put up temporary marks as described above, each should be visited. The angles, which are subtended between one distant but well-defined mark (not necessarily one of those selected) and each of the others, should be carefully observed with a sextant. The observations should be written down as shown below, the angles being written to the right or left of the distant mark a i cording to the direction in which they were seen to be situated. Post 40° 27' Sharp 50° 45' Square. Wood 78 40 (a distanl 52 14 Red. Black 99 <>:} peak). 76 22 Rock. Hal 118 :57 LIS .",(1 Islet. Tower 120 02 This method not only facilitates calculating the angle between any two objects, but prevents the cumulative effects of possible uncorrected errors of the sextant, such as it' Post were reflected to Wood. Wood to Black, Black to Flat, &c. If possible the round of angles should be completed, and, as 120 is about the limit of angular measurement of any sextant, it be necessary to elect another distant but well-defined object and repeat the process, taking care to connect this object with two of the more distant objects of the first series, thus :— Rock 61 22' Blag 22 L0' Mud. 67 I- Tlee. 72 Is Sand 103 16 Towel. P I 2 440 Then, as a check on the correctness of the whole operation, we have Tower 120° 02' Sharp 75° 22' Rock 61°22' Flag 103° 16' Tower, the sum of which angles should equal 360°, or be within a few minutes of it, provided the correct index error has been applied to each angle and the side error taken out. It is now necessary to place the various marks on the sheet of paper, which is called the plotting sheet, in their correct positions relatively to one another. To do this we select two points, such as A and B, Fig. 4, as far apart as possible and so situated that two other points C and D, which are as near the limits of the survey as possible, can be plotted from them by the intersection, at a fairly large angle (60° to 120°), of the two lines which result from plotting the observed angles at A and B. Draw a straight pencil line on the plotting sheet to represent AB, and, with a needle, prick through the points A and B at the requisite distance apart depending on the scale on which it is required to make the survey. As a general rule it will be found convenient to make the scale of the survey an exact number of times that of the published chart as this greatly simplifies the comparison of one with the other. From A and B lay off the angles to C and D and then provisionally prick through either C or D, for choice that one at which the lines intersect most nearly at right angles. In this case we have pricked through D ; from D lay off a line DC at the observed angle to DA. If now all three lines to C intersect at a point, then both C and D can be pricked through Fig. 4. permanently and from the four points A, B, C, and D, other points can be plotted. If the three lines through C do not intersect exactly, the work should be erased and the operation repeated. The accuracy of the observed angles may be checked by taking the sum of the three angles of each triangle, which should not differ from 180° by more than a few minutes. The remaining points of the survey should now be plotted, each being fixed by the intersection of at least three lines the angles between which are not small. When satisfied with the position of each point it should be pricked through. " Cocked hats " are not admissible because if errors are once accepted they tend to accumulate and will lead to Constant trouble. Finally all prick holes should be tinged round in ink. It may very well happen that the positions of some of the points depend solely on bad or doubtful fixes, and one is not justified in pricking them through ; for example, they may have at most only two fines intersecting at them, or only two intersecting at a large angle, due to the unavoidable fact that these marks are not visible from a sufficient number of points. In such a case it may be necessary to anchor a boat in a position which can be fixed by sextant angles making use of the -Ul points already plotted. An angle may then be taken from the boat to verify the position of the object. This method is frequently made use of for fixing points when there is no difficulty in fixing the boat. The final scale used is obtained by measuring the distance between tu.» points which can be identified on the chart, and as far apart as possible, and comparing it with the distance as shown on the chart. The true bearing of one of these points from the other should be taken from the chart and a line, to represent a meridian, should be drawn through one of the points on the plotting sheet, at the correct angle to the line joining them. In the preceding method the scale of the survey has been obtained from the existing chart, and this in most cases wall be sufficiently accurate. In some cases, however, the scale cannot be obtained by this method, for it may not be possible to identify any points on the chart, or the chart may be altogether erroneous, or it may be on too small a scale to enable the distance to be measured satisfactorily. It is there- fore sometimes necessary actually to measure a distance in order to obtain the scale of the survey. This may be done with sufficient accuracy by quite simple methods, provided the survey does not embrace a very large area. Let S, Fig. 5, be the position of the ship at anchor, A and B two points selected so that the angles SAB and ABS are small. The height In:. r>. in feet from the masthead to the waterline having been accurately measured, observers are sent to A and li with sextants. A Hag is hoisted ;ii themasi head of the ship and at a pre-arranged time is dipped smartly, at which signal tin- observers a1 .1 and B observe the masthead angle and immediately afterwards the horizontal angles SAB and ABS. It' idle two observers should be at both 1 and B as then both the vertical and horizontal angles can be observed simultaneously. The observations mould be repeated at regular interval often as oon adored necessary, but three tinn usually sufficient. From each separate series of observations, AS and />'' s ' are first calculated from the observed masthead angle8, whence AB .IN e,, BA8 B& co IBS. Finally the mean is taken of the several values of AB, and thi distance, represented by the length of AB in inche on the plotting sheet, affords 442 a means of obtaining the scale of the survey, provided A and B are sufficiently far apart to be near the limits of the survey. If, however, the points A and B are not near or beyond the limits of the area to be surveyed, AB should be connected by suitable triangles with two points which are so situated, when the distance apart of these may be calculated by plane trigonometry. In the method described above, as the angles are all observed simultaneously or nearly so, the movement of the ship as she swings to her anchor makes no practical difference in the final result ; and in fact this method may be used even if the ship is under way, provided that her way is stopped for the time being, and that there are two observers at both A and B to ensure that all angles are observed simul- taneously. Instead of observing the masthead angles at A and B the distances of A and B from the ship may be observed by range-finder, one distance being observed after the other as quickly as possible when the flag dips, and the angles SAB and SB A being observed at the same time. This method does not give very accurate results and should only be used if A and B are suitable objects for range-finding ; the method by means of masthead angles should generally be used. It is as well to mention here that the range-finder should not be used for general purposes. The main principle of surveying is that the positions of the several points of the survey should be correct relatively to one another, and the positions of the soundings should be correct relatively to those of the points. This result can only be obtained by fixing both points and soundings by angles. A single distance obtained by range-finder may or may not be quite accurate, but any such inaccuracy in this case affects the scale of the whole survey, a fact which is of minor importance so long as the points of the survey are relatively correct. ~ Use may be made of the ship for fixing points when they cannot be fixed in the ordinary way. For example, the ship is at anchor at S, Fig. 6, and a survey of the anchorage is required. The coast is nearly straight, and A, B, and C are three of the principal points that it is required to fix relatively to each other. Observers having been stationed at A, B, and C and using a system of signals similar to that described above, simultaneous angles are observed as follows : — The observer at A measures the angle BAS, the observer at B measures the angle ABS, and the observer at C measures the angle BCS, the three angles being observed simultaneously ; the observations should be repeated three times. The observers at A and C also measure the angles BAC and ACB respectively. The whole angle ABC is also required, but being too large for the observer at B to measure directly, he can wait until either of the other observers joins him. The two observers then measure simultaneously the two angles ABS and SBC, the sum of which is the Fig. 6. 443 angle ABC, this observation being repeated two or three times and the mean taken ; or the observer at B may be able to make use of a distant fixed objeet in the direction of D for example, and measure the two angles ABD and DBC \ or D may be a floating object provided it is sufficiently far off not to move appreciably whilst the two angles are being observed. It would be advisable in the latter ease to repeal the observation of the first angle, observing the angles thus ABD, DBC . ABD and accepting the mean value of ABD. In the event of it being impossible to find a suitable object, some mark on board the ship should selected a- the centre object, the first angle being repeated as before, the whole process repeated several times, and the mean accepted as the correct result. Finally with the angle ABC and the observed value of the angle ABS in. each case, the corresponding value of the angle SBC is obtained. Now being given the angles at A and B in the triangle ABS, the angle ASB may be found ; given the angles at B and C in the triangle SB( '. the angle BSC may be found ; then BC = SB sin BSC cosec BCS SB = AB sin BAS cosec SAB or BC = AB sin BAS cosec ASB sin BSC cosec BCS. AB should now be assumed as equal to any convenient number, say 1,000, and the corresponding value of BC may be found. This process should be repeated three times, using the angles observed ;n each signal, and from the results the mean value of BC may be obtained relatively to AB. Now in the triangle ABC drop a perpendicular from B on to AC, ihen AC = 1,000 cos BAC + BC cos ACB. We now have the relative values of AB, BC, and AC, and if the actual value of AC be found either by the previous method of masthead angles or taken from the chart, B can be plotted with respect to A and C. The position of the ship S with regard to A, B, and C is important. It is evident that to obtain the most accurate results the length of SB should not be much less than that of AB or BC. Theoretically the besl position for S with respect to A, B, and C is such that the angle ABS = SBC, and the angle ASC = 180° — ABS. Naturally the ship cannol always be anchored in the most suitable position, but a boat can be wry well used in place of t he ship,, the same process of signalling by dipping a Hag being carried oul . Any number of points, such as A, 11. C, I>. E, &C, Pig. 7. can be relatively connected in the same way by moving the ship or boat success- ively t<> posil iona S v 8 t , 8 Z &c I'ii.. With ;i straight length "I coast tin- maj "ton be the onlj method available, and with care it i perfectlj accurate provided the positions hi ,s' 6 fce., are suitably elected and the points A,B,C, D, 2?, &c, are fairly equally separated, h is no1 nec< arj for the ship or boat to 444 be actually at anchor provided she is nearly stationary, and that the observations are made simultaneously at the three points. In the preceding methods it has been suggested that the angle at the ship should be calculated and not directly observed. This will be found to be the most convenient method and the least liable to introduce errors. 5. The Field Board. — In order to preserve the plotting sheet from harm, one or more copies of it are made on sheets of paper which have been previously pasted on to drawing-boards. Such a board, on which the various marks are shown and on which all subsequent observations may be plotted at the time of observation, is called a field board. To transfer the various fixed marks from the plotting sheet to the field board, the former is laid over the latter, and is partially covered with weights to keep it quite flat; the various points should then be pricked through, after which they should be ringed round and their names written against them. The area it is proposed to examine should be roughly ringed in pencil, and it is convenient to draw a scale of yards on the board. 6. Sounding. — The value ol a chart depends principally on the accuracy of the soundings, and as errors in the depths are not so easily detected as other errors, it is essential that special pains should be taken to obtain and plot the depths of the water accurately. As it is impossible to take a sounding at every point of the bottom it is necessary to adopt some definite plan ; this consists of taking the soundings at close intervals along fines, a system of lines being so arranged that each, as far as possible, will be at right angles to the probable direction of the various fathom lines which must be assumed to be parallel to the coast line. Sounding consists not merely in obtaining sufficient soundings to fill in the blank spaces on the chart, but in so thoroughly searching the whole area under examination with the lead line as to make sure that the least depths have everywhere been satisfactorily and accurately ascertained. Unless the least depths are so ascertained actual rocks or shoals may be missed. In the case of plans of new anchorages or channels, the resulting chart, through giving a false sense of security and so inducing ships to use it that would otherwise have avoided the locality, may prove to be an even worse danger than having no chart at all. The only method to ensure that the least depths are not missed is close sounding, and a further rigorous examination of the smallest indi- cations of an irregularity in the bottom. By close sounding is meant not only that successive casts of the lead are obtained close together when running along each fine, but also that the lines of soundings them- selves are close together. How close, in order to ensure that irregularities are not missed, must to some extent depend on the depth and on the nature of the bottom. Off flat sandy shores a more evenly sloping bottom may be expected than off irregular or rocky shores, and therefore the fines of soundings may be spaced further apart in the former case than in the latter, with equal confidence of detecting irregularities. As a general rule lines of soundings should be run as close together as the scale of the survey permits. About five lines to the inch is as close as they can be plotted on paper without overcrowding. Therefore the scale (§ 4) should be sufficiently large to ensure that, with the lines at this distance apart on the paper, they may be sufficiently close in reality for a thorough examination according to the probable nature of the bottom. 44o When the depths are over lo fathoms the distance between the lines of soundings may be increased. With regard to the distance apart of successive soundings, the speed of the boat should be regulated so that sounding may be continuous without stopping, as long as the water is shallow enough to enable this to be done ; as the water deepens, the way of the boat should be checked as soon as the leadsman is ready, in order that he may get an up-and-down sounding. When necessary the way should be stopped altogether. In shallow water many more soundings will generally be obtained and entered in the sounding book than can be legibly plotted, and a selection will have to be made, care being taken always to include the shallower casts. It is impossible to plot too many soundings on the field board provided they are legible, and none should be eliminated with the object of improving the appearance of the chart, this being the duty of those in the Hydrographic Department who prepare the w r ork for the engraver. As stated above, the directions of the lines of soundings should, as a rule, be at right angles to the coast line. Points of land or reefs are often prolonged under the water by a narrow shoal ridge or by isolated dangers : radiating Hues should be run round such points and should be unusually close together, and be further supplemented by cross lines to ensure that no narrow tongue or ridge is missed. In particular, all rocky points which are likely to be rounded closely by a ship should receive such close examination. Every portion of the work, as soon as the soundings have been reduced (App. C, § 8) and plotted, should be critically examined to see what irregularities, or indications of such, have so far been revealed. All suspicious areas, or individual soundings which differ considerably from those in the vicinity, should be marked for further examination by circling them with a blue pencil line. As a general rule suspicion should be aroused if the soundings decrease when proceeding from the shore, or if the soundings in any direction decrease and then increase again, both of which conditions indicate a rise of the bottom; all abnormal or sudden changes in the depths require explanation. Having marked all suspicious spots, these must be closely examined by ranning short lines in bet ween the previous one-, and others at right angles to them ; should a .shoal cast be obtained a buoy should be immediately dropped, and a minute examination oarried oul round it to obtain the leasl depth. A barricoe with a line and sinker should be kept ready for this purpose. The buoy may be "-tarred nmud " by ranning lines of soundings radiating from it as centre, or the an a in the vicinity of it' maj be slowly drifted over by the boat, the leadsman holding the leadline and Literally feeling every inch of the bottom m order to detect the summil of the obstruction. Alter having dropped the buoy and fixed it. Further fixing ,iilv nece jarj on obtaining h shoaler cast, and only the shoalest sound] re required to be inked in [see Fig. 8). It must be home in mind that, however closely a spot ma\ appear mii paper to have keen sounded, ye1 the actual sounding may he quite t u enough apart for a rock to exit i undetected. < >n a Bcale of sis inches to the mile a numeral figure occupies a space of nearly 26 yards, while the summil of a pinnacle rock may be onlj a loot or two in diameter. When lounding, a -harp look out must be kept for any appearance of discoloured watol which may indicate the presence of a shoal, ('oral head- in particular may often he detected by the eye, and even in turbid 446 waters, given calm weather and a tideway, rocks may often be detected by a ripple at the surface, particularly when the observer is at a consider- able height. With a muddy bottom a deeper sounding than usual is often an indication of a pinnacle rock, owing to the scour round the base of the rock causing a depression. It is scarcely necessary to say that accuracy is essential ; lead lines should be marked when wet, and the marks invariably tested against measured distances immediately after returning on board. If an error is found to exist, the soundings in the sounding book must be amended accordingly, remembering that if the line is too long the soundings which have been recorded will be.correspondingly too shoal, and vice versa. The leadsman must be constantly watched to see that he calls the sound- ings correctly, and also that his line is invariably up and down. If there is any doubt as to the accuracy of a particular sounding called, the boat should be stopped and the matter cleared up on the spot; a false shoal sounding recorded may otherwise cause an enormous waste of time and trouble when subsequently attempting to verify it. The marking usually adopted for lead lines is not sufficient for survey- ing purposes, and additional marks are required. The system of marking lead lines as adopted in H.M. surveying vessels is shown in Fig. 9, and may be followed with advantage. 7. Boat Sounding. — The lines of soundings it is decided to run should be ruled lightly on the field board, and the boat taken as near as possible to the end of a line where work is to be commenced. The position of the boat should be plotted by a station pointer fix and the boat moved until in the desired position, which should be maintained by dropping the lead on the bottom and keeping the boat vertically over it. The direction of the line of soundings is then found as follows : — Z/>7

c//s7 43 44 45 46 47 ~* *$¥~ ZT ~5~ IT 42 4-1 40 39 38 n ~T "^ 75 ~7t~ 3'4 34- 35 36 37 TT <^ ~7T IT ~f~ 32 31 30 29 2a_ ^. ~r wv ~^>~ ~75 23 |4 25 26 27 22 21 20 19 1 9 7S~ ( ~7lk ~7T ~7^~ "7T 7 13 I* 15 16 IJ ~i zr ~^w ~ir ~iy ir ~z~ ~r ~m~ 12 H 10 9 B i — a — #" a — t i a s i~ a a r~ ~ar /.'/.. m fimu-ki-ii tu i ahovt ■) to fut »••■ "i cudfiitum one kruri i ,,.-., it ..1 .it . ad Sf'fi-t ofeaeh faOiartt , fnr n HuffYcirrU. length of line from tht lead wo as to ensure that at toast 'Jt>fi-4-i (reduced may be- measured ■<( high water spring Sa.in.i, springs r-i.ve 'J~ (.-. I Zl*40 >.;/,./ f li ,■<.■/,,,; h ••./,■ h. ./. 60 /f the boat should be fixed at every few soundings, a check angle being taken occasionally and, if possible, at the extremities of each line. The fixes should be plotted and numbered consecutively, and the nature of the bottom noted at every fix. The entries are made in a book, called the sounding book, as shown below : — Xo. of Fix. Time. Fix. Sounding at Fix. 1 H. M. 10 20 A.M. * Beacon 38° 13' Pier 62° 20' Mill - „ 41° 30' Bat - 71—7 — 6—6—5^. in. 2 10 25 a.m. Beacon 42° 10' Pier 65° 16' Mill - 28 — 28 — 27 — 26 — 26. 30 ft, r Accuracy of fixing is equal in importance to accuracy of sounding : inaccuracy usually results not so much from actual errors in the observa- tions as from making use of badly placed objects. When sounding it is a waste of time to read off the sextant to fractions of a minute of arc The nearest 5 minutes of arc is a sufficient degree of accuracy provided the objects used are well selected, in which case an error of this amount should never appreciably alter the position of the fix. Two officers should be in each boat in order that the two angles of the fix may be observed simultaneously ; one officer should enter the angles and soundings in the sounding book and plot the fixes as ob- tained, while the other " takes charge," watches the leadsman, &c. The larger the scale of the ', by observation - - 261 True, from Mercator's chart 307 Belat .... - 193 Below pole - - 125 Bench mark - - 158 Bergs .... - 221 Beaufort's scale - 188 Brazil current - 213 Breakers, Sound of - 179 British Islands : Tidal streams round - - 251 Tides of - . 233 Weather in - 209 Buoyage system in United Kingdom - 162 Buoys : Caution . 162 Distances between - 180 Buys Ballot's Law - 188 Cable .... . 5 < lables, Strain on - - 182 < lancer, Tropic of - - 180 Capricorn, Tropic of - 189 Celestial : concave - 77 i <|iiator - 77 meridians - - 78 meridian of heavenly body- 81 meridian of observer - - 81 pol< - 77 1 [entering error of sextant 332, 337 Centrifugal force, Effect on at- mosphere - 187 < ''Hi ripetal forces due to moon '111 Chart : tie of - 115, 169 Synoptic- or synchronous i 197 To pre] i - 180 < !bai kbbrevial ions on L56, I.--7. 169, 160, 161, 163 < lorred ion of . IliS 1 .-tidal - 233 1 'it HIM of - . 232 1 defacing pf - r,l I • • ripl i • > 1 1 of . . 168 1 >i-t«u 1 i"ii of, in print in -' - 167 Charts : Example of preparation of - Fathom lines on Isobaric .... Mercator's Necessity for of largest scale - Printing of Reliability of Chemical tube, Depth by Chetwvnd compass, Descrip- tion of - China sea, Monsoons in Chronometer box ..... Error of - Error of, by absolute alti- tudes .... Error of, by equal altitude 149, Error of, by time signal Description of - Driving mechanism of 339, Greenwich test of journal Longitude by Notes on observations for error of - Principle of room - - - - - Rate of. See Rate. Safe distance from electrical instruments - Stowage and care of - Thermal compensation of - To wind and start winding and maintaining mechanism Circle of position - on Mercator's chart - 111, Circumpolar - - - - Clearing bearings - Clearing marks Clocks, Adjustment of, for change of It >nu r it ode . < ilouds, < 'ause of - < 'oast, eli.i 1 1 a ii' it infallible Coast line .... Coasting, general rule - 171, Cocked hat - - - 62, ( ''. < 'orrecl ion of /.". I irrecl ion of ./ 181 158 187 20 18 170 167 169 359 297 190 84 353 139 147 152 142 339 340 348 140 130 154 339 353 351 353 347 352 34 1 111 123 126 176 17.". ss 194 169 L66 179 117 206 3 1 .'{ 279 280 281 1S1 I'M 452 The numbers refer to the Articles. Coefficients, Approximate - 277 Exact - - - 272,278 Relations between exact and approximate - - - 276 Col - - - - 198,205 Co -latitude .... 2 Collimation error - - 332, 335 Comparisons of chronometers 140, 147, 152, 153 Comparison, The mean - 143 Compass : Approximate expression for the deviation of - - 274 between deck, To adjust - 309 Card, Graduation of - - 13 Chetwynd, Description of - 297 Component parts of deviation of 275 Deviation of - - 15,273 Diagram - - - 45, 46 Exact expression for devia- tion of - - - - 272 Expression for deviation of when ship heels - - 290 Gyro. See Gyro-compass, in conning tower - - 304 Landing - - 259,260,261 Magnetic - - - - 13 Magnetic forces at - - 267 Magnetic, Suspension of - 264 Observations for deviation of 306 Principle of correction of - 271 Removal of bubble from - 298 rose ----- 23 Rules for adjustment of - 308 Safe distance from electrical instruments - - - 305 Sluggishness - - - 304 Standard - - - - 15 Thomson, Description of - 300 Compensated balance, Descrip- tion of - - - - 345 Compensation, Thermal, of chronometer --. - - 347 Composite track - - 37 Concave. See Celestial. Conning the ship - - - 185 tower, Compass in - - 304 Constant parameters - - 267 Constellations - - 70 Contour lines - - - 156 Coral regions, caution - - 169 Corrector magnets, Rules for placing - - - - 280 Co-tidal charts - - - 233 Course - - - - 18 Formula for - - - 28 made good 25 to allow for current - - 25 Course : to be by Standard compass - 185 to find by Mercator's chart - 23 Cross -bearings 62 Currents : Cause of - - - - 212 caution - - - - 169 Drift ... . 212 of Atlantic ocean - - 213 of Indian ocean - - - 215 of Pacific ocean - - - 214 Set and drift of - - - 25 Stream - - - - 212 To allow for when shaping course .... 25 To find - - - - 42 Cyclone - - 198, 199, 206 Sequence of weather in - 199 Cyclonic winds - - - 188 Damping of gyroscope Danger angle : Horizontal Vertical Danger line, Limiting Dangers - 318 - 178 - 177 - 169 - 157 Avoidance of, in thick weather 179 clearing marks or danger angles - - - - 180 Distance from - - - 171 Dangerous semi-circle - - 206 Date 84 Change of, on 180th meri- dian .... 88 Greenwich - - - 86 line 89 Datum : Height of tide from - - 242 Level of - - - - 158 of Admiralty charts - - 232 Davis Strait current - - 213 Day 82 Astronomical 84 Civil .... 84 Mean solar 84 Solar - - - - . 83 Dead -reckoning - - - 38 Deck watch 84 minute at last observation - 132,. 141, 154 To determine error of - 140 To take time with - - 141 Declination : Correction of - - 87, 146 of heavenly body - - 78 Parallels of - - - 78 Variation in - - - 79 Departure - - - - 26 Approximate formula for - 29 453 The numbers refer to (fie Articles. Departure : conversion to d Long - - 30 Formula for - - -27 Depression : Distance by angle of - - 59 of terrestrial object - - 54 Depth : by amount of wire out - 360 by chemical tube - - 359 of water .... 158 Derived tidal wave - - 233 Deviation .... 270 Approximate expression for 274 Constant .... 275 Component parts of - - 275 Exact expression for - 272 Necessity for observation of. 311 Observations for determining 306 Quadrantal - - - 275 Rules for applying - - 16 Semicircular - - - 275 Swinging ship for - - 310 Deviation table, Criteria of - 312 Deviation tables - - - 15 Dew : Causes of - - - - 194 Point - - - - 194 Diagrams for plotting position lines - - - - 115 Diagrams, Tidal - - - 243 Dip: Magnetic .... 258 See Horizon. I >i actions, Sailing - - 170 I >i recti ve force : Effect of permanent mag- netism on - 266 of gyroscope 1 316 oi magnetic compass - 264 l)i-i.ince . 18 1 > y great circle track - . 34 Formula for . 28 ol an object i by finder . 50 by vertical angle -5 9,60 SI, ... . 18 To fin'l, 1. .M'-rcator's chart ■1\ to lev. course 44, 174 1 tiurna] inequality 226, 241 Diurnal tid Lunar . 226 Solar - 228 Diurnal \ arial ion of baron L92 Doldrun - 189 Dover, Tides <>f - 282 l taaughl of lii|> - 171 in tea and river trater - Drift ourrei - 212 x 61' Earth : a gyrostat - - - 314 approximately a sphere - 10 Axis of - ... i Figure of - - - - 1 Length of diameters - - 1 Magnetic lines of force of - 258 Movement of - - - 76 Orbit of - 73, 76 Poles of - ... i Rotation of, effect on gyrostat 316 Ebb 232 Echo, Distance of cliff by - 179 Ecliptic - - - - 77 Eddies 250 Electrical instruments' safe distance from compass - 305 Electric current, Magnetic field of - - ' - - 256 Electricity, Atmospheric - 196 Electromagnets - - - 256 Elephanta - - - - 193 English Channel, Fog in - 195 Epoch .... 155 Equal altitudes - - - 146 Comparisons for - - 152 Equation of - - - 149 equation of, Formula for - 150 Errors involved in - - 151 Error of chronometer by - 149 Longitude by - - 131 Table for - - - - 131 Equation of time 95 Correction of - - 98, 146 Equator 1 Celestial - - - - 77 Magnetic - 258 Equatorial counter-current 213, 215 Equatorial current 213, 214, 215 Equilibrium theory - - 222 Equinoctial 77 points 77 Bpring t idea - - - 232 Error In position. See Posi- tion. Error of chronometer. ( 'in-i mometer. ElTOi in .ill nlute altitudes - 148 I oapenu a\ - - 339, 844 i i abli bment : M' . I rn ol ion of - - Mean, To find time of high water fn >m - - - 237 Vulgar - Kl.sinn .... |Q3 oeridian nil it ude - - 1 28 .i. ■r'liii.ii;. pring i id 454 The numbers refer to the Articles. Fathom lines not drawn, caution - - - - 169 Field of magnet - -252 Five fathoms line - - - 169 Fix 61, 66 Running 66 Fixing : by station pointer - - 65 Necessity for 47 Flinders bar - - - - 279 Induction in - - - 294 Quadrantal deviation due to 283 Floes 221 Flood 232 Fog ----- 195 Anchoring in - - 179, 180 Navigation in - - - 179 Use of " stand by " observa- tions in - - - 132 Fog signals - - - - 164 Reliability of - - - 165 Force : Magnetic lines of - - 252 Forecasting the weather - 211 Fort Dauphin - - - 193 Foucault's law - - 315 Four point bearing - - 66 Frigid zone - - - - 138 Frost, Hoar - - - - 194 Fusee 340 Geographical position of heavenly body - 109,110 Gnomonic chart - - 31, 32, 33 Line of bearing on - - 48 Gnomonic projection, when used - - - 167 Gradient, barometric - - 188 Gravity, Direction of - - 154 Great circle track : by gnomonic chart - 31 by calculation - - 35 on Mercator's chart - 34 To find the course 34 Towson's tables - - 36 Greenwich date - - - 86 Greenwich : Royal Observatory - 1 Gregale - - ' - - 193 Ground, Speed over - - 25 Guinea current - - - 213 Gulder - - - - 233 Gulf stream - - - - 213 Gyro-compass - - - 17 Anschutz, Correction of - 325 Damping of - - - 325 Description of - 324 Receivers - - 32 (i Gyro-compass : " Sperry," Correction of - 322 Damping of - - - 322 Description of - - 321 Receivers - - - 323 Gyroscope - - - - 314 Damping of - - - 318 Effect of Earth's rotation on 316, 317 Effect of rolling and pitching on 320 Effect of ship's motion on - 319 Gyrostat - - - - 314 Effect of couple on - 315 Hail, Cause of - - - 194 Halo. - - - - 209 Harbour rate - - - 351 Harbours, Typhoon - - 208 Hard iron - - - - 255 Harmattan - - - - 193 Harmonic analysis of tides - 242 Heavenly body : Geographical position of Position of- - - 78 Heeling : Coefficient - Error, Changes in error, Constant - Correction of, at sea in harbour - Expression for instrument Necessity for correction of Height of eye Heights shown on charts Helm : carried .... When to put, over Helmsman, Orders for - High water, Time of 232, 237, H. W. F. & C. - - 238, Hoar frost - Holding ground, Good - Hour angle - Formula for Horizon, Artificial Dip of sea - - 55 Dip of shore Distance of sea - Distinctness of - Hour angle of bodies on North, South, East, and West points of Observations in artificial 146, Rational - - - 103, Roof error of artificial Shore - 144, 56, 58, 57, 109 , 103 292 296 294 295 294 290 293 295 132 156 185 174 185 239, 240 239 194 159 94 97 145 103 132 163 132 133 126 154 126 148 55 45.") The numbers refer to the Articles. Horizon, Artificial : Latitude : The observer's sea - 55 Angular .... 2 Uncertainty in positkn of by meridian altitude - 126 sea . 117 Difference of 11 Horizontal angle, Determina- Linear - 8 tion of - - 261 Magnetic .... 258 I rae of, when anchoring - 1 SL- Middle .... 29 Horizontal danger angle - ITS Lead. Arming of - - 159 361 Horizontal force. Earth's 258, 265 Leading marks - 172 180 Horizontal fonts, at compass, Libra, First point of 77 when ship heels - 268 Lightning .... 196 Humidity - 186 Effect of, on de\ ia.1 289 Hurricanes - 206 Lights : 1 [ydrometer - - 218 abbreviations on chart- 163 1 1 grometer - 186, 366 Height of, given on chart - 57 Hysteresis - 255 on buoys - System of - 162 163 [ce .... - 221 Visibility of - - 57. L63 Indian Ocean. ( lurrents in - 2 1 5 Light vessels 163 ( '\ clones in - 208 Limb of body observed - 105 154 South-West Mons i in - 190 Line of hearing, Track to coin- [nequahty, Diurnal - 241 cide with 173 Lades error - 332, 336 Line of force of magnel 252 1 ^termination of 132, 154 Line squall - 204 Indicator, l*p and down - 341 Liverpool, Tides of 2:53 [ndraughl into bays 39, 171 Local winds, Tabular sum- Induced magnet ism - 255 mary of ... 193 of ship - 267 Local at t racl ion 263 Induction in soft iron cor- Lodestone 252 rectors - - 284 Log : Instrumental error in absol ute Ktit pies in ship's 38 altitudes . 148 Latent .... 354 Intercept - 112 Longitude : Lavar .... - 347 Angular .... 2 Illuminat ion. 1 !ircle of - 138 h\ chronometer - 130 Intel-mediate course and < lis- by equal alt it ode 131 bance - - - 44, 45, 46 1 Jiff'erence of 11 Iron, 1 [ard and -oft . 255 Linear 8 Lrradiation 1 is. 154 Look-outs in fog - 17!) [sobar - - IS!) Low water. Time | »f 232 1 n of \ I . i ■ - 1 1 • i 1 1 ■ d i p equator 291 252, 256 - 253 - 253 252 252 - 252 - 264 - 264 . 258 456 The numbers refer to the Articles. Magnetic dip : Mile: " field 252 Geographical - 6 field of electric current - 256 Length of - - - 5,7 force - - 258 Nautical - - - 4 induction - - - 255 Nautical, mean length o: 10 latitude - - - - 258 Minimum altitude - - - 127 meridian - - - - 258 Mistral - . - 193 poles - - - 252, 258 Mother tide - - - 233 storms .... 259 Motion work - 339, 343 Magnetic variation - - 14 Molecular theory - - - 254 Changes in 14, 259 Monsoons - - 190 Chart of - - 14 Month - • - 80 Example of finding, on shore 262 Moon - - - 73 Observations for, at sea - 313 Attraction of - - 222 Observations for, on shore - 260 New and full • - 229 Rules for applying - - 16 Moonset : Time of visible - 136 Magnetism - 252 Mooring : Molecular theory of - - 254 ^ line of anchors - - - 181 of earth - - - 252, 258 in selected position - - 183 Magnetism of ship : Effect of sub -permanent - 288 Nautical mile m — 4 Induced - - - - 267 Length of - m . 5 Permanent - - - 266 Mean m _ 10 Sub-permanent - - - 269 Neap, Rise and range Neap tides - m m 232 Magnetism, Red and blue - 252 . - 229 Magnets : Nebular theory . - 74 Effect of temperature on - 257 Nimbus cloud m _ 194 Rules for placing - - 281 North Atlantic, track recom- Magnitudes of stars - - 72 mended - m . 221 Marine barometer - - - 363 North Sea weather m _ 209 Maximum altitude - 127, 131 Note -book _ _ 180 Mean comparison - - - 143 Notices to Mariners _ . 168 Mean establishment. See Esta- blishment - - - 236 < Mean sun 84 Objects Selection of, in pilotage 180 Motion of - - - - 84 Observations, Best time to take Right ascension of - -97, 99 115, 132 M.T.P., Formula for - - 85 Observation spot - - 146 154 Mercator's chart - - 20, 21, 22 Ocean : Circle of position on - 111, 123 Temperature of - - - 220 216 171 To find true bearing from - 307 waves Offing - ■ - * where used- - - - 167 - ■ Meridian altitude : Open marks - - - 172 Position line by - - - 126 Overfalls /~\ CI " _ - - 250 214 Time to take observation - 127 Oya Siwo * Meridian : Celestial - - - - 78 Pacific Ocean currents - - 214 Circle of curvature of - 3 Pampero - - 193 Magnetic 14, 258 Parallax - - 106 Meridian passages of heavenly Effect of, on tides - - 227 bodies .... 125 Horizontal- - - 106 Meridian, Prime ... 1 in altitude - - - 103 Right ascension of - 96 Formula for - - - 106 Meridional parts - - 20, 21 sextant 327, 331 , 336 Mexican current - - - 214 Parameters, Constant - - 267 Microphones - - - - 166 Patent log : Middle : Description of - - - 354 latitude - - - - 29 Error of - - 356 temperature error - 347 Length of line for - - 354 457 The numbers refer to the Articles. Pearl rock : Clearing marks for - - 175 r Horizontal danger angle for 178 Perigee .... 227, 231 Periodic winds - - - 190 Pelorus 303 Permanent magnetism of ship 266 Perpendicularity, Error of 332, 333 Personal error in absolute alti- tude - - - - 148 Peruvian current - - - 214 Pilotage - - - - 156 waters, Track of ship in - 171 Plan, ts - - - 73, 105 Polar distance - - - 78 Polaris : Azimuth of - - - 129 Position line by - - - 129 Tables for - - - - 129 Pole : Altitude of - - - 126 Klevated ... - 77 Poles : Magnetic - .252 uf magnets - - 252,258 Port, Establishment of. See Establishment. Position : Area of - - - -117 by ;i-tronomical observation 115 by astronomical and tern trial observations - - 124 by astronomical observation and sounding - - 1- 1 by bearing and angle- - 63 by bearing and distance - 64 by bearing and sounding - 67 by cross beari] - - 62 by dead reckoning - - 38 by horizontal angles - - 66 by "Longitude bv chrono- meter" - - - L30 by pl"t ting when ; » 1 1 Ltud 123 67 I irele of - - - - ill l i ror in due to error in all it ode - 117 due to < rroi in altil ude uii.l CM T. - 119 due to error in O.M.T. I is, i m Win- 1" , rrorin I he reckon- ing - - - ,120 due toei ror in t he reckon* iiiL r iiiM l all itud - 121 due to eckon- tag, altitudes and O.M.T. 122 Position : Estimated .... 39 Accuracy of - - - 132 Unreliability of - - 47 Line 47 Astronomical- - 103,112 by altitude of Polaris - 129 by compass bearing - 48 by distance 50 by ex-meridian altitude 128 by horizontal angle - 49 by " Longitude by chrono- meter " by meridian altitude Notes on observations for Track to coincide with - Most disadvantageous 117, 130 126 132 171 118, 140 113, 117 90, 93 - 315 Most probable - triangle Precession Predetermined track, Turning ship on to - - - 174 Prediction of tides - 236, 242 I' reparation of chart - 180,184 I 'ressure : Centre of high - - - 187 Centre of low - - - 187 of atmosphere - - - 187 of atmosphere, Effect on tides 2 1 »'. 'Primary tidal wave - - 233 Prime vertical - - - 126 Priming of tide - - 230, 236 Quadrature, Moon in - - 229 Race Radiation - - - - 201 Rain : Cause of - - - -194 cloud - - • -194 Xmi isobaric - - 197 R.A.M.S. - - - 97, 100 i:.\.. - - - 79 I tange-finder, use of - 50, 6 i Rate 139 V cumulated - - - 1 39 Ad JUSI im m of - - - 347 < lhange in, due ti - •'■ i(l Daily - - - 189 Bffi .i of damp on - 361 Effecl of magnel io Beld on Kit' it < >f ship's mo1 i< 'u on 36 1 Kit. i t of temperal lire mi .". I 7 Formula for - - - 349 ( ii. en *1 ions for detrrmmii i • • of ohronometer - - 166 \ arial i< »n i in I :.it ional horizon - - 103 458 The numbers refer to the Articles. Reciprocal bearings - - 306 Reckoning - - - - 39 Accurate keeping of - 132, 179 by calculation - - - 41 by chart 40 by traverse table - - 41 during manoeuvres - -45, 46 in a tideway 43 Refraction : Abnormal - - 52, 56, 132, 148 Astronomical - - 103, 104 effect on visibility - - 163 Terrestrial- - 51, 103 Regulations for preventing collisions at sea, Article 25 180 Revolutions of engines, Speed by .... 357 Revolving storms - - - 206 British Islands - - 209 Indications of approach of - 207 Rules for avoiding - - 208 Rhumb -line - - - - 18 Formulae for - - - 26 Right ascension - - 79, 87, 97 of mean sun : Change in - 99 Correction of - - - 100 of meridian - - 96 Rising of heavenly body, Table of hour angles - 133 Roaring forties - - - 189 Rocks, Isolated - - 169 Rocky shore - - - - 169 Roof error, in absolute altitude 148 Rounding a mark - - - 174 Safe distances : Chronometers Magnetic compass Sailing Directions - St. Elmo's fire Sargasso Sea - Satellites Scirocco Sea, Mean level of Sea rate Seasons Sea water : Colour of - Specific gravity of Secondary cyclone Secular change in variation Semi-circle, dangerous - Semi-diameter Augmentation of moon's Semi-diurnal tide : Lunar Solar - Sensitiveness of marks - - 351 - 305 - 170 - 196 - 213 73 - 193 - 232 - 351 76 - 218 • - 218 198, 200 - 259 - 206 103, 105 - 107 - 226 - 228 - 172 Setting of heavenly bodies, Table of hour angles of - 133 Sextant : Care of - - - - 338 Description of - - - 328 Errors of - - - - 332 Index error of 132, 154, 332, 336 parallax - 327, 328, 331, 336 - 327 327, 332 - 330 - 329 - 330 - 148 - 193 Principle of certificate - telescopes - Vernier Shade error - in absolute altitudes Shamal - 154, 332, 334 96 Side error Sidereal time Signals, Storm Single position line Soft iron correctors, Induction in - - - Solar day. See Day. Solar system - Solar tide ... - Solent, tides of Solstitial points Sound waves Sounding book Sounding machine - Sounding without tubes Soundings : How to take Intervals between Necessity for Plotting, on tracing paper - Use of, in obtaining position 67, 124 Soundings on chart, caution - Southern ocean, Tidal waves in Specific gravity, Sea-water Speed : by measured distance by revolutions of engines - Loss of, whilst turning made good over ground ... " Sperry " gyro-compass, De- scription of - Spring rise Spring tides - Squalls - Standard clock Standard ports Standard time Stand of tide Star, globe or finder Stars Designation of - Identification of - 210 113, 114 284 - 73 - 228 - 233 77 166, 179 - 361 358, 361 - 360 361 361 39 67 169 233 218 355 357 44 25 25 321 232 229, 232 - 204 - 142 - 242 - 89 - 232 - 137 69 71 132, 137 459 The numbers refer to the Artich*. - its : Magnitudes of - - -72 To recognise - - - 75 Station pointer : I description of - - - 362 To test accuracy of - - 302 Us.- of - - - - 65 Stern marks, Steadying the ship on - - - - 17:2 Storm-. See Revolving Btorms. Storm signals - - - 210 Straight isobar - 198, 203 St ream currents - - - 12 Submarine bell - - 106 Sub-permanent magnel ism. The effect of - - - - 288 Sun : Mock .... 209 Rise, visible, Time of - 134 Set, visible, Time of - - 134 Survey, Accuracy of - - 169 Swinging ship - - 3 10 Synoptic : chart - - - - 197 system, of weather analysis 197 Telescope, Sextant 154, 330 Temperature : effect on magnets - 257 effect "ii ratl- - 347 in vicinity of ice - 221 of atmosphere - 187 of i icean - 220 . 221, 366 Zone - - 138 Ten fathom line, caution - 169 Terrestrial magnel ism - 252, 258 Theodolite - 261 Thermometers . 366 M;i \imum - - 307 Minimum - . 368 wet and dry bulb - 366 Thorns* in com] .. - 300 Thunder - lot; storms 196, L'UII Tidal : atls - 25 1 constant* 246 diagram* - - 169, 247, 248, 249 Rati ■ 't 169, round Rritwli I land Ti. 1.. • - 1 I'M - 236, 1 [eight "t coinpoHite - - 229 • Li • - 230 it ing i " ■ 222, 1 [orizonta Tide: Lunar diurnal semi-diurnal - Mother prediction - Printing and lagging of Range of - rips ..... Rise of Single day - - - . Solar diurnal semi-diurnal - Spring, Cause of Stand of - To find height of wave, Primary and derived waves .... Tides : Abbreviations for British Islands - Composition of lunar and solar .... Diurnal inequality of - Effect of atmospheric condi- tions on of earth's rotation - of moon's declination on - of moon's parallax - of sun's parallax i in Equinoctial spring Ext rai irdinary spring I larmonie anah sis of To find height of Irregular .... Lunar and ant i-lunar Neaps .... of Solent .... Solar ami .nit i-solar - Tideway, reckoning in - Time : ' \ 1 1' momica I Change of Civil ( 'mix ersi« 'M "i i" a re Li [uatiorj i if Mean solar Sidereal signal, Error <>t ohron bj Standard - taking, 'i ;> at n »n< »mi< at ion Tornado y sun's tables. iS'( - Cireal circle track, [racing papei Track to coincide with po ition line - - 171 T ratio wind - - . | gg - 220 - 226 - 233 236,242 230, 235 - 232 - 250 - 232 - 24 3 - 228 - 22S - 220 - 232 243 233 241 160 233 229 241 240 225 226 227 228 232 232 242 244 243 224 229 233 228 13 84 85 M 85 95, 'is M or, miet i r I I "I . I 12 I 1 1 193 07 460 The numbers refer to the Articles. Train .... Transfer Transit : Deviation of compass by Objects in - of heavenly body Translation, Error of Travelling rate Traverse : diagram - table Triangle, Astronomical - Trident log, Description of Tropical storms, Nuclei of Tropics - Trough of storm - Turning, Track of ship while Twilight Observations at- Typhoon harbours Typhoons 339, 342 44 - 306 63, 172 ■ 82 - 294 - 351 -45,46 - 30 90,93 - 354 - 189 138, 189 - 206 44 135 115,132,154 - 208 - 206 Variables of Cancer and Cap- ricorn .... 189 Variation. See Magnetic. V-depression - - 198, 204 Veering of wind - - - 199 Venus, Orbit of - - - 74 Vernier, Principle of - - 329 Vertical angle, Distance by - 59 Vertical danger angle - - 177 Vertical force ... 258 Views on charts - - 156 Vigia 157 Vulgar establishment. See Establishment. Water, Specific gravity and colour of 218 Waterspouts, Cause of - - 194 Waves : Cause of - - - - 216 Height of - - 216,217 Waves : Length of - Period of - Weather daily reports forecasting round British Islands North Sea Variations in Wedge Westerly winds ' ' What Star is it ? " See Stars , Identification of Williwaw - Wind: Cause of - Circulation of, about centre of high pressure Cyclonic - effect on tides - Trades - Veering or backing Velocity and direction of - Winds : Anti-cyclonic Local - Periodic . . - - Permanent Wireless Telegraphy, Time by Wreck-marking vessel - 216,217 216,217 - 186 209,211 - 211 and - 209 - 197 198,202 - 189 137 193 188 188 188 246 189 199 188 188 193 190 189 142 162 Year .... 76,77,80 Mean solar 84 Zenith - - - - 90, 103 Zenith distance - - - 92 Calculated and true - - 103 Calculation of - - - 101 Very small - - 111,123 Zodiac 77 Zone : Frigid - - - - 138 Temperate - - - 138 Zones, Tropical - - - 138 Printed under the authority of His Majesty's Stationery Office By Eyre and Spottiswoode, Ltd., East Harding Street, E.C.4, Printers to the King's most Excellent Majesty. /, THE LIBRARY UNIVERSITY OF CALIFORNIA Santa Barbara THIS BOOK IS DUE ON THE LAST DATE STAMPED BELOW. Series 9482 3 1205 00352 4939 UC SOUTH tiiM\i\r wKW^W^m \\\ \\ » u ° 00 293 855 3 •'sSfts ••'-.-- •■■■-•'•■'■■•-• n... '.■ .' ■ ---.',■'■■•