THE 
 VIARINERS' HANDBOOK 
 
 A CONVENIENT REFERENCE BOOK 
 
 ivigators, Yachtsmen, and Seamen of all classes, and 
 tor all persons interested in the Navy, the 
 Merchant Marine, and Nautical 
 Matters generally 
 
 International Correspondence Schools 
 
 SCRANTON, Pa. 
 
 I St Edition, 1 3th Thousand, 3d Impression 
 
 SCRANTON, PA. 
 INTERNATIONAL TEXTBOOK COMPANY
 
 Copyright, 1906. by 
 
 International Textbook Company 
 
 Entered at Stationers' Hall. London 
 
 All Rights Reserved 
 
 FKINTBD IN THB UNITED STATES
 
 PREFACE 
 
 This handbook is intended as a book of 
 ■reference to the young men in the merchant 
 narine, as well as to those in the naval serv^ice. 
 vVhile the treatment of some of the subjects 
 ncluded is necessarily brief, the information 
 given should nevertheless prove very useful and 
 create a desire for further study and investi- 
 igation. 
 
 Ambitious seamen trying to fit themselves 
 for examination to higher rank in either service 
 are often embarrassed by a lack or insufficient 
 knowledge of logarithms; hence, we have incor- 
 porated a thorough and comprehensive article 
 lOn that subject accompanied by tables of com- 
 ;nion logarithms. 
 
 In the subject of navigation, terrestrial and 
 celestial, are included only the standard methods 
 practiced by the up-to-date navigator, and for 
 this reason the book should be of value to the 
 student, as well as to the navigating officer. The 
 treatment of these subjects does not consist 
 :merely of definitions of terms, but rules, formulas, 
 and directions are given for each method, fol- 
 lowed in every case by examples and carefully 
 •worked out solutions illustrating the process or
 
 hr PREFACE 
 
 method explained. Of equal importance to the 
 student and the professional man should be the 
 articles dealing with deviation, the compensation 
 of compasses, and the manipulation of rope. 
 All problems appearing throughout the book 
 involving elements of time are worked out for 
 values given in the Nautical Almanac of 1904. 
 
 It is hoped that the subject of the United 
 States Navy and matters relating to the naval 
 service will prove valuable and instructive not 
 only to men directly connected w4th the Navy, 
 but also to that great auxiliary of the Navy, the 
 officers and men of the Merchant Marine, and 
 that it will, in a measure, tend to draw closer 
 the ties now existing between the two branches. 
 
 This handbook was prepared under the 
 supervision of E. K. Roden, Principal of our 
 School of Navigation. 
 
 International Correspondence Schools.
 
 INDEX 
 
 Additional rewards in the 
 
 Navy, 160. 
 Addition of decimals, 15. 
 
 of fractions, 13. 
 Administrative bureaus of 
 
 Navy, 150. 
 Agonic lines, 70. 
 Air flask of torpedo, 225. 
 Alternation, 17. 
 Altitude, Meridian, of a 
 star. 130. 
 
 Meridian, of the moon, 
 131. 
 
 Meridian, of the sun, 129. 
 
 Observed, 121. 
 
 Parallax in, 123. 
 
 True, 121. 
 Altitudes, Correction of 
 128. 
 
 Equal, near noon, 138. 
 Ammunition car, 211, 
 
 Fixed, 188. 
 Amplitude, Compass, 122. 
 
 True, 122. 
 Aneroid barometer. Indica- 
 tions of weather by, 
 283. 
 Angle, Cosecant of, 65. 
 
 Cosine of, 64. 
 
 Cotangent of, 64. 
 
 Hour, 122. 
 
 Secant of, 65. 
 
 Sine of, 64. 
 
 Spherical. 92. 
 
 Tangent of. 64. 
 Angles. Danger. 115. 
 
 Measure of, 2. 
 Angular distance, 119. 
 Annual parallax, 123. 
 Any root. Extracting, 19. 
 Apparent solar day, 126. 
 Application for admission 
 to citizenship, 321. 
 
 Application of trigonome- 
 try in practice, 66. 
 Apprentices, Naval, 161. 
 Approaching or receding 
 of storm center. To 
 find, 288. 
 Arc, Complement of, 64. 
 
 Supplement of, 64. 
 Arcs, Measure of, 2. 
 Aries, First point of, 119. 
 Arithmetic, 13. 
 Armor. Compound. 250. 
 
 Harveyized, 250. 
 
 Kruppized, 253. 
 
 piercing shells, 204. 
 
 shelf, 250. 
 Armored cruisers, 174. 
 
 decks, 250. 
 Arrangement of code book. 
 International signals, 
 293. 
 Artificer branch, 157. 
 Artificial magnets, 68. 
 Ascension. Right, 122. 
 Asteroids, 124. 
 Astronomical dav, 127. 
 
 terms, 119. 
 Attraction and repxilsion. 
 Magnetic. 69. 
 
 Local, 72. 
 Automatic guns, 188. 
 Autumnal equinox, 119. 
 Avoirdupois weight, 2. 
 Axis, Magnetic, 69. 
 
 of the earth, 92. 
 Azimuth, Compass, 122. 
 
 True, 121. 
 
 Band. Rotating. 198. 
 
 slope, 198. 
 Bands, Locking. 196. 
 Bar. Flinders, 77, 
 
 keel. 239.
 
 INDEX 
 
 Barge Navy, 185. 
 Barometer, aneroid. 
 Weather indications 
 by. 283. 
 
 mercurial, Weather indi- 
 cations by, 281. 
 Base and rate, To find per- 
 centage, 22. 
 
 fuses, 208. 
 Battle drill, 168. 
 
 ships, 174. 
 Bearing, Four-point, 111. 
 
 of an object, 93. 
 Bearings, Bow, 110. 
 
 Cross, 109. 
 
 of same object and dis- 
 tance run, 111. 
 
 reciprocal, Simultaneous, 
 79. 
 Belaying of ropes, 281. 
 Bends and hitches, 277. 
 
 and splices, 270. 
 Bend, Sheet, 277. 
 Bilge keelson, 240. 
 Billet, Station, 169. 
 Black powder, 218. 
 Blackwall hitch, 277, 
 Blasting gelatine, 217. 
 Blocks, Breech. 198. 
 Blue polarity, 69. 
 Boats, Man-of-war. 185. 
 
 Navy, Rigs of, 185. 
 
 Torpedo, 179. 
 
 torpedo, Importance of, 
 233. 
 
 Whale, 185. 
 Boatswain's mates, Duties 
 
 of, 162. 
 Bore, Rifling the, 196. 
 Bottom, Double, 244. 
 Bow-bearings, 110. 
 Bowline How made, 277. 
 Branch, Artificer. 157. 
 
 hydrographic offices, 292. 
 
 Messmen, 158. 
 
 Seamen, 156. 
 
 Special, 158. 
 Breaking strain of manila 
 
 rope, 266. 
 Breasthooks, 242. 
 Breathing, To produce. 316. 
 
 Breech block, 198. 
 
 block, The Driggs- 
 Schroeder, 200. 
 
 block, The Welin. 199. 
 
 closure, Hotchkiss, 199. 
 
 loading gun, 187. 
 
 mechanism, Principles 
 of, 200. 
 
 mechanisms of guns, 198. 
 
 plug. The Elswick, 199. 
 Briggs logarithms, 27. 
 Brown powder, 219. 
 Bugle calls, 185. 
 Built-up gun, 187. 
 Bulkhead, Collision, 246. 
 Bulkheads, 245. 
 Bureau, Chief of, 150. 
 Bureaus, Administrative 
 naval, 150. 
 
 Cable and hawser, 263. 
 Calls, Bugle, 185. 
 Capacity and volume, Mea- 
 sures of, 9. 
 Capped projectiles, 205. 
 Car, Ammunition, 211. 
 Carbodynamite, 216. 
 Card, Compass, 85. 
 Carriage of a gun, 208. 
 Carrick bend, Double, 277. 
 Cast-steel wire ropes. 
 
 Strength of, 269. 
 Celestial equator, 119. 
 
 latitude, 124. 
 
 longitude, 124. 
 
 longitude. Circles of, 123. 
 
 meridians. 120. 
 
 navigation, 119. 
 
 poles. 119. 
 
 sphere, 119. 
 Center keelson, 240. 
 
 of hurricane. To find, 
 287. 
 Chain splice. To make, 
 
 274. 
 Chamber, Immersion, 226. 
 
 slope, 198. 
 Chaplains in Navy^ 152. 
 Characteristic, 28. 
 Charge. Ignition. 202.
 
 INDEX 
 
 Chart, Mercator's, Con- 
 struction of, 105. 
 Charts, foreign, Meridians 
 of, 117. 
 foreiRn, Soundings on, 
 
 118. 
 Great-circle, 109. 
 Chief of bvireau, Navy, 
 
 150. 
 Chinese naturalization 
 
 laws. 322. 
 Circle, 23. 
 Great, 92. 
 Small, 92. 
 Circles, Hour, 120. 
 
 of celestial longitude, 
 123. 
 Circular ring, 27. 
 Citizen, Declaration of in- 
 tention to become, 
 320. 
 Citizenship, Application to 
 receive, 321. 
 Conditions for, 321. 
 Citizens, naturalized. Pro- 
 tection abroad to, 323. 
 Civil day, 127. 
 Classification of enlisted 
 men, 154. 
 of guns, 187. 
 of war ships, 173. 
 Coast navigation. Methods 
 
 in, 109. 
 Cocoa powder, 220. 
 Code book of International 
 signals. Arrangement 
 of, 293. 
 of signals, International, 
 
 293. 
 signals, International, 
 selected, 294. 
 Coefficient B, To compen- 
 sate, 76. 
 C, To compensate, 75. 
 of fineness, 255. 
 Coefficients, Magnetic, 74. 
 Coir rope, 262. 
 Collision bulkhead, 246. 
 Combination primer^ 203. 
 Commerce-dest roying 
 cruiser, 174. 
 
 Commissarv steward. 
 
 Duties of, 163. 
 Commissioned officers. 163. 
 Common fractions, 13. 
 logarithms. Explanation 
 of, 27. 
 Common logarithms. Table 
 of, 46. 
 shells, 204. 
 Compartments, Water- 
 tight, 245. 
 Compass amplitude, 122. 
 azimuth, 122. 
 card, 85. 
 course, 83. 
 
 course, To find true, 80 
 Deviation of, 71. 
 error, 68. 
 management. Remarks 
 
 on, 81. 
 points in various lan- 
 guages, 88. 
 points. Table of, 86. 
 points to degrees, 86. 
 Compasses, Compensation 
 
 of, 73. 
 Compensation of coefficient 
 B, 76. 
 of coefficient C, 75. 
 of compasses, 73. 
 of quadrantal deviation, 
 74. 
 Complement of an arc, 64. 
 Completed warships, 
 Number of, 309. 
 warships. Tonnage of, 
 310. 
 Components, Magnetic, 70. 
 Composite sailing, 94. 
 Composition of gunpowder, 
 218. 
 of steel, 192. 
 of the hull, 238. 
 Compound armor, 250. 
 fractions, Reduction of; 
 
 to simple, 14. 
 proportion, 17. 
 Conditions for citizenship, 
 
 321. 
 Conjunction, Inferior. 124. 
 Superior, 124.
 
 Vlll 
 
 INDEX 
 
 Constants, Table of, 255. 
 Constructing a Mercator- 
 
 ial chart, 105. 
 Construction, gun, Princi- 
 ples of. 189. 
 Cordite powder, 222. 
 Corps, Medical, 151. 
 
 Pav, 152. 
 
 Staff, 151. 
 Correction of altitudes, 12-8. 
 
 of courses, 83. 
 Cosecant of an angle, 65. 
 Cosine of an angle, 64. 
 Cotangent of an angle, 64. 
 Course, Compass, 83. 
 
 Final, 94. 
 
 Initial, 94. 
 
 made good, 93. 
 
 True, 83. 
 Courses, Correction of, 83. 
 Coxswains, Duties of, 162. 
 Crew, Organization of, in 
 
 Navy, 166. 
 Cross-bearings, 108. 
 
 hitch, 277. 
 Cruiser, Commerce- des- 
 troying, 174. 
 Cruisers and gunboats, 
 179. 
 
 Armored, 174. 
 
 Protected, 179. 
 Cubic measure, 1. 
 Curve, Loxodromic, 93. 
 Custom-hotise fees, 323. 
 Cutters, Navy, 185. 
 Cyclones or hurricanes, 284. 
 Cvlinder, 26. 
 
 Frustum of, 26, 
 
 Daily routine in port of 
 
 the Navy, 169. 
 Danger angle. Horizontal, 
 116. 
 angles, 115. 
 angle. Vertical, 116. 
 Dangerous semicircle in 
 
 hurricane, 284. 
 Date, Greenwich, 128. 
 Day. Apparent. 126. 
 Astronomical, 127. 
 
 Day, Civil, 127. 
 Mean, 126. 
 Sidereal. 127. 
 Day's work, 100. 
 Dead reckoning, 94. 
 
 reckoning. Formulas for 
 95. 
 De Bange system of gas 
 
 checking, 201. 
 Decimal fractions, 15. 
 Decimals, Addition of, 15. 
 Division of, 16. 
 Multiplication of, 16. 
 Subtraction of. 15. 
 to fractions, 14. 
 Deck, Armored, 250. 
 Officer of the, 166. 
 stringer, 241. 
 Declaration of intention to 
 
 become citizen, 320. 
 Declination, 122. 
 
 Parallels of. 122. 
 Definition of fleet, 184. 
 of flotilla, 184. 
 of latitude, 92. 
 of longitude, 92. 
 of squadron, 184. 
 Definitions, Astronomical, 
 119. 
 relating to magnetism, 
 68. 
 Degrees to compass points. 
 
 Table, 86. 
 Delayed-action fuses, 208. 
 Denominator. 13. 
 Departure, 93. 
 Description of storm cen- 
 ter, 289. 
 Destroyers, Torpedo-boat, 
 
 184. 
 Determination of latitude, 
 129. 
 of longitude, 135. 
 Deviation of the compass, 
 71. 
 Quadrantal, 72. 
 quadrantal, To compen- 
 sate. 74. 
 Semicircular. 72. 
 To swing a ship for, 79. 
 Diameter of a sphere, 91.
 
 INDEX 
 
 Difference of latitude, 93. 
 
 of latitude, Meridional, 
 94. 
 
 of longitude, 93. 
 Dimensions of notable 
 
 steamships, 314. 
 Dingies, Navy, 185. 
 Dip, Magnetic, 70. 
 
 of the horizon, 123. 
 Director. The torpedo, 232. 
 Displacement and tonnage, 
 256. 
 
 of a ship, 254. 
 Distance, Angular, 119. 
 
 by velocity of sound, 1 15. 
 
 of objects at sea, 114. 
 
 Polar, 122. 
 
 run, 93. 
 
 Zenith, 121. 
 Distances, Sailing, between 
 principal ports, 146. 
 
 Table of, 4. 
 Distant signals, 296. 
 
 signals. Special, 294. 
 Distress signals, 300. 
 Diurnal motion, 120. 
 Division bv logarithms, 38. 
 
 Gun, 167. 
 
 of decimals, 16. 
 
 of fractions, 13. 
 
 of fuses, 206. 
 
 of time on shipboard, 
 171. 
 
 officers, 166. 
 
 Powder, 167. 
 Double bottom, 244. 
 
 carrick bend, 277. 
 
 rule of three, 17. 
 Driggs fuse, 208. 
 
 Schroeder breech block, 
 200. 
 Drill, Battle, 168. 
 Drilling, 167. 
 
 Drowned persons, appar- 
 ently. To restore, 315. 
 Dry measure, 2. 
 Ductility of steel, 192. 
 Duties of line officers, 165. 
 
 Outline of, in the Navy, 
 161. 
 Dynamite, 216. 
 
 Earth, Axis of, 92. 
 
 Magnetic property of, 
 69. 
 
 Meridians of, 92. 
 
 Poles of, 92. 
 Ecliptic, 119. 
 
 Obliquity of the, 120. 
 Educational facilities in 
 
 the Navy, 164. 
 Elastic strength of steel, 
 
 192. 
 Electric primer, 202. 
 Elements of the solar sys- 
 tem, 125. 
 Ellipse, 25. 
 Elongation, 126. 
 Elswick breech plug, 199. 
 Engineer force, 167. 
 
 officers, 166. 
 English money, 5. 
 Enlisted men. Classifica- 
 tion of, 154. 
 
 men. Promotion of, 163. 
 
 men, Rating of, 155. 
 Enlistment record, 169. 
 
 Requirements of, 155. 
 Equal altitudes near noon^ 
 Method of observing,. 
 138. 
 Equation of time, 126. 
 Equator, Celestial, 119. 
 
 Geographical, 92. 
 
 Magnetic, 70. 
 Equinoctial, 119. 
 
 points, 119. 
 Equinox, Autumnal, 119. 
 
 Vernal, 119. 
 Equivalents, Metric, 10. 
 Error, Heeling, 77. 
 
 The compass, 68. 
 Etiquette in the Navy, 
 
 Notes on, 172. 
 Evolution, 19. 
 
 by logarithms, 42. 
 Executive officer, 165. 
 Exercise head of torpedo, 
 
 225. 
 Ex-Meridian of the sun, 
 
 133. 
 Explosives, 214.
 
 IXDEX 
 
 Exponents, 27. 
 Exterior planets, 124. 
 Extracting any root, 
 
 Method of, 19. 
 Eye splice, To make, 274. 
 
 Fees, Custom-house, 323. 
 Fiber ropes, 261. 
 Figure-of-eight knot, 277. 
 Final course, 94. 
 Fineness, Coefficient of ,255. 
 Firing of guns, 201. 
 First points of Aries, 119. 
 Fixed ammunition, 188. 
 Flags, Number used in a 
 hoist, 294. 
 
 Storm-warning, 301. 
 Flat-plate keel, 240. 
 Fleet, Definition of, 184. 
 Flinders bar, 77. 
 Flotilla. Definition of, 184. 
 Force, engineer. Navy, 167. ■ 
 Foreign charts, Meridians 
 of, 117. 
 
 charts, Soundings on, 
 118. 
 
 measures. Value of, 12. 
 
 money. Values of, 6. 
 Formulas for dead reckon- 
 ing, 95. 
 Four-point bearing. 111. 
 
 flag signals, 294. 
 Fourth power of a number, 
 
 19. 
 Fractions, Addition of, 13. 
 
 Common, 13. 
 
 Decimal, 15. 
 
 Division of, 13. 
 
 Multiplication of, 13. 
 
 Sul)traction of, 13. 
 
 Table of, 15. 
 
 to decimals, 14. 
 Frame bar, 238. 
 Frames, 238. 
 Frustum of cylinder, 26. 
 
 of prism, 26. 
 Fuel consumption and 
 
 speed, 259. 
 Fulminate of mercury, 
 217. 
 
 Functions, Trigonometric, 
 
 65. 
 Fuse, Base, 208. 
 
 Delayed-action, 208. 
 
 Navy percussion, 207. 
 
 Percussion, 207. 
 
 The Driggs, 208. 
 
 Time, 206. 
 Fuses, Division of, 206. 
 
 G 
 
 Galvanized-iron wire rope. 
 Breaking strain of, 267. 
 
 steel hawsers, Strength 
 of, 268. 
 Garboard strake, 240. 
 Gas checking, De Bange 
 system of, 201. 
 
 checking, Principle of, 
 201. 
 
 check slope, 198. 
 Gauging, Star, 196. 
 Gear, Obry. 229. 
 Gelatine, Blasting, 217. 
 General quarters. 168. 
 Geographical equator, 92. 
 Grades of line officers, 151. 
 Granny knot, 277. 
 Granulation of powder, 
 
 222. 
 Great circle: 92. 
 
 circle charts, 109. 
 
 circle sailing, 94. 
 
 circle track. To plot. 108. 
 
 circle, Verte.x of, 94. 
 Greenwich date, 128. 
 Gross tonnage, 256. 
 Gunboats and cruisers, 
 
 179. 
 Gun, Breech-loading, 187. 
 
 Built-up, 187. 
 
 carriage, 208. 
 
 construction. Principles 
 of, 189. 
 
 division, 167. 
 
 mounts, 208. 
 
 Powder chamber of, 197. 
 
 Rifled, 187. 
 
 Screw box of, 197. 
 
 steel, 191. 
 
 steel. Treatment of, 193.
 
 INDEX 
 
 Gun, Top carriage of, 209. 
 Guncotton, 216. 
 Gunpowder, Composition 
 
 of, 218. 
 Guns, Automatic, 188. 
 
 Breech mechanisms of, 
 198. 
 
 Classification of, 187. 
 
 Firing of, 201. 
 
 Layers of, 191. 
 
 Machine. 188. 
 
 Manufacture of, 194. 
 
 Naval, 187. 
 
 Rapid-fire, 188. 
 
 Semiautomatic, 189. 
 Gyroscope, 229. 
 
 H 
 
 Handling ships in hurri- 
 canes, 286. 
 Hard iron, 72. 
 Harveyized armor, 250. 
 Hawser and cable, 263. 
 Hawsers, galvanized-steel, 
 Strength of, 268. 
 steel, for heavy towing, 
 Strength of, 268. 
 Heeling error, 77. 
 Height, Metacentric, 237. 
 Hellhoffite, 217. 
 Hemisphere, 92. 
 Hemp ropes, 261. 
 Hitch, Blackwall, 277. 
 Hitches and bends, 277. 
 Horizon, Dip of, 123. 
 Rational, 120. 
 Sea, 121. 
 Sensible, 120. 
 True, 120. 
 Horizontal and vertical 
 iron, 72. 
 danger angle, 116. 
 Horsepower, Indicated, 
 254. 
 Rule for finding, 254. 
 Hotchkiss breech closure, 
 
 199. 
 Hour angle, 122. 
 
 circles, 120. 
 Hull, Composition of the 
 238. 
 
 Hurricanes, Handling of 
 ships in, 286. 
 
 Motion of. 284. 
 
 or cyclones, 284. 
 
 To find center of, 287. 
 Hurricane warning signals, 
 
 301. 
 Hydraulic rammer, 211. 
 Hydrographic offices, 292. 
 Hydrostatic piston, 226. 
 Hyperbolic logarithms, 27. 
 
 Ignition charge, 202. 
 Immersion chamber. 226. 
 Indicated horsepower, 254. 
 Indications of typhoons, 
 289. 
 of weather by aneroid 
 
 barometer, 283. 
 of weather by appear- 
 ance of sky, 283. 
 of weather by mercurial 
 barometer, 281. 
 Indicator, 254. 
 Induction, Magnetic, 70. 
 Inferior conjunction, 124. 
 Initial course, 94. 
 
 tensions in gun con- 
 struction, 189. 
 Insignia of naval officers, 
 
 153. 
 Interior planets, 124. 
 International code of sig- 
 nals, 293. 
 code signals, Selected, 
 
 294. 
 signals, Arrangement of 
 code book, 293. 
 Inversion, 17. 
 Involution, 18. 
 
 by logarithms, 40. 
 Iron, Hard, 72. 
 Soft, 72. 
 Vertical and horizontal, 
 
 72. 
 wire rope, galvanized, 
 Breaking strain of, 267. 
 Isoclinic lines, 70. 
 Isodynamic lines, 71. 
 Isogonic lines, 70.
 
 IXDEX 
 
 K 
 
 Keel, Bar, 239. 
 
 Different tvpes of, 241. 
 
 Flat-plate, 240. 
 
 Side-bar, 240. 
 Keelson, BilK'e, 240. 
 
 Center, 240. 
 
 Side, 240. 
 Kilometers to nautical 
 
 miles, 11. 
 Knot, Figure-of-eight, 277. 
 
 Granny, 277. 
 Knot, Reef, 277. 
 Kruppized armor, 253. 
 
 Largest steamship com- 
 panies. Table of, 312, 
 Latitude, Celestial, 124. 
 
 Definition of, 92. 
 
 determinations, 129. 
 
 Difference of, 93. 
 
 Middle, 93. 
 
 Parairels of, 92. 
 Latitudes. Table of, 104. 
 Launches, Navy, 185. 
 
 Steam, 185. 
 Launching tubes of tor- 
 pedoes, 231. 
 Laws, U.S. naturalization, 
 
 320. 
 Layers of guns, 191. 
 Leeway, 83. 
 
 Length, Measures of, 9. 
 Life-saving signals, 302. 
 Lights in different lan- 
 guages, 118. 
 Linear measure, 1. 
 Line officers, 151. 
 
 officers and their duties, 
 165. 
 
 officers, Grades of, 151. 
 
 officers. Number of, 152. 
 
 of position, 142. 
 
 Sumner, 142. 
 Lines, Agonic, 70. 
 
 Isoclinic, 70. 
 
 Isodynamic, 71. 
 
 Isogonic, 70. 
 Liquid measure, 3. 
 
 List of Weather -Bureau 
 
 stations, 299. 
 Local attraction, 72. 
 
 mean time, 127. 
 Locking bands, 196. 
 Logarithms, 27. 
 
 Briggs, 27. 
 
 common, Table of, 46, 
 
 Divison by, 38. 
 
 Evolution by, 42. 
 
 Hyperbolic, 27. 
 
 Involution by, 40. 
 
 Multiplication by, 36. 
 
 Napierian, 27. 
 
 Natural, 27. 
 Logarithm, To find, of a 
 
 number, 30. 
 Log book, Official, 100. 
 Longitude, Celestial, 124. 
 
 celestial. Circles of, 123. 
 
 Definition of, 92. 
 
 determinations, 135. 
 
 Difference of, 93. 
 Longitudinals 244. 
 Long splice. To make, 272. 
 
 ton table, 2. 
 Loxodromic curve, 93. 
 Lyddite explosive, 218. 
 
 M 
 
 Machine guns, 188. 
 Machinists, Duties of, 162. 
 Magnet, Artificial, 68. 
 
 Natural, 68. 
 Magnetic attraction and 
 repulsion, 69. 
 
 axis, 69. 
 
 coefficients, 74. 
 
 components, 70. 
 
 dip, 70. 
 
 equator, 70. 
 
 induction, 70. 
 
 meridian, 69. 
 
 polarity, 69. 
 
 poles, 68. 
 
 property of the earth, 
 69. 
 
 variation, 70. 
 Magnetism, Definitions re- 
 lating to, 68. 
 
 Retentive, 72.
 
 INDEX 
 
 Magnetism, Subperma- 
 
 nent, 72. 
 Main engine of torpedo, 
 
 228. 
 Manila rope, 261. 
 
 rope. Breaking strain of, 
 266. 
 Man-of-war boats, 185. 
 
 Organization of, 165. 
 Mantissa, 28. 
 
 Manufacture of guns, 194. 
 Marine, Merchant, of the 
 
 world, 311. 
 Mariners, Notice to, 108. 
 Marlinespike, 270. 
 Master-at-arms, Duties of, 
 
 161. 
 Mates in the Navy, 163. 
 Maximum separation. 
 
 Point of, 94. 
 Mean proportional, 17. 
 
 solar day, 126. 
 
 sun, 126. 
 
 time, 126. 
 Measure, Cubic, 1. 
 
 Dry, 2. 
 
 Linear, 1. 
 
 Liquid, 3. 
 
 of angles, 2, 
 
 Square, 1. 
 Measures and weights, 1. 
 
 foreign, Value of, 12. 
 
 of length, 9. 
 
 of money, 5. 
 
 of surface, 9. 
 
 of time, 3. 
 
 of volume, 4. 
 
 of volume and capacity, 
 9. 
 
 of weight, 9. 
 Mechanism, Breech, 200. 
 Medical corps, 151. 
 Melinite, 218. 
 Memoranda, Nautical, 304. 
 Mensuration, 22. 
 Mercator's chart, Con- 
 struction of, 105. 
 
 sailing, 94. 
 Merchant marine. Number 
 and tonnage of ships 
 in, 307. 
 
 Merchant marine of the 
 
 world, 311. 
 Mercurial barometer. 
 Weather indications 
 by, 281. 
 Mercury, Fulminate of, 
 
 217. 
 Meridian altitude of a star, 
 130. 
 altitude of the moon, 
 
 131. 
 altitude of the sun, 129. 
 Magnetic, 69. 
 Prime, 92. 
 Meridians, Celestial, 120. 
 of the earth, 92. 
 used on foreign charts, 
 117 
 Meridional difference of 
 latitude, 94. 
 parts, 94. 
 Messmen branch, 158. 
 Metacenter, 237. 
 Metacentric height, 237. 
 Meteorological o b s e r v a ■ 
 
 tions at sea, 290. 
 Methods in coast naviga- 
 tion, 109. 
 of plating ships, 248. 
 Method, Sumner's, 142. 
 Metric equivalents, 10. 
 
 svstem, 8. 
 Middle latitude, 93. 
 
 latitude sailing, 93. 
 Miles, Nautical, to kilo- 
 meters, 11. 
 Minors, Naturalization 
 
 laws for, 322. 
 Modification of treatment 
 of apparently drowned 
 persons, 319. 
 Money, English, 5. 
 foreign, Values of, 6. 
 Measures of, 5. 
 United States, 5. 
 Monitors, 179. 
 Moon, Meridian altitude of, 
 
 131. 
 Motion, Diurnal, 120. 
 of hurricanes, 284. 
 Mounts, Gun, 208.
 
 XIV 
 
 IXDEX 
 
 Mounts, Turret, 210. 
 Multiplication by 1 o g a- 
 rithms, 36. 
 
 of decimals, 16. 
 
 of fractions, 13. 
 
 N 
 Names of lights in different 
 
 languages, 118. 
 Napierian logarithms, 27. 
 Naturalization laws for 
 Chinese, 322. 
 laws for minors, 322. 
 laws, U.S., 320. 
 Naturalized citizens, Pro- 
 tection abroad to, 322. 
 Natural logarithms 27. 
 
 magnet, 68. 
 Nautical memoranda, 
 304. 
 miles to kilometers, 11. 
 Naval apprentices, 161. 
 guns, 187. 
 
 officers. Insignia of, 153. 
 ordnance, 187. 
 ordnance. U. S., Size and 
 
 power of, 212. 
 powers. Sea strength, 
 Number of ships, 309. 
 Navigable semicircle in 
 
 hurricane, 286. 
 Navigating officer, Navy, 
 
 166. 
 Navigation, 68. 
 
 by dead reckoning, 94. 
 Celestial, 119. 
 steam. Progress of, 304. 
 Terms relating to, 91. 
 Terrestrial, 91. 
 Navy, additional rewards 
 for merit, 160. 
 barge, 185. 
 boats. Rigs of, 185. 
 cutters, 185. 
 dingies, 185. 
 Educational facilities in, 
 
 164. 
 Etiquette in, 172. 
 launches, 185. 
 Mates in the, 163. 
 Organization of, 150. 
 
 Navy, Outline of duties in. 
 161. 
 Pay table for men in, 
 
 156. 
 percussion fuse, 207. 
 Refrigerating ships in, 
 
 165. 
 routine in port, 169. 
 Special pay and privi- 
 leges in, 159. 
 Special schools in, 164. 
 training stations, 151. 
 United States, 150. 
 yards, 150. 
 Net tonnage, 256. 
 Neutral zone, 69. 
 Nickel steel, 193. 
 Nitroglycerine, 216. 
 Notable steamships, 
 
 Dimensions of, 314. 
 Notice to mariners, 108. 
 Number and tonnage of 
 ships built in U. S., 
 308. 
 and tonnage of ships in 
 merchant marine, 307. 
 and tonnage of ships in 
 
 U. S. Navy, 306. 
 Fourth power of, 19. 
 of completed warships, 
 
 309. 
 of flags used in a hoist, 
 
 294. 
 of line officers, Navy, 
 
 152. 
 of revolutions. To find, 
 for certain speed, 258. 
 To cube, 18. 
 To find the logarithm of 
 
 a, 30. 
 To find, whose logarithm 
 
 is given, 34. 
 To square, 18. 
 Numerator, 13. 
 
 Object, Bearings of, and 
 distance run. 111. 
 The bearing of, 93. 
 
 Objects at sea. Distances 
 of, 114.
 
 INDEX 
 
 Obliquity of the ecliptic, 
 
 120. 
 Obry gear. 229. 
 Observations, Meteorolog- 
 ical, at sea, 290. 
 Observed altitude, 121. 
 Occultation, 126. 
 Officer, Executive. 165. 
 
 Navigating, 166. 
 
 of the deck, 166. 
 Officers, Commissioned, 
 163. 
 
 Division, 166. 
 
 Engineer, 166. 
 
 Line, 151. 
 
 line, Duties of, 165. 
 
 Petty. 156. 
 
 Staff 151. 
 
 Titles of, 152. 
 
 Warrant, 152. 
 
 Watch, 166. 
 Official log book. 100. 
 Oil, Use of, in heavy sea, 
 
 303. 
 One-flag signal, 294. 
 Opposition, 126. 
 Ordnance, Naval, 178. 
 
 U. S. naval. Size and 
 power of, 212. 
 Organization of a man-of- 
 war, 165. 
 
 of crew, 166. 
 
 of the Nav>% 150. 
 Outline of duties in the 
 Navy. 161. 
 
 Parallax Annual, 123, 
 
 in altitude, 123. 
 Parallelogram and rect- 
 angle, 24. 
 Parallelopiped or prism. 
 
 26. 
 Parallel sailing, 93. 
 Parallels of declination, 
 122. 
 of latitude, 92. 
 Parts. Meridional. 94. 
 Pav corps, 152. 
 
 table. Navy, 156. 
 Pelorus, Use of, 90. 
 
 Percentage, 22. 
 
 of slip, Rule to find, 258. 
 
 To find, having rate and 
 base, 22. 
 Percussion fuse, 207. 
 
 primer. 202. 
 Persons that are appar- 
 ently drowned. To 
 restore, 315. 
 Pettv officers, 156. 
 Pilot. Signals for. 301. 
 Piston, Hydrostatic. 226. 
 Plane sailing, 93. 
 
 trigonometry, 64. 
 Planets, Exterior. 124. 
 
 Interior, 124. 
 Plating. Methods of, 248. 
 Plotting a great-circle 
 track, 108. 
 
 of Sumner lines, 143. 
 Point of maximum sepa- 
 ration, 94. 
 Points. Equinoctial, 119. 
 
 of compass in variotis 
 languages, 88. 
 
 Solstitial, 120. 
 Polar distance, 122. 
 Polarity. Blue. 69. 
 
 Magnetic. 69. 
 
 Red, 69. 
 Poles, Celestial. 119. 
 
 Magnetic, 68. 
 
 of the earth. 92. 
 Position, Line of, 142. 
 
 of ship in relation to 
 storm track. To find, 
 287. 
 Pound sterling, 8. 
 Powder, Black, 218. 
 
 Brown, 219. 
 
 chamber of a gun, 197. 
 
 Cocoa, 220. 
 
 Cordite, 222. 
 
 division, 167. 
 
 Granulation of, 222. 
 
 Progressive, 222. 
 
 Shimose, 218. 
 
 Smokeless. 221. 
 
 Various forms of, 224. 
 Preliminary considerations 
 in ship building. 235.
 
 XVI 
 
 INDEX 
 
 Prime meridian, 92, 
 
 vertical, 121. 
 Primer, Combination, 203. 
 Electric, 202. 
 Percussion, 202. 
 Primers, 201. 
 
 Principal ports, Sailing dis- 
 tances between, 146. 
 Principle of gas checking, 
 
 201. 
 Principles of gun con- 
 struction, 189. 
 of ship construction, 235. 
 Prism, Frustum of, 26. 
 or parallelepiped, 26. 
 Problems on speed, 257. 
 Progressive powder, 222. 
 Progress of steam naviga- 
 tion, 304. 
 Projectile, Rotating band 
 
 of, 203. 
 Projectiles, 203. 
 Capped, 205. 
 Promotion of enlisted men, 
 
 163. 
 Propellers of torpedo, 228. 
 Propeller, The slip of, 257. 
 Properties of steel, 192. 
 Property, Magnetic, of the 
 
 earth; 69. 
 Proportion, 16. 
 Compound, 17. 
 Simple, 16. 
 Proportional, Mean, 17. 
 Protected cruisers, 179. 
 Protection abroad to nat- 
 uralized citizens, 322. 
 of wire rope, 265. 
 
 Quadrantal deviation, 72. 
 deviation. To compen- 
 sate, 74. 
 
 Quadrature, 126. 
 
 Quartermasters, Duties of, 
 162. 
 
 Quarters, General, 168. 
 
 R 
 
 Rackarock, 217. 
 Radius of a sphere, 91. 
 
 Rammer, Hydraulic, 211. 
 
 Rapid-fire guns, 188. 
 
 Rate and base. To find 
 percentage, 22. 
 
 Rating of enlisted men, 
 155. 
 
 Rational horizon, 120. 
 
 Ratline, 263. 
 
 Reciprocal bearings, Si- 
 multaneous, 79. 
 
 Record, Enlistment, 169. 
 
 Recruiting stations, 154. 
 
 Rectangle and parallelo- 
 gram, 24. 
 
 Red polarity, 69. 
 
 Reduction of compass 
 
 points to degrees, 86. 
 
 of compound to simple 
 
 fractions, 14. 
 of fractions to decimals, 
 
 14. 
 of simple to compound 
 fractions, 14. 
 
 Reef knot, 277. 
 
 Refraction, 123. _ 
 
 Refrigerating ships in the 
 Navy, 165. 
 
 Remarks on compass man- 
 agement, 81. 
 
 Repulsion and attraction, 
 Magnetic, 69. 
 
 Requirements for enlist- 
 ment, 155. 
 
 Retentive magnetism, 72. 
 
 Reverse bar, 238. 
 
 Revolutions, To find, for 
 certain speed, 258. 
 
 Rewards, Additional, in 
 the Navy, 160. 
 
 Rhumb track, 93. 
 
 Rifled gun, 187. 
 
 Rifling the bore, 196. 
 
 Right ascension, 122. 
 of suffrage, 322. 
 
 Rigs of Navy boats, 185. 
 
 Ring, Circular, 27. 
 
 Root, Extraction of any, 
 19. 
 
 Rope, manila. Breaking 
 strain of, 266. 
 White, 262.
 
 INDEX 
 
 Rope. Wire. 263. 
 
 Wire, Protection of, 265. 
 
 vams, 263. 
 Ropes. 261. 
 
 Coir, 262. 
 
 Fiber. 261. 
 
 Hemp, 261. 
 
 How to belay, 281. 
 
 Manila, 261. 
 
 Shroud-laid, 263. 
 
 Splicing, 270. 
 
 Twisting, 262, 
 Rotating band, 198. 
 
 band of projectile, 203. 
 Routine in port of the 
 
 Navy, 169. 
 Rule for characteristic, 29. 
 
 for finding number of 
 horsepower, 254. 
 
 of three. Double, 17. 
 
 of three. Single, 16. 
 Rules for action to avoid 
 
 storm center, 288. 
 Running gear, wire rope 
 for, Strength of, 269. 
 
 Sailing, Composite, 94. 
 
 distances between prin- 
 cipal ports, 146. 
 
 Great-circle, 94. 
 
 Mercator's, 94. 
 
 Middle-latitude, 93. 
 
 Parallel, 93. 
 
 Plane, 93. 
 
 Traverse, 94. 
 Schools. Special, in the 
 
 Navy, 164. 
 Screw box of a gun, 197. 
 Sea horizon, 121. 
 
 strength of Naval pow- 
 ers, 309. 
 
 Use of on in heavy, 303. 
 Seamen branch, 156. 
 
 How to become citizens, 
 321. 
 Secant of an angle, 65. 
 Sector, 25. 
 Segment, 25. 
 Selected International 
 
 Code signals, 294. 
 
 Semiautomatic guns, 189. 
 Semicircle, Dangerous, 284 
 
 Navigable, 286. 
 Semicircular deviation, 72. 
 Sensible horizon, 120. 
 Separation, maximum. 
 
 Point of, 94. 
 Sheepshank, 277. 
 Sheet bend, 277. 
 Shells, Armor-piercing 
 204. 
 Common, 204. 
 Shimose powder, 218. 
 Shipboard, Division of 
 
 time, 171. 
 Ship building, 235. 
 
 Displacement of a. 254. 
 position of. To find, in 
 relation to storm 
 track, 287. 
 To swing, for deviation, 
 79. 
 Ships, Battle, 174. 
 
 Handling, in hurricanes, 
 
 286. 
 in merchant marine. 
 Number and tonnage 
 of, 307. 
 Number and tonnage of, 
 
 in U. S. Navy, 306. 
 Strain in. 238. 
 war. Classification of, 
 173. 
 Ship's writer, 169. 
 Short splice. To make, 271. 
 Shrapnel, 205. 
 Shroud-laid ropes, 263. 
 Side-bar keel, 240. 
 
 keelson, 240. 
 Sidereal day, 127. 
 
 time, 127. 
 Sights, Sunrise and sun- 
 set 139 
 Signal, One-flag, 294. 
 Signals, Distant, 296. 
 distant. Special, 296. 
 for pilot, 301. 
 Four-flag, 294. 
 Hurricane warning, 301. 
 International Code of, 
 293.
 
 INDEX 
 
 Signals, Life-saving, 302. 
 
 of distress, 300. 
 
 Storm, 301. 
 
 Three-flag, 294, 
 
 Two-flag, 294. 
 Simple fractions, Reduc- 
 tion to compound, 14. 
 
 proportion, 16. 
 Simultaneous reciprocal 
 
 bearings, 79. 
 Sine of an angle, 64. 
 Single rule of three, 16. 
 Sinking gear of torpedo, 
 
 231. 
 Size and power of U. S. 
 
 naval ordnance, 212. 
 Slip of the propeller, 257. 
 
 percentage of. Rule to 
 find, 258. 
 Slope, Band, 198. 
 
 Chamber, 198. 
 
 Gas-check, 198. 
 Small circle, 92, 
 
 stuff, 263. 
 Smokeless powder, 221. 
 Soft iron, 72. 
 Solar day. Apparent, 126. 
 
 system, 124. 
 Solstitial points, 120. 
 Soundings on foreign 
 
 charts, 118. 
 Sound, To find distance by, 
 
 115. 
 Special branch, 158. 
 
 distant signals, 296. 
 
 pav and privileges in the 
 Navy, 159. 
 
 schools in the Navy, 164. 
 Speed and fuel consump- 
 tion, 259. 
 
 of vessels. Notes on, 253. 
 
 Problems on, 257. 
 Sphere, 26. 
 
 Celestial, 119. 
 
 Diameter of, 91. 
 
 Radius of, 91. 
 Spherical angle, 92, 
 
 triangle, 92. 
 Splice, chain. To make, 
 274. 
 
 eye. To make, 274. 
 
 Splice, long. To make, 272. 
 
 short. To make, 271. 
 Splices and bends, 270. ' 
 Splicing in wire, 275. 
 of ropes, 270. 
 wire, lools for, 276. 
 Spun yam, 263. 
 Squadron, Definition of, 
 
 184. 
 Square measure, 1. 
 Stability, 236. 
 Staff corps, 151. 
 
 officers, 151. 
 Star gauging, 196. 
 
 Meridian altitude of, 130. 
 Time sight of, 137. 
 Station billet, 169. 
 Stations, Recruiting, 154. 
 Weather-Bureau, List of, 
 299. 
 Steam launches, 185. 
 navigation. Progress of, 
 304. 
 Steamship companies, lar- 
 gest. Table of, 312. 
 Steamships, notable. Di- 
 mensions of, 314. 
 Steel, Composition of, 192, 
 Elastic strength of, 192, 
 gun, 191. 
 
 hawsers for heavv tow- 
 ing. Strength of, 268. 
 Nickel, 193. 
 Properties of, 192. 
 Tensile strength of, 192. 
 Steering of torpedoes, 228. 
 Sterling, Pound, 8. 
 Storm center. Actions to 
 avoid, 288. 
 center, approaching or 
 receding. To find, 288. 
 center. Description of, 
 
 289. 
 signals, U. S., 301. 
 track, To find position 
 of ship in relation to, 
 287. 
 warning flags, 30 1. 
 Strain in ships, 238. 
 Strength of cast-steel wire 
 rope, 269.
 
 INDEX 
 
 Strength, of galvanized- 
 steel hawsers, 268. 
 of steel hawsers for 
 
 heavy towing, 268. 
 of wire rope for running 
 gear, 269. 
 Stringers, 240. 
 Stringer, The deck, 241. 
 Stuff, Small, 263. 
 Subpermanent magnetism, 
 
 72. 
 Subtraction of decimals, 
 15. 
 of fractions, 13. 
 Suffrage, Right of, 322. 
 Sumner line, 142. 
 
 lines, Plotting of, 143. 
 Sumner's method, 142. 
 Sun, Ex-meridian of, 133. 
 Mean, 126, 
 Meridian altitude of, 
 
 129. 
 Time sight of, 135. 
 Sunrise and sunset sights, 
 
 139. 
 Superior conjunction, 124. 
 Supplement of an arc, 64. 
 Surface, Measures of, 9. 
 Swinging a ship for devia- 
 tion, 79. 
 System, Metric, 8. 
 Solar. 124. 
 
 Table, Long-ton, 2. 
 
 of common logarithms, 
 46. 
 
 of compass points, 86. 
 
 of constants, 255. 
 
 of distances, 4. 
 Table of distances of vis- 
 ibility at sea, 114. 
 
 of elements in solar sys- 
 tem, 125. 
 
 of foreign money, 6. 
 
 of completed warships, 
 310. 
 
 of fractions, 15. 
 
 of largest steamship 
 companies, 312. 
 
 of latitudes, 104. 
 
 Table of merchant fleet of 
 
 the world, 311. 
 
 of metric equivalents, 10. 
 
 of naval ordnance. 212. 
 
 of notable merchant 
 
 steamships, 314. 
 of sailing distances, 146. 
 of vessels built in U. S., 
 
 308. 
 Pay, of the Navy, 156. 
 Tables for two bearings 
 and distance run, 112. 
 Traverse, 94. 
 Tangent of an angle, 64. 
 Tensile strength of steel, 
 
 192. 
 Terms, Astronomical, 119. 
 relating to navigation, 
 91. 
 Terrestrial navigation, 91. 
 Three-flag signals, 294. 
 Time, Division of, on ship- 
 board, 171. 
 Equation of, 126. 
 fuse, 206. 
 Local mean, 127. 
 Mean, 126. 
 Measures of, 3. 
 Sidereal, 127. 
 sight of a star, 137. 
 sight of the sun, 135. 
 Titles of officers, 152. 
 To cube a number, 18. 
 find approaching or rece- 
 ding storm center, 288. 
 find center of hurricane, 
 
 287. 
 find logarithm of a num- 
 ber, 30. 
 find number whose loga- 
 rithm is given, 34. 
 produce breathing, 316. 
 restore persons appar- 
 ently drowned, 315. 
 square a number, 18. 
 Tonnage and displace- 
 ment, 256. 
 and number of ships 
 
 built in U. S., 308. 
 and number of ships in 
 U. S. Navy, 306.
 
 INDEX 
 
 Tonnage, Gross, 256. 
 
 Net, 256. 
 
 of completed warships, 
 310. 
 Tools for splicing in wire, 
 
 276. 
 Top carriage of a gun, 209. 
 Torpedo, Air flask of. 225. 
 
 boat destroyers, 184. 
 
 boats, 179. 
 
 boats, Importance of, 
 234. 
 
 director, 232. 
 
 Exercise head of, 225. 
 
 Main engine of, 228. 
 
 Propellers of, 228. 
 
 Sinking gear of, 231. 
 
 War head of, 225. 
 
 Whitehead, 224. 
 Torpedoes, 224. 
 
 Launching tubes of, 231. 
 
 Steering of, 228. 
 Track, great-circle, To 
 plot, 108. 
 
 The rhumb, 93. 
 Training stations, 151. 
 Transit or transition, 123. 
 Trapezium, 25. 
 Trapezoid. 24. 
 Traverse tables, 94. 
 
 sailing, 94. 
 Treatment, M o d i f i e d, of 
 apparently drowned 
 persons, 319. 
 
 of gun steel, 193. 
 Triangle, Spherical, 92. 
 Triangles, 23. 
 Trigonometric functions, 
 
 65. 
 Trigonometry applied in 
 practice, 66. 
 
 Plane, 64. 
 Trov weight. 2. 
 True altitude. 121. 
 
 amplitude, 122. 
 
 azimuth, 121. 
 
 course, 83. 
 
 course. To find compass 
 course from, 84. 
 
 horizon, 120. 
 Turret mounts, 210. 
 
 Twisting of ropes. 262. 
 Two bearings and distance 
 run. Tables oi con- 
 stants for, 112. 
 flag signals, 294. 
 Types of keel, 241. 
 of wire rope. 264. 
 Typhoons, Indications of, 
 289. 
 
 U 
 
 United States money, 5. 
 
 naturalization laws. 320. 
 
 naval ordnance. Size and 
 power of, 212. 
 
 Navy, 150. 
 
 Navy, Number and ton- 
 nage of ships in, 306. 
 
 storm signals, 301. 
 Use of oil in heavy sea, 
 303. 
 
 of pelorus, 90. 
 
 Value of foreign measures, 
 12. 
 of foreign money, 6. 
 Variation, Magnetic, 70. 
 Velocity of sound. To find 
 
 distance by, 115. 
 Vent-sealing, 202. 
 Vernal equinox, 119. 
 Vertex of a great circle, 94. 
 Vertical and horizontal 
 iron, 72. 
 danger angle, 116. 
 Prime, 121. 
 Verticals, 121. 
 Vessels built in United 
 States, Number and 
 tonnage of, 308. 
 speed of. Notes on, 253. 
 Volume [and capacity, 
 Measures of, 9, 
 Measures of, 4. 
 
 W 
 
 War head of torpedo, 225. 
 ships, Classification of, 
 173.
 
 INDEX 
 
 xxi 
 
 Warships, completed. 
 Number of, 309. 
 ships, completed. Ton- 
 nage of, 310. 
 Warrant officers, 152. 
 Watch officers, 166. 
 
 quarter and station 
 book. 169. 
 W a t e r-tight compart- 
 ments, 245. 
 Weather and wind, 281. 
 Bureau stations, List of, 
 
 299. 
 indications by aneroid 
 
 barometer, 283. 
 indications by appear- 
 ance of sky, 283. 
 indications by mercurial 
 
 barometer, 281, 
 observance, 291. 
 'Wedge, 27. 
 
 Weight, Avoirdupois, 2. 
 Measures of, 9. 
 Troy, 2. 
 'Weights and measures, 1. 
 'Welin breech lock, 199. 
 'Whale boats, 185. 
 ^Whitehead torpedo, 224. 
 
 White rope, 262. 
 
 Wind and weather, 281. 
 
 Wire rope, 263. 
 
 rope, cast-steel. Strength 
 
 of, 269. 
 rope for running gear, 
 
 Strength of, 269. _ 
 rope, galvanized-iron. 
 Breaking strain of, 
 267. 
 rope. Protection of, 265. 
 rope. Types of, 264. 
 Splicing of, 275. 
 splicing. Tools for, 276. 
 Work, The dav's, 100. 
 Writer, Ship's, 169. 
 
 Yards, Navy, 150. 
 Yam, Spun, 263. 
 Yams, Rope, 263. 
 Yeomen, 158. 
 Duties of, 163. 
 
 Zenith, 120. 
 
 distance, 121. 
 Zone, Neutral, €
 
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 MARINERS' Handbook 
 
 USEFUL TABLES 
 
 WEIGHTS AND MEASURES 
 
 LINEAR MEASURE 
 
 12 inches (in.) =1 foot ft. 
 
 3 feet = 1 yard yd. 
 
 5i yards = 1 rod rd. 
 
 40 rods = 1 furlong fur. 
 
 8 furlongs =1 mile mi. 
 
 in. ft. yd. rd. fur. mi. 
 
 36 = 3 = 1 
 198= 16.5= 5.5= 1 
 7,920= 660= 220= 40 = 1 
 63,360 = 5,280 = 1,760 = 320 = 8 = 1 
 
 SQUARE MEASURE 
 
 144 square inches (sq. in.) . . = 1 square foot sq. ft. 
 
 9 square feet = 1 square yard sq. yd. 
 
 30 J square yards = 1 square rod sq. rd. 
 
 160 square rods = 1 acre A. 
 
 640 acres =1 square mile sq. mi. 
 
 sq.mi.A. sq. rd. sq. yd. sq. ft. sq. in. 
 
 1 = 640 = 102,400 = 3,097,600 = 27,878,400 = 4,014,489.600 
 
 CUBIC MEASURE 
 
 1,728 cubic inches (cu. in.) . . = 1 cubic foot cu. ft. 
 
 27 cubic feet = 1 cubic yard cu. yd. 
 
 128 cubic feet = 1 cord cd. 
 
 24| cubic feet = 1 perch P. 
 
 1 cu. yd. =27 cu. ft. =46,656 cu. in.
 
 2 USEFUL TABLES 
 
 MEASURE OF ANGLES OR ARCS 
 
 60 seconds (") = 1 minute . . .' 
 
 60 minutes = 1 degree • 
 
 90 degrees = 1 rt. angle or quadrant. . Q 
 
 360 degrees = 1 circle ci •. 
 
 1 cir.=360° = 21,600' = l,296,000'' 
 
 A quadrant is one-fourth the circumference of a circle, or 
 90°; a sextant is one-sixth of a circle, or 60°. A right angle 
 contains 90°. The unit of measurement is the degree or 
 j^ of the circumference of a circle. 
 
 AVOIRDUPOIS WEIGHT 
 
 437^ grains (gr.) = 1 ounce oz. 
 
 16 ounces =1 pound lb. 
 
 100 pounds =1 hundredweight cwt. 
 
 20 cwt., or 2,000 lb =1 ton T. 
 
 1 T. = 20 cwt. =2,000 lb. = 32,000 oz. = 14,000,000 gr. 
 The avoirdupois pound contains 7,000 gr. 
 
 LONG-TON TABLE 
 
 16 ounces = 1 pound lb. 
 
 112 pounds = 1 hundredweight cwt. 
 
 20 cwt., or 2,240 lb = 1 ton T. 
 
 TROY WEIGHT 
 
 24 grains (gr.) = 1 pennyweight pwt. 
 
 20 pennyweights = 1 ounce oz. 
 
 12 otmces = 1 pound lb. 
 
 1 lb. = 12 oz. = 240 pwt. = 5,760 gr. 
 
 DRY MEASURE 
 
 2 pints (pt.) =1 quart qt. 
 
 8 quarts = 1 peck pk. 
 
 4 pecks =1 bushel bu. 
 
 1 bu. = 4 pk.=32 qt. = 64 pt. 
 
 The U. S. struck bushel contains 2,150.42 cu. in. = 1.2444 
 cu. ft. By law, its dimensions are those of a cylinder 18J 
 in. in diameter and 8 in. deep. The heaped bushel is equal 
 to li struck bushels, the cone being 6 in. high. The dry 
 gallon contains 268.8 cu. in., being \ struck bushel.
 
 USEFUL TABLES 
 
 For approximations, the bushel may be taken as 1 J cu. ft.; 
 or 1 cu. ft. may be considered f bu. 
 
 The British bushel contains 2,218.19 cu. in. = 1.2837 cu. ft. 
 = 1.032 U. S. bushels. 
 
 LIQUID MEASURE 
 
 4 gills (gi.) 
 
 2 pints 
 
 4 quarts 
 
 31i gallons 
 
 2 barrels, or 63 gallons 
 
 = 1 pint pt. 
 
 = 1 quart qt. 
 
 = 1 gallon gal. 
 
 = 1 barrel bbl. 
 
 = 1 hogshead hhd. 
 
 1 hhd.=2 bbl. = 63 gal.=252 qt.=504 pt.=2,016 gi. 
 
 The U. S. gallon contains 231 cu. in. = .134 cu. ft., nearly, 
 or 1 cu. ft. contains 7.481 gal. The following cylinders con- 
 tain the given measures very closely; 
 
 Gill... 
 Pint.. 
 Quart. 
 
 Diam. Height 
 ..IJ in. 3 in. 
 . .3^ in. 3 in. 
 . .3i in. 6 in. 
 
 Diam. Height 
 
 Gallon 7 in. 6 in. 
 
 8 gallons. ..14 in. 12 in. 
 
 10 gallons. . .14 in. 15 in. 
 
 When water is at its maximum density, 1 cu. ft. weighs 
 62.425 lb. and 1 gal. weighs 8.345 lb. 
 
 For approximations, 1 cu. ft. of water is considered equal 
 to 7i gal., and 1 gal. as weighing 8i lb. 
 
 The British imperial gallon, both liquid and dry, con- 
 tains 277.274 cu. in. = .16046 cu. ft., and is equivalent to 
 the volume of 10 lb. of pure water at 62° F. To reduce 
 British to U. S. liquid gallons, multiply by 1.2. Conversely, 
 to convert U. S. into British liquid gallons, divide by 1.2; 
 or, increase the number of gallons \. 
 
 MEASURES OF TIME 
 
 60 seconds (sec). 
 
 60 minutes 
 
 24 hours 
 
 7 days 
 
 4 weeks 
 
 12 month 
 
 100 years 
 
 = 1 minute min. 
 
 = 1 hour hr. 
 
 = 1 day da. 
 
 = 1 week wk. 
 
 = 1 month mo. 
 
 = 1 year yr. 
 
 = 1 century C.
 
 4 USEFUL TABLES 
 
 sec. min. hr. da. wk. yr. 
 
 60= 1 
 
 3,600= 60= 1 
 
 86,400= 1,440= 24= 1 
 604,800= 10,080= 168= 7= 1 
 31.556,936 = 525,948 = 8,765 = 365 = 52 = 1 
 
 TABLE OF DISTANCES 
 
 1 statute or land mile = 5,280 ft.; 1,760 yd.; 
 
 320 rd.; 8 fur. 
 
 1 furlong = 40 rd. 
 
 1 league =3 mi. 
 
 1 knot,* or nautical mile = 6,080 ft., or IJ mi. 
 
 1 nautical league =3 naut. mi. 
 
 1 fathom = 6 ft. 
 
 1 meter =3 ft. 3f in., nearly 
 
 1 hand = 4 in. 
 
 1 palm = 3 in. 
 
 1 span = 9 in. 
 
 1 cable's length = 240 yd. 
 
 Austrian mile = 4.09 naut. mi. 
 
 Danish mile = 4.06 naut. mi. 
 
 French kilometre = .54 naut. mi. 
 
 German Ruthen = 4.06 naut. mi. 
 
 Italian mile = 1.00 naut. mi. 
 
 Norwegian mile = 6.01 naut. mi. 
 
 Russian verst = .57 naut. mi. 
 
 Swedish mile = 5.75 naut. mi. 
 
 MEASURES OF VOLUME 
 
 1 cubic foot = 1 ,728 cu. in. 
 
 1 ale gallon = 282 cu. in. 
 
 1 standard, or wine, gallon = 231 cu. in. 
 
 1 dry gallon = 268.8 cu. in. 
 
 1 bushel = 2,150.4 cu. in 
 
 1 British bushel = 2,218.19 cu. in. 
 
 1 cord of wood = 128 cu. ft. 
 
 •A knot is really a measure of speed and not of distance; when used in this 
 sense, it is eijuivalent to 1 naut. mi. in 1 hr. Thus, a vessel running 20 naut. 
 mi. per hr. has a speed oi 20 Icnots.
 
 USEFUL TABLES 
 
 1 perch = 24.75 cu. ft. 
 
 1 ton of round timber =40 cu. ft. 
 
 1 ton of hewn timber =50 cu. ft. 
 
 A box 12^1 in. long, wide, and deep contains 1 bu. 
 
 A box 19f in. long, wide, and deep contains 1 bbl. 
 
 A box 8| in. long, wide, and deep contains 1 pk. 
 
 A box 6/5 in. long, wide, and deep contains i pk. 
 
 A box 4i')| in. long, wide, and deep contains 1 qt. 
 
 MEASURES OF MONEY 
 
 UNITED STATES MONEY 
 
 = 1 cent ct. 
 
 = 1 dime d. 
 
 = 1 dollar I 
 
 =1 eagle E. 
 
 d. $ E. 
 
 10 mills (m) = 
 
 10 cents = 
 
 10 dimes = 
 
 10 dollars = 
 
 m. ct. 
 
 10= 1 
 
 100= 10= 1 
 1.000= 100= 10= 1 
 10,000 = 1,000 = 100 = 10 = 1 
 The term legal tender is applied to money that may be 
 legally offered in payment of debts. All gold coins are 
 legal tender for their face value to any amount, provided 
 that their weight has not diminished more than ^J^. Silver 
 dollars are also legal tender to any amount; but silver 
 coins of lower denomination than $1 are legal tender only 
 for sums not exceeding SIO. Nickel and copper coins are 
 legal tender for sums not exceeding 25 ct. 
 
 ENGLISH MONEY 
 
 4 farthings (far.) . 
 
 12 pence 
 
 20 shillings 
 
 far. 
 4 = 
 48 = 
 
 . = 1 penny d. 
 
 . = 1 shilling s. 
 
 . = 1 pound, or 
 
 sovereign £ 
 
 d. s. £ 
 
 12= 1 
 240 = 20 = 1
 
 USEFUL TABLES 
 
 i? u 
 
 rt [/) 
 
 
 cOOOSrf 
 
 00«3<CtOiMt^OOrt<00>Tjl 
 
 I 
 
 C:(Nr-ikO O O CC O •>* 0> (N ■^ 05 ^ i-H (N 
 
 >_gO 
 
 •. ' ■ ■ ^" ^' ■ ■ ' 
 
 
 o 
 
 
 puw w)tnwi/5 w 
 
 
 Co:,l> OOOOyiWhr 
 
 +i 
 
 ntesi 
 eutz( 
 ntim 
 reis 
 
 nts 
 
 nts 
 
 ntav 
 
 cash 
 
 ntav 
 
 ntav 
 
 e 
 
 ntav 
 
 aster 
 
 ;nni 
 
 ntim 
 
 enni} 
 
 'H 
 
 
 ajv-(u (U(D<D (uo^^ oj'" '±; o'-t' 
 
 P 
 
 u4^So ooooou:ooP.Rua 
 
 >, 
 
 §§§1 §|§§§|§§2§S§ 
 
 
 7 II 7 II II II 11 II 11 II 'i 11 11 11 11 11 
 
 c 
 
 
 o 
 
 
 s 
 
 C '^ U U <D T) ,, 
 
 
 o & c"« ^J5 oi. g o S 2i St^c-^ 
 "^ o c5-i: ^•7:; ^ <U'2 o^ p o p b ca b 
 '» t, C^i: o o <u rt o aj,^; :i oJS >-j2 
 
 T3 
 
 w cAJ w c/i 
 
 ^ 
 
 ^3 T) 'd . . . .-O . 
 
 1 
 
 SO CO ooocAio goooo so 
 
 W 
 
 do do 
 
 
 
 
 
 
 ^-^ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ^ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 "OJ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 :z: 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ■fj 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 a 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 dj 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 X 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 (U 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 to 
 
 1 
 
 
 
 
 
 rt 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 3 
 
 c. 
 
 
 
 
 1 
 
 
 
 
 
 
 
 
 
 
 
 
 O 
 
 .X 
 
 
 
 c 
 
 
 
 
 
 
 
 
 
 
 
 
 CJ 
 
 2 >> 
 
 
 <5 "^ 
 
 
 
 
 
 
 
 
 
 
 
 
 3 >- 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 X P 
 
 
 
 
 
 
 
 
 
 
 
 
 
 C2-^T3 
 
 
 
 
 
 
 
 
 
 
 
 
 ^§ 
 
 
 !'§§ 
 
 
 rt 
 
 
 
 
 
 
 
 
 
 c^; 
 
 !2: rtw 
 
 
 •ii 
 
 •^ u 
 
 
 
 
 ^ 1 
 
 
 <U *-■ w; N • 13 n "^ ^ 
 
 
 
 ih 
 
 C0> 
 
 Ml 
 
 
 u 'Z di u u^ uj^jg o 3 iu o dc.^; w (u i 
 
 
 < 
 
 < 
 
 CQ 
 
 cc 
 
 cq PC 
 
 o 
 
 CJ 
 
 
 
 c 
 
 C 
 
 w 
 
 fl. 
 
 fe 
 
 &. 
 
 c 
 
 1
 
 USEFUL TABLES 
 
 
 
 o C M o 
 
 
 ccccccc£iac(uc 
 
 
 C C 
 
 II II II II II II II II 
 
 II II 
 
 CO 
 
 '^ri'Ti <U U I- c I- 
 
 Co t. i; ^ ■ rti3-ri3 
 
 o V- o ^.b. <u c c^ z „ „.„ „ _ 
 
 (U ra « O IJ P 
 - '-^ ? rt rt <^ "T 
 
 WW CO 
 
 O O 
 
 COS 
 
 
 5 = 
 
 -- 2 r< '-^ J. D 
 
 ^ rt o.t; i_ 
 
 ii W 7D 72 H 
 
 ^S'1 
 
 D>
 
 8 USEFUL TABLES 
 
 The unit of English money is the pound sterling, the 
 vakie of which in United States money is $4.8665. The 
 fineness of English silver is .925; of the gold coins, .916f. 
 What is called sterling silver when applied to solid silver 
 articles has the same fineness. Hence the name sterling 
 silver. 
 
 The other coins of Great Britain are the florin ( = 2 shil- 
 lings), the crown ( = 5 shillings), the half crown ( = 2^ 
 shillings), and the guinea (=21 shillings). The largest 
 silver coin is the crown, and the smallest, the threepence 
 (i shilling). The shilling is worth 25 ct. (24.3 + ct.) in 
 United States money. The guinea is no longer coined. The 
 abbreviation £ is written before the number, while s. and d. 
 follow. Thus, £25 4s. 6d. = 25 pounds 4 shillings 6 pence. 
 
 Rule. — To reduce pounds, shillings, and pence to dollars 
 and cents, reduce the pounds to shillings, add the shillings, if 
 any, and multiply the sum by .24^; if any pence are given, 
 increase this product by twice as many cents as there are pence. 
 
 Example. — Reduce £4 7s. 14d. to dollars and cents. 
 
 Solution.— {4 X 20 + 7) X .24 J + .28 = $21 .45. Ans. 
 
 Rule. — To reduce pounds to dollars, and vice versa, exchange 
 being at $4.8665: Multiply the number of pounds by 73, 
 and divide the quotient fey 15; the result will be the equivalent 
 VI dollars and cents. Or, multiplying the dollars by \b and 
 dividing the product by 73 will give its equivalent in pounds 
 and decimals of a pound. 
 
 Example. — Reduce £6 to dollars and cents. 
 
 Solution. — 6 X 73 H- 15 = $29.20. Ans. 
 
 Example. — Reduce $17 to pounds. 
 
 Solution.— 17X15 -^73 = £3.493. Ans. 
 
 THE METRIC SYSTEM 
 The metric system is based on the meter, which, according 
 to the United States Coast and Geodetic Survey Report of 
 1884, is equal to 39.370432 in. The value commonly used is 
 39.37 in., and is authorized by the United States government. 
 The meter is defined as one ten-millionth the distance from 
 the pole to the equator, measured on a meridian passing near 
 i-aris, France.
 
 USEFUL TABLES 9 
 
 There are three principal units — the meter, the liter (pro- 
 nounced lee-ter), and the gram, the units of length, capacity, 
 and weight, respectively. Multiples of these units are 
 obtained by prefixing to the names of the principal units 
 the Greek words deca (10), hecto (100), and kilo (1,000); 
 the submultiples, or divisions, are obtained by prefixing 
 the Latin words deci (^), centi (t^tj), and milli (ttjW)- These 
 prefixes form the key to the entire system. 
 
 
 MEASURES OF LENGTH 
 
 
 
 10 millimeters . , 
 
 = 1 centimeter 
 
 = 
 
 .394 in. 
 
 10 centimeters., 
 
 = 1 decimeter 
 
 = 
 
 3.937 in. 
 
 10 decimeters. . 
 
 = 1 meter 
 
 = 
 
 3.281 ft. 
 
 10 meters 
 
 = 1 decameter 
 
 32.809 ft. 
 
 10 decameters . , 
 
 = 1 hectometer 
 
 = 
 
 109.363 yd. 
 
 10 hectometers = 1 kilometer = 1,093.63 yd. 
 
 MEASURES OF SURFACE (NOT LAND) 
 
 100 sq. millimeters . . = 1 sq. centimeter. . == .155 sq. in. 
 100 sq. centimeters... = 1 sq. decimeter... = 15.5 sq. in. 
 100 sq. decimeters. . . = 1 sq. meter = 10.764 sq. ft. 
 
 MEASURES OF VOLUME AND CAPACITY 
 
 10 milliliters =1 centiliter = .61 
 
 10 centiliters = 1 deciliter = 6.10 
 
 10 deciliters = 1 liter =61.02 
 
 10 liters = 1 decaliter = .353 
 
 10 decaliters = 1 hectoliter = 3.53 
 
 10 hectoliters = 1 kiloliter = 35.31 cu. ft. 
 
 The liter is equal to the volume occupied by 1 cu. decimeter. 
 
 MEASURES OF WEIGHT 
 
 10 milligrams = 1 centigram . . . = .154 gr. 
 
 10 centigrams = 1 decigram ... = 1.54 gr. 
 
 10 decigrams = 1 gram = 15.43 gr. 
 
 10 grams = 1 decagram. . . . = 154.32 gr, 
 
 10 decagrams = 1 hectogram . . . = .220 lb., avoir. 
 
 10 hectograms = 1 kilogram = 2.204 lb., avoir. 
 
 1,000 kilograms = 1 ton = 2.204 lb., avoir. 
 
 cu. 
 
 in. 
 
 cu. 
 
 m. 
 
 cu. 
 
 m. 
 
 cu. 
 
 ft. 
 
 cu. 
 
 ft.
 
 10 
 
 USEFUL TABLES 
 
 The gram is the weight of 1 cu. cm. of pure distilled 
 water at a temperature of 39.2° F.; the kilogram is the 
 weight of 1 liter of water; the ton is the weight of 1 cu. m. 
 of water. 
 
 METRIC EQUIVALENTS OF POUNDS, FEET, ETC. 
 
 The following table will be found valuable for reference 
 by masters, officers, and stewards in their dealings with 
 ship chandleries and other supply stores in countries where 
 the metric system is used: 
 
 Pounds 
 1 
 
 Kilos. 
 = .454 
 = .909 
 = 1.363 
 = 1.818 
 = 2.272 
 = 2.727 
 = 3.161 
 = 3.636 
 = 4.090 
 = 4.545 
 = 9.060 
 = 13.635 
 = 18.180 
 = 22.725 
 . = 1 metric 1 
 
 Centi- 
 meters 
 = 2.54 
 = 30.48 
 = 91.44 
 = 61.00 
 = 91.44 
 = 122.00 
 = 152.00 
 = 182.88 
 
 Pounds 
 
 60 
 
 70 
 
 80 
 
 Kilos. 
 =. 27 . 270 
 
 2 
 
 3 
 
 .. . = 31.815 
 ... = 36.360 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 90 
 
 100 
 
 200 
 
 300 
 
 400 
 
 500 
 
 600 
 
 700 
 
 800 
 
 900 
 
 1,000 
 
 on (Tonelada 
 
 7 feet 
 
 8 feet 
 
 ... = 40.905 
 . ... = 45.450 
 
 ... = 90.900 
 . ... = 136.350 
 
 ... = 181.800 
 = 227.250 
 
 10 
 
 20 
 
 . ... = 272.700 
 .. . = 318.150 
 
 30 
 
 40 
 
 50 
 
 1.000 kilos 
 
 ... = 363.600 
 .. . = 409.050 
 
 = 454.500 
 
 metrico). 
 
 Centi- 
 meters 
 = 213.00 
 
 1 foot 
 
 = 243 . 84 
 
 1 vard 
 
 9 feet 
 
 =274.32 
 
 2 feet 
 
 10 feet 
 
 = 304.80 
 
 3 feet 
 
 11 feet 
 
 = 335.28 
 
 4 feet . . 
 
 12 feet 
 
 = 365.76 
 
 5 feet . . . 
 
 13 feet 
 
 = 396.24 
 
 6 feet 
 
 14 feet 
 
 = 426.72
 
 USEFUL TABLES 
 
 11 
 
 1 gill = .142 liter 
 
 1 pint = .568 liter 
 
 1 quart = 1 . 136 liters 
 
 1 gallon = 4.543 liters 
 
 1 peck = 9 . 087 liters 
 
 1 bushel = 36.347 liters 
 
 1 quarter = 290 . 781 liters 
 
 1 ounce, avoir = 2.83 decigrams 
 
 1 pound, avoir = .45 kilogram 
 
 1 hundredweight, avoir = 50.80 kilograms 
 
 1 ton. avoir = 1 ,016.05 kilograms 
 
 1 pennyweight, troy = 1 .55 grams 
 
 1 ounce, troy = 31.10 grams 
 
 1 pound, troy = 373.24 grams 
 
 NAUTICAL MILES TO KILOMETERS 
 
 Nautical 
 Miles 
 
 Kilometers 
 
 Nautical 
 Miles 
 
 Kilometers 
 
 1 
 
 1.8532 
 
 20 
 
 37.064 
 
 2 
 
 3 . 7064 
 
 30 
 
 55.596 
 
 3 
 
 5.5596 
 
 40 
 
 74.128 
 
 4 
 
 7.4128 
 
 50 
 
 92.660 
 
 5 
 
 9.2660 
 
 60 
 
 111.190 
 
 6 
 
 ll.li90 
 
 70 
 
 129.720 
 
 7 
 
 12.9720 
 
 80 
 
 148.250 
 
 8 
 
 14.8250 
 
 90 
 
 167.880 
 
 9 
 
 16.7880 
 
 100 
 
 185.320 
 
 10 
 
 18.5320 
 
 110 
 
 203.850 
 
 KILOMETERS TO NAUTICAL MILES 
 
 Kilo- 
 
 Nautical 
 
 Kilo- 
 
 Nautical 
 
 meters 
 
 Miles 
 
 meters 
 
 Miles 
 
 1 
 
 .5396 
 
 20 
 
 10.792 
 
 2 
 
 1.0792 
 
 30 
 
 16.188 
 
 3 
 
 1.6188 
 
 40 
 
 21.584 
 
 4 
 
 2 . 1584 
 
 50 
 
 26.980 
 
 5 
 
 2.6980 
 
 60 
 
 32.375 
 
 6 
 
 3.2375 
 
 70 
 
 37.771 
 
 7 
 
 3.7771 
 
 80 
 
 43.167 
 
 8 
 
 4.3167 
 
 90 
 
 48.563 
 
 9 
 
 4.8563 
 
 100 
 
 53.959 
 
 10 
 
 5.3959 
 
 110 
 
 59.355
 
 12 USEFUL TABLES 
 
 VALUE OF MISCELLANEOUS FOREIGN MEASURES 
 
 The following list contains the value of various foreign 
 measures as given in Monthly Consular Reports published 
 by the Department of Commerce and Labor. Many of 
 the equivalents are probably only approximately correct. 
 Argentine Republic. — 1 frasco = 2.5 qt., 1 baril = 20.1 gal., 
 
 1 libra = 1 lb.. 1 vara = 34.1 in., 1 arroba (dry) =25.3 lb. 
 
 1 quintal = 101.4 lb. 
 Belgium. — 1 last = 85.1 bu. 
 
 Brazil— I arroba = 32.4 lb., 1 quintal = 130 lb. 
 Chile.— I fanega'(dry)=2.5 bu., 1 vara = 33.3 in. 
 China.— I catty = 1.3 lb.. 1 picul = 133.3 lb., 1 chik = 14in., 
 
 1 tsun = 1.4 in., 1 li = 2,115 ft. 
 Costa Rico. — 1 manzana = 1.8 A. 
 Cuba. — 1 vara = 33.4 in., 1 arroba (liquid) = 4.3 gal.. 1 fanega 
 
 (dry) = 1.6 bu., 1 libra = 1 lb. 
 Denmark. — 1 tonde (cereals) =3.9 bu.. 1 centner = 110.1 lb. 
 Greece.—! livre = l.l lb., 1 oke = 2.8 lb.. 1 quintal = 123.2 lb. 
 Japan. — 1 sun = 1.2 in., 1 shaku = 11.9 in., 1 ken = 6 ft., 
 
 1 sho = 1.6 qt., 1 to = 2 pk., 1 koku = 4.9 bu., 1 catty 
 
 = 1.31b., 1 picul = 133.3 lb. 
 Mexico. — 1 carga = 300 lb.; other measures same as Cuba 
 
 and Argentine Republic. 
 Peru.— I vara = 33.4 in., 1 libra = 1 lb.. 1 quintal = 101.4 lb. 
 Portugal. — 1 almuda = 4.4 gal.. 1 arratel = l lb., 1 arroba 
 
 = 32.4 lb. 
 Russia. — 1 vedro = 2.7 gal., 1 korree = 3.5 bu., 1 chetvert 
 
 = 5.7 bu., 1 funt = .9 lb., 1 pood = 36.1 lb., 1 berkovets 
 
 = 361.1 lb., 1 verst = 0.66 mi. 
 Siam. — 1 catty = 1.3 lb., 1 coyan = 2,667 lb. 
 Spain. — 1 pie = .9 ft., 1 vara = .9 yd., 1 arroba(liquid) = 4.3 gal. 
 
 1 fanega (liquid) = 16 gal., 1 butt (wine) = 140 gal., 1 
 
 last (salt) =4.760 lb. 
 Sweden. — 1 tunna = 4.5 bu., 1 sk^lpund = l.l lb., 1 centner 
 
 = 93.7 lb. 
 Turkey.— I pik = 27.9 in., 1 oke = 2.8 1b.. 1 cantar = 124.7 lb. 
 Uruguay. — 1 cuadra= 2 A., 1 suerte = 2,700 cuadras, 1 
 
 fanega (single) =3.8 bu., 1 fanega (double) = 7 7 bu. 
 Zanzibar. — 1 frasila = 35 lb.
 
 ARITHMETIC 13 
 
 ARITHMETIC 
 COMMON FRACTIONS 
 
 Two numbers are required to express a fraction; one 
 is called the numerator and the other the denominator. 
 The numerator is the number that tells how many parts 
 of a whole is taken. Thus, 2 is the numerator of |, as it 
 shows that two of three parts into which the whole is divided 
 are taken. The denominator of a fraction is the number 
 that shows into how many parts the whole is divided. Thus, 
 in the fraction ^ the 3 is the denominator. A common 
 denominator is a denominator that is common to two or 
 more fractions. Thus, \ and f have common denominators; 
 and 12 is a common denominator for \, ^, \, and ^ as they 
 are, respectively, equal to -fn, /i, f^, and i%. 
 
 Addition of Fractions. — If of the same denominator, add 
 together the numerators only. Thus, TB + TB + TB = fB- 
 
 If they have different denominators, change them to 
 fractions with common denominators and then proceed 
 as before. 
 
 Example. — What is the sum of a + i + s? 
 
 Solution. — We have 3 = IS, 4 = M. and 5 = i§; hence, 
 «8 + M + bS = ss- Ans. 
 
 Subtraction of Fractions. — Reduce them to a common 
 
 denominator, take the less from the greater, and reduce 
 
 4.V 1. 7 . 9 . 14-9 5 . ^, ^. 
 
 the result; as, — m. — -7. m. = — -~ — = — ; m. It they are 
 o lb lb lb 
 
 mixed numbers, subtract fractie.ns and whole numbers sepa- 
 rately, placing remainders besic..3 one another; thus, 3| in. 
 -2Hn. = (3-2) + (t-|) = lf in. 
 Multiplication of Fractions. — Multiply the numerators 
 ■together for the numerator and the denominators for the 
 denominator. Thus, 
 
 1^ _3 2 _ 2X3 _ 1 _ J__ 
 2 16 3 2 X 16 X 3 96 16 
 Division of Fractions. — Invert the divisor and multiply. 
 Example. — Divide b\ by f. 
 Solution. — ^Xf = i*2s- Ans.
 
 14 ARITHMETIC 
 
 Reduction of Compound to Simple Fractions. — Mvdtiply 
 the integer by the denominator of the fraction and add 
 the numerator for the new numerator and place it over 
 the denominator. 
 
 Example. — Reduce 5§ to a simple fraction. 
 
 Solution. — 5X3 + 2 = 17, which is the numerator, and 
 the fraction is therefore -\f. Ans. 
 
 Reduction of Simple to Compound Fractions. — Divide the 
 numerator by the denominator and use the remainder as 
 the numerator of the remaining fraction. 
 
 Example. — Reduce -%* to a compound fraction. 
 
 Solution. — 9)64(7 
 
 63 
 ~T 
 
 Hence, the compound fraction is 7^. Ans. 
 
 Reduction of Fractions to Decimals. — Annex ciphers to 
 the numerator, and divide by the denominator and point: 
 off as many decimals places in the quotient as there are 
 ciphers used. 
 
 Example. — Reduce y^g to decimals. 
 
 Solution. — 
 
 1 6 ) 9.0 ( .5 6 2 5. Ans. 
 80 
 
 foo 
 
 _9_6 
 
 ~lo 
 
 32 
 80 
 80
 
 ARITHMETIC 15 
 
 TABLE OF FRACTIONS REDUCED TO DECIMALS 
 
 «^ 
 
 .015625 
 
 ^ 
 
 .265625 
 
 If 
 
 .515625 
 
 
 .765625 
 
 
 .03125 
 
 9 
 
 .28125 
 
 .53125 
 
 .78125 
 
 3 
 
 .046875 
 
 19 
 
 .296875 
 
 35 
 
 .546875 
 
 ti 
 
 .796875 
 
 TB 
 
 .0625 ' 
 
 ^t 
 
 .3i25 
 
 T% 
 
 .5625 
 
 \l 
 
 .8125 
 
 t 
 
 .078125 
 
 jl 
 
 .328125 
 
 If 
 
 .578125 
 
 U 
 
 .828125 
 
 .09375 
 
 .34375 
 
 
 .59375 
 
 H 
 
 .84375 
 
 W 
 
 .109375 
 
 II 
 
 .359375 
 
 if 
 
 .609375 
 
 il 
 
 .859375 
 
 1 
 
 .125 
 
 1 
 
 .375 
 
 1 
 
 .625 
 
 I 
 
 .875 
 
 ix 
 
 .140625 
 
 li 
 
 .390625 
 
 41 
 
 .640625 
 
 If 
 
 .8Q0625 
 
 6 
 
 .lo625 
 
 .40625 
 
 §^ 
 
 .65625 
 
 .90625 
 
 H 
 
 .171875 
 
 II 
 
 .421875 
 
 B5 
 
 .671875 
 
 II 
 
 .921875 
 
 A 
 
 .1875 
 
 TB 
 
 .4375 
 
 ii 
 
 .6875 
 
 TB 
 
 .9375 
 
 li 
 
 .203125 
 
 II 
 
 .453125 
 
 11 
 
 .703125 
 
 li 
 
 .953125 
 
 S 
 
 .21875 
 
 15 
 
 .46875 
 
 |3 
 
 .71875 
 
 M 
 
 .96875 
 
 II 
 
 .234375 
 
 li 
 
 .484375 
 
 ll 
 
 .734375 
 
 II 
 
 .984375 
 
 \ 
 
 .25 
 
 h 
 
 .5 
 
 i 
 
 .75 
 
 ' 
 
 1.0000 
 
 Decimal fractions have for their denominators 10 or a 
 power qi 10, but the denominator is usually omitted. Thus, 
 
 .i = t'<t; .01 = 1^; .ooi=ToW; etc 
 
 Addition of Decimals. — Place the numbers in a column 
 with whole numbers under whole numbers, tenths under 
 tenths, hundredths under hundredths, etc., and proceed as 
 in simple addition, placing the decimal point in the sum 
 directly under the points above. Thus, 
 .00 7 5 
 .63 00 
 1.0 600 
 1 7.93 4 2 
 
 1 9.63 1 7 
 
 Subtraction of Decimals. — Arrange the figures as in addi- 
 tion, and proceed as in simple subtraction. Thus, 
 5.9 8 9 7 8 
 3.2 8 6 94 
 
 2.682 84
 
 16 ARITHMETIC 
 
 Multiplication of Decimals, — Proceed .as in simple multi- 
 plication, pointing? off as many decimal places in the result 
 as there are decimal places in both multiplicand and multi- 
 plier. Thus, 
 
 4.6 7 53 1 
 
 .0 5 3 
 
 1402593 
 2337655 
 .24779143 
 
 Division of Decimals. — Proceed as in simple division and 
 point off as many decimal places in the quotient as the 
 number of decimal places in the dividend exceeds those in 
 the divisor. 
 
 £.ramp/^.— Divide 4.7 5 6 by 3.3. 
 Solution.— 3.3 ) 4.7 5 6 ( 1.4 4 1 2- Ans. 
 3^ 
 1 45 
 1 32 
 136 
 1 32 
 40 
 
 70 
 6^ 
 
 4 
 Example— Divide .006 by 20. 
 Solution.— 2 ) .0 6 ( .0 3. Ans. 
 60 
 
 PROPORTION 
 SIMPLE PROPORTION, OR SINGLE RULE OF THREE 
 
 A proportion is an expression of equality between equal 
 ratios; thus the ratio of 10 to 5 = the ratio of 4 to 2, and is 
 expressed thus: 10:5 = 4:2. 
 
 There are four terms in proportion. The first and last 
 are the extremes, and the second and third are the means.
 
 ARITHMETIC 17 
 
 Quantities are in proportion by alternation when ante- 
 cedent is compared with antecedent and consequent with 
 consequent. Thus, if 10:5 = 4:2, then 10:4 = 5:2. 
 
 Quantities are in proportion by inversion when antecedents 
 are made consequents and the consequents antecedents. 
 Thus, if 10:5 = 4:2, then 5:10 = 2:4. 
 
 In any proportion, the product of the means will equal 
 the product of the extremes. Thus, if 10:5 = 4:2, then 
 5X4 = 10X2. 
 
 A mean proportional between two quantities equals the 
 square root of their products. Thus, a mean proportional 
 between 12 and 3 is the square root of 12X3 or 6. 
 
 If the two means and one extreme of a proportion are 
 given, we find the other extreme by dividing the product 
 of the means by the given extreme. Thus, 10:5 = 4: (?) 
 then 4X5-HlO = 2, and the proportion is 10:5 = 4:2. 
 
 If the two extremes and one mean are given, we find 
 the other mean by dividing the product of the extreme 
 by the given mean. Thus, 10: (?) =4:2, then 10X2-^4 = 5, 
 and the proportion is 10:5 = 4:2. 
 
 Example. — If 6 men unload 30 cars of ballast in a day, 
 how many cars will 10 men unload? 
 
 Solution. — As 10 men will unload more than 6 men, the 
 second term of the proportion must be greater than the 
 first; hence, 6:10 = 30 : ('), then. 
 
 10X30-^-6 = 50 cars. Ans. 
 
 COMPOUND PROPORTION, OR DOUBLE RULE OF 
 THREE 
 
 1. The product of the simple ratios of the first couplet 
 equals the product of the simple ratios of the second couplet. 
 Thus, 
 
 (4:12) f5:101 ^1 7 = 5^y6 
 17:14/ 16:18/ 12^14 10 18' 
 
 2. The product of all the terms in the extremes equals 
 the product of all the terms in the means. Thus, in 
 
 f4:12l _ f5:101 
 17:14/ 16:18/ 
 we have, 4X7X10X18 = 12X14X5X6
 
 IS ARITHMETIC 
 
 3. Any term in either extreme equals the product of the 
 means divided by the product of the other terms in the 
 extremes. Thus, in the same proportion, we have 
 
 _ 5X6X12X 14 
 7X10X18 
 
 4. Any term in either mean equals the product of the 
 extremes divided by the product of the other terms in the 
 means. Thus, in 
 
 f4:121 _ r5:101 
 17:14/ 16:18/ 
 
 we have, 5 = (4X 7X lOX 18) ^(6X 12X 14) 
 
 Rule. — I. Put the required quantity for the first term and 
 the similar known quantity for the second term, and form ratios 
 with each pair of similar quantities for the second couplet, as 
 if the result depended on each pctir and the second term: 
 
 II. Find the required term hy dividing the product of the 
 means by the product of the fourth terms. 
 
 Example. — If 4 men can earn $24 in 7 da., how much can 
 14 men earn in 12 da.? 
 
 Solution.— Sum : $24 
 
 fl4:4| 
 112:7/ 
 
 ^ 24X14X12 ^,^. . 
 Sum = ■ — =$144. Ans. 
 
 4 X / 
 
 Example. — If 12 men, in 35 da., can build a wall 140 rd. 
 lonj?, 6 ft. high, how many men can, in 40 da., build a wall 
 of the same thickness 144 rd. long, 5 ft. high? 
 
 Solution. — 
 
 fl2 : ()■» ^f 140:1441 ^ 12X35X144X5 
 135:40/ 10:5/ 40X140X6 
 
 -;>.r"-~- = 9. Ans. 
 
 INVOLUTION 
 
 To Square a Number. — Multiply the number by itself. 
 Thus, the sfiuare of 4 = 4 \ 4, or 16. 
 
 To Cube a Number. — Multiply the square of the number 
 In- tbf nnm}.fr Thus, the cube of 4 = 16 X 4 = 64.
 
 ARITHMETIC 19 
 
 To Find the Fourth Power of a Number. — Multiply the 
 cube by the number. Thus, the fourth power of 4 = 64X4 
 = 256. 
 
 To Raise a Number to the Sixth Power. — Square its cube. 
 
 To Raise a Number to the Twelfth Power. — Square its 
 sixth power. 
 
 (See logarithms for a shorter method.) 
 
 EVOLUTION 
 
 Rule for Extracting Any Root of Any Number. — I. Point 
 off the number into periods that shall contain as many figures as 
 there are units in the index of the root, beginning with the 
 decimal point. 
 
 II. Find the largest number that, when raised to the power 
 indicated by an exponent having as many units as the index 
 figure of the root, does not exceed the first period; the number 
 thus obtained will be the first figure of the root. 
 
 III. Raise the first figure of the root to the power indicated 
 by an exponent having as many units as the index figure of 
 the root, and subtract the result from the first period; annex the 
 first figure of the second period to the remainder, and call 
 the result the first dividend. 
 
 IV. Raise the first figure of the root to that power indicated 
 by an exponent that has one less unit than the index figure of 
 the root; multiply the result by the index figure, and call the 
 product the first divisor. 
 
 V. Divide the first dividend by the first divisor and obtain 
 two figures of the quotient the second of which may be a decimal. 
 If the quotient is less than 10 and the second figure is o or a 
 greater number, write the first figure of the quotient as the 
 second figure of the root; if less than 5, subtract 1 from the first 
 figure of the quotient for the second figure of the root. If the 
 divisor is greater than the dividend, write a cipher for the second 
 figure of the root. If the dividend contains the divisor 10 or 
 more times, try 9 for the second figure of the root; if 9 is also 
 too large, try 8; and so on. 
 
 VI. Raise that portion of the root already found to the 
 power indicated by an exponent having as many units as the
 
 20 ARITHMETIC 
 
 index figure; subtract the result from the -first two periods; 
 annex the first figure of the third period to the remainder, and 
 call the result the second dividend. 
 
 VII. Raise that portion of the root already found to the 
 power indicated by an exponent having one less unit than the 
 index figure; multiply the result by the index figure, and call 
 the product the second divisor. Divide the second dividend 
 by the second divisor {as described in V) for the third figure 
 of the root. 
 
 VIII. Proceed as in VI and VII for the fourth figure of the 
 root, and so on for more figures, if desired. 
 
 NoTB.— The result obtained in V may be too large or too small; if so, it will 
 be made evident in VI when getting the second dividend, and a smaller (or 
 larger) number must be used for the second figure of the root. If the given 
 number whose root is to be found is wholly decimal, take care that the first 
 period contains as many figures (annexing ciphers, if necessary) as there are 
 units in the index figure of the root. Thus, in extracting the seventh root of 
 .02794, the first period would be .0279400, and the remaining periods, cipher 
 periods. 
 
 Example. — Extract, the square root of 1,971.14. 
 Solution.— 1971. '14(44.398 
 
 42 = 16 
 
 1st divisor = 4X2 =8)37 1st dividend 
 
 4.6; hence, 4 is second figure 
 
 of root 
 1971 1st and 2d periods 
 
 442 = 1936 
 2d divisor = 44 X 2 =88 )'~351 2d dividend 
 
 3.9; hence. 3 is third figure 
 of root 
 197114 1st, 2d, and 3d periods 
 4432= 1962^ 
 
 3d divisor = 443X2 =886) 8650 3d dividend 
 
 9.76 + ; hence. 9 and 8 are, re- 
 spectively, the fourth 
 and fifth figures of 
 root. 
 Required root is 44.398. Ans. 
 Example. — Extract the cube root of 2,571.14.
 
 ARI'l HMETIC 
 
 21 
 
 Solution.— 2'571.'14(13.69 + 
 
 13= 1 
 
 1st divisor = 12X3 =3)15 
 
 1st dividend 
 
 5.0 
 
 2571 
 133= 2197 
 2d divisor = 132X3 =507) 3741 
 
 It is evident that 4 
 as the second figure 
 of the root is too 
 large; hence, use 3 
 1st and 2d periods 
 
 2d dividend 
 
 7.3 
 2571140 
 13.63= 2515456 
 
 hence, 6 is third fig- 
 ure of root 
 
 1st, 2d, and 3d 
 periods 
 
 556840 3d dividend 
 
 10. hence, 9 is fourth 
 figure of root 
 Required root is 13.69 -h. Ans. 
 
 Example.— ^909,203,700,718,879,776 = ' 
 
 First Second Third Fourth 
 Period Period Period Period 
 Solution.— 909 20370 07188 79776 ( 3906 
 
 35 = 243 
 1st divisor = 3^ X 5 = 405 )6662 1st dividend 
 
 16 + 
 Since 16 is greater than 10, we try 9. 
 
 90920370 15/ and 2d periods 
 395 = 90224199 
 2d divisor = 39^ X 5 = 1156720 5) 6961710 2d dividend 
 
 
 Since the divisor is greater than the dividend, we write 
 for the third figure of the root. 
 
 9092037007188 1^^ 2d, 3d pe- 
 3905 = 9022419900000 riods 
 
 3d divisor = 1 =i 15672050000) 696171071887 3d dividend 
 
 ^'"'"^'^ 6 + . Trv6. 
 
 909203700718879776 1st, 2d, 3d, and 4th periods 
 39065 = 909203700718879776
 
 22 ARITHMETIC 
 
 NoTB.— After having obtained the first three figures of the root, the first fig- 
 ure of the quotient, obtained by dividing a dividend by its corresponding 
 divisor, will always be the next figure of the root. If the given number is not 
 a perfect power, find three figures of the quotient when dividing the third divi- 
 dend by the third divisor, and -write ttie first and second figures (increasing the 
 second figure by 1 if the third figure is 5 or a greater digit) as the fourth and 
 fifth figures of the root. It is seldom that more than five figures of the root are 
 required. 
 
 PERCENTAGE 
 
 Percentage means by or on the hundred. Thus, 1 % = 1 on 
 100, 3% =3 on 100, 5% = 5 on 100, etc. 
 
 To Find the Percentage, Having the Rate and the Base. 
 Multiply the base by the rate expressed in hundredths. 
 Thus. 6% of 1.930 is found thus: 
 1930 
 .06 
 
 115.80 
 
 To Find the Amount, Having the Base and Rate. — Multiply 
 the base by 1 plus the rate. Thus, to find the amount of 
 11,930 for 1 year, at 6%, we multiply 1,930 by 1.06. 
 $1,930 XI. 06 = $2,045.80 
 
 To Find the Base, Having the Rate and the Percentage. 
 Divide the percentage by the rate to find the base. Thus, 
 if the rate is 6% and the percentage is 115.80, the base is 
 115.80^.06 = 1,930. 
 
 To Find the Rate, Having the Percentage and the Base. 
 Divide the percentage by the base. Thus, if the percentage 
 is 115.80 and the base 1,930, the rate equals 115.80-1-1,930 
 = .06, or 6%. 
 
 MENSURATION 
 
 In the following formulas, the letters have the meanings 
 here given, unless otherwise stated: 
 Z? = larger diameter; 
 d = smaller diameter; 
 R = radius corresponding to D; 
 r ■= radius corresponding to d; 
 p = perimeter or circumference;
 
 ARITHMETIC 
 
 23 
 
 C =area of convex surface = area of flat surface that can be 
 rolled into the shape shown; 
 
 5= area of entire surf ace = C + area of the end or ends; 
 
 i4 = area of plane figure; 
 
 ir =3.1416, nearly = ratio of any circumference to its diam- 
 eter; 
 
 V = volume of solid; 
 
 The other letters used will be found on the cuts. 
 
 CIRCLE 
 
 ^ = n-rf = 3.1416 d 
 ^ = 27rr = 6.2832 r 
 /) = 2 Vi!^= 3.5449 Va 
 
 P- 
 
 2 A 4 A 
 
 d = ^ = 
 
 n 3.1416 
 
 = .3183p 
 
 rf = 2^^ = 1.1284 VI 
 
 .2832 
 
 = .1592 p 
 
 r= yj~ = .o642<A 
 
 ^ = ^ = .7854 ci2 
 4 
 
 ^ = ^r2 = 3.1416r2 
 A Pr pd 
 
 TRIANGLES 
 
 D = B + C £+B4-C = 180" 
 
 B = D-C £' + 3 + 0=12,0° 
 
 E' = E B' = B. 
 
 The above letters refer to angles.
 
 24 ARITHMETIC 
 
 For a right triangle, c being the hypotenuse, 
 
 c=\a2 + 62 
 
 c = length of side opposite an 
 acute angle of an oblique triangle 
 c=>/o2 + 62^26i 
 
 c = length of side opposite an obtuse angle 
 of an oblique triangle. 
 
 h=Sa2-e2 
 
 For a triangle inscribed in a semicircle; i. e., any right 
 triangle, 
 
 c:b = a:h 
 
 u— ^_£f 
 c a 
 
 a.b + e = e:a = h:c 
 
 L 
 
 For any triangle, 
 
 A fr^ 11.7 
 
 ^4V.-(-±g-/ 
 
 X 
 
 RECTANGLE AND PARALLELOGRAM 
 
 A=ab 
 
 A = b^c^-b' 
 
 TRAPEZOID 
 
 A = ih(a + b)
 
 ARITHMETIC 
 
 25 
 
 TRAPEZIUM 
 
 Divide into two triangles and a trapezoid. 
 
 or, A = ^[hh' + ck + a(h' + h)] 
 
 Or. divide into two triangles by drawing 
 a diagonal. Consider the diagonal as the 
 base of both triangles; call its length /; 
 call the altitudes of the triangles hi and /12; then 
 A = hl{hi+h2) 
 
 n(D + d) 
 
 ELLIPSE 
 
 D 
 
 64 
 
 3(^ 
 
 — (g^^): 
 
 A =iDd=. 7854 Dd 
 4 
 
 €S 
 
 SECTOR 
 
 A = ^lr 
 ._nr2E 
 
 / = length of arc 
 
 008727 r2£ 
 
 SEGMENT 
 
 A = Wr-cir-h)] 
 
 A = 
 
 TT^E 
 
 360 
 
 |(r-/.) 
 
 
 • The perimeter of an ellipse cannot be exactly determined without a very 
 elaborate calculation, and this formula is merely an approximation giTing clos* 
 results.
 
 26 
 
 ARITHMETIC 
 
 CYLINDER 
 
 C = -ndh 
 
 S = 2nrh + 2irr^ 
 
 V = nr2h=.'^d2h 
 4 
 
 y = |^ = . 0796^2;, 
 
 FRUSTUM OF CYLINDER 
 
 h = i sum of greatest and least heights 
 C = ph = ndh 
 
 S = ndh + -zd^ + area of elliptical top 
 
 Ah = -d2h 
 4 
 
 PRISM OR PARALLELOPIPED 
 
 C=Ph 
 S=Ph + 2A 
 V = Ah 
 For prisms with regular polygon as 
 bases, P = length of one side X number of sides. 
 
 To obtain area of base, if it is a polygon, divide it into tri- 
 angles, and find sum of partial areas. 
 
 FRUSTUM OF PRISM 
 
 If a section perpendicular to the edges is a 
 triangle, square, parallelogram, or regular poly- 
 
 ,, sum of lengths of edges^, , . , . 
 
 gon, V = — ,— , ^^Xarea of nght 
 
 number ot edges 
 section. 
 
 SPHERE 
 
 5 = ,r(i^ = 4,rr2 = l2.5664r2 
 r -J7rd3 = j7rr3 = . 5236^3 = 4. 1888r«
 
 LOGARITHMS 
 CIRCULAR RING 
 
 Z) = mean diameter; 
 
 /^ = mean radius. 
 
 S = 47r2/?r = 9.8696Drf 
 V = 2rr2i?r2 = 2.4674L'd2 
 
 WEDGE 
 
 LOGARITHMS 
 
 EXPONENTS 
 
 By the use of logarithms, the processes of multiplication, 
 division, involution, and evolution are greatly shortened, and 
 some operations may be performed that would be impossible 
 without them. Ordinary logarithms cannot be applied to 
 addition and subtraction. 
 
 The logarithm of a number is that exponent by which some 
 fixed number, called the base, must be affected in order to 
 equal the number. Any number may be taken as the base. 
 Suppose we choose 4. Then the logarithm of 16 is 2, because 
 2 is the exponent by which 4 (the base) must be affected in 
 order to equal 16, since 42 = 16. In this case, instead of 
 reading 42 as 4 square, read it 4 exponent 2. With the same 
 base, the logarithms of 64 and 8 would be 3 and 1.5, respect- 
 ively, since 43 = 64, and 4i-5 = 4' = 8. In these cases, as in 
 the preceding, read 4^ and 4}-^ as 4 exponent 3, and 4 expo- 
 nent 1.5, respectively. 
 
 Although any positive number except 1 can be used as a 
 base and a table of logarithms calculated, but two numbers 
 have ever been employed. For all arithmetical operations 
 (except addition and subtraction) the logarithms used are 
 called the Briggs, or common, logarithms, and the base used 
 is 10. In abstract mathematical analysis, the logarithms used 
 are variously called hyperbolic, Napierian, or natural loga- 
 rithms, and the base is 2.718281828-1- . The common loga- 
 rithm of any number may be converted into a Napierian
 
 28 LOGARITHMS 
 
 logarithm by multiplying the common logarithm by 
 2.30258509 + , which is usually expressed as 2.3026, and 
 sometimes as 2.3. Only the common system of logarithms 
 will be considered here. 
 
 Since in the common system the base is 10, it follows that, 
 since 10i = 10, 102 = 100, 103 = 1,000, etc., the logarithm 
 (exponent) of 10 is 1, of 100 is 2, of 1,000 is 3, etc. For the 
 sake of brevity in writing, the words "logarithm of" are 
 abbreviated to "log." Thus, instead of writing logarithm 
 of 100 = 2, write log 100 = 2. When speaking, however, the 
 words for which "log" stands should always be pronounced 
 in full. 
 
 From the above it will be seen that, when the base is 10, 
 since 10°= 1, the exponent O = log 1; 
 
 since 10^= 10, the exponent 1 = log 10; 
 since 102= 100, the exponent 2 = log 100; 
 since 103=1,000, the exponent 3 = log 1,000; etc. 
 
 Also, 
 since 10—^ = iV = -1 . the exponent — 1 =log .1 ; 
 since 10— 2 = xJ5 =01, the exponent — 2 = log .01; 
 since 10-3 = -^^5= 001, the exponent- 3 = log .001; etc. 
 
 From this it will be seen that the logarithms of exact 
 powers of 10 and of decimals like .1, .01, and .001 are the 
 whole numbers 1, 2, 3, etc., and —1, —2, —3, etc., respect- 
 ively. Only numbers consisting of 1 and one or more ciphers 
 have whole numbers for logarithms. 
 
 Now, it is evident that, to produce a number between 1 
 and 10, the exponent of 10 must be a fraction; to produce 
 a number between 10 and 100, it must be 1 plus a fraction; 
 to produce a number between 100 and 1,000, it must be 2 
 plus a fraction, etc. Hence, the logarithm of any number 
 between 1 and 10 is a fraction; of any number between 10 
 and 100, 1 plus a fraction; of any number between 100 and 
 1,000, 2 plus a fraction, etc. A logarithm, therefore, usually 
 consists of two parts; a whole number, called the charac- 
 teristic, and a fraction, called the mantissa. The mantissa is 
 always expressed as a decimal. For example, to produce 20, 
 10 must have an exponent of approximately 1.30103, or 
 101.30103 =-20, very nearly, the degree of exactness depending
 
 LOGARITHMS 29 
 
 on the number of decimal places used. Hence, log 20 
 = 1.30103, 1 being the characteristic, and .30103, the 
 mantissa. 
 
 Referring to the second part of the preceding table, it is 
 clear that the logarithms of all numbers less than 1 are 
 negative, the logarithms of those between 1 and .1 being —1 
 plus a fraction. For, since log .1= —1, the logarithms of 
 .2, .3, etc. (which are all greater than .1, but less than 1) 
 must be greater than —1; i. e., they must equal —1 plus a 
 fraction. For the same reason, to produce a number between 
 .1 and .01, the logarithm (exponent of 10) would be equal to 
 — 2 plus a fraction, and for a number between .01 and .001, 
 it would be equal to —3 plus a fraction. Hence, the loga- 
 rithm of any number between 1 and .01 has a negative 
 characteristic qf 1 and a positive mantissa; of a number 
 between .1 and .01, a negative characteristic of 2 and a 
 positive mantissa; of a number between .01 and .001, a nega- 
 tive characteristic of 3 and a positive mantissa; of a number 
 between .001 and .0001, a negative characteristic of 4 and a 
 positive mantissa, etc. The negative characteristics are dis- 
 tinguished from the positive by the — sign written over the 
 characteristic. Thus, 3 indicates that 3 is negative. 
 
 It must be remembered that in all cases the mantissa is 
 positive. Thus,' thelogarithm 1.30103 means 4-1 -f. 30103, 
 and the logarithm 1.30103 means -1 4- .30103. Were the 
 minus sign written in front of the characteristic, it would 
 indicate that the entire logarithm was negative. Thus, 
 -1.30103= -1 -.30103. 
 
 Rule for Characteristic. — Starting from the unit figure, 
 count the number of places to the first (left-hand) digit of 
 the given number, calling unit's place zero; the number of 
 places thus counted will be the required characteristic. If 
 the first digit lies to the left of the unit figure, the character- 
 istic is positive; if to the right, negative. If the first digit of 
 the number is the unit figure, the characteristic is 0. Thus, 
 the characteristic of the logarithm of 4,826 is 3, since the 
 first digit, 4, lies in the 3d place to the left of the unit figure,^. 
 The characteristic of the logarithm of 0.0000072 is -6 or 6", 
 since the first digit, 7, lies in the 6th place to the right of the
 
 30 LOGARITHMS 
 
 unit figure. The characteristic of the logarithm of 4.391 is 0, 
 since 4 is both the first digit of the number and also the 
 unit figure. 
 
 TO FIND THE LOGARITHM OF A NUMBER 
 
 To aid in obtaining the mantissa of logarithms, tables of 
 logarithms have been calculated, some of which are very 
 elaborate and convenient. In the Table of Logarithms, the 
 mantissas of the logarithms of numbers from 1 to 9,999 are 
 given to five places of decimals. The mantissas of logarithms 
 of larger numbers can be found by interpolation. The table 
 contains the mantissas only; the characteristics may be easily 
 found by the preceding rule. 
 
 The table depends on the principle, which will be 
 explained later, that all numbers having the same figures 
 in the same order have the same mantissa, without regard to 
 the position of the decimal point, which affects the charac- 
 teristic only. To illustrate, if log 206 = 2^1387, then, 
 log 20.6 = 1.31387; log .206 =j..31387; 
 
 log 2.06= .31387; log .0206 = 2.31387; etc. 
 
 To find the logarithm of a number not having more than 
 four figures : 
 
 Rule. — Find the first three significant figures of the number 
 whose logarithm is desired, in the left-hand column; find the 
 fourth figure in the column at the top (or bottom) of the page; 
 and in the column under (or above) this figure, and opposite the 
 first three figures previously found, will be the mantissa or 
 decimal part of the logarithm. The characteristic being found 
 as previously described, write it at the left of the mantissa, and 
 the resulting expression will be the logarithm of the required 
 number. 
 
 Example. — Find from the table the logarithm: (a) of 476; 
 (fc) of 25.47; (c) of 1.073; (d) of .06313. 
 
 Solution. — (a) In order to economize space and make 
 the labor of finding the logarithms easier, the first two figures 
 of the mantissa are given only in the column headed 0. The 
 last three figures of the mantissa, opposite 476 in the column 
 headed N (N stands for number), are 761, found in the 
 column headed 0; glancing upwards, we find the first two
 
 LOGARITHMS 31 
 
 figures of the mantissa, viz., 67. The characteristic is 2; 
 hence, log 476 = 2.67761. Ans. 
 
 NoTB.— Since all numbers in the table are decimal fractions, the decimal 
 point is omitted throughout; this is customary in all tables of logarithms. 
 
 (b) To find the logarithm of 25.47, we find the first three 
 figures, 254, in the column headed N, and on the same hori- 
 zontal line, under the column headed 7 (the fourth figure of 
 the given number), will be found the last three figures of 
 the mantissa, viz., 603. The first two figures are evidently 40, 
 and the characteristic is 1; hence, log 25.47 = 1.40603. Ans. 
 
 (c) For 1.073; in the column headed 3, opposite 107 in 
 the column headed N, the last three figures of the mantissa 
 are found, in the usual manner, to be 060. It will be noticed 
 that these figures are printed *060, the star meaning that 
 instead of glancing upwards in the column headed 0, and 
 taking 02 for the first two figures, we must glance downwards 
 and take the two figures opposite the number 108, in the 
 left-hand column, i. e., 03. The characteristic being 0, log 
 1.073=0.03060, or, more simply, .03060. Ans. 
 
 (d) For .06313; the last three figures of the mantissa are 
 found opposite 631, in column headed 3, to be 024. In this 
 case, the first two figures occur in the same row, and are 80. 
 Since the characteristic is 2, log .06313 = 2.80024. Ans. 
 
 If the original number contains but one digit (a cipher is 
 not a digit), annex mentally two ciphers to the right of the 
 digit; if the number contains but two digits (with no ciphers 
 between, as in 4,008), annex mentally one cipher on the 
 right before seeking the mantissas. Thus, if the logarithm of 
 7 is wanted, seek the mantissa for 700, which is .84510; or, if 
 the logarithm of 48 is wanted, seek the mantissa for 480, 
 which is .68124. Or, find the mantissa of logarithms of 
 numbers between and 100, on the first page of the tables. 
 
 The process of finding the logarithm of a number from 
 the table is technically called taking out the logarithm. 
 
 To take out the logarithm of a number consisting of more 
 than four figures, it is inexpedient to use more than five 
 figures of the number when using five-place logarithms (the 
 logarithms given in the accompanying table are five-place). 
 Hence, if the number consists of more than five figures and
 
 32 LOGARITHMS 
 
 the sixth figure is less than 5, replace all figures after the fifth 
 with ciphers; if the sixth figure is 5 or greater, increase the 
 fifth figure by 1 and replace the remaining figures with 
 ciphers. Thus, if the number is 31, 415, 926, find the logarithm 
 of 31,416,000; if 31.415,426, find the logarithm of 31,415,000. 
 
 Example— Yind log 31,416. 
 
 Solution. — Find the mantissa of the logarithm of the first 
 four figures, as explained above. This is, in the present case, 
 .49707. Now, subtract the number in the column headed 1, 
 opposite 314 (the first three figures of the given number), 
 from the next greater consecutive number, in this case 721, 
 in the column headed 2. 721—707 = 14; this number is 
 called the difference. At the extreme right of the page will 
 be found a secondary table headed P. P., and at the top of 
 one of these columns, in this table, in bold-face type, wall be 
 found the difference. It will be noticed that each column is 
 divided into two parts by a vertical line, and that the figures 
 on the left of this line run in sequence from 1 to 9. Consult- 
 ing the difference column headed 14, we see opposite the 
 number 6 (6 is the last or fifth figure of the number whose 
 logarithm we are taking out) the number 8.4, snd we add 
 this number to the mantissa, found above, disregarding the 
 decimal point in the mantissa, obtaining 49,707 + 8.4 
 = 49,715.4. Now, since 4 is less than 5, we reject it, and 
 obtain for our complete mantissa .49715. Since the charac- 
 teristic of the logarithm of 31.416 is 4, log 31,416 = 4.49715. 
 
 Ans. 
 Example.— Find log 380.93. 
 
 Solution. — Proceeding in exactly the same manner as 
 above, the mantissa for 3,809 is 58,081 (the star directs us to 
 take 58 instead of 57 for the first two figures); the next 
 greater mantissa is 58,092, found in the column headed 0, 
 opposite 381 in column headed N. The difference is 092 
 — 081 = 11. Looking in the section headed P. P. for column 
 headed 11, we find opposite 3, 3.3; neglecting the .3, since it 
 is less than 5, 3 is the amount to be added to the mantissa of 
 the logarithm of 3,809 to form the logarithm of 38,093. 
 Hence, 58,081-1-3 = 58,084. and since the characteristic is 2. 
 log 380.93 = 2.58084. Ans.
 
 LOGARITHMS 33 
 
 Example.— ¥m6. log 1,296,728. 
 
 Solution. — Since this number consists of more than five 
 figures and the sixth figure is less than 5, we find the loga- 
 rithm of 1,296,700 and call it the logarithm of 1,296,728. 
 The mantissa of log 1,296 is found to be 11,261. The differ- 
 ence is 294-261 = 33. Looking in the P. P. section for col- 
 umn headed 33, we find opposite 7, on the extreme right, 
 23.1; neglecting the .1, the amount to be added to the above 
 mantissa is 23. Hence, the mantissa of log 1,296,728 
 = 11,261+23 = 11,284; since the characteristic is 6, log 
 1,296,728 = 6.11284. Ans. 
 
 Example. — Find log 89.126. 
 
 Solution. — Log 89.12 = 1.94998. Difference between this 
 and log 80.13 = 1.95002-1.94998 = 4. The P. P. (propor- 
 tional part) for the fifth figure of the number 6 is 2.4, or 2. 
 Hence, log 89.126 = 1.94998 + .00002 = 1.95000. Ans. 
 
 Example. — Find log .096725. 
 
 Solution.— Log .09672=2.98552. Difference =4. 
 P. P. for 5= 2 
 
 Hence, log .096725 = 2.98554. Ans. 
 
 To find the logarithm of a number consisting of five or 
 more figures: 
 
 Rule. — I. If the number consists of more than five figures 
 and the sixth figure is 5 or greater, increase the fifth figure by 1 
 and write ciphers in place of the sixth and remaining figures. 
 
 II. Find the mantissa corresponding to the logarithm of 
 the first four figures, and subtract this mantissa from the next 
 greater mantissa in the table; the remainder is the difference. 
 
 III. Find in the secondary table headed P. P. a column 
 headed by the same number as that just found for the difference, 
 and in this column, opposite the number corresponding to the 
 fifth figure (or fifth figure increased by 1) of the given number 
 (this figure is always situated at the left of the dividing line 
 of the column), will be found the P. P. (proportional part) 
 for that number. The P. P. thus found is to be added to the 
 mantissa fotind in II, as in the preceding examples, and the 
 result is the mantissa of the logarithm of the given number, as 
 nearly as may be found with five-place tables.
 
 34 LOGARITHMS 
 
 TO FIND A NUMBER WHOSE LOGARITHM IS GIVEN 
 Rule. — I. Consider the mantissa first. Glance along the 
 different columns of the table which are headed 0, until the first 
 iuv figures of the mantissa are found. Then, glance down the 
 same column until the third figure is found (or 1 less than 
 the third figure). Having found the first three figures, glance 
 to the right along the row in which they are situated until the 
 last three figures of the mantissa are found. Then, the number 
 that heads the column in which the last three figures of the 
 mantissa are found is the fourth figure of the required number, 
 and the first three figures lie in the column headed N, and in 
 the same row in which lie the last three figures of the mantissa. 
 
 II. If the mantissa cannot be found in the table, find the 
 mantissa that is nearest to, but less than, the given mantissa, 
 and which call the next less mantissa. Subtract the next less 
 mantissa from the next greater mantissa in the table to obtain 
 the difference. Also, subtract the next less mantissa from the 
 mantissa of the given logarithm, and call the remainder the 
 P. P. Looking in the secondary table headed P. P. for the 
 column headed by the difference just found, find the number 
 opposite the P. P. just found (or the P. P. corresponding most 
 nearly to thai just found); this number is the fifth figure of 
 the required number; the fourth figure will be found at the top 
 of the column containing the next less mantissa, and the first 
 three figures in the column headed N and in the same row that 
 contains the next less mantissa. 
 
 III. Having found the figures of the number as above 
 directed, locate the decimal point by the rules for the character' 
 istic, annexing ciphers to bring the number up to the required 
 number of figures if the characteristic is greater than 4. 
 
 Example. — Find the number whose logarithm is 3.56867. 
 
 Solution. — The first two figures of the mantissa are 56; 
 glancing down the column, we find the third figure, 8 (in 
 connection with 820), opposite 370 in the N column. Glan- 
 cing to the right along the row containing 820, the last" three 
 figures of the mantissa, 867, are found in the column headed 
 4; hence, the fourth figure of the required number is 4, and 
 the first three figures are 370, making the figures of the 
 required number 3,704. Since the characteristic is 3, there
 
 LOGARITHMS 35 
 
 are three figures to the left of the unit figure, and the num- 
 ber whose logarithm is 3.56867 is 3,704. Ans. 
 
 Example. — Find the number whose logarithm is 3.56871. 
 
 Solution. — The mantissa is not found in the table. The 
 next less mantissa is 56,867; the difference between this and 
 the next greater mantissa is 879 — 867 = 12, and the P. P. is 
 56,871-56,867 = 4. Looking in the P. P. section for the 
 column headed 12, we do not find 4, but we do find 3.6 and 
 4.8. Since 3.6 is nearer 4 than 4.8, we take the number 
 opposite 3.6 for the fifth figure of the required number; this 
 is 3. Hence, the fourth figure is 4; the first three figures 
 370, and the figures of the number are 37,043. The charac- 
 teristic being 3, the number is 3,704.3. Ans. 
 
 Example. — Find the number w^hose logarithm is 5.95424. 
 
 Solution. — The mantissa is found in the column headed 0, 
 opposite 900 in the column headed N. Hence, the fourth 
 figure is 0, and the number is 900,000, the characteristic 
 being 5. Had -the logarithm been 5.95424, the number would 
 have been .00009. Ans. 
 
 Example. — Find the number whose logarithm is .93036. 
 
 Solution. — The first three figures of the mantissa, 930, are 
 found in the column, opposite 852 in the N column; but 
 since the last two figures of all the mantissas in this row are 
 greater than 36, we must seek the next less mantissa in the 
 preceding row. We find it to be 93,034 (the star directing us 
 to use 93 instead of 92 for the first two figures), in the 
 column headed 8. The difference for this .case is 039 — 034 
 = 5, and the P. P. is 036-034 = 2. Looking in the P. P. 
 section for the column headed 5, we find the P. P., 2, opposite 
 4. Hence, the fifth figure is 4; the fourth figure is 8; the 
 first three figures 851 , and the number is 8.5184, the character- 
 istic being 0. Ans. 
 
 Example. — Find the number whose logarithm is 2.05753. 
 
 Solution. — The next less mantissa is found in column 
 headed 1, opposite 114 in the N column; hence, the first 
 four figures are 1,141. The difference for this case is 767 — 729 
 = 38. and the P. P. is 753-729 = 24. Looking in the P. P. 
 section for the column headed 38, we find that 24 falls between 
 22.8 and 26.6. The difference between 24 and 22.8 is 1.2.
 
 36 LOGARITHMS 
 
 and between 24 and 26.6 is 2.6; hence, 24 is nearer 22.8 than 
 it is to 26.6, and 6, opposite 22.8, is the fifth figure^ of the 
 number. Hence, the number whose logarithm is 2.05753 
 is .011416. Ans. 
 
 In order to calculate by means of logarithms, a table is 
 absolutely necessary. Hence, for this reason, we do not 
 explain the method of calculating a logarithm. The work 
 involved in calculating even a single logarithm is very great, 
 and no method has yet been demonstrated, of which we are 
 aware, by which the logarithm of a number like 121 can be 
 calculated directly. Moreover, even if the logarithm could 
 be readily obtained, it would be useless without a complete 
 table, such as that which is here given, for the reason that 
 after having used it, say to extract a root, the number cor- 
 responding to the logarithm of the result could not be found. 
 
 MULTIPLICATION BY LOGARITHMS 
 
 The principle upon which the process is based may be 
 illustrated as follows : Let X and Y represent two numbers 
 whose logarithms are x and y. To find the logarithm of 
 their product, we have, from the definition of a logarithm, 
 
 10' =X (1) 
 and 10^ =Y (2) 
 
 Since both members of (1) may be multiplied by the same 
 quantity without destroying the equality, they evidently 
 may be multiplied by equal quantities like 10^' and y. 
 Hence, multiplying (1) by (2), member by member, 
 
 10' X lO'' = 10*+" = XY 
 or, by the definition of a logarithm, x + y = \og X Y. But 
 A' Y is the product of X and Y, and x + y \s the sum of their 
 logarithms; from which it follows that the sum of the loga- 
 rithms of two numbers is equal to the logarithm of their 
 product. Hence, 
 
 To multiply two or more numbers by using logarithms: 
 
 Rule. — Add the logarithms of the several numbers, and the 
 sum will be the logarithm of the product. Find the number 
 corresponding to this logarithm, and the result will be the num- 
 ber sought.
 
 LOGARITHMS 37 
 
 Example.— MvlWav^Y 4.38, 5.217, and 83 together. 
 Solution.— Log 4.38 = .64147 
 
 Log 5.217 = .71742 
 
 Log 83 = 1.91908 
 
 Adding, 3.27797 = log (4.38X5.217X83) 
 
 Number corresponding to 3.27797 = 1,896.6. Hence, 4.38 
 X 5.217X83 = 1,896.6, nearly. Ans. 
 
 By actual multiplication, the product is 1,896.5818, 
 showing that the result obtained by using logarithms was 
 correct to five figures. 
 
 When adding logarithms, their, algebraic sum is always 
 to be found. Hence, if some of their numbers multiplied 
 together are wholly decimal, the algebraic sum of the char- 
 acteristics will be the characteristic of the product. It must 
 be remembered that the mantissas are always positive. 
 
 Example.— UyAtiply 49.82, .00243, 17, and .97 together. 
 
 Solution. — 
 
 Log 49.82 = 1.69740 
 Log .00243 = 3.38561 
 Log 17 = 1.23045 
 Log .97 = 1.98677 
 Adding, 0.30023 = log (49.82X .00243X17X.97) 
 
 Number corresponding to 0.30023 = 1.9963. Hence, 49.82 
 X. 00243 X 17 X. 97 = 1.9963. Ans. 
 
 In this case the sum of the mantissas was 2.30023. The 
 integral 2 added to the positive characteristics makes their 
 sum=^ + l + l=4; sum of negative characteristics = 3 
 +1=4, whence 4+(-4)=0. If, instead of 17, the number 
 had been .17 in the above example, the logarithm of .17 
 would have been 1^23045, and the sum of the logarithms 
 would have been 2.30023; the product would then have 
 been .019963; 
 
 It can now be shown why all numbers with figures in the 
 same order have the same mantissa, without regard to the 
 decimal point. Thus, suppose it were known that log 2.06 
 = .31387. Then, log 20.6 = log (2.06X10) = log 2.06 + log 10 
 = .31387 + 1 = 1.31387. And so it might be proved with the 
 decimal point in any other position.
 
 38 LOGARITHMS 
 
 DIVISION BY LOGARITHMS 
 
 As before, let A' and Y represent two numbers whose 
 logarithms are x and y. To find the logarithm of their 
 quotient, we have, from the definition of a logarithm: 
 
 10" = A' (1) 
 and 10^ = y (2) 
 
 Dividing (1) by (2), lO"""^ = ^> or, by the definition of a 
 
 Y X 
 
 logarithm,;*; — y = log 'y. But y is the quotient of X -^ Y, 
 
 and x — y vs. the difference of their logarithms, from which it 
 follows that the difference between the logarithms of two 
 numbers is equal to the logarithm of their quotient. Hence, 
 to divide one number by another by means of logarithms: 
 
 Rule. — Subtract the logarithm of the divisor from the logarithm 
 of the dividend, and the result will be the logarithm of the 
 quotient. 
 
 Example.— Divide 6,784.2 by 27.42. 
 
 Solution.— Log 6,784.2 = 3.83150 
 Log 27.42 = 1.43807 
 
 difference = 2.39343 = log (6,784.2-^27.42) 
 
 Number corresponding to 2.39343 = 247.42. Hence, 
 6,784.2-^-27.42 = 247.42. 
 
 When subtracting logarithms, their algebraic difference is 
 to be found. The operation may sometimes be confusing, 
 because the mantissa is always positive, and the character- 
 istic may be either positive or negative. When the logarithm 
 to be subtracted is greater than the logarithm from which it is to 
 be taken, or when negative characteristics appear, subtract the 
 mantissa first, and then the characteristic, by changing its sign 
 and adding. 
 
 Example.— Divide 274.2 by 6,784.2. 
 
 Solution.— Log 274.2 = 2.43807 
 
 Log 6.784.2 = 3. 83150 
 
 2.60657 
 
 First subtracting the mantissa .83150 gives .60657 for the 
 mantissa of the quotient. In subtracting, 1 had to be taken 
 from the characteristic of the minuend, leaving a charac- 
 teristic of 1. Subtract the characteristic 3 from this, by
 
 LOGARITHMS 39 
 
 changing its sign and adding 1 — 3 = 2, the characteristic of 
 the quotient. Number corresponding to 2. 60657 = .040418. 
 Hence, 274.2 -i- 6,784.2 = .040418. Ans. 
 
 Example.— Divide .067842 by .002742. 
 
 Solution.— Log .067842 = 2.83150 
 Log .002742 = 3.43807 
 
 difference = 1.39343 
 
 Since .83 1 50 - .43807 = .39343 and -2 + 3 = 1, number cor- 
 responding to 1.39343=24.742. Hence, .067842 h- .002742 
 = 24.742. Ans. 
 
 The only case that is likely to cause trouble in subtract- 
 ing is that in which the logarithm of the minuend has a 
 negative characteristic, or none at all, and a mantissa less 
 than the mantissa of the subtrahend. For example, let it 
 be required to subtract the logarithm 3.74036 from the 
 logarithm 3.55145. The logarithm 3.55145 is equivalent to 
 — 3 + .55145. Now, if we add both +1 and —1 to this 
 logarithm, it will not change its value. Hence, 3.55145 
 = -3 -1 + 1 +.55145 = 4+ 1.55145. Therefore, 3.55145 
 -3.74036 = 
 
 4 + 1.55145 
 3+ .74036 
 
 difference = 7+ .81109 = 7.81109 
 Had the characteristic of the above logarithm been 
 instead of 3, the process would have been exactly the same. 
 Thus, .55145=1 + 1.55145; hence, 
 1 + 1.55145 
 3+ .74036 
 
 difference = 4+ .81109 = 4.81109 
 ^ Example.— mvide .02742 by 67.842. _ 
 Solution.— Log .02742=2.43807=3 + 1.43807 
 Log 67.842 = 1.83150= 1+ .83150 
 
 difference = 4+ .60657 = 4.60657 
 Number corresponding to 4.60657 = .00040417. Hence, 
 .02742 -H 67.842 = .00040417. Ans. 
 
 Example. — What is the reciprocal of 3.1416?
 
 40 LOGARITHMS 
 
 Solution. — Reciprocal of 3.1416= -.^■■o . and log oTITfi 
 = log 1 -log 3.1416 = 0- .49715. Since 0= -1 + 1, 
 1 + 1.00000 
 .49715 
 
 difference = T+ .50285 = T.50285 
 Number whose logarithm is 1.50285 = .31831. Ans. 
 
 INVOLUTION BY LOGARITHMS 
 
 If A' represents a number whose logarithm is x, we have, 
 from the definition of a logarithm, 
 10"^ = X 
 
 Raising both numbers to some power, as the nth, the 
 equation becomes 10"^'" = A" 
 
 But A" is the required power of A, and xn is its logarithm, 
 from which it follows that the logarithm of a number mul- 
 tiplied by the exponent of the power to which it is raised is 
 equal to the logarithm of the power. Hence, to raise a 
 number to any power by the use of logarithms: 
 
 Rule. — Multiply the logarithm of the number by the exponent 
 that denotes the power to which the number is to be raised, and 
 the result will be the logarithm of the required power. 
 
 Example.— 'Whsit is: (a) the square of 7.92? (6) the cube 
 of 94.7? (c) the 1.6 power of 512, that is, the value of 5121-6? 
 
 Solution.— {a) Log 7.92 = .89873; exponent of power = 2. 
 Hence, .89873 X2 = 1.79746 = log 7.922. Number correspond- 
 ing to 1.79746 = 62.727. Hence, 7.922 = 62.727, nearly. Ans. 
 
 (b) Log 94.7 = 1.97635; 1.97635X3 = 5.92905 = log 94.73. 
 Number corresponding to 5.92905 = 849,280, nearly. Hence, 
 94.73 = 849.280, nearly. Ans. 
 
 (c) Log 512i-6 = 1.6Xlog 512 = 1.6X2.70927= 4.334832 
 or 4.33483 (when using five-place logarithms) = log 21,619. 
 Hence, 5121-6 = 21,619, nearly. Ans. 
 
 If the number is wholly decimal, so that the characteristic 
 is negative, multiply the two parts of the logarithm separately by 
 the exponent of the number. If, after multiplying the mantissa, 
 the product has a characteristic, add it, algebraically, to the 
 negative characteristic multiplied by the exponent, and the 
 result will be the negative characteristic of the required power.
 
 LOGARITHMS 41 
 
 Example. — Raise .0751 to the fourth power. 
 
 Solution.— Log .0751^ = 4 X log .0751 =4 X 2.87564. Multi- 
 plying the parts separately, 4X2 = 8 and 4 X .87564 = 3.50256. 
 Adding the 3 and 8, 3 + (-8)= -5; therefore, log .0751* 
 = 5.50256. Number corresponding to this = .00003181. 
 Hence, .0751* = . 00003181. Ans. 
 
 A decimal may be raised to a power whose exponent con- 
 tains a decimal as follows: 
 
 Example. — Raise .8 to the 1.21 power. 
 
 Solution.— Log .8'-2i = 1.21 X 1.90309. There are several 
 ways of performing the multiplication. 
 
 First Method. — Adding the characteristic and mantissa 
 algebraically, the result is —.09691. Multiplying this by 
 1.21 gives —.1172611, or —.11726, when using five-place 
 logarithms. To obtain a positive mantiss^, add +1 and 
 -1; whence, log .8i-2i= -1 + 1 -.11726= 1.88274. Ans. 
 
 Second Method. — Multiplying the characteristic and man- 
 tissa separately gives —1.21 + 1.09274. Adding character- 
 istic and mantissa algebraically, gives —.11726; then, adding 
 + 1 and -1. log .81-21 = 1.88274. Ans. 
 
 Third Method. — Multiplying the characteristic and man- 
 tissa separately gives —1.21 + 1.09274. Adding the decimal 
 part of the characteristic to the mantissa gives — 1 + ( — .21 
 + 1.09274) = 7.88274 = log .8i-2i. The number corresponding 
 to the logarithm 1.88274 = .76338. Ans. 
 
 Any one of the above three methods may be used, but we 
 recommend the first or the third. The third is the most 
 elegant and saves figures, but requires the exercise of more 
 caution than the first method does. Below will be found the 
 entire work of multiplication for both_^8i-2i and .8-21. 
 1.90309 1.90309 
 
 1.21 ^ 
 
 90309 90309 
 
 180618 180618 
 
 ^Q^*^ +1.1896489 
 
 1.0927389 -1-.21 
 
 1.21 
 
 1.9796489, or 1.97965 
 
 1.8827389, or 1.88274
 
 42 LOGARITHMS 
 
 In the second case, the negative decimal obtained by 
 multiplying — 1 and .21 was greater than the positive decimal 
 obtained by multiplying .90309 and .21; hence, +1 and —1 
 were added, as shown. 
 
 EVOLUTION BY LOGARITHMS 
 
 If X represents a number whose logarithm is x, we have, 
 
 from the definition oS a logarithm, 
 
 10' = X 
 
 Extracting some root of both members, as the nth, the 
 
 eq,uation becomes 
 
 I 
 
 10'^= '-v'X 
 
 But ^pC is the required root of X, and - is its logarithm, 
 
 from which it follows that the logarithm of a number divided 
 by the index of the root to be extracted is equal to the 
 logarithm of the root. Hence, to extract any root of a num- 
 ber by means of logarithms: 
 
 Rule. — Divide the logarithm of the number by the index of 
 the root; the result will be the logarithm of the root. 
 
 Example. — Extract (o) the square root of 77,851; (b) the 
 cube root of 698,970; (c) the 2.4 root of 8 964,300. 
 
 Solution.— (a) Log 77,851=4.89127; the index of the 
 root is 2; hence, log >/77,851 =4.89127^2=2.44564; number 
 corresponding to this = 279.02. Hence, "^77^1 = 279.02, 
 nearly. Ans. 
 
 (b) Log -^698,970 = 5.84446 -^3 = 1.94815 = log 88.746; or 
 4698,970 = 88.747, nearly. Ans. 
 
 (c) Log 'v^8,964,3'00 = 6.95251 -i-2.4 = 2.89688 = log 788.64; 
 or. '■i'/8.964,300 = 788.64, nearly. Ans. 
 
 If it is required to extract a root of any number wholly 
 decimal, and the negative characteristic will not exactly 
 contain the index of the root, without a remainder, proceed 
 as follows: 
 
 Separate the two parts of the logarithm; add as many units 
 (or parts of a unit) to the negative characteristic as will make
 
 LOGARITHMS 43 
 
 */ exactly ^contain the index of the root. Add the same number 
 
 to the mantissa, and divide both parts by the index. The 
 
 result will be the characteristic and mantissa of the root. 
 
 Example. — Extract the cube root of .0003181. 
 
 c 7 .- T ^ nnnQioi log .0003181 4.50256 
 
 Solution. — LogF .0003181 =— ^ — ~ = — 
 
 o o 
 
 (4 + 2 = 6) + (2 + .50256 = 2. 50256) 
 
 (6 -h 3 = 2) + (2.50256 h- 3 = .83419) 
 
 or. logf .OOO3T8I =2.83419 = log .068263 
 
 Hence. t^ .0003181 = .068263. Ans. 
 
 Example.— Vmd. the value of ^"v^. 0003181. 
 
 c 7 ,• T i-V/TiT^oT^ log .0003181 4.50256 
 Solution.— L,os y .0003181 = = . 
 
 If —.23 be added to the characteristic, it will contain 1.41 
 exactly 3 times. Hence, 
 
 [ - 4 + ( - .23) = - 4.23] + (.23 + .50256 = .73256) 
 (-4.23 -5- 1.41 =3) + (.73256^-1.41 = . 51955) 
 or, log '■ v^.0003181 =3.51955 = log .0033079 
 
 Hence, '"y^. 0003181 = .0033079. Ans. 
 
 Example. — Solve this expression by logarithms: 
 497 X .0 181X762 _ 
 3.300 X. 651 7 
 
 Solution. — Log 497 = 2.69636 
 
 Log .0181=2.25768 
 Log 762=2.88195 
 
 Log product = 3.83599 
 Log 3,300 = 3.51851 
 Log .6517 = 1.81405 
 
 Log product = 3.33256 
 3.83599 -3.33256 = . 50343 = log 3.1874 
 „ 497 X .0181X762 . ^ __ . . 
 
 "'"^^' 3,300 X. 6517 =3.1874. Ans. 
 
 Example. —Solve-^ 504.203X507 ^ logarithms. 
 \1. 75X71.4X87
 
 44 LOGARITHMS 
 
 Soiunon.— Log 504,203 = 5.70260 
 
 Log 507 = 2.70501 
 
 Log product = 8.40761 
 
 Log 1.75= .24304 
 
 Log 71.4 = 1.85370 
 
 Log 87 = 1.93952 
 
 Log product = 4.03626 
 
 8.40761-4.03626 , ,.^,^ , oo «k 
 — = 1.45/ 12 = log 28.65 
 
 TT 3/504.203X507 90 ^.^ »„, 
 
 Hence, -\ „ ' ^ — :; — ;r= = 28. bo. Ans. 
 
 \ 1.75X71.4X87 
 
 Logarithms can often be applied to the solution of 
 equations. 
 
 Example. — Solve the equation 2.43%^ = -^.0648. 
 Solution.— 2.43a;5 = -^X)648 
 
 Dividing by 2.43, x^ = -^^— 
 
 Taking the logarithms of both numbers, 
 
 5Xlog. = ^-^-^«- log 2.43 
 
 or 5 log x = ^^^^-.38561 
 
 D 
 
 = 1.80193 -.38561 
 
 = 1.41632 
 
 Dividing by 5, log x = 1.88326; 
 
 whence, x = .7643 
 
 Example. — Solve the equation 4.5^ = 8. 
 
 Solution. — Taking the logarithms of both numbers, 
 
 X log 4.5 = log 8, 
 
 log 8 .90309 
 
 whence, x = z -r-z = -£.-001' 
 
 log 4.5 .65321 
 
 Taking logarithms again, _ _ 
 
 log X = log .90309 -log .65321 = 1.95573-1.81505 
 
 = .14068; whence, x = 1.3825 
 
 Remarks. — Logarithms are particularly useful in those 
 
 cases when the unknown quantity is an exponent, as in 
 
 the last example, or when the exponent contains a decimal, 
 
 as in several instances in the examples given on pages 40-44.
 
 LOGARITHMS 45 
 
 Such examples can be solved without the use of logarithms, 
 but the process is very long and somewhat involved, and 
 the arithmetical work required is enormous. To solve the 
 example last given without using the logarithmic table and 
 obtain the value of x correct to five figures would require, 
 perhaps. 100 times as many figures as were used in the 
 solution given, and the resulting liability to error would be 
 correspondingly increased; indeed, to confine the work to 
 this number of figures would also require a good knowledge 
 of short-cut methods in multiplication and division, and 
 judgment and skill on the part of the calculator that can only 
 be acquired by practice and experience. 
 
 Formulas containing quantities affected with decimal 
 exponents are generally of an empirical nature; that is, 
 the constants or exponents or both are given such values 
 as will make the results obtained by the formulas agree 
 with those obtained by experiment. Such formulas occur 
 frequently in works treating on thermodynamics, strength 
 of materials, machine design, etc.
 
 46 
 
 LOGARITHMS 
 
 COMMON LOGARITHMS. 
 
 N. L. 1 
 
 100 
 
 101 
 102 
 
 3 4 
 
 P. P. 
 
 104 
 105 
 106 
 10 
 108 
 1 
 
 no 
 
 111 
 
 112 
 113 
 114 
 115 
 116 
 117 
 118 
 119 
 
 120 
 
 121 
 
 122 
 123 
 124 
 125 
 126 
 12' 
 128 
 129 
 
 130 
 
 131 
 132 
 133 
 134 
 135 
 136 
 137 
 138 
 139 
 
 140 
 
 141 
 142 
 143 
 144 
 145 
 146 
 147 
 148 
 149 
 
 00 000 
 432 
 860 
 
 01 284 
 03 
 
 02 119 
 531 
 938 
 
 03 342 
 743 
 
 04 139 
 532 
 922 
 
 05 308 
 690 
 
 06 070 
 446 
 819 
 
 07 
 555 
 
 217 
 
 561 604 
 *030 
 
 729 
 108 
 483 
 856 
 225 
 591 
 
 08 279 
 636 
 991 
 
 09 342 
 691 
 
 10 037 
 380 
 721 
 
 11 059 
 394 
 727 
 
 12 057 
 385 
 710 
 
 13 033 
 354 
 672 
 988 
 
 14 301 
 613 
 922 
 
 15 229 
 534 
 836 
 
 16 137 
 435 
 732 
 
 17 026 
 319 
 609 
 
 954 
 314 
 
 672 
 *026 
 377 
 726 
 072 
 415 
 755 
 093 
 428 
 
 ~76o; 
 
 090 
 418 
 743 
 066 
 386 
 704 
 #019 
 333 1 
 ~644 
 ^953 
 259 
 564 
 866 
 167 
 465 
 761 
 056 
 348 
 
 N. L. 1 2 3 4 5 6 7 
 
 260 303 
 
 32 
 «115|*157 
 
 I 578 
 
 9531 995 *036 
 3661 407 449 
 7761 816 857 
 *181 *222 *262 
 5831 6231 663 
 981 *021 »060 
 
 346 389 
 "775 
 #1991*242 
 
 620 I 662 
 
 *078 
 
 376 415 
 ~766l~805 
 *154 *192 
 
 538 
 
 918 
 
 296 
 
 454 
 
 "844 
 
 *231 
 
 576 
 
 956 994 
 333: 371 
 707! 744 
 078 *115 
 445! 482 
 809 846 
 
 *171 1*207 
 
 529 
 
 884 
 *237i 
 587 
 934 
 278! 
 6191 
 9241 9581 
 261 1 294 
 594|~628 
 
 926 
 254 
 581 
 905 
 226 
 545 
 862 
 *176 
 489 520 
 799 
 
 959 992 
 287 1 320 
 6131 646 
 9371 969 
 258! 290 
 577 
 
 925 
 #239 
 
 551 
 
 44 
 
 43 
 
 4.4 
 
 4.3 
 
 8.8 
 
 8.6 
 
 13.2 
 
 12.9 
 
 17.6 
 
 17.2 
 
 22.0 
 
 21.5 
 
 26.4 
 
 25.8 
 
 30.8 
 
 30.1 
 
 35.2 
 
 34 4 
 
 39.6 
 
 38.7 1 
 
 4i 
 
 40 
 
 4.1 
 
 4.0 
 
 8.2 
 
 fi.O 
 
 12.3 
 
 12.0 
 
 16.4 
 
 16.0 
 
 20.5 
 
 20.0 
 
 24.6 
 
 24.0 
 
 28.7 
 
 28.0 
 
 32.8 
 
 32.0 
 
 36.9 
 
 36.0 
 
 38 
 
 37 
 
 3.S 
 
 3.7 
 
 7.6 
 
 7.4 
 
 11.4 
 
 11.1 
 
 15.2 
 
 14.8 
 
 19.0 
 
 18.5 
 
 22.8 
 
 22.2 
 
 26.6 
 
 25.9 
 
 30,4 
 
 29 6 
 
 34.2 
 
 33.3 
 
 35 
 
 34 
 
 3.5 
 
 3.4 
 
 7.0 
 
 6.8 
 
 10.5 
 
 10.2 
 
 14.0 
 
 13.6 
 
 17.5 
 
 17.0 
 
 21.0 
 
 20.4 
 
 24.5 
 
 23.8 
 
 2K.0 
 
 27.2 
 
 31.5 
 
 30.6 
 
 32 
 
 31 
 
 3.2 
 
 3.1 
 
 6.4 
 
 6.2 
 
 9.6 
 
 9.3 
 
 12.8 
 
 12.4 
 
 16.0 
 
 15.5 
 
 19.2 
 
 18.6 
 
 22.4 
 
 21.7 
 
 25.6 
 
 24.8 
 
 28.8 
 
 27.9 
 
 P. p.
 
 LOGARITHMS 
 
 47 
 
 
 
 
 
 Table— 
 
 ( Continued) 
 
 
 
 
 
 
 N. 
 
 L. 
 
 1 
 
 !_ 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 P.P. 
 
 ISO 
 
 17 609 
 
 "638 
 
 667 
 
 "696 
 
 "725 
 
 l54 
 
 ^82 
 
 ^TT 
 
 "840 
 
 l69 
 
 
 151 
 
 898 
 
 926 
 
 955 
 
 984 
 
 »013 
 
 *041 
 
 »070 
 
 »099 
 
 »127 
 
 il56 
 
 29 28 
 
 152 
 
 18 184 
 
 213 
 
 241 
 
 270 
 
 298 
 
 327 
 
 355 
 
 384 
 
 412 
 
 441 
 
 1 
 
 2.9 
 
 2.8 
 
 153 
 
 469 
 
 498 
 
 526 
 
 554 
 
 583 
 
 611 
 
 639 
 
 667 
 
 696 1 724 
 
 2 
 
 5.8 
 
 5.6 
 
 154 
 
 752 
 
 7«0 
 
 808 
 
 837 
 
 865 
 
 893 
 
 921 
 
 949 
 
 977,*005 
 
 3 
 
 8.7 
 
 8.4 
 
 155 
 
 19 033 
 
 061 
 
 0»9 
 
 117 
 
 145 
 
 173 
 
 201 
 
 229 
 
 257 
 
 285 
 
 4 
 
 11.6 
 
 11.2 
 
 156 
 
 312 
 
 340 
 
 368 
 
 396 
 
 424 
 
 451 
 
 479 
 
 507 
 
 535 
 
 562 
 
 5 
 
 14.5 
 
 U.O 
 
 157 
 
 590 
 
 618 
 
 645 
 
 673 
 
 700 
 
 728 
 
 756 
 
 783 
 
 811 
 
 838 
 
 6 
 
 17.4 
 
 16.8 
 
 158 
 
 866 
 
 893 
 
 921 
 
 948 
 
 976 
 
 *003 
 
 *030 
 
 *058 
 
 *085 
 
 *112 
 
 7 
 
 20.3 
 
 19.6 
 
 159 
 
 20 140 
 
 167 
 
 194 
 
 222 
 
 249 
 
 276 
 
 303 
 
 330 
 
 358 
 
 385 
 
 8 
 
 23.2 
 
 22.4 
 
 160 
 
 412 
 
 ^439 
 
 466 
 
 193 
 
 "520 
 
 "548 
 
 "575 
 
 602 
 
 629 '"656 
 
 9 
 
 26.1 
 
 25.2 
 
 161 
 
 683 
 
 ^no 
 
 737 
 
 "763 
 
 790 
 
 817 
 
 844 
 
 871 
 
 898 925 
 
 27 26 
 
 162 
 
 952 
 
 978 
 
 «005 
 
 «032 
 
 »059 
 
 *085 
 
 *n2 
 
 *139 
 
 *165 #192 
 
 1 
 
 2.7 
 
 2.6 
 
 163 
 
 21 219 
 
 245 
 
 272 
 
 299 
 
 325 
 
 352 
 
 378 
 
 405 
 
 431' 458 
 
 2 
 
 5.4 
 
 5.2 
 
 164 
 
 484 
 
 511 
 
 537 
 
 564 
 
 590 
 
 617 
 
 643 
 
 669 
 
 696' 722 
 
 3 
 
 8.1 
 
 7.8 
 
 165 
 
 748 
 
 775 
 
 801 
 
 827 
 
 854 
 
 
 906 
 
 932 
 
 958; 985 
 
 4 
 
 10.8 
 
 10.4 
 
 166 
 
 22 Oil 
 
 037 
 
 063 
 
 089 
 
 115 
 
 141 
 
 167 
 
 194 
 
 220 i 246 
 
 5 
 
 13.5 
 
 13.0 
 
 167 
 
 272 
 
 298 
 
 324 
 
 350 
 
 376 
 
 401 
 
 427 
 
 453 
 
 479 505 
 
 6 
 
 16.2 
 
 15.6 
 
 168 
 
 531 
 
 557 
 
 583 
 
 608 
 
 634 
 
 660 
 
 686 
 
 712 
 
 737! 763 
 
 7 
 
 18.9 
 
 18.2 
 
 169 
 
 789 
 
 814 
 
 840 
 
 866 
 
 891 
 
 917 
 
 943 
 
 968 
 
 994 '!019 
 
 8 
 
 21.6 
 
 20.8 
 
 170 
 
 23 045 
 
 "OTO 
 
 ^096 
 
 "m 
 
 147 
 
 l72 
 
 198 
 
 -Wz 
 
 "249 "274 
 
 9 
 
 24.3 
 
 23.4 
 
 171 
 
 300 
 
 325 
 
 350 
 
 376 
 
 "ioi 
 
 ^26 
 
 452 
 
 477 
 
 5021 528 
 
 25 
 
 172 
 
 553 
 
 578 
 
 603 
 
 629 
 
 654 
 
 679 
 
 704 
 
 729 
 
 754 779 
 
 
 2.5 
 
 173 
 
 805 
 
 830 
 
 855 
 
 880 
 
 905 
 
 930 
 
 955 
 
 980 
 
 *005 *030 
 
 
 5.0 
 
 174 
 
 24 055 
 
 080 
 
 105 
 
 1-30 
 
 155 
 
 180 
 
 204 
 
 229 
 
 254 279 
 
 
 7.5 
 
 175 
 
 304 
 
 329 
 
 353 
 
 378 
 
 403 
 
 428 
 
 452 
 
 477 
 
 502 1 527 
 
 
 10.0 
 
 176 
 
 551 
 
 576 
 
 601 
 
 625 
 
 650 
 
 674 
 
 699 
 
 724 
 
 748, 773 
 
 
 12.5 
 
 177 
 
 797 
 
 822 
 
 846 
 
 871 
 
 895 
 
 920 
 
 944 
 
 969 
 
 993 »018 
 
 
 15.0 
 
 178 
 
 25 042 
 
 066 
 
 091 
 
 115 
 
 139 
 
 164 
 
 188 
 
 212 
 
 2371 261 
 
 
 17.5 
 
 179 
 
 285 
 
 310 
 
 334 
 
 358 
 
 382 
 
 406 
 
 431 
 
 455 
 
 479 503 
 
 
 20.0 
 
 180 
 
 527 
 
 551 
 792 
 
 ^75 
 
 816 
 
 "600 
 840 
 
 "624 
 864 
 
 648 
 
 888 
 
 672 
 912 
 
 696 
 935 
 
 720 744 
 959, 983 
 
 22.5 
 
 181 
 
 768 
 
 24 23 
 
 182 
 
 26 007 
 
 031 
 
 055 
 
 079 
 
 102 
 
 126 
 
 150 
 
 174 
 
 198 221 
 
 
 2.4 
 
 2.3 
 
 183 
 
 245 
 
 269 
 
 293 
 
 316 
 
 340 
 
 364 
 
 387 
 
 411 
 
 435 458 
 
 
 4.8 
 
 4.6 
 
 184 
 
 482 
 
 505 
 
 529 
 
 553 
 
 576 
 
 600 
 
 623 
 
 647 
 
 670 ' 694 
 
 
 7.2 
 
 6.9 
 
 185 
 
 717 
 
 741 
 
 764 
 
 788 
 
 811 
 
 834 
 
 858 
 
 881 
 
 905! 928 
 
 
 9.6 
 
 9.2 
 
 186 
 
 951 
 
 975 
 
 998 
 
 *021 
 
 *045 
 
 *068 
 
 *091 
 
 *114 
 
 *138 »161 
 
 
 12.0 
 
 11.5 
 
 187 
 
 27 184 
 
 207 
 
 231 
 
 254 
 
 277 
 
 300 
 
 323 
 
 346 
 
 370 393 
 
 
 14.4 
 
 13.8 
 
 188 
 
 416 
 
 439 
 
 462 
 
 485 
 
 508 
 
 531 
 
 554 
 
 577 
 
 600 623 
 
 
 16.8 
 
 16.1 
 
 189 
 
 646 
 
 669 
 
 692 
 
 715 
 
 738 
 
 761 
 
 784 
 
 807 
 
 830 852 
 
 
 19.2 
 21.6 
 
 18.4 
 20.7 
 
 190 
 
 875 
 
 898 
 
 921 
 
 944 
 
 967 
 
 989 
 
 *012 
 
 *035 
 
 *058'*081 
 
 
 191 
 
 28 103 
 
 126 
 
 Ti9 
 
 171 
 
 194 
 
 217 
 
 "240 
 
 262 
 
 285 307 
 
 22 21 
 
 192 
 
 330 
 
 353 
 
 375 
 
 398 
 
 421 
 
 443 
 
 466 
 
 488 
 
 511 
 
 533 
 
 
 2.2 
 
 2.1 
 
 193 
 
 556 
 
 578 
 
 601 
 
 623 
 
 646 
 
 668 
 
 691 
 
 713 
 
 735 
 
 758 
 
 
 4.4 
 
 4.2 
 
 194 
 
 780 
 
 803 
 
 625 
 
 847 
 
 870 
 
 892 
 
 914 
 
 937 
 
 959 
 
 981 
 
 
 6.6 
 
 6.3 
 
 195 
 
 29 003 
 
 026 
 
 048 
 
 070 
 
 092 
 
 115 
 
 137 
 
 159 
 
 181 
 
 203 
 
 
 8.8 
 
 8.4 
 
 196 
 
 226 
 
 248 
 
 270 
 
 292 
 
 314 
 
 336 
 
 358 
 
 380 
 
 403 
 
 425 
 
 
 11.0 
 
 10.5 
 
 197 
 
 447 
 
 469 
 
 491 
 
 513 
 
 535 
 
 557 
 
 579 
 
 601 
 
 623 
 
 645 
 
 
 13.2 
 
 12.6 
 
 198 
 
 667 
 
 688 
 
 710 
 
 732 
 
 754 
 
 776 
 
 798 
 
 820 
 
 842 
 
 863 
 
 
 15.4 
 
 14.T 
 
 199 
 
 
 907 
 
 929 
 
 951 
 
 973 
 
 994 
 
 *016 
 
 »038 
 
 »060 *081 
 
 8 
 9 
 
 17.6 
 
 16.8 
 
 200 
 
 30 103 
 
 ^5 
 
 ~T46 
 
 168 
 
 190 
 
 211 
 
 ~izz 
 
 ~255 
 
 "276 
 
 298 
 
 19.8 1 10.9 
 
 N. 
 
 L.O 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 P.P.
 
 48 
 
 LOGARITHMS 
 Table— ( Continued). 
 
 N. 
 
 L.O 
 
 1 
 T25 
 
 2 
 lie 
 
 3 
 
 l68 
 
 4 
 
 l90 
 
 5 
 ITT 
 
 6 
 "233 
 
 7 
 
 8 
 
 ± 
 
 P. P. 
 
 200 
 
 30 103 
 
 ~255 276 298 
 
 
 201 
 
 320 
 
 T4T 
 
 "363 
 
 384 
 
 406 
 
 428 
 
 449 
 
 47l| 492I 514 
 
 22 
 
 21 
 
 202 
 
 535 
 
 557 
 
 578 
 
 600 
 
 621 
 
 643 
 
 664 
 
 685 707 1 728 
 
 1 
 
 2.2 
 
 2.1 
 
 203 
 
 750 
 
 
 792 
 
 814 
 
 835 
 
 856 
 
 878 
 
 899; 920 942 
 
 2 
 
 4.4 
 
 4.2 
 
 204 
 
 963 
 
 984 
 
 #006 
 
 *027 
 
 *048 
 
 *069 
 
 *091 
 
 *112,*133,*154 
 
 3 
 
 6.6 
 
 6.3 
 
 205 
 
 31 175 
 
 197 
 
 218 
 
 239 
 
 260 
 
 281 
 
 302 
 
 323 3451 366 
 
 4 
 
 8.8 
 
 8.4 
 
 206 
 
 387 
 
 408 
 
 429 
 
 450 
 
 471 
 
 492 
 
 513 
 
 5341 555 576 
 
 5 
 
 11.0 
 
 10.5 
 
 207 
 
 597 
 
 618 
 
 639 
 
 660 
 
 681 
 
 702 
 
 723 
 
 744' 7651 785 
 
 6 
 
 13.2 
 
 12.6 
 
 208 
 
 80B 
 
 827 
 
 848 
 
 869 
 
 890 
 
 911 
 
 931 
 
 952 9731 994 
 
 7 
 
 15.4 
 
 14.7 
 
 209 
 
 32 015 
 
 035 
 
 056 
 
 077 
 
 098 
 
 118 
 
 139 
 
 160 181 201 
 
 8 
 
 17.6 
 
 16.8 
 
 210 
 
 222 
 
 243 
 
 263 
 
 "284 
 
 l05 
 
 325 
 
 346 
 
 366! 387 408 
 
 9 
 
 19.8 
 
 18.9 
 
 211 
 
 428 
 
 "449 
 
 l69 
 
 490 
 
 510 
 
 531 
 
 552 
 
 572 593 613 
 
 20 
 
 212 
 
 634 
 
 654 
 
 675 
 
 695 
 
 715 
 
 736 
 
 756 
 
 777 1 797 818 
 
 1 
 
 2.0 
 
 213 
 
 838 
 
 858 
 
 879 
 
 899 
 
 919 
 
 940 
 
 960 
 
 980 *001 »021 
 
 2 
 
 4.0 
 
 214 
 
 33 041 
 
 062 
 
 082 
 
 102 
 
 122 
 
 143 
 
 163 
 
 183' 2031 224 
 
 3 
 
 6.0 
 
 215 
 
 244 
 
 264 
 
 284 
 
 304 
 
 325 
 
 345 
 
 365 
 
 385 405! 425 
 
 4 
 
 8.0 
 
 216 
 
 445 
 
 465 
 
 486 
 
 506 
 
 526 
 
 546 
 
 566 
 
 586 i 6061 626 
 
 5 
 
 10.0 
 
 217 
 
 646 
 
 666 
 
 686 
 
 706 
 
 726 
 
 746 
 
 766 
 
 786' 8061 826 
 
 6 
 
 12.0 
 
 218 
 
 846 
 
 866 
 
 885 
 
 905 
 
 925 
 
 945 
 
 965 
 
 9851*005 *025 
 
 7 
 
 14.0 
 
 219 
 
 34 044 
 
 064 
 
 084 
 
 104 
 
 124 
 
 143 
 
 163 
 
 183, 203} 223 
 
 8 
 
 16.0 
 
 220 
 
 242 
 
 "262 
 
 282 
 
 ^01 
 
 ~321 
 
 141 
 
 "361 
 
 "380 
 
 400 420 
 
 9 
 
 18.0 
 
 221 
 
 ~"439 
 
 459 
 
 ~4iy 
 
 498 
 
 "518 
 
 537 
 
 "557 
 
 577 
 
 "596-616 
 
 19 
 
 222 
 
 635 
 
 655 
 
 674 
 
 694 
 
 713 
 
 733 
 
 g 
 
 772 
 
 7921 811 
 
 1 
 
 1.9 
 
 223 
 
 830 
 
 850 
 
 869 
 
 889 
 
 908 
 
 928 
 
 967 
 
 9861*005 
 
 2 
 
 3.8 
 
 224 
 
 35 025 
 
 044 
 
 064 
 
 083 
 
 102 
 
 122 
 
 141 
 
 1601 I8OI 199 
 
 3 
 
 5.7 
 
 225 
 
 218 
 
 238 
 
 257 
 
 276 
 
 295 
 
 315 
 
 334 
 
 353: 372 
 
 392 
 
 4 
 
 7.6 
 
 226 
 
 411 
 
 430 
 
 449 
 
 468 
 
 488 
 
 507 
 
 526 
 
 545 564 
 
 583 
 
 5 
 
 9.5 
 
 227 
 
 603 
 
 622 
 
 641 
 
 660 
 
 679 
 
 698 
 
 717 
 
 736 1 755 
 
 774 
 
 6 
 
 11.4 
 
 228 
 
 793 
 
 813 
 
 832 
 
 851 
 
 870 
 
 
 908 
 
 927 946 
 
 965 
 
 7 
 
 13.3 
 
 229 
 
 984 
 
 *003 
 
 *021 
 
 *040 
 
 *059 
 
 »078 
 
 *097 
 
 *116!*135 
 
 *154 
 
 8 
 
 15.2 
 
 230 
 
 36 173 
 
 192 
 
 211 
 
 229 
 
 248 
 
 267 
 
 286 
 
 305 324 
 
 342 
 
 9 
 
 17.1 
 
 231 
 
 361 
 
 -380 
 
 399 
 
 418 
 
 436 
 
 I55 
 
 -474 
 
 493: 511 
 
 530 
 
 18 
 
 232 
 
 549 
 
 568 
 
 586 
 
 605 
 
 624 
 
 642 
 
 661 
 
 680 1 .698 
 
 717 
 
 1 
 
 1.8 
 
 233 
 
 736 
 
 754 
 
 773 
 
 791 
 
 810 
 
 829 
 
 847 
 
 866 
 
 884 
 
 903 
 
 2 
 
 3.6 
 
 234 
 
 922 
 
 940 
 
 959 
 
 977 
 
 996 
 
 *014 
 
 *033 
 
 *051 
 
 *070 
 
 *088 
 
 3 
 
 5.4 
 
 235 
 
 37 107 
 
 125 
 
 144 
 
 162 
 
 181 
 
 199 
 
 218 
 
 236 
 
 254 
 
 273 
 
 4 
 
 7.2 
 
 236 
 
 291 
 
 310 
 
 328 
 
 346 
 
 365 
 
 383 
 
 401 
 
 420 
 
 438 
 
 457 
 
 5 
 
 9.0 
 
 237 
 
 475 
 
 493 
 
 511 
 
 530 
 
 548 
 
 566 
 
 585 
 
 603 
 
 621 
 
 639 
 
 6 
 
 10.8 
 
 238 
 
 658 
 
 676 
 
 694 
 
 712 
 
 731 
 
 749 
 
 767 
 
 785 
 
 803 
 
 822 
 
 7 
 
 12.6 
 
 239 
 
 840 
 
 858 
 
 876 
 
 894 
 
 912 
 
 931 
 
 949 
 
 967! 985 
 
 *003 
 
 8 
 
 14.4 
 
 240 
 
 38 021 
 
 039 
 
 "057 
 
 075 
 
 "093 
 
 T12 
 
 ^130 
 
 l48 
 
 -166 
 
 184 
 
 9 
 
 16.2 
 
 241 
 
 202 
 
 ^220 
 
 238 
 
 ~256 
 
 "274 
 
 "292 
 
 310 
 
 328 
 
 ^6 
 
 364 
 
 17 
 
 242 
 
 882 
 
 399 
 
 417 
 
 435 
 
 453 
 
 471 
 
 489 
 
 507 
 
 525 
 
 543 
 
 1 
 
 1.7 
 
 243 
 
 561 
 
 578 
 
 596 
 
 614 
 
 632 
 
 650 
 
 668 
 
 686 
 
 703 
 
 721 
 
 2 
 
 3.4 
 
 244 
 
 739 
 
 757 
 
 775 
 
 792 
 
 810 
 
 828 
 
 846 
 
 863 
 
 881 
 
 
 3 
 
 5.1 
 
 245 
 
 917 
 
 934 
 
 952 
 
 970 
 
 987 
 
 »005 
 
 *023 
 
 *041 
 
 *058 
 
 *076 
 
 4 
 
 6.8 
 
 246 
 
 3»094 
 
 111 
 
 129 
 
 146 
 
 164 
 
 182 
 
 199 
 
 217 
 
 235 
 
 252 
 
 6 
 
 8.5 
 
 247 
 
 270 
 
 287 
 
 305 
 
 322 
 
 340 
 
 358 
 
 375 
 
 393 
 
 410 
 
 428 
 
 6 
 
 10.2 
 
 248 
 
 445 
 
 463 
 
 480 
 
 498 
 
 515 
 
 533 
 
 550 
 
 568 
 
 585 
 
 602 
 
 7 
 
 11.9 
 
 249 
 
 620 
 
 637 
 
 655 
 
 672 
 
 690 
 
 707 
 
 724 
 
 742 
 
 759 777 
 
 8 
 
 13.6 
 
 2S0 
 
 794 
 
 811 
 
 829 
 
 l46 
 
 863 
 
 881 
 
 898 
 
 915 
 
 933 
 
 950 
 
 9 
 
 15.3 
 
 N. 
 
 L.O 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 P. P.
 
 LOGARITHMS 
 Table— ( Continued). 
 
 49 
 
 N. 
 
 L.0 
 
 1 2 
 
 3 4 
 
 5 6 7 1 8 9 
 
 P.P. 
 
 250 
 
 39 794 
 
 "§11 "829 
 
 "846 "863 
 
 "881 "898 "915 "933 "950 
 
 
 251 
 
 967 
 
 ~985 »062 
 
 *m9 "(m 
 
 *054:»071i*088 »T06 »T23 
 
 18 
 
 252 
 
 40 HO 
 
 157! 175 
 
 192] 209 
 
 226 243! 261: 278 295 
 
 
 1.8 
 
 253 
 
 312 
 
 329 1 346 
 
 364' 381 
 
 398 1 415 1 432 449 466 
 
 
 3.6 
 
 254 
 
 483 
 
 500 518 
 
 535 1 552 
 
 569 1 586 603; 620 637 
 
 
 5.4 
 
 255 
 
 654 
 
 671 688 
 
 705! 722 
 
 7391 756 1 773, 790 807 
 
 
 7.2 
 
 256 
 
 824 
 
 841 858 
 
 875 892 
 
 909: 926 943 960 976 
 
 
 9.0 
 
 257 
 
 993 
 
 *010 *027 
 
 *044 #061 
 
 *078l*095!*lll #128 *145 
 
 
 10.3 
 
 258 
 
 41 162 
 
 179! 196 
 
 2121 229 
 
 2461 2631 280 296 313 
 
 
 12.6 
 
 259 
 
 330 
 
 347 363 
 
 380 j 397 
 
 414 1 430 447 464 481 
 
 
 14.4 
 
 
 
 
 
 
 
 16.3 
 
 260 
 
 497 
 
 514; 531 
 
 547) 564 
 
 "5811 "597 |~614 "631 "647 
 
 
 
 
 
 
 
 
 I7_ 
 
 261 
 
 664 
 
 "681^697 
 
 714| 731 
 
 747 1 764 j 780 797 814 
 
 262 
 
 830 
 
 847 863 
 
 880 896 
 
 913 929 946 963 979 
 
 
 1.7 
 
 263 
 
 996 
 
 »012 »029 »045 *062 
 
 *o-8 *095 nn nil nn 
 
 
 3.4 
 
 264 
 
 42 160 
 
 177, 193 
 
 210 226 
 
 243 259 275 292 308 
 
 
 5.1 
 
 265 
 
 325 
 
 341 357 
 
 3741 390 
 
 4061 423 439 455 472 
 
 
 6.3 
 
 266 
 
 488 
 
 504 521 
 
 537 553 
 
 570 i 586 602 619 635 
 
 
 8.5 
 
 267 
 
 651 
 
 607 1 684 
 
 700i 716 
 
 732 1 7491 765 781 797 
 
 
 10.3 
 
 268 
 
 813 
 
 830 ! 846 
 
 862 878 
 
 8941 911 1 927 943 959 
 
 
 11.9 
 
 269 
 
 975 
 
 991*008 
 
 *024 1*040 
 
 #056 >072 *088 »104 »120 
 
 
 13.6 
 15.3 
 
 270 
 
 43 136 
 
 152 i 169 
 
 ItejloT 
 
 "2T7:"233 "249,^65 "281 
 
 271 
 
 297 
 
 313, 329 
 
 345 
 
 361 
 
 377. 393, 409 425 441 
 
 16 
 
 272 
 
 457 
 
 473 489 
 
 505 
 
 521 
 
 537 1 553, 569 584 600 
 
 
 1.6 
 
 273 
 
 616 
 
 632, 648 
 
 664 
 
 680 
 
 696, 7121 727 743 759 
 
 
 3.3 
 
 274 
 
 775 
 
 791 807 
 
 823 
 
 838 
 
 854 870 886 902 917 
 
 
 4.8 
 
 275 
 
 933 
 
 649 965 
 
 981 
 
 996 
 
 *012 *028:*044 *059 #075 
 
 
 6.4 
 
 376 
 
 44 091 
 
 1071 122 
 
 138 
 
 154 
 
 170, 1851 201 217 232 
 
 
 8.0 
 
 277 
 
 248 
 
 264 279 
 
 295 
 
 311 
 
 326 342 358 373 389 
 
 
 9.6 
 
 278 
 
 404 
 
 420 j 436 
 
 451 
 
 467 
 
 483i 498| 514 529 545 
 
 
 11.3 
 
 279 
 
 560 
 
 576; 5»2 
 
 607 
 
 623 
 
 638 
 
 654! 669 685 700 
 
 8 
 9 
 
 12.3 
 14.4 
 
 280 
 
 716 
 
 "731 "747 
 
 "762 
 
 778 
 
 "793 
 
 809i"824 "840 "§55 
 
 
 
 281 
 
 871 
 
 "886 "902 
 
 "917 
 
 "932 
 
 "948 
 
 "063i~979 "994 #010 
 
 '5 J 
 
 282 
 
 45 025 
 
 040 056 
 
 0711 086 
 
 102 
 
 117 133 148 163 
 
 
 1.5 
 
 283 
 
 179 
 
 194 209 
 
 225 240 
 
 255 
 
 271 ' 286 301' 317 
 
 
 3.0 
 
 284 
 
 332 
 
 347, 362 
 
 378 1 393 
 
 408 
 
 423 439 454 469 
 
 
 4.5 
 
 285 
 
 484 
 
 500 515 
 
 530! 545 
 
 561 
 
 576 591 606 621 
 
 
 6.0 
 
 286 
 
 637 
 
 652 667 
 
 6821 697 
 
 712 
 
 728, 743 758 773 
 
 
 7.5 
 
 287 
 
 788 
 
 803 818 
 
 834 1 849 
 
 864 
 
 879 894 909 924 
 
 
 9.0 
 
 288 
 
 939 
 
 954 969 
 
 984,*000 
 
 #015 
 
 *030,#045 #060 #075 
 
 
 10.51 
 
 289 
 
 46 090 
 
 105 j 120 
 
 135 
 
 150 
 
 165 
 
 I80! 195, 210 225 
 
 
 12.0 
 13.5 
 
 290 
 
 240 
 
 255] 270 
 
 285 
 
 300 
 
 315 
 
 330, 3451 359 374 
 
 
 
 291 
 
 389 
 
 404' 419 
 
 434 
 
 449 
 
 464 
 
 479' 494, 509 523 
 
 1* 
 
 292 
 
 538 
 
 553 568 
 
 583 
 
 598 
 
 61 3 1 627 1 642 657 1 672 
 
 
 1.4 
 
 293 
 
 687 
 
 702 716 
 
 731' 746 
 
 761, 7761 790 805' 820 
 
 
 2.8 
 
 294 
 
 835 
 
 850 864 
 
 879 894 
 
 909 9231 938 953 967 
 
 
 4.3 
 
 295 
 
 982 
 
 997 *012 
 
 *026 ■^041 
 
 #056! #070 #085 #100 #114 
 
 
 5.6 
 
 296 
 
 47 129 
 
 144 159 
 
 173 188 
 
 202: 217 232 246 261 
 
 
 7.0 
 
 297 
 
 276 
 
 290, 305 
 
 319 334 
 
 349 363! 378 392 407 
 
 
 8.4 
 
 298 
 
 422 
 
 436 451 
 
 465 1 480 
 
 494 509! 524 538 553 
 
 
 9.8 
 
 299 
 
 567 
 
 582 596 
 
 611 625 
 
 640) 654 
 
 669, 683, 698l 
 
 
 11.2 
 
 300 
 
 712 
 
 727 741 
 
 756 770 
 
 784 799 
 
 813 
 
 828' 842 
 
 
 12.6 
 
 N. 
 
 L.O 
 
 1 2 
 
 3 4 
 
 5 
 
 6 
 
 7 
 
 8 9 
 
 P.P.
 
 50 
 
 LOGARITHMS 
 
 Table— ( Continued). 
 
 N. 
 
 L.O 
 
 1 
 
 2 
 
 ±I-L 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 P.P. 
 
 800 
 
 47 712 
 
 871 
 
 "741 
 
 885 
 
 756 
 900 
 
 770 
 "914 
 
 "784 
 929 
 
 "799 
 943 
 
 "813 
 
 958 
 
 "828 
 972 
 
 "842 
 986 
 
 
 801 
 
 857 
 
 
 302 
 
 48 001 
 
 015 
 
 029 
 
 044 
 
 058 
 
 073 
 
 087 
 
 101 
 
 116 
 
 130 
 
 "5. 
 
 803 
 
 144 
 
 159 
 
 173 
 
 187 
 
 202 
 
 216 
 
 230 
 
 244 
 
 259 
 
 273 
 
 304 
 
 287 
 
 302 
 
 316 
 
 330 
 
 344 
 
 359 
 
 873 
 
 387 
 
 401 
 
 416 
 
 
 1.& 
 
 305 
 
 430 
 
 444 
 
 458 
 
 473 
 
 487 
 
 501 
 
 515 
 
 530 
 
 544 
 
 558 
 
 
 8.0 
 
 306 
 
 572 
 
 586 
 
 601 
 
 615 
 
 629 
 
 643 
 
 657 
 
 671 
 
 686 
 
 700 
 
 
 4.5 
 
 307 
 
 714 
 
 728 
 
 742 
 
 756 
 
 770 
 
 785 
 
 799 
 
 813 
 
 827 
 
 841 
 
 
 6.0 
 
 308 
 
 855 
 
 869 
 
 883 
 
 897 
 
 911 
 
 926 
 
 940 
 
 954 
 
 968 
 
 982 
 
 
 7.5 
 
 309 
 
 996 
 
 »010 
 150 
 290 
 
 *024 
 "l64 
 304 
 
 *038 
 
 178 
 318 
 
 *052 
 
 "m 
 
 332 
 
 *066 
 206 
 346 
 
 #080 
 "220 
 360 
 
 #094 
 234 
 374 
 
 #108 
 248 
 388 
 
 #122 
 262 
 402 
 
 8 
 9 
 
 9.0 
 10.5 
 12.0 
 
 SIO 
 
 49 136 
 
 311 
 
 276 
 
 18.5 
 
 812 
 
 415 
 
 429 
 
 443 
 
 457 
 
 471 
 
 485 
 
 499 
 
 513 
 
 527 
 
 541 
 
 
 313 
 
 554 
 
 568 
 
 582 
 
 596 
 
 610 
 
 624 
 
 638 
 
 651 
 
 665 
 
 679 
 
 
 814 
 
 693 
 
 707 
 
 721 
 
 734 
 
 748 
 
 762 
 
 776 
 
 790 
 
 803 
 
 817 
 
 
 815 
 
 831 
 
 845 
 
 859 
 
 872 
 
 886 
 
 900 
 
 914 
 
 927 j 941 
 
 955 
 
 14 
 
 816 
 
 969 
 
 982 
 
 996 
 
 #010 
 
 #024 
 
 #037 
 
 #051 
 
 #065! #079 
 
 #092 
 
 
 1.4 
 
 317 
 
 50 106 
 
 120 
 
 133 
 
 147 
 
 161 
 
 174 
 
 188 
 
 202 
 
 215 
 
 229 
 
 
 2.8 
 
 318 
 
 243 
 
 256 
 
 270 
 
 284 
 
 297 
 
 311 
 
 325 
 
 338 
 
 352 
 
 365 
 
 
 4.3 
 
 319 
 
 379 
 
 393 
 
 406 
 
 420 
 
 433 
 
 447 
 
 461 
 
 474 
 
 488 
 
 501 
 
 
 5.6 
 
 
 
 529 
 
 ~542 
 
 ^56 
 
 569 
 
 1 
 583 
 
 "696 
 
 "610 
 
 "623 
 
 "637 
 
 
 7.0 
 
 8.4 
 
 S20 
 
 515 
 
 321 
 
 651 
 
 "664 
 
 "678 
 
 691 
 
 "705 
 
 718 
 
 732 
 
 745 
 
 759 
 
 772 
 
 
 9.8 
 
 322 
 
 786 
 
 799 
 
 813 
 
 826 
 
 840 
 
 853 
 
 866 
 
 880 
 
 893 
 
 907 
 
 8 
 
 11.2 
 
 323 
 
 920 
 
 934 
 
 947 
 
 961 
 
 974 
 
 987 
 
 #001 
 
 #014 
 
 #028 
 
 #041 
 
 9 
 
 12.8 
 
 324 
 
 51 055 
 
 068 
 
 081 
 
 095 
 
 108 
 
 121 
 
 135 
 
 148 
 
 162 
 
 175 
 
 
 325 
 
 188 
 
 202 
 
 215 
 
 228 
 
 242 
 
 255 
 
 268 
 
 282 
 
 295 
 
 308 
 
 
 326 
 
 322 
 
 335 
 
 348 
 
 362 
 
 375 
 
 388 
 
 402 
 
 415 
 
 428 
 
 441 
 
 
 827 
 
 455 
 
 468 
 
 481 
 
 495 
 
 508 
 
 521 
 
 534 
 
 548 
 
 561 
 
 574 
 
 13 
 
 328 
 
 587 
 
 601 
 
 614 
 
 627 
 
 640 
 
 654 
 
 667 
 
 680 
 
 693 
 
 706 
 
 1 
 
 l.S 
 
 329 
 
 720 
 
 733 
 
 746 
 
 759 
 
 772 
 
 786 
 
 799 
 
 812 
 
 825 
 
 838 
 
 2 
 
 2.6 
 
 330 
 
 851 
 
 865 
 
 878 
 
 891 
 »022 
 
 904 
 #035 
 
 "917 
 
 #048 
 
 930 
 ^61 
 
 943 
 
 #075 
 
 957 
 
 #088 
 
 970 
 #101 
 
 
 3.9 
 5.2 
 6.5 
 
 831 
 
 983 
 
 1961*009 
 
 832 
 
 52 114 
 
 127 
 
 140 
 
 153 
 
 166 
 
 179 
 
 192 
 
 205 
 
 218 
 
 231 
 
 
 7^8 
 
 333 
 
 244 
 
 257 
 
 270 
 
 284 
 
 297 
 
 310 
 
 323 
 
 336 
 
 349 
 
 362 
 
 
 9.1 
 
 334 
 
 375 
 
 388 
 
 401 
 
 414 
 
 •42" 
 
 440 
 
 453 
 
 466 
 
 479 
 
 492 
 
 
 10 4 
 
 335 
 
 504 
 
 517 
 
 530 
 
 543 
 
 556 
 
 569 
 
 582 
 
 595 
 
 608 
 
 621 
 
 
 nil 
 
 336 
 
 634 
 
 647 
 
 660 
 
 673 
 
 686 
 
 699 
 
 711 
 
 724 
 
 737 
 
 750 
 
 
 337 
 
 763 
 
 776 
 
 789 
 
 802 
 
 815 
 
 827 
 
 840 
 
 853 
 
 866 
 
 879 
 
 
 338 
 
 892 
 
 905 
 
 917 
 
 930 
 
 943 
 
 956 
 
 969 
 
 982 
 
 994 
 
 #007 
 
 
 339 
 
 53 020 
 
 033 
 
 046 
 
 058 
 
 071 
 
 084 
 
 097 
 
 110 
 
 122 
 
 135 
 
 12 
 
 340 
 
 148 
 
 leijTTS 
 
 186 
 
 199 
 
 212 
 
 224 
 
 237 
 
 250 
 
 263 
 
 
 1.2 
 
 841 
 
 275 
 
 288 
 
 301 
 
 314 
 
 326 
 
 ~339 
 
 T52 
 
 364 
 
 377 
 
 390 
 
 
 2.4 
 3.6 
 4.8 
 6.0 
 7.2 
 8.4 
 9.6 
 10.8 
 
 342 
 
 403 
 
 415 
 
 428 
 
 441 
 
 453 
 
 466 
 
 479 
 
 491 
 
 504 
 
 517 
 
 843 
 
 529 
 
 542 
 
 555 
 
 567 
 
 580 
 
 593 
 
 605 
 
 618 
 
 631 
 
 643 
 
 344 
 
 656 
 
 668 
 
 681 
 
 694 
 
 706 
 
 719 
 
 732 
 
 744 
 
 757 
 
 769 
 
 845 
 
 782 
 
 794 
 
 807 
 
 820 
 
 832 
 
 845 
 
 857 
 
 870 
 
 882 
 
 895 
 
 346 
 
 908 
 
 920 
 
 933 
 
 945 
 
 95H 
 
 970 
 
 983 
 
 995 #008 
 
 •020 
 
 847 
 
 54 033 
 
 045 
 
 058 
 
 070 
 
 083 
 
 095 
 
 108 
 
 120 
 
 133 
 
 145 
 
 348 
 
 158 
 
 170 
 
 183 
 
 195 
 
 208 
 
 220 
 
 233 
 
 245 
 
 258 
 
 270 
 
 849 
 
 283 
 
 295 
 
 307 
 
 320 
 
 332 
 
 345 
 
 357 
 
 370 
 
 382 
 
 394 
 
 
 850 
 
 407 
 
 419 
 
 432 
 
 444 
 
 456 
 
 469 
 
 481 
 
 l94 
 
 ^06 
 
 TTi 
 
 
 N. 
 
 L.O 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 P.P.
 
 LOGARITHMS 
 
 51 
 
 Table— ( Continued). 
 
 N. 
 
 L.O 
 
 1 2 1 3 1 4 
 
 5 1 6 
 
 7|8j9 
 
 P.P. 
 
 350 
 
 54 407 
 
 ~419'~432 "444 ~456 
 
 169^81 
 
 494; 506' 518 
 
 
 351 
 
 531^ 543 555! 568 580 
 
 593 605 
 
 ~6r7;"630 ~642 
 
 
 352 
 
 6541 667, 679 691, 704 
 
 716! -28 
 
 741, 753: 765 
 
 13 
 
 353 
 
 777 
 
 790 
 
 802' 814 1 827 
 
 839 1 851 
 
 864' 876' 888 
 
 354 
 
 900 
 
 913 
 
 925 
 
 937, 949 
 
 962 974 
 
 986 998 »011 
 
 1 
 
 l.S 
 
 855 
 
 55 023 
 
 035 
 
 047 
 
 060 i 072 
 
 084 096 
 
 108; 121) 133 
 
 2 
 
 2.6 
 
 856 
 
 145 
 
 157 
 
 169 
 
 1821 194 
 
 206 218 
 
 2301 242! 255 
 
 3 
 
 3.9 
 
 357 
 
 267 
 
 279 291 
 
 303 315 
 
 3281 340 
 
 352 364 376 
 
 4 
 
 5.2 
 
 358 
 
 388 
 
 400: 413: 425 437 
 
 449 1 461 
 
 4731 4851 497 
 
 5 
 
 6.5 
 
 359 
 
 509 522 j 534 546 558 
 
 570 i 582' 594 606' 618 
 
 6 
 
 7 
 8 
 
 7.8 
 9.1 
 10.4 
 
 360 
 
 630 
 
 642 1 654 666 678 
 
 691 703; 715 727' 739 
 
 361 
 
 751 
 
 763 j 7751 787 799 
 
 811 823 835 847 859 
 
 9 
 
 ll.T 
 
 362 
 
 871 
 
 883 i 895' 907; 919 
 
 931 943 955 967 979 
 
 
 363 
 
 991 *003 *015 #027 *038 
 
 *050 *062 *074 *086 *098 
 
 
 364 
 
 56 110, 122i 1341 146: 158 
 
 170 j 182 194' 2051 217 
 
 
 865 
 
 229 2411 253! 265' 277 
 
 289 301' 312 324' 336 
 
 12 
 
 366 
 
 348' 360, 372 1 384 396 
 
 407 
 
 419 431 443 455 
 
 1 
 
 1.2 
 
 367 
 
 467! 478, 490, 502 514 
 
 526 
 
 538 549: 561 i 573 
 
 2 
 
 2.4- 
 
 368 
 
 585 i 597; 608, 620. 632 
 
 644 
 
 656 667, 679: 691 
 
 3 
 
 3.6 
 
 369 
 
 703| 714| 726 738. 750 
 
 761 
 
 773, 785 797] 808 
 
 4 
 
 4.8 
 
 370 
 
 820 
 
 832 i 844 855 867 
 
 879; 891 902; 914: 926 
 996i'^08 »019*03l -^43 
 
 5 
 6 
 7 
 
 6.0 
 7.2 
 
 371 
 
 937 
 
 949 
 
 961 972 984 
 
 8.4 
 
 372 
 
 57 054 
 
 066 
 
 078! 089 101 
 
 113 
 
 124 
 
 136, 148] 159 
 
 8 
 
 9.S 
 
 373 
 
 171 
 
 183 
 
 194 206 217 
 
 229 
 
 241 
 
 252 
 
 264 276 
 
 9 
 
 lO.ti 
 
 874 
 
 287 
 
 299 
 
 310 322! 334 
 
 345 
 
 357 
 
 368 
 
 380 392 
 
 
 375 
 
 403 
 
 415 
 
 426 438 449 
 
 461 
 
 473 
 
 484 
 
 496 507 
 
 
 376 
 
 519 
 
 530 
 
 542 553. 565 
 
 576 
 
 588 
 
 600 
 
 611 623 
 
 
 S77 
 
 634 
 
 646 
 
 657 1 669 680 
 
 692 i 7031 715 
 
 726' 738 
 
 II 
 
 378 
 
 749 
 
 761 
 
 772 784 795 
 
 80- 818, 830 
 
 841' 852 
 
 1 
 
 1.1 
 
 379 
 
 864 
 
 875 
 
 887! 898 910 
 
 9211 933 944 
 
 955' 967 
 
 2 
 
 2.2 
 
 S80 
 
 978 
 
 "990 'KIOl ^31^24 
 
 ^35|*047,^58 »070 «081 
 
 3 
 
 4 
 5 
 6 
 7 
 8 
 9 
 
 3.J 
 4.4 
 
 5.5 
 6.6 
 
 7.7 
 8.3 
 9.9 
 
 381 
 
 58 092! 104 
 
 115i 127 
 
 138 
 
 T49 j 1611172, "184 I95 
 
 382 
 
 2061 218 
 
 229 240 
 
 252 
 
 263 274 286! 297 i 309 
 
 383 
 
 320 
 
 331 
 
 343 354 
 
 365 
 
 377! 388! 399: 410! 422 
 
 884 
 
 433 
 
 444 
 
 456 467 
 
 478 
 
 490 501 i 512 524' 535 
 
 385 
 
 546 
 
 557 
 
 569 580 
 
 591 
 
 602 
 
 614 625^ 636 647 
 
 386 
 
 659 
 
 670 
 
 681 : 692 
 
 704 
 
 715 
 
 7261 737; 749 760 
 
 387 
 
 771 
 
 782 794' 805! 816 
 
 827 
 
 838 ( 8.50 861' 872 
 
 
 388 
 
 8831 8941 906i 917: 928 
 
 939 
 
 950 961 973 984 
 
 
 389 
 
 995 *006 'H)17 *028 *040 
 
 •^51 *062 *073 *084 *<)95 
 
 10 
 
 890 
 
 59 106 
 
 118' 129i 140 151 
 
 162! 173 184 195 ^ 207 
 
 2 
 3 
 
 4 
 5 
 6 
 7 
 8 
 9 
 
 1.0 
 
 391 
 
 218 
 
 229, 240: 251 262 
 
 273 
 
 284! 295; 306] 318 
 
 2.0 
 8.0 
 4.0 
 5.0 
 6.0 
 7.0 
 8.0 
 9.0 
 
 392 
 
 329 
 
 340 1 351' 362 373 
 
 384 
 
 395 
 
 406! 417 i 428 
 
 393 
 
 439 
 
 450; 461 472 483 
 
 494 
 
 506 
 
 517 
 
 528 ^39 
 
 894 
 
 550 
 
 561 572 1 5831 594 
 
 605 
 
 616 
 
 627 
 
 638 649 
 
 895 
 
 660 1 671! 6821 693 | 704 
 
 715 
 
 726 
 
 737 
 
 748 759 
 
 396 
 
 770! 780' 791 8O2! 813 
 
 824 
 
 835' 846 
 
 857! 868 
 
 397 
 
 8791 890 901] 912^ 923 
 
 934 
 
 945 956 
 
 966 977 
 
 398 
 
 988! 999*010*021 #032 
 
 »<)43 K154 '►065 #076 »086 
 
 399 
 
 60 097 
 
 108 119, 130 141 
 
 152 163^ 173' 184] 195 
 ~260 "271]~282j~293J~304 
 
 
 400 
 
 206 
 
 '2T7|~228 ~239 "249 
 
 
 N. 
 
 L.O 
 
 1 
 
 2 3 1 4 
 
 ~5~ 6 
 
 7 8 9 
 
 P.P.
 
 52 
 
 LOGARITHMS 
 
 
 
 
 
 Table— ( Continued) 
 
 
 
 
 N. 
 
 L.O 
 
 1 
 "in 
 
 2 
 
 ^28 
 
 3 4 
 
 "239 "249 
 
 5 6 7 
 
 8 9 
 
 P.P. 
 
 400 
 
 60 206 
 
 "260 "271 "282" 
 
 "293 "304 
 
 
 401 
 
 314 
 
 325 
 
 3361 347 358 
 
 369 379 390 401 412 
 
 
 402 
 
 423, 433 
 
 4441 455 
 
 466 
 
 477! 487 1 498 509 520 
 
 
 403 
 
 531 1 541 
 
 552 563 
 
 574 
 
 584! 595 606 617! 627 
 
 
 404 
 
 638^ 649 
 
 660! 670 
 
 681 
 
 692i 703! 713; 724! 735 
 
 
 405 
 
 746' 756 
 
 767 
 
 778 
 
 788 
 
 799> 810 821 ! 831 842 
 
 
 406 
 
 853, 863 
 
 874 
 
 885 895 
 
 906 917 927 938 949 
 
 II 
 
 407 
 
 959 970 
 
 981 
 
 991 
 
 *002 
 
 *013 *023 #034 *045 *055 
 
 
 
 408 
 
 61 066 077 
 
 087 
 
 098 
 
 109 
 
 119 130 140 151 162 
 
 
 
 409 
 
 1721 183 
 
 194 
 
 204 
 
 215 
 
 2251 236 247! 257 268 
 
 
 
 
 
 
 
 
 
 
 
 410 
 
 278, 289 
 
 300 
 
 310 
 
 321 
 
 331 342 352 363 374 
 
 411 
 
 384 1 395! 405 
 
 416 
 
 l26 
 
 437 1 448 458 469 479 
 
 412 
 
 490 1 500 
 
 511 
 
 521 
 
 532 
 
 542 1 553 563 574; 584 
 
 
 
 413 
 
 595 606 
 
 616 
 
 627 
 
 637 
 
 648 658 669 679 690 
 
 
 8 8 
 
 414 
 
 700 711 
 
 721 
 
 731 
 
 742 
 
 752 763 773 1 784 794 
 
 a 
 
 9.9 
 
 415 
 
 805 815 
 
 826 
 
 836 
 
 847 
 
 857 868 878 888 > 899 
 
 
 
 416 
 
 909' 920 
 
 930 
 
 941 
 
 951 
 
 962 972 982 993 *003 
 
 
 417 
 
 62 014, 024 
 
 034 
 
 045 
 
 055 
 
 066 076 086 097 107 
 
 
 418 
 
 118 128 
 
 138 
 
 149 
 
 159 
 
 170 180 190 201! 211 
 
 
 419 
 
 221 232 
 
 242 
 
 252 263 
 
 273 284 ^94 304 315 
 
 
 420 
 
 325 335 
 
 ~346 ^ "366 
 
 ^77 "387 "397 l08 "418 
 
 
 421 
 
 428; 439 
 
 ~449 
 
 459 S 469 
 
 480 490 500 511, 521 
 
 10 
 
 422 
 
 531] 542 
 
 552 
 
 562 
 
 572 
 
 583 5931 603 613' 624 
 
 1 ■ " 
 
 l.U 
 
 423 
 
 634 1 644 
 
 655 
 
 665 
 
 675 
 
 685 6961 706 716 726 
 
 2 
 
 2.0 
 
 424 
 
 737: 747 
 
 757 
 
 767 
 
 778 
 
 788 798 i 808,, 818 829 
 
 3 
 
 425 
 
 839 i 849 
 
 859 
 
 870 
 
 880 
 
 890 900 910; 921 931 
 
 4 
 
 
 426 
 
 941! 951 
 
 961 
 
 972 
 
 982 
 
 992 *002 *012 »022 »f033 
 
 5 
 
 
 427 
 
 63 043, 053 
 
 063 
 
 073 
 
 083 
 
 094 104 114 124 134 
 
 6 
 
 
 428 
 
 144 1 155 
 
 165 
 
 175 
 
 185 
 
 195 205 215 225 236 
 
 7 
 
 
 429 
 
 246 j 256 
 
 266 
 
 276 
 
 286 
 
 296! 306 3171 327 337 
 
 8 
 
 8.0 
 
 
 
 
 
 
 9 
 
 SO 
 
 430 
 
 347 
 
 i£! 
 
 "367 
 468 
 
 177JJ87 
 
 4781 488 
 
 ~397-"407,"4T7,"428 "438 
 ^98 "508 "518 "528 "538 
 
 
 431 
 
 448 
 
 458 
 
 
 432 
 
 548 
 
 458 
 
 568 
 
 579! 589 
 
 599 609 619 629 639 
 
 
 433 
 
 649 
 
 659 
 
 669 
 
 679 i 689 
 
 699 709! 719 729 739 
 
 
 434 
 
 749 
 
 759 
 
 769 
 
 779 1 789 
 
 799 809 819 829 839 
 
 
 435 
 
 849! 859 
 
 869 
 
 879 889 
 
 899 909 919 929 939 
 
 
 436 
 
 949 
 
 959 
 
 969 
 
 979 988 
 
 998 «008 *018 *028 *038 
 
 9 
 
 437 
 
 64 048 
 
 058 
 
 068 
 
 078 088 
 
 098 108! 118 128 137 
 
 
 9 
 
 438 
 
 147 
 
 157 
 
 167 
 
 177 1 187 
 
 197i 2071 217 227 237 
 
 
 
 439 
 
 246 
 
 256 
 
 _266 
 
 276 j 286 
 
 296 306 316 326 335 
 
 
 
 440 
 
 345, 355 
 
 365 
 
 375, 385 
 
 395, 404 414 424 434 
 
 
 
 441 
 
 444 
 
 454 
 
 464 
 
 473 
 
 483 
 
 493 503 513 523 532 
 
 442 
 
 542 
 
 552 
 
 562 
 
 572 
 
 582 
 
 591 601 61 ll 621 631 
 
 443 
 
 640 
 
 650 
 
 660 
 
 670 
 
 680 
 
 689! 699| 709 719 729 
 
 444 
 
 738 
 
 748 
 
 758 
 
 768 
 
 777 
 
 787; 797 1 807 816! 826 
 
 445 
 
 836 
 
 816 
 
 856 
 
 865 
 
 875 
 
 885! 8951 904 914! 924 
 
 446 
 
 933 
 
 943 
 
 953 i 963! 972 
 
 982! 992 *002!»011,#O21 
 
 
 447 
 
 65 031 
 
 040 
 
 050 
 
 060 070 
 
 079 089! 0991 108 118 
 
 
 448 
 
 128 
 
 137 
 
 147 
 
 157 167 
 
 176' 186| 196' 205] 215 
 
 
 449 
 
 225 
 
 234 
 
 244 
 
 2541 263 
 
 273 283 292 302 312 
 
 
 450 
 
 321 
 
 331 
 
 341 
 
 350 360 
 
 "369 "379 ^89 198 1 408 
 
 
 N. 
 
 L.O 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 6 7 
 
 T 
 
 9 
 
 P.P.
 
 LOGARITHMS 
 
 53 
 
 Table— ( Continued). 
 
 N. 
 
 L.O 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 1 
 
 6 
 
 7 1 8 
 
 9 
 
 P. P. 
 
 
 450 
 
 65 321 
 
 13T 
 
 ^41 
 
 "350 
 
 l60 
 
 "369 
 
 "379 "389!^98 
 
 ^08 
 
 
 
 451 
 
 418 
 
 427 
 
 437 
 
 447 
 
 456 
 
 466 
 
 475' 485 495 
 
 504 
 
 
 
 452 
 
 514 
 
 523 
 
 533 
 
 543 
 
 552 
 
 562 
 
 571 581 591 
 
 600 
 
 
 
 453 
 
 610 
 
 619 
 
 629 
 
 639 
 
 648 
 
 658 j 
 
 667 677 
 
 686 
 
 696 
 
 
 
 454 
 
 706 
 
 715 
 
 725 
 
 734 
 
 744 
 
 753 
 
 849! 
 
 763 772 
 
 782 
 
 792 
 
 
 
 455 
 
 801 
 
 811 
 
 820 
 
 830 
 
 839 
 
 858 868 
 
 877 
 
 887 
 
 
 
 456 
 
 896 
 
 906 
 
 916 
 
 925 
 
 935 
 
 944 
 
 954' 963 973' 982 
 
 m 
 
 
 457 
 
 992 
 
 *001 
 
 #011 
 
 *020 
 
 *030 
 
 *039 *049 *058 »068 «077 
 
 1 
 
 1.0 
 
 
 458 
 
 66 087 
 
 096 
 
 106 
 
 115 
 
 124 
 
 134 
 
 143 153 182, 172 
 
 2 
 
 2.0 
 
 
 459 
 
 181 
 
 191 
 
 200 
 
 210 
 
 219 
 
 229 
 
 238 247 257! 266 
 
 3 
 
 3.0 
 
 
 460 
 
 276 
 
 ^85 
 
 "295 
 
 -Wi 
 
 ^14 
 
 3p 
 
 "^32 "342 "351 "361 
 
 4 
 5 
 
 4.0 
 5.0 
 
 
 461 
 
 370 
 
 "380 
 
 "389 
 
 393 
 
 "408 
 
 417 
 
 1271^436 "iiSlISS 
 
 6 
 
 7 
 8 
 9 
 
 6.0 
 
 7.0 
 8.0 
 9.0 
 
 
 462 
 
 464 
 
 474 
 
 483 
 
 492 
 
 502 
 
 511| 
 
 521 530 539 549 
 
 
 463 
 
 558 
 
 567 
 
 577 
 
 586 
 
 596 
 
 605! 
 
 614 624 633; 642 
 
 
 464 
 
 652 
 
 661 
 
 671 
 
 680 
 
 689 
 
 699 
 
 708 717 7271 738 
 
 
 465 
 
 745 
 
 755 
 
 764 
 
 773 
 
 783 
 
 792 
 
 801 811 820 829 
 
 
 466 
 
 839 
 
 848 
 
 857 
 
 867 
 
 876 
 
 885' 
 
 894 904 913 922 
 
 
 
 467 
 
 932 
 
 941 
 
 930 
 
 960 
 
 969 
 
 978, 
 
 987! 997 *008^015 
 
 
 
 468 
 
 67 025 
 
 034 
 
 043 
 
 052 
 
 082 
 
 071' 
 
 080 089 099 108 
 
 
 
 469 
 
 117 
 
 127 
 
 136 
 
 !45 
 
 154 
 
 164 
 
 173 182 191 201 
 
 
 
 470 
 
 210 
 
 219 
 
 228 
 
 237 
 
 247 
 
 256 
 
 "265 "274 "284 ^93 
 
 
 
 471 
 
 302 
 
 311 
 
 1m 
 
 330 
 
 "339 
 
 348 
 
 "357 "367 "376 "385 
 
 9 
 
 
 472 
 
 394 
 
 403 
 
 413 
 
 422 
 
 431 
 
 440 
 
 449 459 468 477 
 
 1 
 
 0.9 
 
 
 473 
 
 486 
 
 495 
 
 504 
 
 514 
 
 523 
 
 532 
 
 541 550 560 569 
 
 2 
 
 1.8 
 
 
 474 
 
 578 
 
 587 
 
 596 
 
 605 
 
 614 
 
 624. 
 
 633 642 651 680 
 
 3 
 
 2.T 
 
 
 475 
 
 689 
 
 679 
 
 688 
 
 697 
 
 -06 
 
 715! 
 
 7241 733 742 752 
 
 
 3.6 
 
 
 476 
 
 761 
 
 852 
 
 770 
 861 
 
 779 
 
 870 
 
 788 
 879 
 
 797 
 
 888 
 
 806 
 897' 
 
 815; 825! 834 843 
 
 6 
 
 4.5 
 
 5.4 
 
 
 477 
 
 906 916 925' 934 
 
 
 478 
 
 943 
 
 952 
 
 961 
 
 970 
 
 979 
 
 988 
 
 997 ^006 ^015 *024 
 
 
 6.3 
 
 
 479 
 
 68 034 
 
 043 
 
 052 
 
 081 
 
 070 
 
 079 
 
 088 097 106 115 
 
 
 7.2 
 
 
 480 
 
 124 
 
 l33 
 
 "142 
 
 151 
 
 "160 
 
 189 
 
 178 187 : 196 205 
 
 1 a.i 
 
 
 481 
 
 215 
 
 224 
 
 233 
 
 242 
 
 251 
 
 280 
 
 269 278 287 296 
 
 
 
 482 
 
 305 
 
 314 
 
 323 
 
 332 
 
 341 
 
 350! 
 
 359 388 377 386 
 
 
 
 483 
 
 395 
 
 404 
 
 413 
 
 422 
 
 431 
 
 440 
 
 449 458 467 476 
 
 
 
 484 
 
 485 
 
 494 
 
 502 
 
 511 
 
 520 
 
 529 
 
 538 547 556 565 
 
 
 
 485 
 
 574 
 
 583 
 
 592 
 
 801 
 
 610 
 
 619 
 
 628 637 646 655 
 
 
 
 486 
 
 664 
 
 673 
 
 681 
 
 690 
 
 
 708 
 
 717 728 735 744 
 
 II 
 
 
 487 
 
 753 
 
 762 
 
 771 
 
 780 
 
 789 
 
 797 
 
 808 815 824 833 
 
 1 
 
 S 
 
 
 488 
 
 842 
 
 851 
 
 860 
 
 869 
 
 878 
 
 886 
 
 895 904 913 922 
 
 2 
 
 
 
 489 
 
 931 
 
 940 
 
 949 
 
 958 
 
 966 
 
 975 
 
 984 993 ^002 ^^11 
 
 3 
 
 
 
 490 
 
 69 020 
 
 "028 
 
 ~037 
 
 "046 
 
 055 
 
 064 
 
 "073 "082 "090 "099 
 
 4 
 5 
 
 
 
 491 
 
 108 
 
 ~va 
 
 l26 
 
 135 
 
 144 
 
 152 
 
 luu Tfij T79 "188 
 
 6 
 
 7 
 8 
 9 
 
 
 
 492 
 
 197 
 
 205 
 
 214 
 
 223 
 
 232 
 
 241 
 
 249 258 267, 276 
 
 
 493 
 
 2^5 
 
 294 
 
 302 
 
 311 
 
 320 
 
 329 
 
 338 348 355' 364 
 
 
 494 
 
 373 
 
 381 
 
 390 
 
 399 
 
 408 
 
 417 
 
 425 434 443 452 
 
 
 495 
 
 461 
 
 469 
 
 478 
 
 487 
 
 496 
 
 504 
 
 513 522 531 ! 539 
 
 
 496 
 
 548 
 
 557 
 
 566 
 
 574 
 
 583 
 
 592 
 
 601 609: 618 i 627 
 
 
 
 497 
 
 636 
 
 644 
 
 653 
 
 662 
 
 671 
 
 679 
 
 688 697; 705! 714 
 
 
 
 498 
 
 723 
 
 732 
 
 740 
 
 749 
 
 758 
 
 767 
 
 775 784 7931 801 
 
 
 
 499 
 
 810 
 
 819 
 906 
 
 827 
 914 
 
 836 
 923 
 
 845 
 932 
 
 854 
 940 
 
 862 871, 880 
 949, 958 966 
 
 888 
 975 
 
 
 
 500 
 
 897 
 
 
 N. 
 
 L.O 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 1 7 8 
 
 9 
 
 P. P.
 
 54 
 
 LOGARITHMS 
 
 
 
 
 
 Table— ( Continued) 
 
 • 
 
 
 
 N. 
 
 L.O 
 
 69" 897 
 
 1 2 
 
 3 
 
 A 
 
 5 
 
 6 7 
 
 8 
 
 9 
 
 r 
 
 P. 
 
 500 
 
 '906|'9T4 
 
 "923 932 
 
 "940 
 
 "949 "958 
 
 966 
 
 ■975 
 
 
 
 501 
 
 984 
 
 "992,*O01 
 
 *010|'^)18 
 
 *027 
 
 *O36#044 
 
 »053*062 
 
 
 
 602 
 
 70 070 
 
 079 
 
 088 
 
 096 
 
 105 
 
 114 
 
 122 131 
 
 140! 148 
 
 
 
 503 
 
 157 
 
 165 
 
 174 
 
 183 
 
 191 
 
 200 
 
 209 
 
 217 
 
 226 
 
 234 
 
 
 
 504 
 
 243 
 
 252 
 
 260 
 
 269 
 
 278 
 
 286 
 
 295 
 
 303 
 
 312 
 
 321 
 
 
 
 505 
 
 329 
 
 338 
 
 346 
 
 355 
 
 364 
 
 372 
 
 381 
 
 389 
 
 398 
 
 406 
 
 
 
 606 
 
 415 
 
 424 
 
 43.2 
 
 441 
 
 449 
 
 458 
 
 467 
 
 475 
 
 484 
 
 492 
 
 
 .». 
 
 507 
 
 501 
 
 509 
 
 518 
 
 526 
 
 535 
 
 544 
 
 552 
 
 561 
 
 569 
 
 678 
 
 
 508 
 
 586 
 
 595 
 
 603 
 
 612 
 
 621 
 
 629 
 
 638 
 
 646 
 
 655 
 
 663 
 
 
 1.8 
 
 609 
 
 672 
 
 680 
 
 689 
 
 697 
 
 706 
 
 714 
 
 723 
 
 731 
 
 740 
 
 749 
 
 
 2;t 
 
 510 
 
 757 
 
 "766 
 
 774 
 
 l83 
 
 ~791 
 
 "800 
 
 808 
 
 817 
 
 "825 
 
 "834 
 
 s 
 
 S.» 
 4.5 
 
 6.4 
 6.3 
 7.2 
 8.1 
 
 511 
 
 842 
 
 ~851 
 
 l59 
 
 868 
 
 ^6 
 
 "8851^93 
 
 "902 
 
 910 
 
 919 
 
 512 
 
 927 
 
 935 
 
 944 
 
 952 
 
 961 
 
 969 
 
 978 
 
 986 
 
 995 
 
 *003 
 
 513 
 
 71 012 
 
 020 
 
 029 
 
 037 
 
 046 
 
 054 
 
 063 
 
 071 
 
 079 
 
 088 
 
 614 
 
 096 
 
 105 
 
 113 
 
 122 
 
 130 
 
 139 
 
 147 
 
 155 
 
 164 
 
 172 
 
 515 
 
 181 
 
 189 
 
 198 
 
 206 
 
 214 
 
 223 
 
 231 
 
 240 
 
 248 
 
 257 
 
 516 
 
 265 
 
 273 
 
 282 
 
 290 
 
 299 
 
 307 
 
 315 
 
 324 
 
 332 
 
 341 
 
 
 
 517 
 
 349 
 
 357 
 
 366 
 
 374 
 
 383 
 
 391 
 
 399 
 
 408 
 
 416 
 
 425 
 
 
 
 618 
 
 433 
 
 441 
 
 450 
 
 458 
 
 466 
 
 475 
 
 483 
 
 492 
 
 500 
 
 608 
 
 
 
 619 
 
 517 
 
 525 
 
 533 
 
 542 
 
 550 
 
 569 
 
 567 
 
 575 
 
 584 
 
 692 
 
 
 
 520 
 
 600 
 
 609 
 
 "617 
 
 625 
 
 634 
 
 642 
 
 650 
 
 659 
 
 667 
 
 675 
 
 
 
 521 
 
 684 
 
 692 
 
 700 
 
 709 
 
 717 
 
 725 
 
 734 
 
 742 
 
 750 
 
 759 
 
 
 8 
 
 522 
 
 767 
 
 775 
 
 784 
 
 792 
 
 800 
 
 809 
 
 817 
 
 825 
 
 834 
 
 842 
 
 1 
 
 0.8 
 
 523 
 
 850 
 
 858 
 
 867 
 
 875 
 
 883 
 
 892 
 
 900 
 
 908 
 
 917 
 
 925 
 
 2 
 
 1.6 
 
 524 
 
 933 
 
 941 
 
 950 
 
 958 
 
 966 
 
 975 
 
 983 
 
 991 
 
 999*008 
 
 3 
 
 2.4 
 
 525 
 
 72 016 
 
 024 
 
 032 
 
 041 
 
 049 
 
 057 
 
 066 
 
 074 
 
 0821 090 
 
 4 
 
 3.3 
 
 526 
 
 099 
 
 107 
 
 115 
 
 123 
 
 132 
 
 140 
 
 148 
 
 156 
 
 165 173 
 
 6 
 
 4.0 
 
 527 
 
 181 
 
 189 
 
 198 
 
 206 
 
 214 
 
 222 
 
 230 
 
 239 
 
 247 
 
 255 
 
 6 
 
 4.8 
 
 528 
 
 263 
 
 272 
 
 280 
 
 288 
 
 296 
 
 304 
 
 313 
 
 321 
 
 329 
 
 337 
 
 7 
 
 6.6 
 
 529 
 
 346 
 
 354 
 436 
 
 518 
 
 362 
 444 
 "526 
 
 370 
 452 
 534 
 
 378 
 460 
 ~542 
 
 387 
 469 
 550 
 
 395 
 
 477 
 "558 
 
 403 
 
 485 
 567 
 
 411 
 "493 
 
 "575 
 
 419 
 ~50i 
 "583 
 
 8 
 9 
 
 6.4 
 7.2 
 
 530 
 
 428 
 
 531 
 
 509 
 
 
 532 
 
 591 
 
 599 
 
 607 
 
 616 
 
 624 
 
 632! 640 
 
 648 
 
 656 
 
 665 
 
 
 
 533 
 
 673 
 
 681 
 
 689 
 
 697 
 
 705 
 
 713 
 
 722 
 
 730 
 
 738 
 
 746 
 
 
 
 634 
 
 754 
 
 762 
 
 770 
 
 779 
 
 787 
 
 795 
 
 803 
 
 811 
 
 819 
 
 827 
 
 
 
 535 
 
 835 
 
 843 
 
 852 
 
 860 
 
 868 
 
 876 
 
 884 
 
 892 
 
 900 
 
 908 
 
 
 
 536 
 
 916 
 
 925 
 
 933 
 
 941 
 
 949 
 
 957 
 
 965' 973 
 
 981 
 
 989 
 
 
 7 
 
 537 
 
 997 
 
 *006 
 
 *014 
 
 *022 
 
 *030 
 
 *0:!8!*046 «054 
 
 «062 
 
 #070 
 
 
 0.7 
 
 538 
 
 73 078 
 
 086 
 
 094 
 
 102 
 
 111 
 
 119 
 
 127 
 
 135 
 
 143 
 
 151 
 
 
 1.4 
 
 539 
 
 159 
 
 167 
 
 175 
 
 183 
 
 191 
 
 199 
 
 207 
 
 215 
 
 223 
 
 231 
 
 
 2.1 
 
 540 
 
 ~239 
 
 "247 
 
 ^5 
 
 263 
 
 272 
 
 280 
 
 ~288 
 
 "m 
 
 304 
 
 "312 
 
 
 2.8 
 
 3.5 
 4.2 
 4.9 
 5.6 
 6.3 
 
 641 
 
 320 
 
 128 
 
 "33^ 
 
 344 
 
 352 
 
 360 
 
 368 
 
 376 
 
 384 
 
 392 
 
 542 
 
 400 
 
 408 
 
 416 
 
 424 
 
 i32 
 
 440 
 
 448 
 
 45(> 
 
 464 
 
 472 
 
 543 
 
 480 
 
 488 
 
 496 
 
 504 
 
 512 
 
 520 
 
 528 
 
 5;-6 
 
 544 
 
 652 
 
 544 
 
 560 
 
 568 
 
 576 
 
 584 
 
 592 
 
 600 
 
 608 
 
 6.6 
 
 624 
 
 632 
 
 645 
 
 640 
 
 648 
 
 656 
 
 664 
 
 672 
 
 679 
 
 687 
 
 695 
 
 703 
 
 711 
 
 646 
 
 719 
 
 727 
 
 735 
 
 743 
 
 751 
 
 759 
 
 767 
 
 775 
 
 783 
 
 791 
 
 
 
 647 
 
 799 
 
 807 
 
 815 
 
 823 
 
 830 
 
 838 
 
 846 
 
 854 
 
 862 
 
 870 
 
 
 
 548 
 
 878 
 
 886 
 
 894 
 
 902 
 
 910 
 
 918 
 
 926 
 
 933 
 
 941 
 
 949 
 
 
 
 649 
 
 957 
 
 965 
 
 973 
 
 981 
 
 989 
 
 997 
 
 #005 
 
 *013 
 
 »020 
 
 #028 
 
 
 
 550 
 
 74 036 
 
 "044 
 
 "052 
 
 060 
 
 068 
 
 076 
 
 084 
 
 092 
 
 ^9 
 
 107 
 
 
 
 N. 
 
 L.O 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 P 
 
 P.
 
 LOGARITHMS 
 
 55 
 
 
 
 
 
 Table— 
 
 ( Continued) 
 
 • 
 
 
 
 N. 
 
 L.O 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 8 
 
 9 
 
 P.P. 
 
 550 
 
 74 036 
 
 "044 
 
 "052 
 
 "060 
 
 "068 
 
 "076 
 
 "084 
 
 ~092 "099! 107 
 
 
 
 
 
 
 
 
 
 
 
 
 551 
 
 115 
 
 123 
 
 131 
 
 139 
 
 147 
 
 l55 
 
 162 
 
 170 178; 186 
 
 
 552 
 
 194 
 
 202 
 
 210 
 
 218 
 
 225 
 
 233 
 
 241 
 
 24«i 257' 265 
 
 
 553 
 
 273 
 
 280 
 
 288 
 
 296 
 
 304 
 
 312 
 
 320 
 
 327 1 335 1 343 
 
 
 554 
 
 351 
 
 359 
 
 367 
 
 374 
 
 382 
 
 390 
 
 398 
 
 40k| 414 421 
 
 
 555 
 
 429 
 
 437 
 
 445 
 
 453 
 
 461 
 
 468 
 
 476 
 
 484! 492 i 500 
 
 
 556 
 
 507 
 
 515 
 
 523 
 
 531 
 
 539 
 
 547 
 
 554 
 
 5621 570! 578 
 
 
 557 
 
 586 
 
 593 
 
 601 
 
 609 
 
 617 
 
 624 
 
 632 
 
 640 6481 656 
 
 
 568 
 
 663 
 
 6711 679 
 
 687 
 
 695 
 
 702 
 
 710 
 
 718, 726! 733 
 
 
 559 
 
 741 
 
 749 757 
 
 764 
 
 772 
 
 780 
 
 788 
 
 796 803 1 811 
 
 
 560 
 
 819 j 827 834 
 
 "842 
 
 "850 
 
 "858 
 
 865 
 
 873 881 889 
 
 , A 
 
 561 
 
 896| 904 912 
 
 920 
 
 927 
 
 "935 
 
 "943 
 
 "950 1 "958 "966 
 
 562 
 
 9-4 
 
 9811 989 
 
 997 
 
 *005 
 
 *012 
 
 *020 
 
 «028:*035 *043 
 
 2 
 
 u.o 
 1.6 
 2.4 
 3.3 
 4.0 
 4.8 
 5.6 
 6.4 
 7.2 
 
 563 
 
 75 051 
 
 059 1 066 
 
 074 
 
 082 
 
 089 
 
 097 
 
 105 
 
 113 120 
 
 564 
 
 128 
 
 136i 143 
 
 151 
 
 159 
 
 166 
 
 174 
 
 182 
 
 189 197 
 
 565 
 
 205 
 
 213| 220 
 
 228 
 
 236 
 
 243 
 
 251 
 
 259 
 
 266 274 
 
 566 
 
 282 
 
 289 
 
 297 
 
 305 
 
 312 
 
 320 
 
 328 
 
 335 
 
 343 351 
 
 567 
 
 358 
 
 366 
 
 374 
 
 381 
 
 289 
 
 397 
 
 404 
 
 412 
 
 420 1 427 
 
 568 
 
 435 
 
 442 
 
 450 
 
 458 
 
 465 
 
 473 
 
 481 
 
 488 
 
 496 1 504 
 
 569 
 
 511 
 
 519 
 
 526 
 
 534 
 
 542 
 
 549 
 
 557 
 
 565 
 
 572 580 
 
 570 
 
 587 
 
 ^95 
 
 603 
 
 610 
 
 618 
 
 626 
 
 633 
 
 641 648 j 656 
 
 
 571 
 
 664 
 
 ~671 
 
 "679 
 
 ~686 
 
 "694 
 
 "702 
 
 709 
 
 717| 724i 732 
 
 
 572 
 
 740 
 
 747 
 
 755 
 
 762 
 
 770 
 
 778 
 
 785 
 
 793 1 800 ! 80» 
 
 
 573 
 
 815 
 
 823 
 
 831 
 
 838 
 
 846 
 
 853 
 
 861 
 
 868! 8761 884 
 
 
 574 
 
 891 
 
 899 
 
 906 
 
 914 
 
 921 
 
 929 
 
 937 
 
 944 952! 959 
 
 
 575 
 
 967 
 
 974 
 
 982 
 
 989 
 
 997 
 
 *005 
 
 *012 
 
 *020 *027 *035 
 
 
 576 
 
 76 042 
 
 050 
 
 057 
 
 065 
 
 072 
 
 080 
 
 087 
 
 095! 103 110 
 
 
 577 
 
 118 
 
 125 
 
 133 
 
 140 
 
 148 
 
 155 
 
 163 
 
 170 
 
 1781 185 
 
 
 578 
 
 193 
 
 200 
 
 208 
 
 215 
 
 223 
 
 230 
 
 238 
 
 245 
 
 253 1 260 
 
 
 579 
 
 268 
 
 275 
 
 283 
 
 290 
 
 298 
 
 305 
 
 313 
 
 320 
 
 328 335 
 
 
 580 
 
 343 
 
 350; 358 
 425 433 
 
 ^5 
 440 
 
 373 
 
 448 
 
 380 
 455 
 
 "388 
 462 
 
 "395: "4031 "410 
 "470,"477l~485 
 
 
 581 
 
 418 
 
 7 
 
 582 
 
 492 
 
 500 507 
 
 515 
 
 522 
 
 530 
 
 537 
 
 545; 552 i 559 
 
 1 
 
 0.7 
 
 583 
 
 567 
 
 574! 582 
 
 589 
 
 597 
 
 604 
 
 612 
 
 619; 626 634 
 
 2 
 
 1.4 
 
 584 
 
 641 
 
 649 1 656 
 
 664 
 
 671 
 
 678 
 
 686 
 
 693, 701 708 
 
 3 
 
 2.1 
 
 585 
 
 716 
 
 7231 730 
 
 738 
 
 745 
 
 753 
 
 760 
 
 768! 775 782 
 
 
 2.8 
 
 586 
 
 790 
 
 797 
 
 805 
 
 812 
 
 819. 
 
 827 
 
 834 
 
 842 849, 856 
 
 
 3.5 
 
 587 
 
 864 
 
 871 
 
 879 
 
 886 
 
 893 
 
 901 
 
 908 
 
 916: 923 930 
 
 
 4.2 
 
 588 
 
 938 
 
 945 
 
 953 
 
 960 
 
 967 
 
 975 
 
 982 
 
 989! 997 *004 
 
 
 4.9 
 
 589 
 
 77 012 
 
 019 
 
 026 
 
 034 
 
 041 
 
 048 
 
 056 
 
 063 
 
 070| 078 
 
 
 5.6 
 6.3 
 
 590 
 
 085 
 
 093 
 
 100 
 
 "107 
 
 IT5 
 
 "122 
 
 I29 
 
 137 
 
 144 
 
 151 
 
 
 
 691 
 
 159 
 
 1661 173 
 
 181 
 
 188 
 
 "195 
 
 ^03 
 
 "2T0 
 
 "217 
 
 225 
 
 
 592 
 
 232 
 
 240! 247 
 
 254 
 
 262 
 
 
 276 
 
 283 
 
 291 
 
 298 
 
 
 593 
 
 305 
 
 313 
 
 320 
 
 327 
 
 335 
 
 342 
 
 349 
 
 357 
 
 364 
 
 371 
 
 
 594 
 
 379 
 
 386 
 
 393 
 
 401 
 
 408 
 
 415 
 
 422 
 
 430 
 
 437 
 
 444 
 
 
 595 
 
 452 
 
 459 
 
 466 
 
 474 
 
 481 
 
 488 
 
 495 
 
 503 
 
 510 
 
 517 
 
 
 596 
 
 525 
 
 532 
 
 539 
 
 546 
 
 554 
 
 561 
 
 568 
 
 576 
 
 583 
 
 590 
 
 
 597 
 
 597 
 
 605 
 
 612 
 
 619 
 
 627 
 
 634 
 
 641 
 
 648 
 
 656 
 
 663 
 
 
 598 
 
 670 
 
 677 
 
 685 
 
 692 
 
 699 
 
 706 
 
 714 
 
 721 
 
 728 
 
 735 
 
 
 599 
 
 743 
 
 750 
 822 
 
 757 
 830 
 
 764 
 837 
 
 772 
 "844 
 
 779 
 ~851 
 
 786 
 «59 
 
 793 
 "866 
 
 801 
 "873 
 
 808 
 ^80 
 
 
 600 
 
 815 
 
 
 N. 
 
 L.O 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 ~8~ 
 
 9 
 
 P.P.
 
 56 
 
 LOGARITHMS 
 
 Table— ( Continued). 
 
 N. 
 
 L.O 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 p. p. 
 
 600 
 
 77 815 
 
 "822 
 895 
 
 "830 
 902 
 
 "837 
 909 
 
 ^44 
 916 
 
 J51 
 924 
 
 "859 
 931 
 
 166 
 938 
 
 "873 
 945 
 
 "880 
 952 
 
 
 601 
 
 887 
 
 
 602 
 
 960 
 
 967 
 
 974 
 
 981 
 
 988 
 
 996 
 
 *003 
 
 *010 
 
 *017 
 
 *025 
 
 
 603 
 
 78 032 
 
 039 
 
 046 
 
 053 
 
 061 
 
 068 
 
 075 
 
 082 
 
 089 
 
 097 
 
 
 604 
 
 104 
 
 111 
 
 118 
 
 125 
 
 132 
 
 140 
 
 147 
 
 154 
 
 161 
 
 168 
 
 
 605 
 
 176 
 
 183 
 
 190 
 
 197 
 
 204 
 
 211 
 
 219 
 
 226 
 
 233 
 
 240 
 
 
 606 
 
 247 
 
 254 
 
 262 
 
 269 
 
 276 
 
 283 
 
 290 
 
 297 
 
 305 
 
 312 
 
 8 
 
 607 
 
 319 
 
 326 
 
 333 
 
 340 
 
 347 
 
 355 
 
 362 
 
 369 
 
 376 
 
 383 
 
 1 
 
 0.8 
 
 608 
 
 390 
 
 398 
 
 405 
 
 412 
 
 419 
 
 426 
 
 433 
 
 440 
 
 447 
 
 455 
 
 2 
 
 1.6 
 
 609 
 
 462 
 
 469 
 
 476 
 
 483 
 
 490 
 
 497 
 
 504 
 
 512 
 
 519 
 
 526 
 
 3 
 
 2.4 
 
 610 
 
 533 
 
 540 
 611 
 
 547 
 618 
 
 625 
 
 "56T 
 633 
 
 "569 
 640 
 
 576 
 647 
 
 ^83 
 654 
 
 590 
 661 
 
 597 
 
 668 
 
 4 
 5 
 6 
 7 
 8 
 9 
 
 3.2 
 4.0 
 4.8 
 5.6 
 6.4 
 7.2 
 
 611 
 
 604 
 
 612 
 
 675 
 
 682 
 
 689 
 
 696 
 
 704 
 
 711 
 
 718 
 
 725 
 
 732 
 
 739 
 
 613 
 
 746 
 
 753 
 
 760 
 
 767 
 
 774 
 
 781 
 
 789 
 
 796 
 
 803 
 
 810 
 
 614 
 
 817 
 
 824 
 
 831 
 
 838 
 
 845 
 
 852 
 
 859 
 
 866 
 
 873 
 
 880 
 
 615 
 
 
 
 902 
 
 909 
 
 916 
 
 923 
 
 930 
 
 937 
 
 944 
 
 951 
 
 616 
 
 958 
 
 965 
 
 972 
 
 979 
 
 986 
 
 993 
 
 *000 
 
 *007 
 
 *fll4 
 
 *021 
 
 
 617 
 
 79 029 
 
 036 
 
 043 
 
 050 
 
 057 
 
 064 
 
 071 
 
 078 
 
 085 
 
 092 
 
 
 618 
 
 099 
 
 106 
 
 113 
 
 120 
 
 127 
 
 134 
 
 141 
 
 148 
 
 155 
 
 162 
 
 
 619 
 
 169 
 
 176 
 
 183 
 
 190 
 
 197 
 
 204 
 
 211 
 
 218 
 
 225 
 
 232 
 
 
 620 
 
 239 
 
 246 
 "316 
 
 253 
 323 
 
 260 
 ^30 
 
 267 
 337 
 
 274 
 344 
 
 "281 
 ~35T 
 
 288 
 
 295 
 
 302 
 372 
 
 
 621 
 
 309 
 
 358! 365 
 
 7 
 
 • 622 
 
 379 
 
 38fi 
 
 393 
 
 400 
 
 407 
 
 414 
 
 421 
 
 428 
 
 435 
 
 442 
 
 1 
 
 0.7 
 
 623 
 
 449 
 
 456 
 
 463 
 
 470 
 
 477 
 
 484 
 
 491 
 
 498 
 
 505 
 
 511 
 
 2 
 
 1.4 
 
 624 
 
 518 
 
 525 
 
 632 
 
 539 
 
 546 
 
 553 
 
 560 
 
 567 
 
 574 
 
 581 
 
 3 
 
 2.1 
 
 625 
 
 588 
 
 595 
 
 602 
 
 609 
 
 616 
 
 623 
 
 630 
 
 637 
 
 644 
 
 650 
 
 4 
 
 2.8 
 
 626 
 
 657 
 
 664 
 
 671 
 
 678 
 
 685 
 
 692 
 
 
 706 
 
 713 
 
 720 
 
 5 
 
 3.5 
 
 627 
 
 727 
 
 734 
 
 741 
 
 748 
 
 754 
 
 761 
 
 768 
 
 775 
 
 782 
 
 789 
 
 6 
 
 4.2 
 
 628 
 
 796 
 
 803 
 
 810 
 
 817 
 
 824 
 
 831 
 
 837 
 
 844 
 
 851 
 
 858 
 
 7 
 
 4.9 
 
 629 
 
 865 
 
 872 
 
 879 
 
 886 
 
 893 
 
 900 
 
 906 
 
 913 
 
 920 
 
 927 
 
 8 
 9 
 
 5.6 
 
 6.8 
 
 630 
 
 934 
 
 "94T 
 "010 
 
 "948 
 
 "on 
 
 "955 
 "024 
 
 ~962 
 1(30 
 
 ^9 
 ~037 
 
 ^75 
 044 
 
 ~982 
 "051 
 
 989 
 "058 
 
 996 
 "065 
 
 631 
 
 80 003 
 
 
 632 
 
 072 
 
 079 
 
 085 
 
 092 
 
 099 
 
 106 
 
 113 
 
 120 
 
 127 
 
 134 
 
 
 633 
 
 140 
 
 147 
 
 154 
 
 161 
 
 168 
 
 175 
 
 182 
 
 188 
 
 195 
 
 202 
 
 
 634 
 
 209 
 
 216 
 
 223 
 
 229 
 
 236 
 
 243 
 
 250 
 
 257 
 
 264 
 
 271 
 
 
 635 
 
 277 
 
 284 
 
 291 
 
 298 i 305 
 
 312 
 
 318 
 
 325 
 
 332 
 
 339 
 
 
 636 
 
 346 
 
 353 
 
 359 
 
 366! 373 
 
 380 
 
 387 
 
 393 
 
 400 
 
 407 
 
 A 
 
 637 
 
 414 
 
 421 
 
 428 
 
 434 
 
 441 
 
 448 
 
 455 
 
 462 
 
 468 
 
 475 
 
 
 06 
 
 638 
 
 482 
 
 489 
 
 496 
 
 502 
 
 509 
 
 516 
 
 523 
 
 530 
 
 536 
 
 543 
 
 
 1.2 
 
 639 
 
 650 
 
 557 
 "625 
 
 564 
 632 
 
 570 
 638 
 
 577 
 645 
 
 584 
 652 
 
 591 
 659 
 
 598 
 
 604 
 
 611 
 679 
 
 9 
 
 1.8 
 
 640 
 
 618 
 
 665 672 
 
 2.4 
 3.0 
 3.6 
 4.2 
 4.8 
 5.4 
 
 641 
 
 686 
 
 693 
 
 699 
 
 706 713 
 
 720 
 
 726 
 
 "733 1 "740 
 
 747 
 
 642 
 
 754 
 
 760 
 
 767 
 
 774 
 
 781 
 
 787 
 
 794 
 
 801 1 808 
 
 814 
 
 043 
 
 821 
 
 828 
 
 835 
 
 841 
 
 848 
 
 855 
 
 862 
 
 8681 875 
 
 882 
 
 644 
 
 889 
 
 895 
 
 902 
 
 909 
 
 916 
 
 922 
 
 929 
 
 936 943 
 
 949 
 
 645 
 
 956 
 
 963 
 
 969 
 
 976 
 
 983 
 
 990 
 
 996 
 
 #003 *010 
 
 »017 
 
 646 
 
 81 023 
 
 030 
 
 037 
 
 043 
 
 050 
 
 057 
 
 064 
 
 070 077 
 
 084 
 
 
 647 
 
 090 
 
 097 
 
 104 
 
 111 
 
 117 
 
 124 
 
 131 
 
 I37I 144 
 
 151 
 
 
 648 
 
 158 
 
 164 
 
 171 
 
 178 
 
 184 
 
 191 
 
 198 
 
 204 211 
 
 218 
 
 
 649 
 
 224 
 
 231 
 
 238 
 
 245 
 
 251 
 
 258 
 
 265 
 
 271 
 
 278 
 
 285 
 
 
 650 
 
 291 
 
 298 
 
 l05 
 
 311 
 
 318 
 
 J25 
 
 "331 
 
 "338 
 
 "345 
 
 351 
 
 
 N. 
 
 L.O 
 
 1 
 
 •2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 P. P. 
 
 
 
 
 
 
 
 
 
 
 
 

 
 LOGARITHMS 
 
 57 
 
 
 
 
 
 Table— 
 
 {Continued). 
 
 
 
 N. 
 
 L.O 
 
 i 1 2 1 3 
 
 |4 
 
 5 1 6 1 7 
 
 8 9 
 
 P.P. 
 
 650 
 
 81 291 
 
 "298i'305i"3TT 
 
 318 
 
 325, 331 j "338 
 
 "345 "351 
 
 
 651 
 
 358 
 
 365: 371 37h 
 
 "3S5 
 
 391 
 
 398 1 405 
 
 411 418 
 
 
 652 
 
 425 
 
 431 438 
 
 445 
 
 451 
 
 458 
 
 465 
 
 471 
 
 478 485 
 
 
 653 
 
 491 
 
 498 i 505 
 
 511 
 
 518 
 
 525 
 
 531 
 
 538 
 
 544 551 
 
 
 654 
 
 558 
 
 564 571 
 
 578 
 
 584 
 
 591 
 
 598 
 
 604 
 
 61li 617 
 
 
 655 
 
 624 
 
 631 637 
 
 644 
 
 651 
 
 657 
 
 664 
 
 671 
 
 6771 684 
 
 
 656 
 
 690 
 
 697 1 704 
 
 710 
 
 717 
 
 723 
 
 730 
 
 737 
 
 743 750 
 
 
 657 
 
 757 
 
 763: 770i 776 
 
 783 
 
 790 
 
 796 
 
 803 
 
 809 816 
 
 
 658 
 
 823 
 
 829, 8361 842 
 
 849 
 
 856' 862, 869 
 
 875 882 
 
 
 659 
 
 889 
 
 895 902 1 908 
 
 915 
 
 921 928 i 935 
 
 941 948 
 
 
 660 
 
 954 
 
 961 968 974 
 
 981 
 
 987 
 
 994 *000 
 
 *00"7 *014 
 
 
 661 
 
 S2 020 
 
 ~027 ~033 "040 
 
 W6 
 
 "053 
 
 "060 ^066 
 
 073 079 
 
 7_ 
 
 662 
 
 086 
 
 092 099 105 
 
 112 
 
 119 
 
 125! 132 
 
 138 145 
 
 1 
 
 0.7 
 
 663 
 
 151 
 
 158 164! 171 
 
 178 
 
 184 
 
 191 1 197 
 
 204 210 
 
 2 
 
 1.4 
 
 664 
 
 217 
 
 223 230 
 
 2?6 
 
 243 
 
 249 
 
 256 263 
 
 
 3 
 
 
 665 
 
 282 
 
 289 295 
 
 302 
 
 308 
 
 315 
 
 321 ! 328 
 
 334 341 
 
 4 
 
 
 666 
 
 347 
 
 354 360 
 
 367 
 
 373 
 
 S80 
 
 3871 393 
 
 400 406 
 
 5 
 
 
 667 
 
 413 
 
 419 426 
 
 432 
 
 439 
 
 445 452 1 458 
 
 465, 471 
 
 6 
 
 
 668 
 
 478 
 
 4841 491' 497 
 
 504 
 
 510 5171 523 
 
 530 536 
 
 7 
 
 
 669 
 
 543 
 
 549 556 562 
 
 569 
 
 575 1 582 588 
 
 595 601 
 
 8 
 9 
 
 
 670 
 
 607 
 
 614 620 627 
 
 633 
 
 640 "646 653 
 
 659 666 
 
 671 
 
 672 
 
 "679 "685|~692 
 
 ~698 
 
 '705'"7Tl ^718 
 
 "724|-730 
 
 
 672 
 
 737 
 
 743: 750 j 756 
 
 763 
 
 7691 776 
 
 782 
 
 789 1 795 
 
 
 673 
 
 802 
 
 808: 814! 821 
 
 827 
 
 834 840 
 
 847 
 
 853! 860 
 
 
 674 
 
 866 
 
 8721 8791 885 
 
 892 
 
 898 905 
 
 911 
 
 918' 924 
 
 
 675 
 
 930 
 
 837 943! 950 
 
 956 
 
 963 969 
 
 975 
 
 982 988 
 
 
 676 
 
 995 *001 #008>014 
 
 *020 
 
 *027,»033;*040 
 
 *046;*052 
 
 
 677 
 
 83 059 
 
 065 i 072 
 
 078 
 
 085 
 
 091 1 097 104 
 
 no! 117 
 
 
 678 
 
 123 
 
 129! 136 
 
 142 
 
 149 
 
 1551 161 168 
 
 174 181 
 
 
 679 
 
 187 
 
 193 
 
 200 
 
 206 
 
 213 
 
 2191 225 232 
 
 238: 245 
 
 
 680 
 
 251 
 
 257 
 
 264 
 
 270 
 
 276 
 
 283 289 296 
 
 302 308 
 
 
 681 
 
 315 
 
 321 
 
 327 
 
 l34 
 
 "340 
 
 "347 
 
 353 
 
 359 
 
 "366 "372 
 
 6 
 
 682 
 
 378 
 
 385 
 
 391 
 
 398 
 
 404 
 
 410 
 
 417 
 
 423 
 
 429 436 
 
 1 
 
 0.6 
 
 683 
 
 442 
 
 448 
 
 455 
 
 461 
 
 467 
 
 474 
 
 480 
 
 487 
 
 493 499 
 
 3 
 
 1.2 
 
 684 
 
 506 
 
 512 
 
 518 
 
 525 
 
 531 
 
 537 
 
 544 
 
 550 
 
 556 563 
 
 3 
 
 1.3 
 
 685 
 
 569 
 
 575 
 
 582 
 
 588 
 
 594 
 
 601 
 
 607 
 
 613 
 
 620 626 
 
 4 
 
 2.4 
 
 686 
 
 632 
 
 639 
 
 645 
 
 651 
 
 658 
 
 664 
 
 670 
 
 677 
 
 683 689 
 
 5 
 
 3.0 
 
 687 
 
 696 
 
 702 
 
 708 
 
 715 
 
 721 
 
 727 
 
 734, 740 
 
 746 753 
 
 6 
 
 3.6 
 
 688 
 
 759 
 
 765 771 
 
 778 
 
 784 
 
 790 
 
 797 803 
 
 809 816 
 
 7 
 
 4.2 
 
 689 
 
 822 
 
 828 835 
 
 841 
 
 847 
 
 853 
 
 860 866 
 
 872 879 
 
 8 
 
 4.3 
 
 690 
 
 885 
 
 891 
 954 
 
 -897 
 960 
 
 904 
 967 
 
 910 
 973 
 
 916 
 979 
 
 923 1 929 
 985 i 992 
 
 "935 "942 
 998 *004 
 
 » 
 
 5.4 
 
 691 
 
 948 
 
 
 692 
 
 84 Oil 
 
 017 
 
 023 
 
 029 
 
 036 
 
 042 
 
 048 
 
 055 
 
 061 067 
 
 
 693 
 
 073 
 
 080 
 
 086 
 
 092 
 
 098 
 
 105 
 
 111 
 
 117 
 
 123 130 
 
 
 694 
 
 136 
 
 142 
 
 148 
 
 155 
 
 161 
 
 167 
 
 173 
 
 180 
 
 186 192 
 
 
 695 
 
 198 
 
 205 
 
 211 
 
 217 
 
 223 
 
 230 
 
 236 
 
 242 
 
 248 255 
 
 
 696 
 
 261 
 
 267 
 
 273 
 
 280 
 
 286 
 
 292 
 
 298 305 
 
 311 317 
 
 
 
 323 
 
 330 
 
 336' 342 
 
 348 
 
 354 
 
 361 : 367 
 
 373 379 
 
 
 698 
 
 386 
 
 392 
 
 398! 404 
 
 410 
 
 417 
 
 4231 429 
 
 435 1 442 
 
 
 699 
 
 448 
 
 454 
 516 
 
 460 
 ~522 
 
 466 
 
 ~528 
 
 473 
 535 
 
 479 
 541 
 
 485 491 
 l47^ 
 
 497 504 
 "559 ~566 
 
 
 700 
 
 510 
 
 
 N. 
 
 L.O 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 ' 
 
 8 9 
 
 P.P.
 
 58 
 
 LOGARITHMS 
 
 
 
 
 
 Table— 
 
 (.Continued) 
 
 • 
 
 
 
 N. 
 
 L.O 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 ' 
 
 8 1 9 
 
 P.P. 
 
 700 
 
 84 510 
 
 "516 
 
 "522 
 
 "528 
 
 T35 
 
 "541 
 
 "547 
 
 "553 
 
 "559 "566 
 
 
 701 
 
 572 
 
 578 
 
 584 
 
 590 
 
 597 
 
 "603 
 
 "609 
 
 615 
 
 621 628 
 
 
 702 
 
 634 
 
 640 
 
 646 
 
 652 
 
 658 
 
 665 
 
 671 
 
 677 
 
 683 689 
 
 
 703 
 
 696 
 
 702 
 
 708 
 
 714 
 
 720 
 
 726 
 
 733 
 
 739 
 
 745 751 
 
 
 704 
 
 757 
 
 763 
 
 770 
 
 776 
 
 782 
 
 788 
 
 794 
 
 800 
 
 907 1 813 
 
 
 705 
 
 819 
 
 825 
 
 831 
 
 837 
 
 844 
 
 850 
 
 856 
 
 862 
 
 868 874 
 
 
 706 
 
 880 
 
 887 
 
 893 
 
 899 
 
 905 
 
 911 
 
 917 
 
 924 
 
 930 936 
 
 7 
 
 707 
 
 942 
 
 948 
 
 954 
 
 960 
 
 967 
 
 973 
 
 979 
 
 
 9911 997 
 
 
 0.7 
 
 708 
 
 85 003 
 
 009 
 
 016 
 
 022 
 
 028 
 
 034 
 
 040 
 
 046 
 
 052' 058 
 
 
 
 709 
 
 065 
 
 071 
 132 
 
 077 
 138 
 
 083 
 144 
 
 089 
 150 
 
 095 
 156 
 
 101 
 163 
 
 107 
 169 
 
 114 120 
 I75J 181 
 
 8 
 9 
 
 
 710 
 
 126 
 
 sis 
 
 6.S 
 
 711 
 
 187 
 
 193 
 
 199 
 
 205 
 
 211 
 
 217 
 
 224 
 
 230 
 
 236 242 
 
 712 
 
 248 
 
 254 
 
 260 
 
 266 
 
 272 
 
 278 
 
 285 
 
 291 
 
 297 i 303 
 
 713 
 
 309 
 
 315 
 
 321 
 
 327 
 
 333 
 
 339 
 
 345 
 
 352 
 
 358 364 
 
 714 
 
 370 
 
 376 
 
 382 
 
 388 
 
 394 
 
 400 
 
 406 
 
 412 
 
 418 425 
 
 715 
 
 431 
 
 437 
 
 443 
 
 449 
 
 455 
 
 461 
 
 467 
 
 473 
 
 479, 485 
 
 716 
 
 491 
 
 497 
 
 503 
 
 509 
 
 516 
 
 522 
 
 528 
 
 534 
 
 540 646 
 
 
 717 
 
 652 
 
 558 
 
 564 
 
 570 
 
 576 
 
 582 
 
 588 
 
 594 
 
 600 606 
 
 
 718 
 
 612 
 
 618 
 
 625 
 
 631 
 
 637 
 
 643 
 
 649 
 
 655 
 
 661 667 
 
 
 719 
 
 673 
 
 679 
 
 685 
 
 691 
 
 697 
 
 703 
 
 709 
 
 715 
 
 721: 727 
 
 
 720 
 
 733 
 
 739 
 
 745 
 
 751 
 
 757 
 
 ^63 
 
 "^69 
 
 T75 
 
 "781, "788 
 
 
 721 
 
 794 
 
 800 
 
 806 
 
 812 
 
 818 
 
 824 
 
 830 
 
 "836 
 
 842' 848 
 
 8 
 
 722 
 
 854 
 
 860 
 
 866 
 
 872 
 
 878 
 
 884 
 
 890 
 
 896 
 
 902, 908 
 
 
 0.5 
 
 723 
 
 914 
 
 920 
 
 926 
 
 932 
 
 938 
 
 944 
 
 950 
 
 956 
 
 962 968 
 
 
 1.2 
 
 724 
 
 974 
 
 980 
 
 986 
 
 992 
 
 998 
 
 *004 
 
 *010 
 
 #016 
 
 *022 »028 
 
 
 1.8 
 
 725 
 
 86 034 
 
 040 
 
 046 
 
 052 
 
 058 
 
 064 
 
 070 
 
 076 
 
 082! 088 
 
 
 2.4 
 
 726 
 
 094 
 
 100 
 
 106 
 
 112 
 
 118 
 
 124 
 
 130 
 
 136 
 
 141 ! 147 
 
 
 3.0 
 
 727 
 
 153 
 
 159 
 
 165 
 
 171 
 
 177 
 
 183 
 
 189 
 
 195 
 
 201 207 
 
 
 3.6 
 
 728 
 
 213 
 
 219 
 
 225 
 
 231 
 
 237 
 
 243 
 
 249 
 
 255 
 
 261 267 
 
 
 4.2 
 
 729 
 
 273 
 
 279 
 
 285 
 
 291 
 
 297 
 
 303 
 
 308 
 
 314 
 
 320 326 
 
 
 4.3 
 
 730 
 
 332 
 
 338 
 
 344 
 
 ~35l) 
 
 "356 
 
 "362 
 
 368 
 
 3-4 
 
 380 : 386 
 
 731 
 
 392 
 
 398 
 
 ~404 
 
 lio 
 
 ~415 
 
 421 
 
 427 
 
 433 
 
 439, 445 
 
 
 732 
 
 451 
 
 457 
 
 463 
 
 469 
 
 475 
 
 481 
 
 487 
 
 493 
 
 499; 604 
 
 
 733 
 
 510 
 
 516 
 
 522 
 
 528 
 
 534 
 
 540 
 
 546 
 
 552 
 
 558 564 
 
 
 734 
 
 570 
 
 576 
 
 581 
 
 587 
 
 593 
 
 599 
 
 605 
 
 611 
 
 617 623 
 
 
 735 
 
 629 
 
 635 
 
 641 
 
 646 
 
 652 
 
 658 
 
 664 
 
 670 
 
 676 682 
 
 
 73fi 
 
 688 
 
 694 
 
 700 
 
 705 
 
 711 
 
 717 
 
 723 
 
 729 
 
 735; 741 
 
 s 
 
 737 
 
 747 
 
 753 
 
 759 
 
 764 
 
 770 
 
 776 
 
 782 
 
 788 
 
 794 1 800 
 
 
 0.5 
 
 738 
 
 806 
 
 812 
 
 817 
 
 823 
 
 829 
 
 835 
 
 841 
 
 847 
 
 853! 859 
 
 
 1.0 
 
 739 
 
 864 
 
 870 
 
 876 
 
 882 
 
 
 894 
 
 900 
 
 906 
 
 911 917 
 
 
 1.5 
 
 740 
 
 ~923 
 
 929 
 
 935 
 
 "941 
 
 "947 
 
 "953 
 
 958 
 
 "964 
 
 976 1 976 
 
 8 
 
 2.0 
 2.5 
 3.0 
 3.5 
 4 
 
 741 
 
 9H2 
 
 "988 
 
 "994 
 
 "999 
 
 *005 
 
 »ori 
 
 »017 
 
 #023 
 
 *«29 ^35 
 
 742 
 
 87 040 
 
 046 
 
 052 
 
 058 
 
 064 
 
 070 
 
 075 
 
 081 
 
 087 093 
 
 743 
 
 099 
 
 105 
 
 111 
 
 116 
 
 122 
 
 128 
 
 134 
 
 140 
 
 •146 151 
 
 744 
 
 157 
 
 163 
 
 169 
 
 1-5 
 
 181 
 
 186 
 
 192 
 
 198 
 
 204 210 
 
 
 4.5 
 
 745 
 
 216 
 
 221 
 
 227 
 
 233 
 
 239 
 
 245 
 
 251 
 
 256 
 
 262 268 
 
 746 
 
 274 
 
 2H0 
 
 2H6 
 
 291 
 
 297 
 
 303 
 
 309 
 
 315 
 
 320 1 826 
 
 
 747 
 
 332 
 
 338 
 
 344 
 
 349 
 
 355 
 
 361 
 
 367 
 
 373 
 
 379 384 
 
 
 748 
 
 390 
 
 396 
 
 402 
 
 408 
 
 413 
 
 419 
 
 425 
 
 431 
 
 437 442 
 
 
 749 
 
 448 
 
 454 
 
 460 
 
 466 
 
 371 
 
 477 
 
 483 
 
 489 
 
 495] 600 
 
 
 750 
 
 506 
 
 ~612 
 
 518 
 
 ;623 
 
 529 
 
 535 
 
 541 
 
 647 
 
 552 
 
 558 
 
 
 N. 
 
 L.0 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 P. P.
 
 LOGARITHMS 
 
 59 
 
 Table— ( Continued). 
 
 N. 
 
 L.0 
 
 87 506 
 
 1 
 
 "512 
 
 2 
 
 "518 
 
 3 
 
 "523 
 
 4 
 
 ~b29 
 
 5 
 
 -535 
 
 6 
 
 "541 
 
 7 1 8 ! 9 
 
 P 
 
 P. 
 
 750 
 
 ^47;-552 "558 
 
 
 751 
 
 564 
 
 570 
 
 576 
 
 581 
 
 "587 
 
 "593 
 
 599 
 
 6041 610 616 
 
 
 752 
 
 622 
 
 628 
 
 633 
 
 639 
 
 045 
 
 651 
 
 656 
 
 662 668 674 
 
 
 753 
 
 679 
 
 685 
 
 691 
 
 697 
 
 703 
 
 708 
 
 714 
 
 720; 726 731 
 
 
 754 
 
 
 743 
 
 749 
 
 754 
 
 760 
 
 766 
 
 772 
 
 777, 783 789 
 
 
 755 
 
 795 
 
 800 
 
 806 
 
 812 
 
 818 
 
 823 
 
 829 
 
 835' 841 846 
 
 
 756 
 
 852 
 
 858 
 
 864 
 
 
 875 
 
 881 
 
 887 
 
 892 898 904 
 
 
 757 
 
 910 
 
 915 
 
 921 
 
 927 
 
 933 
 
 938 
 
 944 
 
 950 955 961 
 
 
 758 
 
 967 
 
 973 
 
 978 
 
 984 
 
 990 
 
 996 
 
 *001 
 
 *007 »013 >01(- 
 
 
 759 
 
 88 024 
 081 
 
 030 
 "087 
 
 036 
 
 041 
 
 047 
 
 053 
 
 058 
 
 064 070 076 
 
 
 760 
 
 "093 
 
 098 
 
 104 
 
 110 
 
 116 
 
 121 127 133 
 
 
 761 
 
 138 
 
 144 
 
 lob 
 
 "156 
 
 161 
 
 "167 
 
 173 
 
 178 184 190 
 
 6 
 
 762 
 
 195 
 
 201 
 
 20- 
 
 213 
 
 218 
 
 224 
 
 230 
 
 235 241 247 
 
 
 0.6 
 
 763 
 
 252 
 
 258 
 
 264 
 
 270 
 
 275 
 
 281 
 
 287 
 
 292 298 304 
 
 
 1.2 
 
 764 
 
 309 
 
 315 
 
 32] 
 
 326 
 
 332 
 
 338 
 
 343 
 
 349 355 360 
 
 
 1.3 
 
 765 
 
 366 
 
 372 
 
 377 
 
 383 
 
 389 
 
 395 
 
 400 
 
 406 412 417 
 
 
 2.4 
 
 766 
 
 423 
 
 429 
 
 434 
 
 440 
 
 446 
 
 451 
 
 457 
 
 463 468 474 
 
 
 3.0 
 
 767 
 
 480 
 
 485 
 
 491 
 
 497 
 
 502 
 
 508 
 
 513 
 
 519 525 530 
 
 
 3.6 
 
 768 
 
 536 
 
 542 
 
 547 
 
 553 
 
 559 
 
 564 
 
 570 
 
 576 581 587 
 
 
 *l 
 
 769 
 
 593 
 
 598 
 
 604 
 
 610 
 
 615 
 
 621 
 
 627 
 
 632 638 643 
 
 8 
 
 *•! 
 
 770 
 
 649 
 
 655 
 
 660 
 
 "666 
 
 672 
 
 677 
 
 683 
 
 689 694 700 
 
 9 1 ^.s 
 
 771 
 
 705 
 
 711 
 
 717 
 
 -72'2 
 
 728 
 
 734 
 
 739 
 
 745 750 756 
 
 
 772 
 
 762 
 
 767 
 
 773 
 
 779 
 
 784 
 
 790 
 
 795 
 
 801 807 812 
 
 
 773 
 
 818 
 
 824 
 
 829 
 
 835 
 
 840 
 
 846 
 
 852 
 
 857 863 868 
 
 
 774 
 
 874 
 
 880 
 
 885 
 
 891 
 
 897 
 
 902 
 
 908 
 
 913 919 925 
 
 
 775 
 
 930 
 
 936 
 
 941 
 
 947 
 
 953 
 
 958 
 
 964 
 
 969 975 981 
 
 
 776 
 
 986 
 
 992 
 
 997 
 
 *003 
 
 »009 
 
 *014 
 
 *020 
 
 *025 *031 '037 
 
 
 777 
 
 89 042 
 
 048 
 
 053 
 
 059 
 
 064 
 
 070 
 
 076 
 
 081 087 092 
 
 
 778 
 
 098 
 
 104 
 
 109 
 
 115 
 
 120 
 
 126 
 
 131 
 
 137 143 148 
 
 
 779 
 
 154 
 
 159 
 
 165 
 
 170 
 
 176 
 
 182 
 
 187 
 
 193 198 204 
 
 
 780 
 
 209 
 
 215 
 
 221 
 
 226 
 
 "232 
 
 ^37 
 
 "243 
 
 "248 "254 "260 
 
 
 781 
 
 265 
 
 Tri 
 
 -276 
 
 282 
 
 "287 
 
 "293 
 
 "298 
 
 304 310 315 
 
 5 
 
 782 
 
 321 
 
 326 
 
 332 
 
 337 
 
 343 
 
 348 
 
 354 
 
 360 365 371 
 
 1 
 
 0.5 
 
 783 
 
 376 
 
 382 
 
 387 
 
 393 
 
 398 
 
 404 
 
 409 
 
 415 421 426 
 
 2 
 
 1.0 
 
 784 
 
 432 
 
 437 
 
 443 
 
 448 
 
 454 
 
 459 
 
 465 
 
 470 476 4M 
 
 3 
 
 1.5 
 
 785 
 
 487 
 
 492 
 
 498 
 
 504 
 
 509 
 
 515 
 
 520 
 
 526 531 537 
 
 4 
 
 2.0 
 
 786 
 
 542 
 
 548 
 
 553 
 
 559 
 
 564 
 
 5-0 
 
 575 
 
 581 5S6 592 
 
 5 
 
 2.5 
 
 787 
 
 597 
 
 603 
 
 609 
 
 614 
 
 620 
 
 625 
 
 631 
 
 636 642 647 
 
 6 
 
 3.0 
 
 788 
 
 653 
 
 658 
 
 664 
 
 669 
 
 675 
 
 680 
 
 686 
 
 691 697 702 
 
 7 
 
 3.5 
 
 789 
 
 708 
 
 713 
 
 719 
 
 724 
 
 730 
 
 735 
 
 741 
 
 746 752 75T 
 
 8 
 
 4.0 
 
 790 
 
 763 
 
 768 
 
 774 
 
 "779 
 
 785 
 
 790 
 
 796 
 
 801 807 812 
 
 9 
 
 4.5 
 
 791 
 
 818 
 
 "823 
 
 "829 
 
 "834 
 
 840 
 
 "845 
 
 "851 
 
 856 862 ^67 
 
 
 792 
 
 873 
 
 878 
 
 883 
 
 889 
 
 894 
 
 900 
 
 905 
 
 911 916 922 
 
 
 793 
 
 92- 
 
 933 
 
 938 
 
 944 
 
 949 
 
 955 
 
 960 
 
 966 971 977 
 
 
 794 
 
 982 
 
 988 
 
 993 
 
 998 
 
 »«04 
 
 *009 
 
 *015 
 
 *020 *026 '■031 
 
 
 795 
 
 90 037 
 
 042 
 
 048 
 
 053 
 
 059 
 
 064 
 
 069 
 
 075 080 086 
 
 
 796 
 
 091 
 
 097 
 
 102 
 
 108 
 
 113 
 
 119 
 
 124 
 
 129 135 140 
 
 
 797 
 
 146 
 
 151 
 
 157 
 
 162 
 
 168 
 
 173 
 
 179 
 
 184 189 195 
 
 
 798 
 
 200 
 
 206 
 
 211 
 
 217 
 
 222 
 
 227 
 
 233 
 
 238 244 249 
 
 
 799 
 
 255 
 
 260 
 
 266 
 
 271 
 
 276 
 
 282 
 
 287 
 
 293 298 304 
 
 
 800 
 
 309 
 
 314 
 
 820 
 
 325 
 
 331 
 
 336 
 
 342 
 
 "347 "352 "358 
 
 
 N. 
 
 L.O 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 T 
 
 7 1 8 1 9 
 
 P.P.
 
 60 
 
 LOGARITHMS 
 
 
 
 
 
 Table— 
 
 ( Continued] 
 
 . 
 
 
 
 N. 
 
 L.0| 1 2 3 4 
 
 5 6 7 1 8 
 
 9 
 
 P.P. 
 
 800 
 
 90 309 314 320 325 | 331 
 
 l36 ir2 "347|'352 
 
 "358 
 
 
 801 
 
 363; 369 2741 380 385 
 
 390 
 
 396 401 
 
 407 
 
 412 
 
 
 802 
 
 417 423 428 434 439 
 
 445 
 
 450! 455 
 
 461 
 
 466 
 
 
 803 
 
 472 477 482 488 493 
 
 499 
 
 504 
 
 509 
 
 515 
 
 520 
 
 
 804 
 
 526 531 1 636 542' 547 
 
 553 
 
 558 
 
 563 
 
 569! 574 
 
 
 805 
 
 580' 585' 590 j 5961 601 
 
 607 
 
 612 
 
 617 
 
 623 
 
 628 
 
 
 806 
 
 634 639 i 644! 650 1 655 
 
 660 
 
 666 
 
 671 
 
 677 
 
 682 
 
 
 807 
 
 687 693. 698. 703 709 
 
 714 
 
 720 
 
 725 i 730 
 
 736 
 
 
 808 
 
 7411 747; 752! 757 763 
 
 768 
 
 773! 779! T84 
 
 789 
 
 
 809 
 
 7951 800; 806! 811 816 
 
 822 
 
 827 8321 838 
 
 843 
 
 
 810 
 
 849; 8541 859 865 | 870 
 
 ^75 88l!'886i 891 
 
 "897 
 
 
 811 
 
 902, 907 913 918 924 
 
 929 
 
 934' 940 945 950 
 
 .8 
 
 812 
 
 956 961 966 972 
 
 977 
 
 982 
 
 988 9931 998.*004 
 
 
 
 813 
 
 91 009 014 020 i 025 
 
 030 
 
 036 
 
 041 046 052 
 
 057 
 
 
 
 814 
 
 062, 068. 0731 078 
 
 084 
 
 
 094 100 105 
 
 110 
 
 
 
 815 
 
 116' 121 
 
 126 
 
 132 
 
 137 
 
 142 
 
 148; 153! 158 
 
 164 
 
 
 
 816 
 
 169 
 
 174 
 
 180 
 
 185 
 
 190 
 
 196 
 
 201 ! 206' 212 
 
 217 
 
 
 
 817 
 
 222 
 
 228 
 
 233 
 
 238 
 
 243 
 
 249 
 
 254! 259, 265 
 
 270 
 
 
 
 818 
 
 275 
 
 281 
 
 286 
 
 291 
 
 297 
 
 302 
 
 307! 312 1 318 
 
 323 
 
 
 
 819 
 
 328 
 
 334 
 
 339! 344 
 
 350 
 
 355 
 
 360 365 371 
 
 376 
 
 9 
 
 
 820 
 
 381 i 387 392] 397 
 
 403 
 
 408i 413! 418; 424 
 
 429 
 
 821 
 
 434! 4401 445 
 
 450 
 
 455 
 
 "461 '466!'471'~477 
 
 482 
 
 
 822 
 
 487 1 492 498 
 
 503 
 
 508 
 
 514 519! 524 529 
 
 535 
 
 
 823 
 
 540 1 545! 551 
 
 556 
 
 561 
 
 566 572! 5771 582! 587 
 
 
 824 
 
 5931 598 603 
 
 609 
 
 614 
 
 619 624 630 635 640 
 
 
 825 
 
 645 
 
 651 656 
 
 661 
 
 666 
 
 672! 6771 682; 687 
 
 693 
 
 
 826 
 
 698 
 
 703 709 
 
 714 
 
 719 
 
 724 730 ! 7351 740 
 
 745 
 
 
 827 
 
 751 
 
 756 761 
 
 766 
 
 772 
 
 777 782 1 787 793 
 
 798 
 
 
 828 
 
 803 
 
 808 814 
 
 819 
 
 824 
 
 829 834! 840 845 
 
 850 
 
 
 829 
 
 855 
 
 861 866 
 
 871 
 
 876 
 
 882 j 887 j 892 
 
 897 
 
 903 
 
 
 830 
 
 908 
 
 913 918 
 
 924 1 929 
 
 934' 939 
 
 944 
 
 950 
 
 "955 
 
 
 831 
 
 960 
 
 965 971 
 
 976 
 
 981 
 
 986 
 
 991 
 
 997 
 
 *002 1*007 
 
 5 
 
 832 
 
 92 012 
 
 018 023 
 
 028 
 
 033 
 
 038 
 
 044 
 
 049 
 
 054 059 
 
 1 
 
 0.5 
 
 833 
 
 065 
 
 070 075 
 
 080 
 
 085 
 
 091 
 
 096 
 
 101 
 
 106 111 
 
 3 
 
 1.0 
 
 834 
 
 117 
 
 122 127 
 
 132 
 
 137 
 
 143 
 
 148 
 
 153 
 
 158 163 
 
 3 
 
 1.5 
 
 835 
 
 169 
 
 174 179 
 
 184 
 
 189 
 
 195 
 
 200 
 
 205 210' 215 
 
 4 
 
 2.0 
 
 836 
 
 221 
 
 226 231 
 
 236 
 
 241 
 
 247 
 
 252 
 
 257 262 
 
 267 
 
 5 
 
 2.5 
 
 837 
 
 273 
 
 278 283 
 
 288 
 
 293 
 
 298 
 
 304 
 
 309 314 
 
 319 
 
 6 
 
 3.0 
 
 838 
 
 824 
 
 330 335 340 
 
 345 
 
 350 
 
 355 
 
 361 366 
 
 371 
 
 7 
 
 3.5 
 
 839 
 
 376 
 
 381; 387! 392 397 
 
 402 
 
 407 412 418 
 
 423 
 
 8 
 
 4.0 
 
 840 
 
 428 433 1 438; 443 ^ 449 
 
 ^454 
 
 "459i"46ll"469 
 
 474 
 
 9 
 
 4.5 
 
 £41 
 
 4801 485 490, 495! 500 
 
 505 
 
 '5lii~5i6r521 1526 
 
 
 842 
 
 531 536 542 
 
 547! 552 
 
 557 
 
 562 i 567! 572 
 
 578 
 
 
 843 
 
 583 588 593 
 
 5981 603 
 
 609 
 
 614 619 
 
 624 
 
 629 
 
 
 844 
 
 634! 639 645 
 
 650 655 
 
 660 
 
 665 670 
 
 675 
 
 681 
 
 
 845 
 
 686 691 696 
 
 701 1 706 
 
 711 
 
 716 722 
 
 727 
 
 732 
 
 
 846 
 
 737 742' 747 
 
 7521 758 
 
 763 768 773 
 
 778 
 
 783 
 
 
 847 
 
 788 793 799 1 804 i 809 
 
 814 819 824 
 
 829 
 
 334 
 
 
 848 
 
 840 845' 850, 855 
 
 860 
 
 865 
 
 870 875 
 
 881 
 
 886 
 
 
 849 
 
 891 996 901 906 
 
 911 
 
 916 
 
 921 927 
 
 932 
 
 937 
 
 
 850 
 
 942 947 
 
 952 957 
 
 962 
 
 967 
 
 973 
 
 978 
 
 988 
 
 988 
 
 
 N. 
 
 L.O 
 
 1 
 
 2 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 P.P.
 
 LOGARITHMS 
 
 61 
 
 Table— ( Continued). 
 
 N. 
 
 L.O 
 
 1 ! 2 1 3 r-4 
 
 5 6 
 
 ' 
 
 8 9 
 
 P. P. 
 
 850 
 
 92 942 1 947' 952 1 9571 962 
 
 "967 "973 1 "978 
 
 "983 "988 
 
 
 851 
 
 993, 998 *«03,*<)08 »013 
 
 K)18,»O24»029*034 *039 
 
 
 852 
 
 93 044; 049 0541 0591 064 
 
 0691 075 OsO 
 
 085; 090 
 
 
 853 
 
 0951 lOOl 105 1101 115 
 
 120 
 
 125 131 
 
 136 141 
 
 
 854 
 
 146 15l[ 156| 161 
 
 166 
 
 171 
 
 176 181 
 
 186] 192 
 
 
 855 
 
 197 
 
 202! 207! 212 
 
 217 
 
 222 
 
 227 232 
 
 237! 242 
 
 
 856 
 
 247 
 
 2521 258! 263 
 
 268 
 
 273 
 
 278 283 
 
 288] 293 
 
 fl 
 
 85" 
 
 298 
 
 303 308! 313 
 
 318 
 
 323 
 
 328 334 
 
 339 344 
 
 1 
 
 s 
 
 8=i8 
 
 349 
 
 354 i 359 364 
 
 369 
 
 374 
 
 379 384 
 
 389 394 
 
 2 
 
 1.2 
 
 859 
 
 399 
 
 404! 409! 414 
 
 420 
 
 425 
 
 430 435 
 
 440 : 445 
 
 3 
 
 1.3 
 
 860 
 
 4501 455 460 465 
 
 ~470 
 
 475 
 
 ~480 "485 
 
 490 495 
 
 4 
 5 
 
 2.* 
 3 9 
 
 861 
 
 5001 505 510 515 
 
 "520 
 
 ^26 
 
 ~531|"536 
 
 ~541:"546 
 
 6 
 
 7 
 8 
 9 
 
 4.3 
 5.4 
 
 862 
 
 551 556, 5611 566 
 
 571 
 
 576 
 
 581] 586 
 
 591) 596 
 
 863 
 
 601 6061 611 1 616 
 
 621 
 
 626 
 
 631 636 
 
 641! 646 
 
 864 
 
 651 656 661 
 
 666 
 
 671 
 
 676 
 
 682 687 
 
 8921 897 
 
 865 
 
 702 7071 712 
 
 717 
 
 722 
 
 727 
 
 732! 737 
 
 742 1 747 
 
 866 
 
 752 757 762 
 
 767 
 
 772 
 
 777 
 
 782] 787 
 
 792 1 797 
 
 
 867 
 
 802 ! 807 ! 812 
 
 817 
 
 822 
 
 827 
 
 832; 837 
 
 842; 847 
 
 
 868 
 
 852 
 
 8571 862 
 
 867 
 
 872 
 
 877 
 
 882] 887 
 
 892 1 897 
 
 
 869 
 
 902 
 
 907 912 
 
 917 
 
 922 
 
 927 
 
 932 937 
 
 942 1 947 
 
 
 870 
 
 952 
 
 957, 962 i 967 i 972 
 "007 1)12 "on, "022 
 
 977 
 
 982 987 
 
 992, 997 
 1)42 ~047 
 
 
 871 
 
 94 002 
 
 "0271^32 T37 
 
 5 
 
 872 
 
 052 
 
 057 062 
 
 067 072 
 
 077 
 
 082 
 
 086 
 
 0911 096 
 
 1 
 
 0.5 
 
 873 
 
 101 
 
 106 HI 
 
 116 121 
 
 126 
 
 131 
 
 136 
 
 141 146 
 
 2 
 
 1.0 
 
 874 
 
 151 
 
 156 161 
 
 166! 171 
 
 176 
 
 181 
 
 186 
 
 191 1 196 
 
 3 
 
 1.5 
 
 875 
 
 201 206 211 
 
 216| 221 
 
 226 
 
 231 
 
 236 i 
 
 240] 245 
 
 4 
 
 2.0 
 
 876 
 
 250 255 260 
 
 265 270 
 
 275 
 
 280 
 
 285 
 
 290 i 295 
 
 5 
 
 2.5 
 
 877 
 
 300 
 
 305, 3101 315 320 
 
 325 
 
 330 335 
 
 340 345 
 
 6 
 
 3.0 
 
 878 
 
 349 
 
 354 359! 364 369 
 
 374 
 
 379! 384 
 
 389 1 394 
 
 T 
 
 3.5 
 
 879 
 
 399 
 
 404: 4091 414 419 
 
 424 
 
 429 433 
 
 4381 443 
 
 8 
 9 
 
 4.0 
 4.5 
 
 880 
 
 448 
 
 453 458 1 463 468 
 
 ^l 
 
 478 483 
 "527(~532, 
 
 488, 493 
 537 542 
 
 881 
 
 498 
 
 "563 ~507i~5r21~5r7 
 
 
 882 
 
 547 552 5571 562 i 567 
 
 571 
 
 5761 581 ! 
 
 586: 591 
 
 
 883 
 
 596 601 606 611. 616 
 
 621 626! 630 
 
 635 640 
 
 
 884 
 
 645 650 655 660 665 
 
 670 
 
 675 680 
 
 685, 689 
 
 
 885 
 
 694| 699 704; 709, 7U 
 
 719 
 
 724, 7291 
 
 734: 738 
 
 
 886 
 
 743: 748 7531 758 1 763 
 
 768 
 
 773: 7-8 
 
 783 787 
 
 4 
 
 887 
 
 792' 797 802 8071 812 
 
 817 
 
 822] 827 
 
 8321 836 
 
 1 
 
 0.4 
 
 888 
 
 841 i 846 851 856 861 
 
 866 
 
 871 ! 876 
 
 880] 885 
 
 2 
 
 0.8 
 
 889 
 
 890] 895; 900 905] 910 
 
 915 
 
 919! 924 
 
 929 934 
 
 3 
 
 1.2 
 
 890 
 
 939 944 949 954 959 
 
 963! 968 973 
 
 "978 
 
 983 
 
 
 1.6 
 2.0 
 2.4 
 
 891 
 
 983, 993, 998 #002 #007 
 
 *012 *017,*022 »027 
 
 *032 
 
 892 
 
 95 036 041 046 051; 056 
 
 061 ! 066 
 
 071 
 
 075 
 
 080 
 
 
 2 3 
 
 893 
 
 085 090, 095i 100| 105 
 
 109 114 
 
 119 
 
 124 
 
 129 
 
 32 
 
 894 
 
 1341 139 1431 148! 153 
 
 158 163 
 
 168 
 
 173 
 
 177 
 
 
 3.6 
 
 895 
 
 182 
 
 1871 1921 197 i 202 
 
 207 211 
 
 216 
 
 221 
 
 226 
 
 
 
 896 
 
 231 
 
 236 240 2451 250 
 
 255 260] 265 
 
 270 
 
 2-4 
 
 
 897 
 
 279 
 
 284 289 294| 299 
 
 303! 308 313 
 
 318 
 
 323 
 
 
 898 
 
 328 
 
 332 337: 342 347 
 
 352! 357 361 
 
 366 
 
 371 
 
 
 899 
 
 376 
 
 381 386 390 395 
 
 400 405 410 
 
 415 
 
 419 
 
 
 900 
 
 424 
 
 L.O 
 
 ^29 "434 
 
 439 
 
 444 
 
 ^448 ~453'^58 
 
 463 
 
 468 
 
 
 N. 
 
 1 2 
 
 3 
 
 4 
 
 5 6 1 7 
 
 T 
 
 9 
 
 P.P.
 
 LOGARITHMS 
 
 Table— ( Continued). 
 
 N. 
 
 L.0ll|2|3 
 
 4 
 
 5 
 
 6 7 1 8 9 
 
 P. P. 
 
 900 
 
 95 424 429 434 439 
 
 ~444 
 
 ~448 
 
 ^453 "458; "463 ["468 
 
 
 901 
 
 472 477 482 t 487 
 
 "492 
 
 ^97 
 
 501 506; Cn 516 
 
 
 902 
 
 521 525 530 1 535 
 
 540 
 
 545 
 
 550 554 j 559 564 
 
 
 903 
 
 569 574 578 583 
 
 588 
 
 593 
 
 5981 602; 607! 612 
 
 
 904 
 
 617 622 626: 631 
 
 636 
 
 641 
 
 646 650^ 655 660 
 
 
 905 
 
 665i 670; 674 679 
 
 684 
 
 689 
 
 694' 698' 703 708 
 
 
 906 
 
 713 7181 722 
 
 727 
 
 732 
 
 737 
 
 742; 746 751 756 
 
 
 907 
 
 761 766 770 
 
 775 
 
 780 
 
 785 
 
 789 794! 799' 804 
 
 
 908 
 
 809, 813 818 
 
 823 
 
 828 
 
 832 
 
 837 842; 8471 852 
 
 
 909 
 
 856! 861 866 
 
 871 
 
 875 
 
 880 
 
 885 890, 895! 899 
 
 
 910 
 
 904 909 914 
 
 "918 
 
 '92'3 
 
 ~928 
 
 933! 938, 942 947 
 
 
 911 
 
 952 957 961 
 
 "966 
 
 ~971 
 
 976 
 
 980 985' 990 995 
 
 , 5 
 
 912 
 
 999 *004 *009 *014 
 
 *019 
 
 *023 
 
 *028 *038 *038 *042 
 076; 080! 085 090 
 
 1 
 
 0.5 
 
 913 
 
 96 047 052 1 057 
 
 061 
 
 066 
 
 071 
 
 2 
 
 1.0 
 
 914 
 
 095 099 104 
 
 109 
 
 114 
 
 118 
 
 123 
 
 128 133! 137 
 
 3 
 
 1.5 
 
 915 
 
 142 1471 152 
 
 156 
 
 161 
 
 166 
 
 171 
 
 175! 180' 185 
 
 4 
 
 2.0 
 
 916 
 
 190 194 199 
 
 204 
 
 209 
 
 213 
 
 218 
 
 223 2271 282 
 
 5 
 
 2.5 
 
 917 
 
 237; '2421 246 
 
 251 
 
 256 
 
 261 
 
 265 
 
 270 275 i 280 
 
 6 
 
 3.0 
 
 918 
 
 284: 289, 294 
 
 298 
 
 803 
 
 308 
 
 313 
 
 317 322' 327 
 
 7 
 
 3.5 
 
 919 
 
 832 336 341 
 
 346 
 
 350 
 
 855 
 
 860 ! 365' 869 374 
 
 8 
 
 4.0 
 4.5 
 
 920 
 
 379, 884 388 
 
 393 
 
 398 
 
 402 
 
 "407 j "412 "417 ^21 
 
 921 
 
 426 431 435 
 
 "440 
 
 ~445 
 
 ~450 
 
 "454|l59 l64 168 
 
 
 922 
 
 473 478' 483 
 
 487 
 
 492 
 
 497 
 
 501! 506! 511 515 
 
 
 923 
 
 520 525 1 530 
 
 534 
 
 539 
 
 544 
 
 548! 553; 558 562 
 
 
 924 
 
 567 572 j 677 
 
 581 
 
 586 
 
 591 
 
 595 600, 605! 609 
 
 
 925 
 
 614 619, 624 
 
 628 
 
 633 
 
 638 
 
 642, 647 652 656 
 
 
 926 
 
 661 666 i 670 
 
 675 
 
 680 
 
 685 
 
 689 694 6991 703 
 
 
 927 
 
 708 7131 717 
 
 722 
 
 727 
 
 731 
 
 736, 741' 745' 750 
 
 
 928 
 
 755 1 759 764 
 
 769 
 
 774 
 
 778 
 
 783 788! 792' 797 
 
 
 929 
 
 802 806 811 
 
 816 
 
 820 
 
 825 
 
 830 ; 834! 839! 844 
 
 
 830 
 
 848 853 858 
 
 862 
 
 "867 
 
 872 
 
 l76' "881,186 190 
 
 
 931 
 
 895 900 904 
 
 ~909 
 
 914 
 
 "918 
 
 923 928 932 937 
 
 4 
 
 932 
 
 942! 946 951 
 
 956 
 
 960 
 
 965 
 
 970 974 979 984 
 
 1 
 
 0.4 
 
 933 
 
 9M8 993 997 
 
 *002 
 
 *007 
 
 *011 
 
 *016 *021 »025 X030 
 
 2 
 
 0.8 
 
 934 
 
 97 035 039, 044 
 
 049 
 
 053 
 
 058 
 
 063 067 072 077 
 
 3 
 
 1.2 
 
 935 
 
 081 : 086 090 
 
 095 
 
 100 
 
 104 
 
 109 114 118 123 
 
 4 
 
 1.6 
 
 936 
 
 128; 132 137 
 
 142 
 
 146 
 
 151 
 
 155 160! 165 169 
 
 5 
 
 2.0 
 
 937 
 
 174! 179 
 
 183 
 
 188 
 
 192 
 
 197 
 
 202 206 211 216 
 
 6 
 
 2.4 
 
 938 
 
 220 225 
 
 230 
 
 234 
 
 239 
 
 243 
 
 248; 253: 257 262 
 
 7 
 
 2.8 
 
 939 
 
 267 271 
 
 276 
 
 280 
 
 285 
 
 290 
 
 294 299 304 308 
 
 8 
 
 3.2 
 
 
 
 
 
 
 
 
 9 
 
 3.6 
 
 940 
 
 313 In 
 
 322 
 
 327 
 
 331 
 
 "336 
 
 340 345 350 354 
 
 941 
 
 359 364 368 
 
 373 
 
 ~377 
 
 382 
 
 "387i"391 ~396 lOO 
 
 
 942 
 
 405 410 414 
 
 419 
 
 424 
 
 428 
 
 433; 437, 442, 447 
 
 
 943 
 
 451 456 460] 465 
 
 470 
 
 474 
 
 479 483 488 493 
 
 
 944 
 
 497 5(12 506 511 
 
 516 
 
 520 
 
 525 529 534 539 
 
 
 945 
 
 543 548 552 1 557 
 
 562 
 
 566 
 
 571 575 580 ; 585 
 
 
 946 
 
 589, 594, 59^ 603 
 
 607 
 
 612 
 
 617 621 626 630 
 
 
 947 
 
 635 640 644 64'.l 
 
 653 
 
 658 
 
 663 667 672 676 
 
 
 948 
 
 681 685 
 
 690 695 
 
 699 
 
 704 
 
 708 713 717: 722 
 
 
 949 
 
 727 731 
 
 736 
 
 740 
 
 745 
 
 749 
 
 754 759; 763 768 
 
 
 950 
 
 772 l77 
 
 782 
 
 786 
 
 791 
 
 795 
 
 loo loi 809 lis 
 
 
 N. 
 
 L.O 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 ~6 1 7 8 9 
 
 P.P. 
 
 
 
 
 
 
 
 
 

 
 LOGARITHMS 
 
 63 
 
 Table— ( Continued). 
 
 N. 
 
 L.O 
 
 1 2 3 1 -I 
 
 5 6 ! 7 8 9 
 
 P.P. 
 
 950 
 
 97 772 
 
 Tn l82 ^ "791 
 
 ~795|800'"804 "809 "813 
 
 
 951 
 
 818 823 1 8271 832 836 
 
 ~84l|"845 "850'1;55 ~859 
 
 
 95J 
 
 864 868' 873! 877 8b2 
 
 886 891 896 900 905 
 
 
 953 
 
 909! 9u' 918' 923 928 
 
 932 9371 941 946 950 
 
 
 954 
 
 955 959' 9641 868 973 
 
 978: 982 987 991 996 
 
 
 955 
 
 98 OOOi 005 009: 014 019 
 
 023; 028 032 037 041 
 
 
 956 
 
 046 050! 055 1 059 064 
 
 068, 073 078 082 087 
 
 
 957 
 
 0911 096 100 105 109 
 
 114' 118 123 127 132 
 
 
 958 
 
 137 1411 146 150 155 
 
 159 164 168 173 177 
 
 
 959 
 
 182 1 186 191 i 195 200 
 
 204 209 214 218 223 
 
 
 960 
 
 227 232 j 2361 241: 245 
 
 250 '254 '259 263 268 
 
 
 961 
 
 272i 277] 281 1 286, 290 
 
 295: 299 304, 3081 313 
 
 5 
 
 962 
 
 3181 322' 327 331 336 
 
 340 345 349 354' 358 
 
 1 ~ ' 
 
 u.» 
 
 963 
 
 363 367 372 1 3761 381 
 
 385 390 394 399 403 
 
 2 
 
 1.0 
 
 964 
 
 408 
 
 412 417 421 426 
 
 430, 435 439 444 448 
 
 3 
 
 1.5 
 
 965 
 
 453 
 
 4571 462 4661 471 
 
 4751 480 484 489 493 
 
 4 
 
 2.0 
 2.5 
 
 966 
 
 498 
 
 502 507 511 516 
 
 520 525 529 534 538 
 
 5 
 
 967 
 
 543 
 
 5471 552 556 561 
 
 565 570 574 579 583 
 
 6 
 
 3.0 
 
 968 
 
 588 
 
 592 i 597, 601 605 
 
 610, 614 619 623 628 
 
 7 
 
 3.5 
 
 969 
 
 632 
 
 637 641, 646 650 
 
 6551 659 664 668 673 
 
 8 
 9 
 
 4.0 
 4.5 
 
 970 
 
 677 682, 686 691, 695 
 
 ^700 ^04 709 ^13,'717 
 
 971 
 
 722; 726; 731 735 740 
 
 Tu "749 ^53 ^58 "762 
 
 
 972 
 
 767l 771 7761 780 784 
 
 789: 793, 798 802 807 
 
 
 973 
 
 811 8161 820' 825 829 
 
 834 838 843 847 851 
 
 
 974 
 
 856' 860 1 865 869 874 
 
 878 883 887 892 896 
 
 
 975 
 
 900 905 909 1 914 918 
 
 923 927 932 936 941 
 
 
 976 
 
 945 949' 954 958 963 
 
 967 972 1 9761 981 985 
 
 
 977 
 
 989 994 998 *003 '007 
 
 *012 »016 '021 '025 *029 
 
 
 978 
 
 99 034 038: 043 1 047 052 
 
 056' Oeil 065 069 074 
 
 
 979 
 
 078 083, 087, 092 096 
 
 100 105| 109, 114 118 
 
 
 980 
 
 123 127] 131 136 140 
 
 ~145 I49 "1541158 l62 
 
 
 981 
 
 167' 1711 1761 180 185 
 
 l89 "l93 "1981^02 ~207 
 
 4 
 
 982 
 
 211 216 220 224 229 
 
 233 238 242 247 251 
 
 1 
 
 0.4 
 
 983 
 
 255 i 260 264 269 273 
 
 277 282 286 i 291' 295 
 
 2 
 
 0.8 
 
 984 
 
 300 304 3081 313 317 
 
 322 326, 330 335 339 
 
 3 
 
 1.2 
 
 985 
 
 3441 348 352 357 361 
 
 366 370 1 374 379 383 
 
 4 
 
 1.6 
 
 986 
 
 3881 392, 396 401 405 
 
 410 414 419 423 427 
 
 5 
 
 2.0 
 
 987 
 
 432 436 441 i 445 449 
 
 454' 458 463 467 47 l| 6 
 
 2.4 
 
 988 
 
 476 
 
 480 484 489 493 
 
 498 502: 506 511 515 
 
 7 
 
 2.8 
 
 989 
 
 520 
 
 524 528 533 537 
 
 542 546'; 550 555 559 
 
 8 
 9 
 
 3.2 
 3.6 
 
 990 
 
 564 
 
 568; 572, 577 1 581 
 
 ~585 ^90 ^94 , ^99 1 ~603 
 
 991 
 
 607 
 
 612 616 621 625 
 
 "629 "634 "638 "642 "647 
 
 
 992 
 
 651 j 6561 660' 664 669 
 
 673 677 682 686 691 
 
 
 993 
 
 695 6991 704 7081 712 
 
 717, 721 1 726, 730| 734 
 
 
 994 
 
 739' 743 747 752 1 756 
 
 760 765, 769 774 j 778 
 
 
 995 
 
 782, 787 791 795' 800 
 
 804 808 813: 817' 822 
 
 
 996 
 
 826 830 835 839 843 
 
 848 852' 856' 861 1 865 
 
 
 997 
 
 870 874' 878 883, 887 
 
 891 896 900 904! 909 
 
 
 998 
 
 9131 9171 922 926 930 
 
 935 939 944 948' 952 
 
 
 999 
 
 957 961 
 
 965 j 970 974 
 
 978, 983, 987, 991 
 
 99b 
 
 
 lOM 
 
 00 006 [ 004 
 
 ~oo9J"ol3 "on 
 
 022 026 
 
 030 
 
 035 
 
 "039 
 
 
 N. 
 
 L.O 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 P.P.
 
 64 
 
 TRICOXOMETRY 
 
 TRIGONOMETRY 
 
 Plane Trigonometry treats of the solution of plane tri- 
 angles. In every triangle there are six parts — three sides 
 and three angles. These parts are so related that when 
 three of the parts are given, one being a side, the other 
 parts may be found. 
 
 An angle is measured by the arc included between its 
 sides, the center of the circumference being at the vertex 
 of the angle. For the purpose of measuring angles, the 
 circumference is divided into 360 equal parts called degrees, 
 each degree being divided into 60 equal parts called minutes. 
 
 The complement of an arc is 90° minus the arc. 
 The supplement of an arc is 180° minus the arc. 
 
 In trigonometry, instead of comparing the angles of 
 triangles, or the arcs that measure them, we compare the 
 sine, cosine, tangent, cotangent, secant, and cosecant. 
 
 The sine of the angle aoc. Fig. 1, 
 f „ ^s the line a b drawn from a per- 
 
 pendicular to o c. 
 
 The cosine of the angle a o c is 
 
 
 B 
 
 c,-"-""^^^ 
 
 a 
 
 
 C 
 
 b 
 
 Fig. 2 
 
 
 the sine of its complement; or, it is the distance ob i = d a) 
 •from the foot of the sine to the center of the circle. 
 
 The tangent of the angle a o c is the line c e that is per- 
 pendicular to the radius o c at the extremity c, and which 
 is limited by a line passing through the center of the circle 
 and the other extremity a. 
 
 The cotangent of the angle a o c is equal to the tangent 
 of its complement; or, it is the line f g perpendicular to f o 
 and limited by the line o g passing through the extremity a.
 
 TRIGOXOMETRY 65 
 
 The secant of the angle a o c is a line drawn from the center o 
 through the extremity o and limited by the tangent of the 
 same angle. Thus, o e \s the secant of the angle ao c. 
 
 The cosecant of, the angle is the secant of the complement 
 of that angle. Thus, o g is the cosecant of the angle a o c. 
 
 All of these are known as trigonometric functions, and 
 are usually denoted by the abbreviations sin, cos, tan, cot, 
 sec, and cosec. 
 
 The ratios existing between the trigonometric functions 
 are best explained by means of a right triangle ABC, 
 Fig. 2, where C is the right angle. They are as follows: 
 
 sin i4 =- = opposite side h- hypotenuse 
 
 cos A=- = adjacent side -^hypotenuse 
 
 tan A = T = opposite side -e- adjacent side 
 
 cot A=- = adjacent side -h opposite side 
 a 
 
 sec A =-r = hypotenuse -H adjacent -ide 
 
 cosec A =-=hypotenuse -J- opposite side 
 a 
 
 The hypotenuse is the side c opposite the right angle. 
 The adjacent side h is the side that, with the hypotenuse, 
 includes the angle. The opposite side a is the side that joins 
 the adjacent side and the hypotenuse. 
 
 From the relations shown, we derive the following simple 
 principles: 
 
 1 . The sine of an arc equals the sine of its supplement, and 
 the cosine of an arc equals the cosine of its supplement. 
 
 2. The tangent of an arc equals the tangent of its supplement, 
 and the cotangent of an arc equals the cotangent of its supplement. 
 
 3. The secant of an arc equals the secant of its supplement, 
 and the cosecant equals the cosecant of its supplement. 
 
 Thus, the sine of 70° = the sine of 110° 
 
 the cosine of 70° = the cosine of 110° 
 
 the tangent of 70° = the tangent of 110° 
 
 the cotangent of 70° = the cotangent of 110® 
 
 the secant of 70° = the secant of 110° 
 
 the cosecant of 70° = the cosecant of 110°
 
 66 TRIGOXOMETRY 
 
 Thus, if you want to find the sine of an angle of 120'' 30', 
 look for the sine of 180° -120° 30', or 59° 30'. etc. 
 Functions of the sum and difference of two angles: 
 sin (A + B) = sin A cos B + cos A sin B 
 cos {A + B)= cos A cos 5 — sin A sin B 
 sin (A — B)= sin A cos B — cos A sin B 
 cos iA-B)= cos A cos B + sin A sin B 
 There are two kinds of trigonometrical tables that may be 
 used in the computation of the sides and angles of a triangle, 
 viz. : natural sines, tangents, etc., and logarithmic sines, tangents, 
 etc. Natural sines, tangents, etc., are calculated for a circle 
 whose radius is unity, and logarithmic sines, tangents, etc., are 
 calculated for a circle whose radius is 10,000,000,000. With 
 natural sines, etc., long and tedious operations in multiplica- 
 tion and division are necessary. With logarithmic sines, etc., 
 these operations, in conjunction with a table of logarithms of 
 numbers, are reduced to simple addition and subtraction. 
 
 ILLUSTRATIONS OF TRIGONOMETRY 
 APPLIED IN PRACTICE 
 
 Example. — Referring to Fig. 1. suppose that the angle v 
 subtended by the lighthouse is 15° and that the height h 
 of the light is 144 ft.; what is the distance d? 
 
 Solution.- 
 
 Fig. 1 
 —In this case we have 
 
 d ^ ^^* 
 
 tan V tan 15° 
 
 log 144 = 2.15836 
 tan 15° = 9.42805 
 
 log (f = 2.73031 
 d = 537.4 ft. Ans.
 
 TRIGONOMETRY 
 
 67 
 
 Example. — Referring to Fig. 2, suppose that a ship 
 from C sails N E by N, or N 33° 45' E, a distance of 115 mi.; 
 how much northing and how much easting has she made? 
 
 Solution. — In this case, A B represents the easting and 
 C A the northing; we have then, 
 
 AB = BCX sin 33° 45' 
 C^=SCXcos33° 45' 
 log 115 = 2.06070 log 115 = 2.06070 
 
 sin 33° 45' = 9.74474 cos 33° 45' = 9.91985 
 
 log A 5 = 1.80544 log C^ = 1.98055 
 
 A B = 63.89 mi. Ans. C ^ = 95.6 mi. 
 
 Example. — A ship sails N 69° E for a distance of 
 
 Ans. 
 
 and is then found to have made good a course due east and 
 
 Fig. 2 
 
 Fig. 3 
 
 covered a distance of 103 mi. in that direction; find the 
 direction and distance of the current that has acted on 
 the vessel. 
 
 Solution. — If N S, Fig. 3, represents the meridian, A C iz 
 the course and distance run, and A D the course and distance 
 made good; the line CD { = A B) will then represent the 
 direction and distance of the current that has acted on the 
 ship during her run. Using natural functions, we find 
 the required quantities, the angle E C D and the distance
 
 68 NAVIGATION 
 
 CD, as follows* From the vertex C draw C E perpendicu- 
 lar to A D, thus forming two right triangles A E C and 
 CED. In the triangle AEC.the side d is known, as is also 
 the angle C A E. We then have 
 
 C E = dsm C A £ = 80 X sin 21° = 80 X .3583= 28.7 
 and m = dcosCA £ = 80 X cos 21° = 80 X .9336= 74.7 
 
 whence, n = >l i9-m = 103-74. 7 = 28.3 
 
 In the triangle CED, we have 
 
 tan£CZ; = ^ = ||| = 44°36' 
 
 EC 28.7 28.7 ^- _ 
 
 and a = wt^t^^ . .„ „„ -7 = -v,-^ = 40.3 
 
 cos EC D cos 44° 36' .712 
 
 Therefore, C D or the direction of the current is S 44° 
 
 36' E and the drift or distance 40.3 mi, Ans. 
 
 Note. — For other examples showing tlT« application of Trigonometry in 
 pr»otice, see Navigation by Dead Reckoning. 
 
 NAVIGATION 
 
 THE COMPASS ERROR 
 
 TERMS AND DEFINITIONS RELATING TO THE MAG- 
 NETIC NEEDLE 
 
 Magnetism is the name given the phenomenon displayed 
 by magnets of attracting small pieces of iron and steel. 
 
 Magnets are of two kinds, natural and artificial. The ore 
 commonly known as lode stone, which possesses the property 
 of magnetism, is a natural magnet. The chemical composi- 
 tion of this ore is about 72 parts of iron and 28 parts of 
 oxygen. When a bar or needle is rubbed with a piece of 
 lode stone, it acquires magnetic properties similar to those • 
 of the lode stone without the latter losing any of its own | 
 magnetism. Such bars or needles are called artificiaJ j 
 magnets. 
 
 Magnetic Poles. — When an ordinary bar magnet is plunged 
 into iron filings it does not become uniformly covered 
 but instead the filings arrange themselves around the end^
 
 NAVIGATION 69 
 
 of the bar in feathery tufts that grow smaller as the middle 
 of the bar is approached, leaving that portion bare. The 
 points around which the filings concentrate are called the 
 poles of the magnet, while the middle portion of the bar 
 which has no visible magnetic force is called the neutral 
 zone. 
 
 Magnetic axis is the line connecting the two poles of a 
 magnet. 
 
 Magnetic Polarity. — A magnetized needle suspended on 
 its center of gravity will lay itself in a definite direction 
 pointing toward north and south. This tendency, called 
 polarity, applies to all magnets. The end pointing north- 
 wards is called the north-seeking, or red, pole, and the 
 opposite the south-seeking, or blue, pole. In other words, 
 the north-seeking end of the needle is said to have red 
 polarity, while the south-pointing end has blue polarity. 
 
 Magnetic Attraction and Repulsion. — When two magnet- 
 ized bars, or needles, are brought close together, the north- 
 seeking, or red, pole of one magnetic needle will repel the 
 north-seeking end of the other needle, while it will attract 
 the south-seeking end. From this, the following law for 
 magnetic attraction and repulsion may be enunciated: 
 Poles of contrary names attract each other, while poles of 
 the same name repel each other; or, the red pole of one 
 magnet will repel the red of another, but attract the blue, 
 and vice versa. 
 
 Magnetic Property of the Earth. — The fact that a suspended 
 needle takes up a fixed position has led to the theory that 
 the earth itself is a huge magnet having its red and blue 
 magnetic poles in the neighborhood of the geographical 
 poles, and that the magnetic needle turns to these poles 
 as to the poles of an ordinary magnet, according to the law 
 just given. Since the north-seeking end of a needle has 
 red polarity, it follows that the magnetic pole of the earth 
 situated in the northern hemisphere must be a blue pole 
 and that in the southern a red pole. 
 
 Magnetic meridian is the direction that the horizontally 
 suspended magnetic needle assumes when not influenced 
 by local disturbances.
 
 70 iV.-l 17(7.4 r/O.V 
 
 Magnetic Components. — The magnetic force of the earth 
 may be resolved into two components, one horizontal and 
 one vertical ; the former represents the directive element of 
 the compass needle; the latter acts only in a vertical direc- 
 tion. A magnetic needle mounted at its center of gravity 
 would be acted upon by both components. 
 
 Mag^netic dip is the effect of the vertical component of 
 the earth's magnetic force, or the inclination, or downward 
 deflection from the horizontal, of a magnetic needle free to 
 move in the vertical plane. The amount of dip varies from 
 0° to 90°, being 0° at the magnetic equator and gradually 
 increasing until 90° is reached at the magnetic poles. 
 
 Magnetic equator is a narrow belt or zone embracing all 
 points on the earth's surface where the magnetic dip is 
 zero; it encircles the equatorial part of the earth and inter- 
 sects it, but never recedes more than 16° on either side of the 
 geographical equator. 
 
 Magnetic induction is the property of a magnet imparting 
 magnetism to a body of iron or steel in its immediate vicinity. 
 Thus, the earth being a magnet will impart or communicate 
 magnetism to the hull of an iron vessel. The vessel is then 
 said to be magnetized by induction. 
 
 Magnetic variation is the angle that the magnetic meridian 
 makes with the geographical meridian, or, what is the same, 
 the angle that the direction of the suspended needle makes 
 with the true meridian; it is caused by the magnetic poles 
 of the earth not coinciding with the geographic poles. 
 Variation is not constant, but undergoes a progressive 
 change, the annual amount of which is invariably marked 
 on charts. 
 
 Isogenic lines are curves or lines connecting points of 
 equal variation. Charts on which such lines are plotted 
 are called isogenic, or variation, charts. 
 
 Agonic lines are curves or lines connecting all places on 
 the earth's surface where the variation of the compass is 
 zero. 
 
 Isoclinic lines are curves or lines that are drawn inter- 
 mediate to the poles and equator connecting all places 
 where the dip of the magnetic needle is the same.
 
 NAVIGATION 
 
 N 
 
 Isodynamic lines are curves or lines connecting all places 
 where the intensity of the earth's magnetic force is the same. 
 
 Deviation. — A compass placed on board an iron or 
 steel vessel is subjected to various disturbances from the 
 magnetism of the surrounding metal, and the errors thus 
 produced are collectively known as the deviation of the 
 compass. Deviation may also be defined as the deflection 
 of the compass needle from the magnetic meridian. At 
 the same time, the needle is acted upon by variation and the 
 combined eflfect of the two may properly be termed the 
 total error of the compass. Deviation and variation must not 
 be confounded with 
 one another; varia- Jffaff 
 tion, being caused by 
 the magnetic force of 
 the earth, affects the 
 compass alike on all 
 courses, while devia- 
 tion, being caused by 
 the magnetism of the 
 iron in the hull and 
 fittings of the vessel 
 itself, varies for dif- 
 ferent headings of the 
 ship. The reason 
 why deviation varies 
 as indicated will be 
 readily understood 
 
 by remembering that, through induction of magnetism from 
 the earth, any iron or steel vessel may be considered as a 
 large magnet having red and blue polarity that affects 
 the compass needle in exactly the same manner as an ordinary 
 magnet. Suppose that the vessel has blue polarity in the 
 bow and red polarity in the stern and that no other magnetic 
 disturbances have any effect on the compass needle; then, 
 when heading in the direction of the magnetic meridian, 
 as (a) in the appended figure, it is evident there will be no 
 deflection of the needle. But when turning the bow in any 
 other direction, for example to east, as in (6), there will 
 
 (3 
 
 rw 
 
 Caj
 
 72 NAVIGATION 
 
 necessarily be a deflection due to the influence of the altered 
 position of the ship's magnetic poles. Hence, the cause 
 of the deviation being different for different positions of 
 the ship's head. 
 
 Subpermanent magnetism is the magnetic condition of 
 a more or less enduring character possessed by a ship when 
 launched and which was acquired when building, by induc- 
 tion from the earth and rendered permanent, or nearly so, 
 by hammering. 
 
 Retentive magnetism is the temporary magnetism com- 
 municated to an iron ship when her head is kept in one 
 direction for some time; as, for example, when moored to 
 a pier, or when steering a continuous course for several 
 days. Retentive magnetism frequently remains for days 
 after the cause is removed. 
 
 Semicircular deviation is the effect of the combined action 
 of the subpermanent magnetism and the transient magnet- 
 ism from the vertical soft iron of the ship. It is called 
 semicircular because it has the contrary name and maximum 
 value in opposite semicircles. 
 
 Quadrantal deviation is the deviation produced by the 
 transient magnetism of horizontal soft iron. It is called 
 quadrantal because it is greatest on the quadrantal points, 
 and because it changes its name in each successive quadrant. 
 
 Soft Iron is iron that becomes magnetized as soon as it 
 is exposed to the influence of some magnetic body but 
 which has not power to retain the magnetism thus acquired. 
 Malleable and cast iron belong to this class. 
 
 Hard Iron is iron combined with a certain percentage of 
 carbon (steel) and which has the property of retaining its 
 magnetism permanently, or nearly so, when magnetized. 
 
 Vertical and horizontal iron refer to the structure of a 
 vessel built of iron or steel To the first named, belongs 
 all iron running in a vertical direction, such as frames, stan- 
 chions, bulkheads, etc.; to the latter, all iron running hori- 
 zontally, such as the keel, deck beams, deck plates, etc. 
 
 Local attraction is any disturbance, temporary or other- 
 wise, caused by any iron, steel, dynamo, electric wiring, 
 etc., in the immediate vicinity of the compass and which
 
 NAVIGATION 
 
 73 
 
 is not included in the stationar/ metal surrounding the 
 compass. In this expression is included also the magnetic 
 influences due to the locality in which the ship happens to 
 be, for example, when in dock alongside of iron ships, cranes, 
 pillars, etc., or when in close proximity to iron-bearing 
 mountains or volcanic islands. The effect on the compass 
 of cargo containing iron, such as iron ore, machinery, etc., 
 may also be classed as local attraction. 
 
 COMPENSATION OF COMPASSES 
 
 The general principle of compensating a compass is to 
 counteract the magnetic disturbances by means of magnets 
 and soft iron placed in the immediate neighborhood of the 
 compass and in such position as to cause a disturbance 
 contrary to that caused by the iron of the ship. The mag- 
 netic needle will thus be left comparatively free. This 
 may be illustrated 
 as follows: Bear- 
 ing in mind that 
 the north - seeking 
 end of the compass rimi 
 needle always pos- 
 sesses red polarity 
 and that red polar- 
 ity repels red and 
 attracts blue, and 
 vice versa, assume 
 a needle to be de- 
 flected from mag- 
 netic north A' to n. 
 Fig. 1. Then, in 
 order to bring the needle back to its proper position N, or, 
 what is the same thing, to counteract the effect of the sur- 
 rounding iron and steel, magnets may be placed in any of the 
 positions shown at a suitable distance from the needle. It 
 will be noticed in each case, that is, if the magnets are used 
 singly or in pairs, or in any other combination, that the 
 whole operation of compensating is simply an application 
 of the law of magnetic attraction and repulsion.
 
 74 
 
 NAVIGATION 
 
 The two principal errors of a compass to compensate are 
 the semicircular deviation and the quadrantal deviation. 
 The semicircular error is the combined effect of subper- 
 manent magnetism of the ship and the induced magnetism 
 of vertical iron; but, as a whole and for the purpose of 
 compensation, it is convenient to divide this error into two 
 parts and consider each part as a separate force, one acting 
 in a fore-and-aft, and the other in an athwartship direction. 
 The first part of that error, which affects the compass 
 needle when heading on easterly and westerly courses, is 
 usually denoted by the letter i5; while the second part, which 
 affects the needle when heading on northerly and southerly 
 courses, is denoted by the letter C. The quadrantal deviation, 
 resulting from horizontal iron and which attains its maxi- 
 mum value when the ship is heading on any of the quadrantal 
 points, is denoted by D. These forces B, C, and D are 
 technically known as coefficients. 
 
 When compensating a compass, it has been found good 
 practice to correct the quadrantal deviation first and then 
 
 the two parts of the 
 ^ ^^ semicircular error. 
 
 To Compensate the 
 Quadrantal Deviation. 
 Since this error which 
 is caused by the mag- 
 netism of horizontal soft 
 iron, attains its maxi- 
 mum value on the quad- 
 rantal points, the ship is 
 swung in the direction of 
 one of these points, for 
 example, N E, as shown 
 in Fig. 2; and since the 
 error is caused by soft 
 iron, it is necessary to 
 compensate it by using hollow soft-iron spheres. These 
 spheres are so placed in the plane of the compass card as to 
 cause an opposite effect to the magnetism of horizontal iron. 
 The error to be corrected being easterly in the N E and S W
 
 NAVIGATION 
 
 75 
 
 quadrants and westerly in the N W and S E quadrants in 
 almost every ship, the spheres are placed athwartship on the 
 same horizontal plane and at equal distances from the cen- 
 ter of the compass, the distance being determined by trial, 
 moving them to and fro in their respective, slits until the com- 
 pass shows the correct quadrantal point on which the ship is 
 headed. The quadrantal deviation is constant in all lati- 
 tudes, provided that the surrounding iron remains in the 
 same position, and hence its compensation remains constant 
 everywhere. 
 
 To Compensate Coefficient C. — Swing the ship's head 
 toward magnetic north, according to some compass not 
 influenced by the magnetism of the ship (for instance by a 
 compass on shore), or, better still, by permanent marks on 
 land, the bearing be- 
 tween which coincides 
 with the magnetic me- 
 ridian. If the compass 
 in -^his position does not 
 show exactly north, but 
 is deflected to the east, 
 as shown in Fig. 3, place 
 a magnet on the fore- 
 and-aft line with its red 
 pole to starboard. 
 
 The distance of the 
 magnet must be deter- 
 mined by trial; begin by 
 placing the magnet at 
 some distance from the 
 compass and gradually 
 approach it until the 
 compass shows correct 
 magnetic north, when the magnet is secured to the deck. 
 If the needle had been deflected to the west, it is evident 
 that the red end, or pole, of the magnet should have been 
 placed to the port side. In case this error is large, the ship 
 is swung toward magnetic south and a similar operation 
 is performed on that heading. 
 
 Cbmpensalion 
 
 ofC. 
 
 Fig. 3
 
 76 
 
 NAVIGATION 
 
 lo Compensate Coefficient B. — --The ship is swung magnetic 
 east or %vest. If swung to east and the compass north on that 
 heading is deflected to the west, as in Fig. 4, place a magnet 
 on the athwartship line with its blue pole forwards and at a 
 distance from the . compass sufficient to correct the error. 
 The compass north being deflected to the east, the compen- 
 sating magnet is reversed. A similar operation is then per- 
 formed, if necessary, with the ship's head swung west. 
 
 The foregoing applies to ships not equipped with a com- 
 pensating binnacle. It becomes necessary then to have 
 fore-and-aft and athwartship lines run out on the deck and 
 
 Compen^aiion of B, 
 
 Fig. 4 
 
 intersecting at a point vertically below the center of the 
 compass to be compensated. The magnets are then placed 
 perpendicularly with their centers on these lines, as shown 
 in Figs. 3 and 4. 
 
 At present, however, and particularly in iron ships, com- 
 pensating magnets are seldom, if ever, fastened to the deck, 
 but are fitted to slide into horizontal fore-and-aft and 
 athwartship receptacles within the binnacle. In most 
 binnacles, the receptacles are arranged in such a manner 
 as to be moved up or down, nearer to, or farther from, the 
 compass, as may be required, and then secured by means
 
 NAVIGATION 11 
 
 of clamp screws that cannot be touched except by opening 
 the door of the binnacle; in others, the movement of the 
 magnets is controlled from the outside of the binnacle by 
 means of a crank-key, thus enabling the adjuster to watch 
 the compass while he is altering the position of the magnets, 
 and to move them the exact amount required; after the 
 adjustment is completed, the crank-key is removed and the 
 casing locked, making it impossible for any one to tamper 
 with the magnets. The principle of magnets being stored 
 within the binnacle is precisely the same as in securing them 
 to the deck, both the magnets for B and C being exactly 
 parallel to the ship's deck or to the plane of the compass 
 card when the ship is in an upright position. 
 
 As previously stated, the compensation of the quadrantal 
 error is good for all latitudes. Such, however, is not the 
 case with that part of the semicircular error caused by the 
 induced magnetism of vertical iron. Since the amount of 
 this magnetism depends on the magnetic dip, it is evident 
 that the deviation resulting from it will depend on the 
 magnetic dip also. To distinguish this latter error from 
 that produced by subpermanent magnetism and to apply 
 to it a proper compensation is a difficult task, requiring 
 skill, good judgment, and an intimate knowledge of the 
 magnetic condition of the ship. The usual method of cor- 
 recting or compensating this error is by means of a vertical 
 iron bar, called the Flinders bar, which is placed within or 
 outside the binnacle either immediately before or abaft the 
 compass. This bar, which received its name from its inventor, 
 Captain Flinders, of the British Navy, is not a permanent 
 magnet; it is made of soft iron, and consequently receives 
 its magnetism by induction from the earth. 
 
 The object, therefore, to be attained by the Flinders bar 
 is to place it in such a position within the binnacle that the 
 gradual change of its magnetism, produced by the change 
 in latitude, will counterbalance the effect of the likewise 
 varying magnetism of the vertical iron of the ship. 
 
 Heeling Error. — When, from some cause, the ship has a 
 list to either side, a new error is created, which is generally 
 known as the heeling error. The principal cause of this
 
 78 NAVIGATION 
 
 error may be explained as follows: When the ship heels 
 over from the pressure of wind, shifting of cargo, or unequal 
 trimming of coal bunkers, all horizontal iron, such as the 
 deck beams, tends to assume a vertical position, and in 
 doing so will receive magnetism by induction from the earth. 
 Thus, for a ship in the northern hemisphere, the upper ends 
 of the beams, whether heeling to port or starboard, will 
 acquire blue polarity and the lower ends red polarity. In 
 the southern hemisphere, these conditions are reversed. 
 As a consequence, the north end of the compass needle will 
 be attracted by the upper ends of the beams in north mag- 
 netic latitudes and repelled in south magnetic latitudes, and 
 the amount of this error will evidently depend on the extent 
 of heeling. As a general rule, the heeling error is greatest 
 on northerly and southerly courses and least on easterly 
 and westerly courses. The simplest method of compensa- 
 ting the heeling error is to place a magnet vertically below 
 the center of the compass bowl. Before compensating, the 
 ship is swung into a north-and-south direction and heeled 
 over at least 5°, for instance, to starboard. If in this posi- 
 tion the compass north is deflected toward the uppermost 
 or windward side (as is usually the case), the compensating 
 magnet is placed with its red pole uppermost, and at a dis- 
 tance from the compass bowl that is determined by raising 
 or lowering the magnet until the compass points correctly. 
 In the very exceptional case of the needle being deflected 
 toward the lower or leeward side, the blue pole of the mag- 
 net is placed uppermost. 
 
 The compensation for heeling error is good only for the 
 latitude in which it is made, and it therefore becomes a 
 necessity to renew it when the ship has changed her latitude 
 considerably, usually for every change of 10° in latitude. 
 At the magnetic equator, the error is at its minimum; and 
 when entering the southern hemisphere, it again increases 
 in amount, although of a different character; in southern 
 magnetic latitudes, therefore, the vertical magnet will have 
 to be reversed. 
 
 The foregoing remarks on compensation are general, and 
 while the operations may appear easy of execution, they
 
 NAVIGATION 79 
 
 nevertheless require a certain amount of skill and experi- 
 ence to meet all conditions that may arise; and for this 
 reason it is advisable always to employ a professional com- 
 pass adjuster, the cost of this being insignificant when com- 
 pared with the importance of the subject. 
 
 SWINGING A SHIP FOR DEVIATION 
 
 Preparatory to swinging a ship for finding the amount of 
 deviation remaining after the compass is compensated, a 
 well-defined distant object on land should be selected, the 
 correct magnetic bearing of which is known. If the ship's 
 position is accurately fixed, the magnetic bearing of the 
 selected object may be taken directly from the chart; or, 
 it may be conveniently found by taking the mean of all 
 compass bearings of the object after the ship is swung. 
 Regularly established ranges, such as are found in the princi- 
 pal ports, are, however, to be preferred whenever available. 
 
 The magnetic bearing of the object being determined, 
 the ship is gradually swung round so as to bring her head 
 successively upon each of the 32 points of the standard 
 compass, steadying at each. The difference between the 
 •correct magnetic bearing of the object and the successive 
 bearings, as observed with the compass on board v/hen the 
 ship's head is on the several points, will show the error on 
 each of these points, or, in other words, the deviation of 
 the standard compass according to the direction in which 
 the ship's head was placed. 
 
 When no suitable object by which a range may be estab- 
 lished is in sight, the deviation may be found by what is 
 known as simultaneous reciprocal bearings. This method 
 consists of a compass being brought on shore and placed on 
 a tripod in ^ carefully selected spot, where it will be free 
 from the magnetic influence of any iron and where its loca- 
 tion can be distinctly seen from the standard compass on 
 board. As the ship is swung around, with her head suc- 
 cessively upon each of the 32 points of the standard com- 
 pass, simultaneous observations, or bearings, are taken by 
 the observer stat'oned at each compass, according to some 
 prearranged signals.
 
 80 
 
 NAVIGATION 
 
 The bearings should be strictly simultaneous, and in order 
 to guard against any mistake regarding the exact instant at 
 which bearings are taken, both observers should note the 
 time of each observation by watches previously compared. 
 To obtain the deviation resulting from observations by this 
 method, the bearings taken by the shore compass must be 
 reversed and considered as correct magnetic. The rule to be 
 followed in naming the deviation when comparing bearings is: 
 
 Rule. — // the correct magnetic bearing lies to the right of 
 the compass bearing, the deviation is easterly; if to the left, 
 the deviation is westerly. 
 
 Illustration. — Referring to the figure^ suppose that when 
 the vessel is heading W by N the shore compass bears E N E 
 and that the bearing of the ship by shore compass (taken 
 at the same time) is W by S. W by S reversed is E by N, 
 
 E 
 
 Fig. 5 
 
 which is the correct magnetic bearing. The difference 
 between this and the compass bearing is one point. Hence, 
 the deviation for the heading W by N is one point, or 
 11° 15' east, because the magnetic bearing falls to the right 
 of the compass bearing, as shown in Fig. 5. 
 
 The deviation determined ,by either method belongs, of 
 C'Durse, only to the compass by which the observations are 
 made, and is not applicable to that compass if removed or 
 rilaced in some other position on the ship. 
 
 When deviations are small, as is usually the case in ships 
 where compasses are carefully adjusted, it is sufficient to
 
 NAVIGATION 
 
 81 
 
 determine the deviation for the eight principal points only, 
 and then find the deviation for intermediate points by 
 means of the various diagrams in use. 
 
 The following forms will be found convenient for tabulating 
 bearings and the resulting deviations. 
 
 
 BEARINGS OF A DISTANT OB 
 
 JECT 
 
 Ship's 
 
 Head 
 
 by 
 
 Standard 
 
 Compass 
 
 Bearing of 
 Distant 
 
 Obiect by 
 Standard 
 Compass 
 
 Bearing 
 
 Referred 
 
 to 
 
 East Point 
 
 Deviation 
 
 of 
 Standard 
 Compass 
 
 N 
 NE 
 
 E 
 SE 
 
 S 
 S W 
 
 W 
 N W 
 
 N41°E 
 N30°E 
 N 11° E 
 N 12° W 
 N33° W 
 N27° W 
 
 N 
 N 28° E 
 
 E 49° X 
 E 60° N 
 E 79° N 
 E 102° N 
 E 123° N 
 E li7° N 
 E 90° N 
 E 62° N 
 
 36° 15' W 
 25° 15' W 
 
 6° 15' W 
 16° 45' E 
 37° 45' E 
 31°45'E 
 
 4° 45' E 
 23° 15' W 
 
 682 
 
 Sum = 682°- 
 
 E 85.25° N = E 85° 15' N 
 
 Corr. magnetic bearing = 
 = N4°45'E 
 
 When bearings have different names, or do not lie in the 
 same quadrant, it is advisable always to refer them to some 
 convenient cardinal point, as shown. . This will prevent any 
 mistake in finding the mean or correct magnetic bearing of 
 the object. 
 
 Remarks on Compass Management. — The accuracy of 
 deviation tables should be tested whenever practicable, or 
 whenever there is reason to believe a change of the magnetic 
 condition of the ship has taken place. After coming out of 
 dry dock, after target practice, after considerable altera- 
 tions in the fittings of the vessel, and after taking in or 
 unloading some cargo of a magnetic character, such as 
 machinery, iron ore, etc., a new deviation table should be 
 made in case the given values do not conform with actual
 
 82 
 
 NAVIGATION 
 
 conditions. A navigator should ever be watchfvxl about 
 the proper performance of the compass, and particularly so 
 in modem steamships, where new forms of disturbances are 
 likely to appear at any time. The principal cause of the 
 directive force of a magnetic needle being lessened are vibra- 
 tions. If the compass is exposed or subjected to vibrations 
 from the propeller or engine room for any length of time, 
 it will begin to act sluggishly, and the needles will have to be 
 recharged or remagnetized. 
 
 V^'.th the introduction of electricity on board ships, a 
 new form of compass disturbances has been created, inas- 
 
 RECIPROCAL BEARINGS 
 
 
 Ship's 
 Head by 
 
 the 
 Standard 
 Compass 
 
 Simultaneous Bearings 
 
 Deviation 
 
 Time 
 
 By the 
 Standard 
 Compass 
 
 By the 
 
 Shore 
 
 Compass 
 
 (Reversed) 
 
 of 
 Standard 
 Compass 
 
 7h 56m 
 7h59m 
 8h 3m 
 8h 5m 
 
 8h 8m 
 
 North 
 NbvE 
 
 N N E 
 
 N Eby N 
 
 NE 
 
 S 25.3° E 
 S 30 9° E 
 S 35.2° E 
 S 38.7° E 
 S 40.8° E 
 
 S 30.8° E 
 S 32.5° E 
 S 34.3° E 
 S 35.4° E 
 S 36.3° E 
 
 5.5° W 
 
 1.6° W 
 
 .9° E 
 
 3.3° E 
 
 4.5° E 
 
 much as the magnetisrti of the large electromagnets used in 
 the dynamos and the electric currents in general may dis- 
 turb a compass at a considerable distance. The committee 
 of Lloyd's Register of British and Foreign Shipping has 
 made the following suggestions in reference to protecting 
 compasses from the influence of electricity on shipboard: 
 
 1, That dynamos and *Jectric motors should be placed 
 as far as possible from all compasses and at a distance, of 
 at least 30 ft. from the standard compass. 
 
 2. That wires conducting electric currents should not 
 come nearer than 16 ft. to any compass, whereas wires con- 
 ducting strong currents should be at a still greater distance.
 
 NAVIGATION 83 
 
 3. That the compensating of compasses should be done 
 when the dynamos are at rest, while the operations for 
 determining the deviation should be performed when the 
 dynamos are running. 
 
 CORRECTION OF COURSES 
 
 Compass course is the course steered by a ship. It may 
 be affected by variation, deviation, and leeway; and in 
 order to find the corresponding true course proper allowance 
 must be made for any or all of these errors. 
 
 True course is equal to the compass course corrected for 
 variation, deviation, and leeway; or, it is the angle that 
 the ship's track over ground makes with the true, or geo- 
 graphical, meridian. 
 
 Leeway is the result of the pressure that- the sea or wind 
 exerts on the hull and sails of a ship, causing her to drift 
 sideways. The amount of leeway varies with the strength 
 of wind, form of hull under water, etc. It is usually esti- 
 mated by eye, the observer being guided by the angle 
 between the ship's wake and fore-and-aft line, and is 
 expressed in points and fractions of a point. 
 
 To find the true course from a given compass course apply 
 easterly variation and deviation to the right, and westerly 
 variation and deviation to the left. Allow leeway in direc- 
 tion toward which the wind is blowing. 
 
 Example. — Compass course is S W by W ^ W, deviation 
 14° W, variation 20° E, wind S S E, leeway 2i points; 
 find the true course. 
 
 Solution. — Comp. course = S W by W i W 
 
 Leeway (to the right) =2} points 
 
 Course through water = W ^ S 
 
 or = S 84° 22' W 
 Dev.= 14° O'W 
 
 Mag. course = S 70° 22' W 
 Var. = 20° 0' E 
 
 True course = S 90° 22' W 
 or = west. Ans.
 
 84 NAVIGATION 
 
 Example. — Compass course S E by S, deviation 11° E, 
 variation 25° W, wind S W by S, leeway i point; required 
 the true course. 
 
 Solution. — Comp. course = S E by S 
 
 Leeway (to the left) = i point 
 Course through water = S E f S 
 
 or = S36°34' E 
 Dev.= 11° 0' E* 
 Mag. course = S 25° 34' E 
 Var. = 25° 0' W 
 
 True course = S 50° 34' E 
 
 or = S51° 0' E. Ans. 
 To find the compass course from a given true course 
 
 apply westerly variation and deviation to the right, and 
 easterly variation and deviation to the left. If leeway, 
 apply against the wind. 
 
 Example. — Required the compass course, having given 
 true course N 8° W, variation 17° 10' W, deviation 3° 20' E; 
 the wind is easterly and the leeway estimated to -J point. 
 Solution. — 
 
 True course = N 8° 0' W 
 
 Var.= 17° 10' W 
 
 Mag. course = N 9° 10' E 
 
 Dev. = 3° 20' E 
 
 N 5° 50' E 
 Leeway h point = 5° 37' (against the wind) 
 Comp. course = N 11° 27' E 
 
 or = N by E, nearly. Ans. 
 iLxam pic- -The true course to a certain point is N 30° E, 
 the variation is 28° W, deviation 6° E; find what course 
 to steer b\- the compass. 
 Solution. — 
 
 True course = N 30° E 
 Var. = 28° W 
 
 Mag. course = N 58° E 
 Dev. = 6° E 
 
 Comp. course = N 52° E. Ans.
 
 NAVIGATIO.y 
 
 85 
 
 In correcting courses, it is well to bear in mind that, 
 since the compass card is the representation of the visible 
 horizon, the position of the observer is considered to be 
 at the center of the compass card. Hence, when applying 
 corrections, whether to right or left, always consider yourself 
 
 to be stationed at the center of the card and looking in 
 the direction of the course to be corrected. 
 
 In the above figure, representing a compass card, quarter- 
 points are indicated by small triangles, and half-points by 
 elongated diamonds; each subdivision is designated by refer- 
 ence to the compass points between which they are situated, 
 as shown in the following tables.
 
 86 
 
 NAVIGATION 
 
 
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 NAVIGATION 
 
 1 
 
 C 
 
 1 
 
 e 
 
 T. quarto G. 
 
 G. T. 
 G. quarto T. 
 
 Greco. 
 G. quarto L. 
 
 G. L. 
 L. quarto G. 
 
 c 
 > 
 
 L. quarto S. 
 
 S. L. 
 S. quarto L. 
 
 Scirocco 
 S. quarto O. 
 
 O. S. 
 O. quarto S. 
 
 C/3 
 
 13 
 1 
 
 . . ^ d . . 
 o o - ■ = O 2 
 
 . ■ o ^ o • 
 
 6 
 
 ^ o - . ^ d o 
 
 :=! ■ -n O 'i^ . = 
 
 ddo^o^^ 
 
 c 
 
 a 
 
 CO 
 
 c 
 2 
 
 W 2: pq w 
 i^ w "C . "B w '^' 
 
 2; ^' z w 
 
 o 
 to 
 
 w 
 
 W W CO w 
 
 "^ w •§ . u cii ^ 
 o . rt H cfl ^ o 
 
 . t CO P . g CO t 
 rt . ^ CO " . rt 
 
 S w w w ^ g 
 
 W CO CO CO 
 
 
 o 
 
 ;2; 
 
 • ■ 'z d . • 
 
 oo , . -oz 
 
 . . o z o . . 
 22^ ^oo 
 
 6 
 
 . . d CO 
 
 S CO ^. ° > S 
 
 d d ^ ^ ° CO CO 
 CO OQ 
 
 
 1 
 
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 2^ ^^ ^^ ^ 
 rlz: w W W §• 
 
 ^' 2 ^' W 
 
 w 
 
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 1 
 
 t 
 
 o 
 
 2; 2 " 
 
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 w 

 
 NAVIGATION 
 
 89 
 
 c 
 
 .5 
 
 Ostro. 
 O. quarto L. 
 
 O. L. 
 L. quarto O. 
 
 Libeccio 
 L. quarto P. 
 
 P. L. 
 P. quarto L. 
 
 Ponente. 
 P. quarto M. 
 
 P. M. 
 M. quarto P, 
 
 Maestro. 
 M. quarto T. 
 
 M. T. 
 T. quarto M. 
 
 1 
 
 Syd. 
 
 S. till W. 
 
 S. S. W. 
 
 S. W. till S. 
 
 S. W. 
 S. W. till W. 
 
 w. s. w. 
 
 W. till s. 
 
 West 
 
 W. till N. 
 
 W. N. W. 
 
 N. W. till W. 
 
 N. W. 
 
 N. W. till N. 
 
 N. N. W. 
 
 N. till W. 
 
 C/2 
 
 Sur. 
 S. cuarto S. O. 
 
 S. S. O. 
 S. O. cuarto S. 
 
 S.O. 
 S. O. cuarto 0. 
 
 O.S. O. 
 O. cuarto S. 0. 
 
 Oeste. 
 O. cuarto N. 0. 
 
 O. N. O. 
 N. 0. cuarto O. 
 
 N. O. 
 N. O. cuarto N. 
 
 N. N. O. 
 N. cuarto N. O. 
 
 C 
 
 o 
 
 Sud. 
 
 S. zu W. 
 
 S. S. W. 
 
 S. W. zu S. 
 
 S. W. 
 
 S. W. zu W. 
 
 W. S. W. 
 
 W. zu S. 
 
 West 
 
 W. zu N. 
 
 W. N. W. 
 
 N. W. zu W. 
 
 N. W. 
 
 N. W. zu N. 
 
 N. N. W. 
 
 N. zu W. 
 
 XI 
 
 Sud. 
 S. quart S. O. 
 
 S. S. 0. 
 S. O. quart S. 
 
 S.O. 
 S. 0. quart 0. 
 
 0. S. O. 
 0. quart S. 0. 
 
 Ouest. 
 0. quart N. O. 
 
 O. N. O. 
 N. O. quart O. 
 
 N. O. 
 N. O. quart N. 
 
 N. N. 0. 
 N. quart N. 0. 
 
 1 
 
 C 
 
 South 
 
 Sby W 
 
 SS W 
 
 S WbyS 
 
 SW 
 
 SWby W 
 
 WS W 
 
 WbyS 
 
 West 
 
 Wby N 
 
 W N W 
 
 NWby W 
 
 N W 
 
 N Wby N 
 
 N N W 
 
 Nby W
 
 90 NAVIGATION 
 
 THE USE OF PELORUS IN HEADING A SHIP IN ANY 
 DESIRED MAGNETIC DIRECTION 
 
 On the date of observation, select, beforehand, a suitable 
 hour of local apparent time, and estimate also, in advance, 
 by dead reckoning, the position of the ship for the hour 
 in which the observation is to be made. With the latitude of 
 the position thus found and the declination, enter the azimuth 
 tables and find the true azimuth or bearing of the sun 
 for the selected hour of apparent time; apply to this true 
 azimuth the variation of the locality taken from the chart; 
 the result will be the magnetic bearing of the sun for the time 
 selected. Shortly before the time selected, and when the 
 ship has reached the position decided on, set that point of the 
 pelorus corresponding with the required magnetic direction to 
 the ship's head and turn the sight vanes of the instrument 
 to correspond with the magnetic bearing of the sun pre- 
 viously found. Then clamp the plate and sight vanes 
 of the instrument. Turn the ship by means of the rudder 
 until the sight vanes are direfcted toward the sun, and keep 
 them in this position until the exact instant of the local 
 apparent, time selected. At that instant the ship's head 
 will correspond with the correct magnetic direction required; 
 any difference shown by the compass at that instant will 
 be the deviation for that heading. 
 
 Illustration. — Let it be required, on September 12, 1904, 
 to head the ship correct magnetic North at 2:20 p. M. 
 local apparent time. At the hour selected the ship is 
 estimated to be near Cape Flattery in lat. 44° 30' N and 
 long. 126° W, the variation for that locality being about 
 23° E. Proceed as follows: First find the Greenwich 
 apparent time corresponding to the local apparent time- 
 selected, and then the declination; thus, 
 
 L. App. T., Sept. 12 = 2^ 20"' P. m. 
 Long. W. in time = 8'' 24 *" 
 G. App. T., Sept. 12 = 10" 44"< p. m. 
 Sun's Decl. = N 4° 14' 58" Change in l^-S?" 
 
 Corr. for lO.?"- -10' 10" X 10.7^ 
 
 Corr. Decl. = N 4° 4' 48" 609^9 
 
 Corr. = 10' 9.9"
 
 TERRESTRIAL NAVIGATION 91 
 
 The azimuth tables are then entered with the local apparent 
 time, the latitude, and th6 declination; the corresponding 
 true azimuth is found to be N 132° W. The variation 
 applied to this will give the sun's magnetic azimuth, or 
 bearing; thus, 
 
 True azimuth = N 132° W 
 Variation = 23° E 
 Sun's Mag. bearing = N 155° W or S 25° W, at 2:20 p. m. 
 
 Before reaching the locality decided on, set the north 
 point of the pelorus to correspond with the ship's head, and 
 the sight vanes to S 25° W, clamping both plate and vanes. 
 A few minutes before 2 :20 p. m. turn the ship so that the 
 vanes point directly toward the sun; keep them in this 
 direction by means of the helm until the watch set to local 
 apparent time (or its equivalent in mean time) shows 
 2 :20 P. M. At that instant, the ship is heading correct mag- 
 netic north. Suppose the steering compass at that time 
 shows N ^ W; the deviation will then be * point or 5.5° E, 
 because the compass north falls to the right of the magnetic 
 north. 
 
 If it be required at any time to find the true course the 
 ship is heading, the sight vanes of the pelorus are set and 
 clamped at an angle equal to the true azimuth, corresponding 
 to time, declination, and latitude at observation; at the 
 proper time the sight vanes are swung in the direction of the 
 sun, when the lubber line of the pelorus will give the true 
 course on which the ship is heading. By applying to this 
 the variation of the locality the deviation for heading is 
 readily found. 
 
 TERRESTRIAL NAVIGATION 
 
 TERMS RELATING TO NAVIGATION 
 A sphere is a solid bounded by a surface every point of 
 which is at equal distance from a fixed common point 
 called the center. A radius of a sphere is a straight line 
 drawn from the center to the surface. A straight line 
 passing through the center and terminated at both ends 
 by the surface is called a diameter of the sphere.
 
 92 TERRESTRIAL NAVIGATION 
 
 A great circle is a section of a sphere made by a plane 
 passing through its center. The shortest distance measured 
 on the surface between two points on a sphere is the arc 
 of the great circle joining these two points. 
 
 A small circle is a section of a sphere made by a plane 
 that does not pass through the center. 
 
 Hemisphere. — A great circle divides the sphere into 
 two equal parts, each of which is called a hemisphere. 
 
 A spherical angle is the angle subtended between two 
 great circles. 
 
 A spherical triangle is a portion of a sphere bounded by 
 three arcs of great circles. 
 
 The axis of the earth is the diameter around which the 
 earth daily revolves with uniform motion from west to 
 east; the revolution being completed in 24 hr. 
 
 The poles of the earth are the extremities of its axis, 
 or the points in which the axis meets the surface. 
 
 The equator is a great circle on the earth's surface equidistant 
 from the poles. It divides the earth into two equal parts — 
 the northern hemisphere and the southern hemisphere. The 
 poles of the earth are the poles of the equator, every point 
 of the latter being 90° from either pole. The equator of 
 the earth is generally referred to as the terrestrial or geo- 
 graphical equator. 
 
 The meridians of the earth are great circles that pass 
 through the poles of the earth, and are therefore perpen- 
 dicular to the equator. 
 
 Prime Meridian. — The first, or prime, meridian is that 
 fixed meridian by reference to which the longitude of places 
 on the earth is measured; as, for example, the meridian 
 of Greenwich. 
 
 Parallels of latitude are small circles whose planes are 
 parallel to the plane of the equator. 
 
 Latitude. — The latitude of any place is the distance 
 north or south from the equator measured on the meridian 
 that passes through the place; it may be of any value from 
 0° to 90° N or S. 
 
 Longitude. — The longitude of any place is the distance 
 in arc east or west measured on the equator from the first
 
 TERRESTRIAL NAVIGATION 93 
 
 meridian to the meridian passing through that place. Lon- 
 gitude is reckoned from 0° to 180° E or W, but is never 
 considered greater than 180° either way. Longitude is 
 also measured in hours, minutes, and seconds, each hour 
 being equal to 15°. 
 
 Difference of latitude is the arc of a meridian contained 
 between the two latitude parallels passing through any 
 two places. 
 
 Difference of longitude is the portion of the equator 
 contained between the meridians passing through any 
 two places. 
 
 Rhumb. — When a ship is kept on one continuous course, 
 her track crosses the meridians at the same angle. The 
 line representing this track is called the rhiimb or loxodromic 
 curve. 
 
 The distance between two places, or the distance run 
 by the ship on any course, is the length of the rhumb joining 
 the two places, expressed in miles. 
 
 Departure is the distance made good by a ship due east 
 or west, or the distance between any two places measured 
 on one of their parallels; it is expressed in miles. 
 
 The course made good is equivalent to true course, or the 
 angle between a meridian and the ship's track over ground. 
 
 The bearing of an object or place is the angle that the 
 direction of the object or place makes with the meridian, 
 and is the same as the course toward it. 
 
 Plane sailing is the method of finding the ship's position 
 by assuming the surface sailed over to be a plane. It is 
 used only for short runs. 
 
 Middle latitude of two plages is the latitude of a parallel 
 midway between the two places; or, it is equal to half the 
 stim of the two latitudes when the places considered are 
 on the same side of the equator. 
 
 Parallel sailing is the method of calculating a ship's position 
 when the ship has run a continuous course true east or true west. 
 
 Middle-latitude sailing is a combination of plane and 
 parallel sailing, or a method of calculating the position of 
 a ship by assuming that the departure made by the ship 
 is equal to the distance along the middle-latitude parallel.
 
 94 TERRESTRIAL NAVIGATION 
 
 Mercator's sailing is a method of calculating the position of 
 a ship by using meridional parts. 
 
 Meridional parts of a certain latitude give the length, 
 expressed in minutes of the equator, of the line on a 
 Mercator's chart that represents the latitude. 
 
 Meridional difference of latitude is the difference between 
 the meridional parts for any two latitudes; or, the length 
 of the line on a Mercator's chart that represents the differ- 
 ence of latitude. 
 
 Traverse sailing is the method of reducing to a single 
 course and distance the several courses and distances run 
 by a vessel during a certain period of time. 
 
 Traverse tables are a collection, in tabular form, of the 
 lengths of the sides of a right triangle in which one acute 
 angle (course) varies from 1° to 89°, and the hypotenuse 
 (distance) from 1 to 300 mi.; or, they contain the true differ- 
 ence of latitude and departure corresponding to every 
 course from 0° to 90°, and for every distance from 1 to 
 300 mi. 
 
 Great-circle sailing is the various methods of determining, 
 graphically, or by calculation, the compass courses and 
 distances to be run in order to follow the great-circle track 
 from one place to another. 
 
 Initial course is the first course run along a great-circle 
 track. 
 
 Final course is the last course run along a great-circle 
 track. 
 
 Point of maximum separation is the point of a great-circle 
 track that is farthest from the rhumb track. At this point, 
 the courses on both tracks are parallel with each other. 
 
 Vertex of a great circle is the point on a great circle having 
 the highest latitude. 
 
 Composite sailing is a combination of great-circle and 
 parallel sailing. 
 
 NAVIGATION BY DEAD RECKONING 
 
 The cases of sailing that most frequently present them- 
 selves in the actual navigation of a vessel may consistently 
 be said to be two in number, as follows:
 
 TERRESTRIAL NAVIGATION 
 
 95 
 
 1. When the latitude and longitude of two places are 
 known, to find the course, distance, and departure from 
 one place to the other. 
 
 2. When the place left and the course and distance 
 run are known, to find the latitude and longitude of the 
 place arrived at. 
 
 Either of these cases may be worked by middle latitude 
 or Mercator's sailing, according to formula given in the 
 accompanying table. 
 
 Cases 
 
 Middle-Latitude 
 Sailing 
 
 Mercator's 
 Sailing 
 
 Both latitudes 
 and longitudes 
 given, to find 
 course, distance, 
 and departure. 
 
 Dep. = D. Long. X 
 cos M. Lat. 
 
 tan C = cos M. Lat. 
 X D. Long. ^ D. 
 Lat. 
 
 tanC = Dep.H-D.Lat. 
 
 Dist. = D. Lat. X 
 sec C 
 
 Dist. = Dep. X co- 
 sec C 
 
 tan C = D. Long. ^ 
 
 M. D. Lat. • 
 Dist. = D. Lat. X 
 
 secC 
 Dep. = D. Lat. X 
 
 tanC 
 Dep. = (D. Lat. X 
 
 D. Long.) -^ M. 
 
 D. Lat. 
 
 Place left, course 
 and distance known, 
 to find difference of 
 latitude, departure, 
 and difference of lon- 
 gitude 
 
 D. Lat. = Dist. X 
 
 cosC 
 Dep. = Dist. X sin C 
 D. Long. = Dep. X 
 
 sec M. Lat. 
 D. Long. = D. Lat. X 
 
 tan C X sec M. Lat. 
 
 Dep. = Dist.X sinC 
 D. Lat. = Dist. X 
 
 cos C 
 D. Long. = M. D. 
 
 Lat. X tan C 
 D. Long. = (Dep.X 
 
 X M. D. Lat.) -r 
 
 D. Lat. 
 
 If the distance is less than 300 mi., the middle-latitude 
 method may be used; if greater than 300 mi., Mercator's 
 method should be employed, except in cases where the 
 course is large or very near east or west, when it is pref- 
 erable to use the former method. 
 
 The reason it is preferable to use the middle-latitude 
 method in finding the difference of longitude when the 
 course is large, is that tangents for angles between 80 — 90°
 
 96 TERRESTRIAL NAVIGATION 
 
 change very rapidly, and hence when using the formula 
 D. Long. = M. D. Lat. X tan C, if there is an error 
 in the course, the resulting D. Long, will be considerably 
 in error. Therefore, when the course is large or nearly 90°, 
 it is better to find the difference of longitude by the middle- 
 latitude formula, D. Long. = Dep. X sec M. Lat., in which 
 the tangent is not used. 
 
 Example. — A ship in lat. 37° 3' N and long. 23° 18' W 
 is bound for a point, the latitude and longitude of which 
 are. respectively, 32° 38' N and 31° 13' W; required the 
 true course and the number of miles to be covered. 
 Solution By Middle-Latitude Method. — 
 Lat. left = 37° 3' N 
 Lat. in = 32° 38' N 
 D. Lat. = 4° 25' = 265' S 
 Sumof Lats. = 69° 41' 
 
 i sum = 34° 50' = M. Lat. 
 Long, left = 23° 18' W 
 Long. in = 31° 13' W 
 D. Long. = 7° 55' = 475' W 
 tan C = cos M. Lat.XD. Long.s-D. Lat. 
 log cos 34° 50' = 9.91425 
 log 475= 2.67669 
 a. c. log 265= 7.576 75 
 log tan C = 10.16769 
 
 Course = S55° 48' W. Ans. 
 Dist. = D. Lat. X sec C. 
 log 265= 2.42325 
 log sec 55° 48' = 10. 2=^020 
 log Dist.= 2.67345 
 
 Dist. = 471.5 mi. Ans. 
 By Traverse Tables. — Enter the Tables with the M. Lat. 
 34° 50' (or 35° nearly) as course and the D. Long. 475' in 
 the distance column, when the departure will be found 
 in the latitude column. Thus, 
 
 for 300 we get 245.7 
 
 for 175 we get 143.4 
 
 Whence, for 475 we get 389.1 mi. as departure
 
 TERRESTRIAL NAVIGATION 97 
 
 Having found the departure, enter the Tables again 
 with 132.5 (half D. Lat.) and 194.5 (half Dep.) in a latitude 
 and departure column, respectively, and find the corre- 
 sponding course and distance. The course thus found 
 is nearly 56°, or 5 points and half the distance is 235, which, 
 when doubled, gives the distance as 470 mi. Ans. 
 
 Example.— X ship in lat. 32° 15' N and long. 67° 52' W 
 is bound for a point in lat. 49° 57' N and long. 8° 12' W; 
 find the true course and distance to be run. 
 
 Solution. — By Mcrcator's Sailing. — First find the D. Lat., 
 the M. D. Lat., and the D. Long, as follows, and then 
 calculate the course and distance according to proper formulas 
 taken from the preceding table. 
 
 1st Lat. = 32° 15' N M. P. = 2,033.9 
 
 2d Lat. = 49° 57' N M. P. = 3,452.2 
 
 Lat. = 1,418.3 
 
 D. Lat. 
 or 
 
 = 17° 42' 
 = 1,062' N. 
 
 1st Long. 
 
 2d Long. 
 
 M. D. 
 
 = 67° 52' W 
 = 8° 12' W 
 
 
 D. Long, 
 or 
 
 = 59° 40' 
 = 3,580' E 
 
 tan 
 log 
 
 C = D. Long 
 
 3,580 ( + 10) = 
 
 log 1,418.3 = 
 
 log tan C = 
 
 Course = 
 
 ^M. D. Lat 
 13.55388 
 3.15168 
 
 
 10.40220 
 
 -N 68° 23' E 
 
 Ans. 
 
 Dist. = D. Lat. X sec. C 
 log 1,062= 3.02612 
 log sec 68° 23' = 10.43369 
 log Dist.= 3.45981 
 
 Dist. = 2,883 mi. Ans. 
 By Traverse Tables. — Enter the Tables with M. D. Lat. 
 in a latitude column and the D. Long, in a departure column, 
 and find the corresponding course. Then, with this course 
 and the D. Lat., find the required distance. In this case, 
 the numbers 1,418 and 3,580 are too large, and we, there- 
 fore, divide each by 100 and enter the Tables with 14.1 and
 
 98 TERRESTRIAL NAVIGATION 
 
 35.8 instead and get a course of 68°. Then, with the corre- 
 sponding course 68° and the D. Lat. worked by similar 
 artifice, 1,062-^10 = 106.2, the distance found is 2,835. 
 Now, this distance does not agree with that obtained by 
 calculation, but can be made much closer by a simple pro- 
 portion, if deemed necessary. The correct course is 68° 23', 
 not 68°, and we therefore must make an allowance for the 
 23'; thus, 
 
 with 68° as course and 1,062 D. Lat., the dis- 
 tance is 2,835 mi. 
 
 and with 69° as course and 1,062 D. Lat., the dis- 
 tance is 2,963 mi. 
 
 The difference, therefore, for 60' of the course is 128 mi. 
 
 23 X 128 
 Whence, for 23' it must be — ^77 — = 49 mi. This, when 
 oO 
 
 added to the distance corresponding to the lesser course, will 
 
 produce a more correct value of the required distance, or 
 
 49 + 2,835 = 2,884 mi., which very nearly agrees with that 
 
 derived by computation. Ans. 
 
 Example. — From a place in lat. 52° 6' N and long. 38° 
 27' W, a vessel runs N 56° W, 229 mi.; find her latitude 
 and longitude in. 
 
 Solution. — By the Middle-Latitude Method. — 
 
 D. Lat. = Dist. X cos C Lat. left = 52° 6' N 
 
 log 229= 2.35984 D. Lat.= 2° 8.1' N 
 
 log cos 56°= 9.74756 , ^ . -.„,.,, ., . 
 
 Lat. in = 54° 14.1' N. Ans. 
 
 log D. Lat.= 2.10740 Sum of Lats. = 106° 20.1' 
 
 D. Lat. = 128.1' N i sum= 53° 10' = M. Lat. 
 
 D. Long. = D. Lat. X tan CXsec M. Lat. 
 
 log 128.1= 2.10740 
 
 log tan 56° = 10.17101 
 
 log sec 53° 10' = 10.222 22 
 
 log D. Long. = 2.50063 
 
 D. Long. = 316.7' W 
 
 Long, left = 38° 27' W 
 D. Long. = 316.7'= 5° 16.7' W 
 
 Long, in = 43° 43.7' W. Ans.
 
 TERRESTRIAL NAVIGATION 99 
 
 By Traverse Tables. — Enter Tables with course 56° and 
 distance 229 and find the corresponding D. Lat. 128.1 and 
 Dep. 189.8 in their respective columns. Then, with the 
 M. Lat. as course and the Dep. just found, enter the Tables 
 again with Dep. in a latitude column when the required 
 D. Long, is found in the distance column. Thus, 
 
 for 144.4 we get 240' D. Long. 
 
 for 45.4 we get 76' D. Long. 
 
 Whence, for 189.8 we get 316' D. Long. 
 This applied to the longitude left will give the longitude 
 in as 43° 43' W. Ans. 
 
 Example. — From a point situated in lat. 49° 52' S and 
 long. 27° 15' W, a ship steams 513.5 mi., steering a true 
 course N 26° 36' E; find the latitude and longitude in. 
 Solution.- — By Mercator's Sailing. — 
 
 D. Lat. = Dist.Xcos C 
 log 513.5 = 2.71054 
 log cos 26° 36' = 9.95141 
 
 log D. Lat. = 2.66195 
 
 D. Lat. = 459.1' N 
 
 Lat. left = 49° 52' S 
 
 D. Lat.= 7°39' N M. P. =3444.5 
 
 T * • .00 iQ, c M. P. = 2783.8 
 Lat. m = 42° 13' S 
 
 M. D. Lat.= 660.7 
 D. Long. = M. D. Lat. X tan C 
 
 log 660.7 =2.82000 Long, left = 27° 15' W 
 
 log tan 26° 36' = 9.69963 D. Long.= 5° 31' E 
 
 log D. Long. = 2.51963 Long, in = 21° 44' W. Ans. 
 
 D. Long. = 330.8' E 
 
 By Traverse Tables.— Entering the Tables with N 26° 
 36' E and the distance 513.5, the corresponding D. Lat. 
 is found to be 459.4'. This value is obtained by taking the 
 mean of the D. Lat. for 26° and 27°, respectively, the corre- 
 sponding course being 26^°, nearly. To find the D. Long., 
 the Tables are entered again in a similar manner with 
 course and the M. D. Lat., 660.7, in a latitude column when 
 the required D. Long, is found in the departure column. Ans.
 
 100 TERRESTRIAL NAVIGATION 
 
 THE DAY'S WORK 
 
 The operation of calculating at each noon the course and 
 distance made good during the past 24 hr. is commonly 
 known as the day's work. Each compass course run dur- 
 ing the day is converted to true and, together with its dis- 
 tance, entered in a traverse, whence the course and distance 
 made good and the latitude and longitude in are found from 
 the total D. Lat. and Dep.. either by calculation or by 
 inspection of the Traverse Tables, as shown in the following 
 example. Strictly speaking, the day's work includes the 
 finding of the ship's position both by dead reckoning and 
 astronomical observations. In the example that follows 
 only the former method is considered. 
 
 The official log book of a ship should contain a carefully 
 prepared record of the day's work, and, in fact, all important 
 happenings that may occur on board ship. In it should be 
 entered courses and distances run, with amount of leeway, 
 variation, and deviation applicable to each. This is usually 
 done at the end of each watch by the officer in charge of the 
 deck, who inserts them in a scrap log; from the scrap log they 
 are subsequently transferred to the official log book. 
 
 Example. — On June 16, 1904, at noon, a point in lat. 
 51° 53' N and long. 55° 22' Wbore NNW by compass, the 
 estimated distance being 48 mi. When bearing was taken 
 the ship headed S E by S, the deviation for that point being 
 recorded in the appended log account. From the place 
 where bearing was taken the following compass courses and 
 distances were run; find course and distance made good 
 and the latitude and longitude of the ship at noon June 17, 
 assuming a current setting correct magnetic east, li mi. 
 per hr., to have uniformly affected the ship during the 
 entire run from noon to noon.
 
 TERRESTRIAL NAVIGATION 
 LoG-BooK Account 
 
 101 
 
 June 16 
 
 e 
 
 i2 
 
 in 
 
 5 
 
 
 
 
 
 
 § 
 
 
 
 c 
 
 C 
 
 Courses 
 
 Wind 
 
 A 
 
 Dev. 
 
 Remarks 
 
 K 
 
 W 
 
 ^ 
 
 
 
 
 
 1 
 
 12 
 
 
 
 South 
 
 ESE 
 
 i 
 
 
 
 p. M. 
 
 2 
 
 11 
 
 5 
 
 
 
 
 
 
 3 
 
 13 
 
 
 
 
 
 
 
 
 4 
 
 13 
 
 5 
 
 
 
 
 
 
 5 
 
 13 
 
 5 
 
 SSE 
 
 East 
 
 
 
 11" W 
 
 
 6 13 
 
 5 
 
 
 
 
 
 
 7 ! 12 
 
 5 
 
 
 
 
 
 Var.36°W 
 
 8 
 
 12 
 
 5 
 
 
 
 
 
 
 9 
 
 12 
 
 5 
 
 SE by S 
 
 Eby N 
 
 i 
 
 18° W 
 
 
 10 
 
 12 
 
 5 
 
 
 
 
 
 
 11 
 
 13 
 
 
 
 
 
 
 
 
 12 
 
 12 
 
 
 
 
 
 
 
 Midnight 
 
 June 17 
 
 1 
 
 12 
 
 
 
 ESE JE 
 
 NE 
 
 1 
 
 27° W 
 
 A. M. 
 
 2 
 
 12 
 
 
 
 
 
 
 
 
 3 
 
 12 
 
 
 
 
 
 
 
 
 4 
 
 12 
 
 
 
 
 
 
 
 
 5 
 
 12 
 
 
 
 E i N 
 
 NNE 
 
 i 
 
 29° W 
 
 
 6 
 
 11 
 
 5 
 
 
 
 
 
 
 7 
 
 12 
 
 
 
 
 
 
 
 Var.36° W 
 
 8 
 
 10 
 
 5 
 
 
 
 
 
 
 9 
 
 10 
 
 5 
 
 S by E J E 
 
 East 
 
 i 
 
 8°W 
 
 
 10 
 
 10 
 
 
 
 
 
 
 
 
 11 
 
 11 
 
 5 
 
 
 
 
 
 
 12 
 
 12 
 
 
 
 
 
 
 
 Noon 
 
 Solution. — Correct each compass course for variation, 
 deviation, and leeway; take the sum of distances run on 
 each course. Correct current for variation and consider it 
 as a separate course run. Reverse bearing, apply the 
 necessary corrections, and enter it with the estimated dis- 
 tance in the Traverse as the first course and distance run. 
 Thus,
 
 102 TERRESTRIAL NAVIGATION 
 
 1st Comp. C. = South 2d Comp. C. = S 22° 30' E 
 
 Leeway = 2° 49' Dev.= 11° 0' W 
 
 S 2° 49' W S 33° 30' E 
 
 Var. = 36° 0' W Var. = 36° 0' W 
 
 True C = S33° 11' E True C = S 69° 30' E 
 
 Dist. 50 mi. Dist. 52 mi. 
 
 8d Comp. C. = S33°45' E 4th Comp. C.= 
 Leeway = 2° 49' Leeway = 
 
 Dev. = 18° 0' W Dev. 
 
 S30° 
 18° 
 
 56' 
 0' 
 
 E 
 W 
 
 S48° 
 36° 
 
 56' 
 0' 
 
 E 
 W 
 
 S 
 
 70° 
 
 19' 
 
 E 
 
 
 11° 
 
 15' 
 
 
 S 
 
 59° 
 
 4' 
 
 E 
 
 
 27° 
 
 0' 
 
 W 
 
 s 
 
 86° 
 
 4' 
 
 E 
 
 
 36° 
 
 0' 
 
 W 
 
 Var. = 36° 0' W Var. 
 
 True C. = S84°56' E True C. = S 122° 4' E 
 
 Dist. 50 mi. or = N57°56'E 
 
 Dist. 48 mi. 
 6th Comp. C. = N 84° 22' E 6th Comp. C. = S 14° 4' E 
 
 Leeway = 5° 38 Leeway = 5° 38' 
 
 Dev. = 29° 0' W Dev. 
 
 N 90° 
 = 29° 
 
 0' E 
 0' W 
 
 N61° 
 ' 36° 
 
 O'E 
 0' W 
 
 S 8° 
 
 26' 
 
 E 
 
 = 8° 
 
 0' 
 
 W 
 
 S 16° 
 
 26' 
 
 E 
 
 = 36° 
 
 0' 
 
 W 
 
 Var. = 36° 0' W Var. 
 
 True C. = N 25° C E True C. = S 52° 26' E 
 
 Dist. 46 mi. Dist. 44 mi. 
 
 Bearing rev'd. = S 22° 30' E Current (mag.) = N 90° E 
 Dev. for SE by S= 18° 0' W Var.= 36° W 
 
 S 40° 30' ¥ True set = N 54° E 
 
 Var. = 36° 0' W Rate or distance 
 
 True rev'd. bear. = S 76° 30' E for24h = 36mi. 
 
 Dist. 48 mi. 
 Enter the true courses thus found in a Traverse arranged 
 in the form shown, and find from Traverse Tables the D. Lat. 
 and Dcp. corresponding to each course and distance. The 
 total D. Lat. and Dep. made by the ship is found, respect- 
 ively, by taking the algebraic sum of northerly and southerly 
 differences of latitudes and easterly and westerly departures.
 
 TERRES TRIAL NA VIGA TION 
 
 103 
 
 
 TRAVERSE 
 
 
 
 
 D. Lat. 
 
 Dep. 
 
 True 
 
 .1 
 
 
 
 
 Courses 
 
 
 
 
 
 
 
 N 
 
 S 
 
 E 
 
 W 
 
 S77° E 
 
 48 
 
 
 10.8 
 
 46.8 
 
 
 S33°E 
 
 50 
 
 
 41.9 
 
 27.2 
 
 
 S 70° E 
 
 52 
 
 
 17.8 
 
 48.9 
 
 
 S85°E 
 
 50 
 
 
 4.4 
 
 49.8 
 
 
 N 58° E 
 
 48 
 
 25.4 
 
 
 40.7 
 
 
 N 25° E 
 
 46 
 
 41.7 
 
 
 19.4 
 
 
 S52°E 
 
 44 
 
 
 27.1 
 
 34.7 
 
 
 N 54° E 
 
 36 
 
 21.2 
 
 
 29.1 
 
 
 
 88.3 102.0 296.6 E = Dep. 
 
 
 D. Lat.= 
 
 88.3 
 
 5 
 
 
 
 13.7' i 
 
 
 
 Lat. 
 
 left = 51° 53' N 
 
 
 Lat. in = 51°39.3' N. 
 M. Lat. = 51° 46' 
 
 Ans. 
 
 For Course 
 
 tan C" = Dep.-^D. Lat 
 
 log 296.6= 2.47217 
 
 log 13.7= 1.13672 
 
 log tan C = 11.33545 
 
 Course = S 87° 21' E. Ans. 
 
 For Distance 
 
 Dist. = D. Lat. X sec C 
 
 log 13.7 = 1.13672 
 
 log sec C = 1.33503 
 
 log Dist. = 2.47175 
 
 Dist. = 296.3 mi. Ans. 
 
 For Diff. Longitude For Longitude In 
 
 D. Long. = Dep. X sec M. Lat. Long, left = 55° 22' W 
 log 296.6 = 2.47217 D. Long.= 7° 59.3' E 
 
 log sec M. Lat. = .20840 Long, in = 47° 22.7' W. Ans. 
 
 log D. Long. = 2.68057 
 D. Long. = 479.3' E 
 
 The required data are found also by inspection of Traverse 
 Tables in the usual manner. Thus, the nearest whole 
 degree course corresponding to the D. Lat. 13.7 and Dep. 
 296.6 is S 87° E, the distance by tables being 297 mi.; 
 with M. Lat. 52° as course and 29.6 in a latitude column.
 
 104 
 
 TERRESTRIAL NAVIGATION 
 
 the corresponding number found in distance column is 48, 
 which multiplied by 10 gives the D. Long, as 480'. 
 
 LENGTHS, IN NAUTICAL MILES, OF A DEGREE OF 
 
 LONGITUDE FOR EACH DEGREE OF LATITUDE 
 
 FROM 0° TO 90° 
 
 Lat. 
 
 
 Lat. 
 
 
 Lat. 
 
 
 De- 
 
 Miles 
 
 De- 
 
 Miles 
 
 De- 
 
 Miles 
 
 grees 
 
 
 grees 
 
 
 grees 
 
 
 1 
 
 59.99 
 
 31 
 
 51.43 
 
 61 
 
 29.09 
 
 2 
 
 59.96 
 
 32 
 
 50.88 
 
 62 
 
 28.17 
 
 3 
 
 59.92 
 
 33 
 
 50.32 
 
 63 
 
 27.74 
 
 4 
 
 59.85 
 
 34 
 
 49.74 
 
 64 
 
 26.30 
 
 5 
 
 59.77 
 
 35 
 
 49.15 
 
 65 
 
 25.36 
 
 6 
 
 59.67 
 
 36 
 
 48.54 
 
 66 
 
 24.40 
 
 7 
 
 59.55 
 
 37 
 
 47.92 
 
 67 
 
 23.44 
 
 8 
 
 59.42 
 
 38 
 
 47.28 
 
 68 
 
 22.48 
 
 9 
 
 59.26 
 
 39 
 
 46.63 
 
 69 
 
 21.50 
 
 10 
 
 59.09 
 
 40 
 
 45.96 
 
 70 
 
 20.52 
 
 11 
 
 58.89 
 
 41 
 
 45.28 
 
 71 
 
 19.53 
 
 12 
 
 58.69 
 
 42 
 
 44.59 
 
 72 
 
 18.54 
 
 13 
 
 58.46 
 
 43 
 
 43.88 
 
 73 
 
 17.54 
 
 14 
 
 58.22 
 
 44 
 
 43.16 
 
 74 
 
 16.54 
 
 15 
 
 57.95 
 
 45 
 
 42.43 
 
 75 
 
 15.53 
 
 16 
 
 57.67 
 
 46 
 
 41.68 
 
 76 
 
 14.52 
 
 17 
 
 57.38 
 
 47 
 
 40.92 
 
 77 
 
 13.50 
 
 18 
 
 57.06 
 
 48 
 
 40.15 
 
 78 
 
 12.48 
 
 19 
 
 56.73 
 
 49 
 
 39.36 
 
 79 
 
 11.45 
 
 20 
 
 56.38 
 
 50 
 
 38.57 
 
 80 
 
 10.42 
 
 21 
 
 56.01 
 
 51 
 
 37.76 
 
 81 
 
 9.38 
 
 22 
 
 55.63 
 
 52 
 
 36.94 
 
 82 
 
 8.35 
 
 23 
 
 55.23 
 
 53 
 
 36.11 
 
 83 
 
 7.31 
 
 24 
 
 54.81 
 
 54 
 
 35.27 
 
 84 
 
 6.27 
 
 25 
 
 54.38 
 
 55 
 
 34.41 
 
 85 
 
 5.23 
 
 26 
 
 53.93 
 
 56 
 
 33.45 
 
 86 
 
 4.18 
 
 27 
 
 53.46 
 
 57 
 
 32.68 
 
 87 
 
 3.14 
 
 28 
 
 52.97 
 
 58 
 
 31.79 
 
 88 
 
 2.00 
 
 29 
 
 52.48 
 
 59 
 
 30.09 
 
 89 
 
 1.05 
 
 30 
 
 51.96 
 
 60 
 
 30.00 
 
 90 
 
 .00
 
 TERRESTRIAL NAVIGATIOX 105 
 
 CONSTRUCTING A MERCATORIAL CHART 
 
 First, determine the limits of the proposed chart — in other 
 words, the number of degrees and minutes it is to contain, 
 both of latitude and of longitude. Then draw a straight 
 line near the lower margin of the paper, if the chart is to 
 represent north latitude; near the upper margin, if it is to 
 represent south latitude; or at a suitable position in 
 the center, if both north and south latitudes are to be 
 represented. Divide this base line into as many equal 
 parts as the number of degrees of longitude required; for 
 instance, if the chart is to contain 15° of longitude, divide 
 the line into 15 equal parts; if it is to contain 4° of longi- 
 tude, divide it into 4 equal parts. At each extremity of 
 the base line, erect lines perpendicular to it. Take from 
 the Tables of Meridional Parts CI. C. S. Nautical Tables, or 
 Bowditch) the meridional parts for each degree of latitude, 
 for the limits between which the chart is to be drawn, and 
 take the difference between each successive pair, thus 
 obtaining the meridional differences of latitude. Reduce 
 these meridional differences to degrees by dividing them 
 by 60; the result will be the lengths, measured on the longi- 
 tude scale, between the chosen degrees of latitude. Lay 
 off these lengths successively on the perpendicular lines, 
 and through the points thus obtained draw straight lines 
 parallel to the base line, to represent latitude parallels. 
 At convenient intervals, or through each division on the 
 base line, draw lines parallel to the perpendiculars to rep- 
 resent meridians. 
 
 The accuracy of the frame of the chart thus completed 
 should be tested by measuring the two diagonals of the 
 rectangle formed; if they are of the same length, the frame 
 is perfect. Then graduate the scale into suitable divisions 
 of 5' or 10' each, or if deemed necessary divide each degree 
 into 60 divisions, which will then represent minutes. The 
 principal points in the chart are now laid down according 
 to their respective latitudes and longitudes, and whatever 
 formations and contours of water or land are required, 
 together with other useful items, are drawn in freehand. 
 Compass diagrams may also be inserted at convenient
 
 106 TERRESTRIAL NAVIGATION 
 
 places, remembering that the direction of the meridians 
 indicates true north and south. 
 
 Example. — Construct a Mercator's chart extending from 
 lat. 40° to 43° N and from long. 105° to 108° E, on a scale 
 of 2 in. to a degree of longitude. On this chart, plot the 
 following positions: A lat. 41° 10' N, long. 105° 36' E; 
 B lat. 42° 15' N, long. 107° 30' E; and C lat. 42° 40' N, 
 long. 106° 12' E. Find the true course from A to B, then 
 from B to C. 
 
 Solution. — Referring to the chart, draw a line a 6 at 
 the bottom margin of the paper to. represent the 40th 
 parallel. On this base line, lay off three lengths of .2 in. 
 each and divide each length into 60 equal parts, repre- 
 senting minutes or nautical miles. This is conveniently 
 done by the method shown in the lower right-hand corner 
 of the chart, which consists in drawing a pencil line b c at 
 an angle of about 45° from the extremity of a degree and 
 dividing it into a desired number of equal divisions directly 
 from the rule used; the last division of this line is then con- 
 nected with the other extremity d of the degree, and lines 
 parallel to this line are drawn from each division: the lines 
 thus drawn will divide the degree into the desired number 
 of equal parts, as shown. Proceed similarly in graduating 
 the other degrees. Next, consult the Table of Meridional 
 Parts and take out the values corresponding to each degree 
 of latitude and obtain the meridional differences of latitude 
 as indicated below. 
 
 Lat. M. P. M. D. Lat. 
 
 40° 2,607. 9| 78.6-J-60 = l° 18.6' 
 
 ^^° 2.686. 5 1 79.8^60 = 1° 19.8' 
 
 42° 2,766.3{ 1-60-1° 21 1' 
 
 43° 2,847.4) ^^'^ '^""^ ^^'^ 
 
 This being complied with, take, with a pair of dividers, 
 1" 18.6' from the longitude scale and lay it off on each per^ 
 pendicular from the base line; and through the points thus 
 obtained, draw the parallel of 41°. In like manner, from 
 the parallel 41°. lay off the next length 1° 19.8' taken from 
 the longitude scale, and draw the parallel of 42°. Proceed
 
 TERRES TRIAL NA VIGA TION 
 
 107 
 
 similarly and get the parallel of 43°. Divide this last 
 parallel into degrees and minutes the same as the parallel 
 
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 Ad 
 
 fr 
 
 2 /nchea 'V Unf/tu(A. 
 
 of 40", at the bottom of the chart, and draw the meridians of 
 106° and 107° east longitude. The frame of the chart is then
 
 108 TERRESTRIAL NAVIGATION 
 
 completed and the positions A, B, and C may now be plotted 
 in the usual manner. 
 
 Joining A and B with a straight line, we find the course 
 between the two points to be N 53° E. In like manner, we 
 find the course from 5 to C to be N 66*° W, nearly. Ans. 
 
 It is very useful to a navigator, in case charts are lost or 
 destroyed, to be able to construct a substitute for temporary 
 use. 
 
 In connection with the use of charts, especially old charts, 
 care should be taken that all changes in the position or 
 character of lights, the establishment of new or discontin- 
 uation of existing lights, buoys, landmarks, etc., are properly 
 noted on the chart before it is used, also the exact location 
 of sunken wrecks and other obstructions as given in Notice 
 to Mariners. This work of correcting charts is, as a rule, 
 performed free of cost by officers in charge of Branch Hydro- 
 graphic Offices located in the principal ports along the 
 seaboard. 
 
 PLOTTING A GREAT-CIRCLE TRACK 
 
 Let the appended diagram represent a gnomonic, or 
 great-circle chart, the straight line A B being the great- 
 circle track between the two places A and B. In order to 
 transfer this track to a Mercator's chart, select a few points 
 along the line and find, by inspection, the latitude and 
 longitude of each. Plot these points carefully on the 
 Mercatorial chart and draw a uniform curve passing through 
 all points thus established. This curve will be the great- 
 circle track and the courses and distance to be run, in order 
 to follow this track, may be conveniently found as follows: 
 Get the difference between the initial course and the course 
 at the point of maximum separation (equal to the rhumb 
 course) and find how many quarter points are contained in 
 it. Divide the distance between the first place and the 
 point of maximum separation by this number of quarter 
 points; the result will be the number of miles to be sailed 
 on each quarter-point course. 
 
 For instance, assume the initial course to be N W, the 
 course at the point of maximum separation W N W, and
 
 TERRESTRIAL NA VIGA TION 
 
 109 
 
 the distance between these points 800 mi. Now, the difTer- 
 ence between N W and W N W is 2 points, or 8 quarter 
 points; hence, dividing 800 mi. by 8 will give 100 mi. for 
 each quarter-point course. In other words, the course will 
 have to be changed one-quarter of a point to the west for 
 every 100 mi. run. 
 
 Proceed, similarly, to find the course and distance front 
 the point of maximum separation to the point of destination.- 
 It is evident that the difiference between the courses cari 
 be divided into still smaller divisions if required; for instance, 
 in the case just mentioned, it may be divided into eighths of 
 a point ; the course will then 
 have to be changed one- 
 eighth of a point for each 
 50 mi. run. For ordinary 
 practice, however, quarter 
 points will suffice. 
 
 The courses thus found 
 are true and must be cor- 
 rected for variation, devia- 
 tion, and leeway, if any. 
 
 On great-circle charts 
 published by the United 
 States Hydrographic Office 
 will ibe found a Great-Circle 
 Course Diagram, by which 
 courses and distances along 
 
 the track are conveniently found by inspection. Directions 
 how to use this diagram are printed on the chart under the 
 head of Explanation. 
 
 A I \ \ 
 
 USEFUL METHODS IN COAST NAVIGATION 
 
 Cross-Bearings. — When the bearings of two selected 
 objects are corrected for deviation, due to the direction of 
 the ship's head at the time of observing them, place the 
 parallel ruler on the nearest magnetic compass rose on the 
 chart so that the edge passes through the center and the 
 requisite degree or point on the circumference. Then move 
 the ruler, step by step, until the edge passes through the
 
 110 
 
 TERRESTRIAL NA \ 'IGA TION 
 
 object when a light pencil line drawn along the edge will 
 represent one of the bearings. The ship will then be some- 
 where on the line. Proceed similarly with the other bearing. 
 Now, the ship will be somewhere on this line also, and since 
 the only common point of two lines intersecting each other 
 is at their point of intersection, the position of the ship on 
 the chart must necessarily be at the point where the two 
 bearings intersect. 
 
 It is evident that the objects selected for cross-bearings 
 should be so situated that the 
 lines of bearing do not inter- 
 sect at a very acute angle, since 
 the point of intersection in such 
 cases is somewhat doubtful. To 
 obtain accurate results, the 
 angle between the bearings 
 should be as near as possible to 
 90°, or 8 points. 
 
 Bow-Bearings. — A compass 
 bearing is taken of a light or 
 other prominent known object 
 when it is 2, 3, or 4 points off 
 the bow, and the time and log 
 noted. When the bearing has 
 doubled, the log and time are 
 again noted. (If a patent log is 
 used, it is not necessary to note 
 the time, but simply the indi- 
 cator of the log at both bear- 
 ings.) The distance of the ship 
 from the object is then equal to the distance run in the 
 interval between the first and second bearing, or, the differ- 
 ence of readings of the patent log at the two bearings. 
 
 By using this method when the object bears 2 or 3 points 
 off the bow, the distance of vessel from A is known before 
 the object is abeam, as shown in the figure. 
 
 Illustration. — Referring to the figure, suppose that the 
 reading of the patent log when at B is 69.6 mi., and when at 
 D, or when bearing is doubled, it is 74.2 mi. The distance 
 
 Fig. 1
 
 TERRESTRIAL NAVIGATION 111 
 
 of ship from A is then 74.2 — 69.6 = 4.6 mi. In other words, 
 B D = D A; also, incase C and E are considered, C E = E A. 
 This method is frequently used when the ship is at D, or 
 when object bears 4 points off the bow, and is then known 
 as 4-point bearing. Doubling this angle, the ship is exactly 
 abeam of object. 
 
 Bearings of Same Object and Distance Run. — A compass 
 bearing is taken of some known object at any instant and 
 the number of points, or degrees, contained between its 
 direction and the ship's head, or course, are noted. A 
 straight continuous course is then kept until the bearing of 
 the object has altered at least 3 points, when another bearing 
 is taken and the number of points between it and the ship's 
 head are again noted. 
 
 These angles, if expressed in points, are then entered in 
 the table found on page 112, or, if expressed in degrees, in 
 the table on the following page, and the distance is found as 
 follows: "With the first number of points, or degrees, at 
 the top and the second angle at the side column, find the 
 corresponding number; multiply this by the number of 
 miles run in the interval between bearings. The product 
 is the distance, in miles, at the time the second bearing 
 was taken. 
 
 Example. — A certain lighthouse bore N N W; 2 hr. later, 
 after the ship had run true west 12 mi., the bearing of the 
 same light was N E by N; required, the distance of the ship 
 from the light at the second bearing. 
 
 Solution. — The number of points included between the 
 first bearing and the ship's head is 6; between the second 
 bearing and the ship's head there are 11 points. Entering 
 the proper Table with 6 points at the top and with 1 1 points 
 in the side column, we find, below the former and opposite 
 the latter, the number 1.11; multiplying this by 12, the 
 number of miles run in the interval between bearings, 
 the product, 1.11X12 = 13.3 mi., which will be the distance 
 of the ship from the light at the time of taking the second 
 bearing. Ans.
 
 112 
 
 TERRESTRIAL NAVIGATION 
 
 2 
 
 c 
 
 bo 
 c 
 
 m 
 
 u 
 
 s 
 
 3 
 
 C 
 
 1 
 
 ■ 8 
 
 1 
 
 Q 
 
 o 
 
 1 S 
 
 o 
 
 .-ICC 
 
 OS 
 
 OeoiN 
 
 C<i(N--H 
 
 Oi 
 
 CDOOI^iC 
 
 00 
 
 Oi d .-h' r-^ --^ 
 
 00 
 
 2.61 
 2.12 
 1.80 
 1.58 
 1.41 
 1.29 
 
 
 CD -H t^ lO Tt< d (M 
 (N <N -^ ^ T-i -1 ^ 
 
 i> 
 
 CDOOt^iOCftt^OOr-^' 
 
 oq d ^ -J ^' -h' r-; ^ 
 
 CD 
 
 
 to 
 
 Tt< Ci CD rt CO (N_ r-* C p C5 
 
 
 or^oc;io^cDO»o(MO 
 
 C000i000(Mf-HOOCTi0>0> 
 
 Csi ^ ^ ^ r^ r-; r-; ^ 
 
 « 
 
 I^CDO— lOOOOOTfON IC* 
 
 .-H t^ u'; CO ^ q q Ci q 00 00 00 
 
 HO 
 
 (NTt<C3(>3Cr. OCOOO'*— •ClX^- 
 CD CO (M_ o q q 00 00 00 t^_ t>; t^. 
 
 tH 
 
 00 iq (M '-^_ q q 00 00 1> t>; t>; t>; i>; r>. 
 
 CO 
 
 C0>OTt<OO(MC0(N05C0i0-<*C0'*i0 
 
 qco^_qqoqt--;t>;qqqqqqcq 
 
 CO 
 
 lo X o 00 oi (N t>-co o 00 r- CO CO CO r> 00 
 rj<_^_qooi^r-.qqqo4r5u5io»o»o»o 
 
 hn 
 
 coo»0'<**r^^t^co<-iajoor^r^r^oooi'H 
 (M_ q 00 1>: q q >o lo lo T(H -^^ ■* ■<*; ■*_ r^ -*_ lo 
 
 C<l 
 
 O'-^CnO-^OcOCO.-iOOlQOOOOOOO^CO 
 
 q 00 q q »c lo ^_ Tt -"t rf CO CO CO CO CO ^ ■>*_ Tf 
 
 ^ IS L CJ ct! 
 
 tC "nl b <U <U 
 
 Tj<-<^lO»OCOCOt^l^0000050500^'
 
 TERRESTRIAL NAVIGATION 
 
 113 
 
 
 •c 
 
 CQ 
 
 m 
 
 C 
 c3 
 
 1 
 1 
 
 1 
 
 i 
 
 Q 
 
 2 
 
 2.82 
 2.28 
 
 
 8 
 
 2.88 
 2.33 
 1.97 
 
 
 § 
 
 — CC C: rf< 
 
 O3f0C5r>. 
 
 C^ (N — -I 
 
 
 § 
 
 O CC O I^ o 
 
 d csi d — ■ ^ 
 
 
 g 
 
 CN (M" — — — ^ 
 
 
 S 
 
 (NC^ — — — — — 
 
 ^ 
 
 t2 
 
 (N C^J — — ■ ^ — --I 
 
 3 
 
 o 
 
 2.75 
 2.22 
 1.88 
 
 1.4() 
 1 .33 
 1 .23 
 1.15 
 1.08 
 
 i 
 
 § 
 
 2.65 
 2.14 
 1.81 
 1 ..')8 
 1.41 
 1.28 
 1.18 
 1.11 
 1.05 
 1.00 
 
 1 
 
 8 
 
 2.53 
 2.05 
 1.73 
 1.51 
 1.35 
 1.22 
 1.13 
 1.06 
 1.00 
 .95 
 .92 
 
 .s 
 
 S 
 
 
 i 
 
 8 
 
 cvi — — — — — — 
 
 E 
 
 ^ 
 
 o cc ^ c^ — o c; X Xt^ t^i^ i^i^ 
 
 2 
 
 E 
 
 5 
 
 XMX!MO-H^x-*'-HOoc;i-':'*Tf 
 x lO CM — q q 00 1> t^_ t^_ q q q q q 
 
 > 
 
 ts 
 
 XOtOOO:; — iOOCOOO — C^XXt^X 
 
 q oc — q X 3C t^_ i> q q q iq »c »o in o 
 
 "5 
 
 8 
 
 ■*_'-; q x t>; t>- q q »o "O »o lo iq lo »o o lO 
 
 3 
 
 ^ 
 
 N q 00 t>. q q iq iq •* -* •*_ -^^ •rf rji rt l rt ■>:}< -^^ 
 
 "a 
 
 g 
 
 O — XClCOX'^'MCiXOiCiOTfTtTfL.'lico 
 OXO«0»0-*-*-*C0C000fCC0C0C0C^0000C0 
 
 M 
 
 rH 
 
 n\ 
 
 c 
 
 Q 
 
 Between 
 
 Course and 
 
 Second 
 
 Bearing 
 
 Q 
 
 OiOOOO»COiOO«00»CO»00»OOiOO 
 
 Tf*»r:»oo«Dr^i>wwc5 0>oo--Hrt<Ncsic»o 
 
 c 
 c 
 
 7 
 
 z
 
 114 
 
 TERRESTRIAL XAVIGATION 
 
 DISTANCES OF OBJECTS AT SEA, IN NAUTICAL MILES 
 
 The maximum distance at which an object is visible at 
 sea according to its elevation and that of the observer, 
 the weather being clear and the refraction normal, is shown 
 by the following table: 
 
 Height 
 
 Distance 
 
 Height 
 
 Distance 
 
 Feet 
 
 Nautical Miles 
 
 Feet 
 
 Nautical Miles 
 
 5 
 
 2.56 
 
 110 
 
 12.07 
 
 10 
 
 3.63 
 
 120 
 
 12.60 
 
 15 
 
 4.44 
 
 130 
 
 13.12 
 
 20 
 
 5.15 
 
 140 
 
 13.62 
 
 25 
 
 5.75 
 
 150 
 
 14.08 
 
 30 
 
 6.30 
 
 200 
 
 16.26 
 
 35 
 
 6.81 
 
 250 
 
 18.18 
 
 40 
 
 7.27 
 
 300 
 
 19.92 
 
 45 
 
 7.71 
 
 350 
 
 21.51 
 
 50 
 
 8.13 
 
 400 
 
 23.00 
 
 55 
 
 8.53 
 
 450 
 
 24.39 
 
 60 
 
 8.91 
 
 500 
 
 25.71 
 
 65 
 
 9.27 
 
 550 
 
 26.97 
 
 70 
 
 9.62 
 
 600 
 
 28.17 
 
 75 
 
 9.96 
 
 650 
 
 29.32 
 
 80 
 
 10.28 
 
 700 
 
 30.43 
 
 85 
 
 10.60 
 
 800 
 
 32.53 
 
 90 
 
 10.91 
 
 900 
 
 34.50 
 
 95 
 
 11.21 
 
 1,000 
 
 36.36 
 
 100 
 
 11.50 
 
 
 
 The distances of visibility given in the above table are 
 those from which an object may be seen by an observer 
 whose eye is at the sea level; in practice, therefore, it is 
 necessary to add to these a distance of visibility correspond- 
 ing to the height of the observer's eye above sea level. 
 
 Example. — A light 90 ft. high is seen just at the horizon; 
 height of observer is 15 ft. What, under ordinary condi- 
 tions of the atmosphere, is its distance from the observer? 
 
 Solution. — Distance corresponding 
 
 to 90 ft. is 10.91 
 
 Add distance corresponding to height 
 
 of observer's eye above sea level, 
 
 15 ft 4.44 
 
 Distance of light is 15.35 naut. mi. Ans.
 
 TERRESTRIAL XAVIGATION 115 
 
 Example. — A vessel is running for a certain port. At the 
 time the lighthouse at the entrance of the harbor is expected 
 to become visible, a man is sent aloft; his height above 
 the water-line is 60 ft. After a while he discovers the light, 
 the height of which is 75 ft. ; what is the distance of the ship 
 from the light, in nautical miles? 
 
 Solution. — Entering table, we find that 
 distance corresponding to 60 ft. is 8.91 
 distance corresponding to 75 ft. is 9.96 
 
 Hence, distance from light is 18.87 naut. mi. Ans. 
 
 Distances corresponding to heights not included in the 
 above table may be found by the form-ula, 
 
 in which H = elevation, or height, in feet, of the object above 
 sea level; 
 £? = corresponding distance of visibility, in nautical 
 miles. 
 
 The formula is based on the mean curvature of the earth 
 and is corrected for ordinary- atmospheric refraction. The 
 distance of visibility of a light may be augmented by abnor- 
 mal atmospheric refraction, which usually increases with 
 the height of the barometer and a falling temperature. 
 
 Distance by the Velocity of Sound, — A convenient method, 
 whenever available, is to determine the distance by noting 
 the number of seconds elapsed between seeing the flash and 
 hearing the report of a gun fired. The velocity of sound is 
 1 naut. mi. in 5.6 sec. or .18' ( = 1,092 ft.) in 1 sec. Hence, 
 the following rule: 
 
 Rule. — Divide the number of seconds elapsed by 5.6, or, 
 multiply them by .18; the result is the required distance expressed 
 in miles. 
 
 Thus, if the number of seconds counted in the interval of 
 
 time between the flash and report of a gun is 14, the required 
 
 14 
 distance is --^ = 2.5; or, =14X. 18 = 2.52 mi. 
 
 O.D 
 
 Danger Angles. — The danger angle, which may be either 
 vertical or horizontal, is the name given to a method that 
 is used when coasting to avoid hidden dangers, such as rocks.
 
 116 
 
 TERRESTRIAL NAVIGATION 
 
 shoals, sunken derelicts, and other obstructions situated 
 immediately at or below the water level. By its use, any 
 such dangerous obstacle may be passed or rounded at any 
 desired distance. 
 
 The vertical danger angle is based on the principle that 
 the distance to an object will remain the same as long as 
 
 the angle subtended 
 by the height of the 
 object remains the 
 same. Tables con- 
 taining angles corre- 
 sponding to different 
 heights and distances 
 expressed in miles 
 and fractions of a 
 mile have accord- 
 ingly been prepared 
 for the use of navi- 
 gators. Thus, if an 
 object is 190 ft. high 
 and it is required to 
 round it at a distance 
 of, for example, 2 mi., 
 the angle that the ob- 
 ject should subtend Is 
 53.7'; the sextant is 
 then set and clamped 
 at that angle and 
 the vessel's course 
 altered so that the 
 angle will remain the 
 Fig. 2 same. If the angle 
 
 referred to becomes larger, the ship is inside the 2-mi. limit; 
 if smaller it is outside, or the distance of the ship from the 
 object is greater than 2 mi. 
 
 The horizontal danger angle is an application of the 
 geometrical properties of the circle, namely, that angles 
 inscribed in the same segment are equal. The following 
 example will serve to explain this method: Suppose that
 
 TERRESTRIAL NAVIGATION 117 
 
 when steaming along a coast it is necessary to avoid some 
 hidden rocks R, Fig. 2, by passing ^ mi. outside of them. 
 On the shore, there are two known objects in sight, a light- 
 house L and a church C, both being marked on the chart. 
 Then, to find the danger angle corresponding to a distance 
 of \ mi. from the rocks, proceed as follows: With the outer- 
 most rock as a center and a radius equal to ^ mi., describe 
 a circle on the chart. Then, through the most seaward 
 point a of this circle and the points C and L, describe another 
 circle; connect a with C and L; measure, with a protractor, 
 the angle C a L formed by the lines a C and a L. Assume 
 it to be 52°, as in the figure. This is the required horizontal 
 danger angle. Now, set that angle on the sextant (neglect- 
 ing the index error if it is small) and watch the two selected 
 objects C and L, holding the instrument in a horizontal 
 position. When the two objects appear in the horizon 
 glass, the ship is close to the circle of safety Oi a a^, and 
 when they come in contact, the ship is on that circle; once 
 on the circle, change the course of the ship so that the two 
 images will remain in contact until the danger is passed. 
 As long as this is being done, the ship will be on the circle 
 of safety ai a ao, since the angles C ai L, C a L, and C a2 L 
 are all equal, being angles in the same segment. If the 
 angle increases, the ship is on the inside of the circle of 
 safety and consequently nearer the danger than is desirable, 
 if it becomes smaller, the ship is outside of the ^-mi. limit. 
 When circumstances permit the selection of a vertical 
 and a horizontal danger angle the latter should always be 
 preferred as being more reliable, because much larger, than 
 the former. 
 
 NOTES RELATING TO THE USE OF FOREIGN CHARTS 
 
 Meridians Used on Foreign Charts. — On English, Dutch, 
 Scandinavian, Russian, Austrian, and American charts, 
 Greenwich meridian is used as the first, or prime, meridian. 
 On French charts, the meridian passing through Paris is 
 used; its long, is 2° 20' 15" or, 0'' 9" 218 east of the Greenwich 
 meridian. The meridian of San Fernando, used on Spanish 
 charts, is in long. 6° 12' 24", or 0^ 24" 49.6' west of the
 
 118 
 
 TERRES TRIAL NA VIGA TION 
 
 Greenwich meridian. On Portuguese charts, the meridian 
 passing through the Marine Observatory, Lisbon, is used; 
 its long, is 9° 11' 10", or O*' 36"^ 44.7^ west of Greenwich. 
 The meridian of Pulkowa Observatory, St. Petersburg, 
 which is sometimes used on Russian charts, lies in long. 
 30° 19' 40", or 2^ l" 18. 7> east of Greenwich. The observa- 
 tory of Naples, the meridian of which is sometimes used on 
 Italian charts, is in long. 14° 15' 7.3" or, 0^ 57" 0.5» east of 
 Greenwich. 
 
 NAMES OF LIGHTS USED ON CHARTS IN DIFFERENT 
 LANGUAGES 
 
 English 
 
 German 
 
 French 
 
 Italian 
 
 Fixed light 
 
 Festes feuer 
 
 Feu fixe 
 
 Luce fissa 
 
 Fixed and 
 flashing light 
 
 Festes feuer 
 mit BHnken 
 
 Feu fixe a 
 Eclats 
 
 Luge bianca 
 a splendori 
 
 Revolving 
 light 
 
 Blinkfeuer 
 
 Feu tournant 
 et feu a echpses 
 
 Luge a 
 splendori 
 
 Quick flashing 
 light 
 
 Funkelfeuer 
 
 Feu scintillant 
 
 Luge 
 scintillante 
 
 Group flashing 
 light 
 
 Gruppen- 
 blinkfeuer 
 
 Feu k eclats 
 
 Luge a gruppi 
 di splendori 
 
 Flashing light 
 
 Blitzfeuer 
 
 Feu cliquotant 
 
 Luge 
 scintillante 
 
 Intermittent or 
 occulting light 
 
 Unter- 
 brochenes feuer 
 
 Feu 
 intermittent 
 
 Luge 
 intermittente 
 
 Alternating 
 light 
 
 Wechselfeuer 
 
 Feu altematif 
 
 Luge 
 alternate 
 
 For symbols and abbreviations in use on the pfficial charts 
 of the principal maritime nations, the reader should consult 
 U. S. Hydrographic Office Publication No. 121. 
 
 Soundings on Foreign Charts. — In order to facilitate the 
 reduction of measurements of depth given on foreign charts 
 to English standards, the following, may prove useful.
 
 CELESTIAL NAVIGATION 119 
 
 Feet Fathoms 
 
 Danish and Norwegian Fawn = 6.175 = 1.029 
 
 Dutch (old) Vadem = 5.575 = .929 
 
 Dutch (recent) Elle = 3.281 = .547 
 
 French .Metre = 3.281 = .547 
 
 Portuguese Braca = 6.004 = 1.000 
 
 Prussian Faden = 5.906 = .984 
 
 Spanish Metro = 3.281 = .547 
 
 Swedish Famn = 5.843 = .974 
 
 Russian, equal to English feet and fathoms. 
 
 The Spanish, Portuguese, and Italian Metro, and the 
 Dutch Elle and French Metre are identical. 
 
 CELESTIAL NAVIGATION 
 
 ASTRONOMICAL TERMS AND DEFINITIONS 
 
 Angular distance is the arc contained between lines drawn 
 from two objects toward an observer; it must not be con- 
 founded with the actual linear distance between the objects; 
 it is expressed in angular measure and must necessarily be 
 the same at any points along the lines at equal distance 
 from the observer. 
 
 Celestial sphere is the apparent spherical surface, called the 
 sky, that surrounds the earth on every side and to which all 
 the heavenly bodies seem to be attached. The center of the 
 celestial sphere is regarded to be at the center of the earth. 
 
 Celestial Poles. — The position of the celestial poles is 
 indicated by the prolongation of the axis of the earth. 
 
 Celestial equator is the great circle formed by the plane of 
 the earth's equator extended toward the celestial sphere; 
 it is also known as the equinoctial. 
 
 Ecliptic is the great circle that the sun's apparent path 
 describes on the celestial sphere. It is inclined to the 
 equator at an angle that may be assumed to be 23° 27', 
 crossing it in two opposite points called the equinoctial 
 points. The point at which the sun passes from south to 
 north of the equinoctial is called the first point of Aries, or 
 vernal equinox, while the opposite point is called the autumnal 
 equinox.
 
 120 
 
 CELESTIAL NAVIGATION 
 
 Solstitial points are those points of the ecliptic that are 
 farthest north or south from the equator and situated 
 therefore midway between the equinoctial points. 
 
 Obliquity of the ecliptic is the angle between the ecliptic 
 and the celestial equator. 
 
 Celestial meridians are great circles passing through the 
 celestial poles and intersecting the celestial equator at 
 right angles. They are identical to meridians of the earth 
 extended toward the celestial sphere. The celestial meridian 
 most freqtiently in use by navigators passes through the 
 zenith, and consequently through the north and south point 
 of the horizon, as shown in Fig. 1. It is known as the 
 meridian. Celestial meridians are also called hour circles, 
 because the arcs of the equator intercepted between them are 
 used as measures of time. 
 
 z 
 
 Jiuiionnl Horizon 
 
 Fig. 1 
 
 Diurnal motion is the apparent daily motion of the 
 heavenly bodies from east to west caused by the rotation 
 of the earth on its axis. 
 
 Zenith is the point Z, Fig. 1 , of the celestial sphere that is 
 vertically above the head of an observer. The zenith of 
 any point on the surface of the earth is indicated by the 
 direction of the plumb-line at that point. 
 
 Rational horizon is the great circle whose plane is per- 
 pendicular to the zenith and passes through the center of 
 the earth. 
 
 Sensible, or true, horizon is the plane passing through the 
 point where the observer stands; it is perpendicular to
 
 CELESTIAL NAVIGATION 
 
 121 
 
 the observer's zenith and consequently parallel with the 
 rational horizon, as shown in Fig. 2. 
 
 Sea horizon is the apparent boundary between the sky 
 and the sea, forming a circle at the center of which the 
 observer stands. 
 
 Verticals. — Circles of altitude, or verticals, are great 
 circles that pass through the zenith intersecting the rational 
 horizon at right angles. 
 
 Prime vertical is the vertical at right angles to the merid- 
 ian; it passes through the east and west point of the horizon, 
 as shown in Fig. 1. 
 
 True altitude is the angular distance of a celestial body 
 from the rational horizon; it is measured along the vertical 
 passing through the body, as shown in Fig. 1. 
 
 Sensible ^ 
 
 a 
 
 Horixon. 
 
 ^^y^^ji 
 
 ^Hx^^. 
 
 ^^^ 
 
 JSatibnalt 
 
 
 1 1 fforixon. 
 
 % 
 
 
 § 
 
 ^ 
 
 ^ 
 
 f . 
 
 Fig. 2 
 
 Observed altitude is the distance of a celestial body above 
 the sea horizon, expressed in angular measure. 
 
 Zenith distance is the distance of the observed body from 
 the observer's zenith; it is the complement of the altitude. 
 
 True azimuth is the arc of the horizon intercepted between 
 the true north or south and the vertical passing through 
 the body; it is measured from north or south toward east 
 or west and may be of any value from 0° to 180°.
 
 122' 
 
 CELES TIA L NA VIGA TION 
 
 Compass azimuth is the azimuth measured by the ship's 
 compass; the difiference between the true and compass azi- 
 muths is the total error of the compass. 
 
 True amplitude is the complement of the true azimuth; 
 it is measured along the horizon from the prime vertical 
 toward north or south. 
 
 Compass amplitude is the amplitude measured by the 
 ship's compass; it is affected by variation and deviation. 
 
 Hour angle is the angle at the pole subtended between 
 the meridian and the hour circle passing through a celestial 
 body. It is measured from the meridian westwards and 
 may be of any magnitude from O*" to 24^. 
 
 Equator 
 
 Fig. 3 
 
 Declination is the angular distance of a body north or 
 south frorri the celestial equator; it is measured by the arc 
 of the hour circle passing through the object and intercepted 
 between it and the equator. 
 
 Polar distance is the distance of a celestial body from the 
 nearer pole; it is measured by the arc of the hour circle 
 intercepted between the pole and the body. The polar 
 distance is, therefore, the complement of the declination, as 
 shown in Fig. 3. 
 
 Parallels of declination are small circles parallel to the 
 celestial equator. 
 
 Right ascension is the arc of the celestial equator measured 
 eastwards from the vernal equinox to the hour circle passing
 
 CELESTIAL NAVIGATIOS 123 
 
 through a celestial body. It is reckoned from O*" to 24''. 
 Thus, in Fig. 3, the right ascension of the star 5 is about Z^, 
 while that of the star s' is about \b^. The approximate 
 position of the vernal equinox in the sky is easily fixed any 
 clear night by following an imaginary line from Polaris that 
 passes through or very near the stars Alpha, Andromeda, 
 and Algenib. At a distance of 90° from Polaris, along that 
 line, is the vernal equinox. Hence, the right ascension of 
 all stars to the left of that line is small, while that of stars 
 to the right is large. 
 
 Annual parallax is the greatest angle subtended at a star 
 by the radius of the earth's orbit. The parallax of only a 
 few stars has, as yet, been determined, and in no case does 
 it amount to as much as 1 sec. 
 
 Parallax in altitude is the angle subtended by a line joining 
 a celestial body with the point of observation and a line 
 joining the same body with a certain point of reference, 
 such as the center of the earth. A correction for parallax 
 is used when correcting observed altitudes, and is always 
 additive. This correction is maximum when the body is 
 near .the horizon and vanishes on approaching the zenith. 
 
 Dip is the angular distance between the sensible horizon 
 and a line drawn from the observer's eye to the sea horizon, 
 as shown in Fig. 2. The amount of dip depends on the 
 height above the surface of the sea, increasing as the height 
 of the eye increases. The correction for dip is always 
 subtractive. 
 
 Refraction is the downward deflection of a ray of light 
 on entering the atmosphere of the earth, causing a celestial 
 body to appear higher than it kctually is. It is least in 
 high altitudes, and increases toward the horizon. The 
 correction for refraction is subtractive. 
 
 Transit, or transition, is the passage of a celestial body, such 
 as a star, across the meridian of a certain place, either above 
 or below the pole ; it is identical to meridian passage and cul- 
 mination. Thus, when the sun reaches its highest altitude 
 on any day, it is said to be in culmination or transition. 
 
 Circles of celestial longitude are great circles perpendicular 
 to the ecliptic and passing through the poles of the ecliptic.
 
 124 CELESTIAL NAVIGATION 
 
 Celestial latitude is the angular distance of a star or planet 
 from the ecliptic measured along the circle of longitude that 
 passes through the object. 
 
 Celestial longitude is the arc of the ecliptic measured 
 eastwards from the vernal equinox to the circle of longitude 
 passing through a celestial object. 
 
 The Solar System. — A body, like the earth, that performs a 
 circuit about the sun, is called a planet. A smaller body, like 
 the moon, that revolves about a planet, is called a satellite of 
 tliat planet. The sun, planets, and satellites constitute what 
 is called the solar system. Including the earth, there are 
 eight known planets, which are divided into two classes — 
 interior and exterior planets. Interior planets are those 
 whose orbits lie within that of the earth; viz.. Mercury and 
 Venus; exterior planets are. those whose orbits are greater 
 than that of the earth and, consequently, lie outside of it; 
 they are. Mars, Jupiter, Saturn, Uranus, and Neptune. The 
 principal elements of the solar system are given in the table . 
 
 Between the orbits of Mars and Jupiter, there are a num- 
 ber of small planets, called asteroids, of which at present 
 about 384 are known ; they are supposed to be the fragments 
 of a burst planet. A number of these small planets have 
 not been observed since their discovery and are practically 
 lost. Hence, it is sometimes a matter of doubt, until cer- 
 tain elements have been computed, whether a supposed 
 new pTanet is really new or only an old one rediscovered. 
 All the exterior planets are attended by moons, similar to 
 ours, that move around them in the same direction that 
 the planets themselves revolve around the sun. Th3 only 
 exceptions are the satellites of Uranus and Neptune, which 
 revcilve in the opposite direction. 
 
 Conjunction. — A planet is said to be in conjunction with 
 another body when both lie on the same line, or is seen in 
 the same direction in the heavens. In the case of interior 
 planets this conjunction is of two kinds: the one when the 
 planet is between the earth and the sun, called inferior 
 conjunction; and the other when at the opposite pomt oi 
 its (irbit, with the sun between the planet and the earth, 
 called superior conjunction.
 
 CELESTIAL NAVIGATION 
 
 125 
 
 Gravity 
 at Surface 
 Earth = 1 
 
 
 s§§ 
 
 
 (N (N X O t^ <N '- <N (N 
 
 h 
 
 1.310,000 
 
 .05 
 
 .92 
 
 1.00 
 
 .15 
 
 1 ,309 . 00 
 
 721 .00 
 
 65 . 00 
 
 85 . 00 
 
 
 
 Mean 
 
 Diameter 
 
 Miles 
 
 866.400 
 
 3,030 
 
 7,700 
 
 7,910 
 
 4,230 
 
 86,500 
 
 71,000 
 
 31.900 
 
 34,800 
 
 lis 
 
 87.96 
 
 224 . 70 
 
 365.25 
 
 686.95 
 
 4,332.58 
 
 10,759.22 
 
 30,686.82 
 
 60,181.11 
 
 Mean 
 Distance 
 From Sun 
 Expressed 
 in Millions 
 of Miles 
 
 c w X >o ro o C5 o 
 
 CCXiOiThXXxS 
 •-(•^Xt^t^ 
 
 s 
 
 2 
 
 c 
 
 
 
 
 11
 
 126 CELESTIAL NAVIGATION 
 
 Opposition. — A planet is said to be in opposition when 
 the earth is directly between it and the sun, at which time 
 it is most brilliant. 
 
 Elongation is the angle formed by lines connecting the 
 earth with a planet and sun, respectively. 
 
 Quadrature. — Two heavenly bodies are said to be in 
 quadrature when they are half way between conjunction 
 and opposition. 
 
 Occultation. — The moon, in her orbital motion, often 
 passes before, and hides from a spectator on the earth, certain 
 of the fixed stars, and occasionally one of the planets; these 
 occurrences are called occultations. 
 
 EXPLANATIONS OF TERMS RELATING TO TIME 
 
 Apparent solar day is the interval of time between two 
 successive transits of the sun over the same meridian; 
 apparent time is measured by the hour angle of the true sun. 
 
 Mean Sun. — The intervals between the successive returns 
 of the sun to the same meridian are not exactly equal, owing 
 to the varying motion of the earth around the sun, and to 
 the obliquity of the ecliptic, and for this reason the length 
 of the apparent solar day is not the same at all times of the 
 year and cannot be measured by a clock whose rate is 
 uniform. To avoid the irregularity that would arise from 
 using the true sun as the measure of time, a fictitious sun, 
 called the mean sun has been devised, which is supposed 
 to move along the celestial equator with a uniform velocity. 
 This mean sun is supposed to keep, on the average, as near 
 the real sun as is consistent with perfect uniformity of 
 motion; it is sometimes in advance of it, and sometimes 
 behind it, the greatest deviation being about 16 min. of time. 
 
 Mean time, which is perfectly equable in its increase, is 
 measured by the motion of the mean sun. The clocks in 
 ordinary use and chronometers are regulated to mean time. 
 
 Mean solar day is the average, or mean, of all the apparent 
 solar days in a year; or, the interval of time between two 
 successive mean noons. 
 
 Equation of time is the difference between apparent and 
 mean time; its value for every day of the year is recorded
 
 CELESTIAL NAVIGATION 127 
 
 in the Nautical Almanac. By means of the equation of 
 time, we change apparent to mean time, or the reverse, 
 by adding or subtracting it acording to directions in the 
 Almanac. 
 
 Sidereal time is the time measured by the daily motion of 
 the stars; or for astronomical purposes, by the daily motion 
 of that point in the equator from which the true right 
 ascension of the stars is counted. This point is the vernal 
 equinox, and its hour angle is called sidereal time. Astro-' 
 nomical clocks, regulated to sidereal time, are called sidereal 
 clocks. 
 
 Sidereal day is the interval between two successive upper 
 transits of the vernal equinoctial point, and begins when 
 the vernal equinoctial point is on the meridian. It is about 
 3 min. and 56 sec. shorter than the mean solar day; and is 
 divided into 24 sid. hr. 
 
 Astronomical Day. — When mean time is used in astro- 
 nomical work, the day begins at mean noon and is called 
 the astronomical day; astronomical mean time is reckoned 
 continuously up to 24 hr. 
 
 Civil Day. — When mean time is used in the ordinary 
 affairs of life it is called civil time and the civil day begins 
 at midnight, 12 hr. earlier than the astronomical day. 
 Thus, Jan. 9, 2 o'clock a. m., civil time, is Jan. 8, 14 hr., 
 astronomical time; and Jan. 9, 2 o'clock p. m., civil time, 
 is also Jan. 9, 2 hr., astronomical time. The rule for con- 
 verting civil time into astronomical time is this: If the 
 civil time is marked a. m., take 1 from the date and add 
 12 to the hours, and the result is the astronomical time 
 wanted; if the civU time is marked p. m., take away the 
 designation p. m., and the astronomical time is had without 
 further change. 
 
 To change astronomical to civil time, we simply write 
 P. M. after it if it is less than 12 hr. If greater than 12 hr., 
 we subtract 12 hr. from it, increase the date by 1, and write 
 A. M. For example, Jan. 3, 23 hr., astronomical time, is 
 Jan. 4, 11 o clock a. m., civil time. 
 
 Local mean time (L. M. T.) is the mean time at a certain 
 place or locality, as, for example, the mean time at ship; at
 
 128 CELESTIAL NAVIGATION 
 
 no time can the mean time be the same at two places unless 
 they are situated on the same meridian. 
 
 Greenwich date (G, D.) is the local mean time at Green- 
 wich shown by the chronometer and with proper date 
 appended; the Greenwich date should be expressed astro- 
 nomically. Chronometer being marked up to 12 hr. only, it 
 cannot always be decided, especially where longitude is 
 large, whether the Greenwich mean time (G. M. T.) is more 
 or less than 12 hr. In such cases, it is advisable to get an 
 approximate value of the G. D. by applying to the local 
 time the hours and minutes of the ship's longitude, adding 
 if in west, subtracting if in east, longitude. In case the 
 difference between this approximation and the time by the 
 chronometer is nearly 12 hr., add 12 hr. to the latter and 
 put the day back 1, if necessary. 
 
 Example. — The local time at a ship in longitude 150" 30' W 
 is 5*^ 40"' p. M., Dec. 16. The chronometer indicates 2^ 22™ 10', 
 its error on G. M. T. being 10™ 50' slow. Find G. D. 
 
 Solution. — Ship's time, Dec. 16= 5'' 40" 
 
 Long. (W) in time= +10'' 2'" 
 
 Approx. G. D., Dec. 16 = 
 
 15b 42-» 
 
 
 3h22"' 
 
 10' 
 
 -t-lO-" 
 
 50' 
 
 Chron. = 
 
 Error = 
 
 G. M. T., Dec. 16= Sb as-n 
 
 Add= 12h 
 
 G. M. T. or G. D., Dec. 16= 15" SS"" 
 In this case 12'' must be added to the time indicated by 
 the chronometer. This gives the G. D., corresponding to 
 ship time, as Dec. 16, 15'' SS-". Ans. 
 
 Notes on the Correction of Altitudes. — The altitude of a 
 celestial object, as measured with a sextant, is called the 
 observed altitude; but in order to obtain the true altitude 
 some or all of the following corrections must be applied: 
 (1) Index error of the sextant, (2) dip of the horizon, 
 (3) refraction, (4) parallax, (5) semi-diameter. The cor- 
 rection for dip and refraction are taken from nautical 
 tables; parallax of the sun is also found in tables, while that 
 of the moon is tabulated in the Nautical Almanac. The
 
 CELESTIAL NAVIGATION 129 
 
 semi-diameter of the sun that is taken from the Nautical 
 Almanac is applied according to what limb is brought in 
 contact with the horizon; if lower limb is observed, it is 
 additive; if upper limb, subtractive. 
 
 In correcting altitudes, it should be remembered that 
 the observed altitude is that read off the sextant. When 
 this has been corrected for index error, dip, and semi- 
 diameter, the result is the apparent altitude of the center, 
 and the application to this of the corrections for refraction 
 and parallax produces the true altitude of the center of the 
 observed body, as if the observation had been made at the 
 center of the earth and the altitude had been measured 
 from the rational horizon. 
 
 The observed altitude of a star has to be corrected only for 
 index error, dip, and refraction. When an artificial horizon 
 is used, apply index error to the double altitude read off the 
 sextant, divide by 2, and apply the other corrections as usual, 
 except that for dip. When correcting altitudes of the sun, 
 use refraction and parallax corresponding to the apparent 
 altitude of the upper or lower limb; for altitude of the moon, 
 use the apparent altitude of the moon's center. 
 
 Since the value of dip depends on the height of the eye 
 above surface of the sea. it is advisable always to ascertain 
 beforehand the exact vertical distance from water-line to 
 the bridge, or other place usually occupied by observer, 
 when measuring altitudes. And due allowance should be 
 made for any reduction or increase in this vertical distance 
 when ship is loaded, or light, or when having a considerable 
 list to either side. 
 
 LATITUDE DETERMINATIONS 
 Meridian Altitude of the Sun. — The measurement shovild 
 begin a short time before noon, say 10 or 15 min. The 
 altitude will increase gradually until apparent noon, when 
 it will stop and begin to decrease. The highest altitude 
 attained is the desired meridian altitude. Apply to this 
 observed altitude the necessary corrections, and subtract 
 the true altitude thus found from 90°. The result is the 
 zenith distance, which is named opposite to the direction
 
 130 CELESTIAL NAVIGATION 
 
 the observer is facing when measuring the altitude. Find, 
 from the Nautical Almanac, the sun's declination and correct 
 it for the G. D. Take the algebraic sum of the declination 
 and zenith distance, and name it the same as the larger 
 quantity. The result is the required latitude. 
 
 Example.— On Sept. 23, 1904, in longitude 11° 45' W, by 
 dead reckoning, the observed meridian altitude of the sun's 
 lower limb was 33° 37' 40", the observer facing south; index 
 error = + 1' 40"; height of eye = 23 ft. Find the latitude. 
 
 Solution.— L. App. T. Sept. 23 = 0'> C" 0^ 
 Long. (W) in time = 0'' 47™ 0» 
 
 Corr. 
 
 Decl. 
 
 for 47'" 
 
 G. D. Sept. 
 = S0°0' 11.6" 
 + 46.7" 
 
 23 = 
 
 -.Qh 47m OS 
 
 Change in I*" 
 
 = 58.4" 
 X.8h 
 
 Con 
 
 -. Decl. 
 
 = S 0°0'58.3" 
 Obs. Mer. Alt. 
 L E. 
 
 = 33 
 
 Corr. = 
 ° 37' 40" 
 + 1' 40" 
 
 = 46.72" 
 
 33° 39' 20" 
 
 Dip = -4' 42" 
 
 33° 34' 38" 
 
 S. D.= +15' 59" 
 
 App. Alt. = 33° 50' 37" 
 Ref.= -1'26" 
 
 Parallax 
 
 = 
 
 + 0' 
 
 7" 
 
 
 True Mer. Alt. 
 
 = 33° 
 90° 
 
 49' 
 0' 
 
 18" 
 0" 
 
 
 Z. D. 
 
 Decl. 
 
 Latitude 
 
 = 56° 
 = 0° 
 = 56° 
 
 10' 
 0' 
 9' 
 
 42" 
 58" 
 44" 
 
 N 
 S 
 
 "n 
 
 Ans. 
 
 In this case, the bearing of the sun being south, the zenith 
 distance is north; the declination being south, the latitude 
 is therefore equal to the difference between the two, having 
 tlie same name as the larger quantity. 
 
 Meridian Altitude of a Star. — Select a bright star that is 
 near and about to cross your meridian. Be sure that the 
 star selected is identified without doubt. Find to the nearest
 
 CELESTIAL NAVIGATION 131 
 
 minute the local apparent time of its meridian passage, by 
 subtracting from the star's right ascension the right ascen- 
 sion of the sun, and thence the correspdnding mean time. 
 Be ready with the sextant a few minutes before that time 
 and proceed exactly as in the case of observing the sun. 
 
 Example. — On Oct. 19, 1904, an opportunity presented 
 itself to observe the meridian altitude of the star Sirius 
 (a Canis Majoris); the altitude when measured was 45° 34 
 20", the observer facing south; index error = -2' 20"; height 
 of eye = 23 ft. Find the latitude. 
 
 Solution. — For approximate time of meridian passage. 
 R. A. ( + 24h)=30i' 41'» 
 R. A.' Sun = 13^35^ 
 L. App. T. = 17h G"" 
 Eq. of T. =_-L5^ 
 L. M. T. = 16h Si-" p. M. 
 Approx. L. M. T. of passage = 4'' 51™ a. m. 
 
 Obs. Mer. Alt. = 45° 34' 20" 
 I. E.= -2' 20" 
 
 45° 32' 0" 
 Dip = - 4' 42" 
 
 45° 27' 18" 
 Ref . = - 0' 56" 
 
 True Alt. = 45° 26' 22" 
 90° 0' 0" 
 
 Z. D. = 44°33' 38" N 
 Decl. = 16°35' 5" S 
 
 Latitude = 27° 58' 33" N Ans. 
 
 The star's declination, which is practically constant, is 
 taken directly from the catalog of fixed stars in the Nau- 
 tical Almanac. 
 
 Meridian Altitude of the Moon. — Find, from the Nautical 
 Almanac, the mean time of the moon's meridian passage at 
 Greenwich, If your local time is P. m., take it out for the 
 given date; if a. m., for the day preceding. Apply to it a 
 correction equal to the hourly difference multiplied by the 
 longitude in time, adding this correction when longitude is
 
 132 CELESTIAL NAVIGATION 
 
 west, but subtracting it wher^ east; the result is the local 
 time of transition. Then find the corresponding G. M. T. 
 by applying the longitude in time. For the G. D. thus 
 found, correct the moon's semi-diameter declination and 
 parallax as shown in the example that follows: Measure 
 the altitude at the proper time and reduce it to true, whence 
 the latitude is found as usual. 
 
 Example. — On Aug. 22, 1904, in the evening, a meridian 
 altitude of the moon's lower limb measured in an artificial 
 horizon was 61° 46' 30", the observer facing south; index error 
 of sextant = +1' 30" ; long. = 75° 45' W. Find the latitude. 
 
 Solution. — Find, first, the local time of meridian passage and 
 
 the requisite elements of the moon in the Nautical Almanac. 
 
 Mer. pass. Aug. 22 = 9^40.5'° Change in 1^ = 2"' 
 
 Corn for long. = + lO-^ X5*' 
 
 L. M. T. of pass.= 9^^ 50.5°^ p. m. Corr. = 10°' 
 
 Long, in time= +5"^ 3™ 
 G. M. T. Aug. 22 = 141' 53.5m 
 
 Moon's S.D. at midnight = 14' 56" (nearly) 
 Corr. for Alt. = +7" 
 Corr. S. D. = 15' 3" 
 
 Hor. Par. at midnight = 54' 42" 
 
 Decl. at 14»> Aug. 22 = S 16° 43' 28" Change 1^ = 4" 
 
 Cor. for 53.5'"= -3' 34" X53.5'° 
 
 Corr. Decl. = S 16° 39' 54" 214.0" 
 
 Obs. double Alt. = 61° 46' 30" Corr. =3' 34" 
 
 I. E.= +1'30" 
 
 2)61° 48 0" 
 
 Obs. Mer. Alt. = 30° 54' 0" 
 
 S. D.= + 15' 3" 
 
 App. Alt. center = 31° 9' 3" 
 Par. Ref.= +45' 13" 
 
 True Mer. Alt. = 31° 54' 16"
 
 CELESTIAL NAVIGATION 133 
 
 True Mer. Alt. = 31° 54' 16" 
 90° 0' 0" 
 
 Z. D. = 58° 5' 44" N 
 Decl. = 16°39' 54" S 
 
 Latitude = 41° 25' 50" N Ans. 
 
 The correction for parallax and refraction is taken from 
 I. C. S. Nautical Tables, page 170, or from Table 24, Bow- 
 ditch. 
 
 Ex-Meridian of the Sun. — Measure an altitude within 
 1 hr. of noon (either p. m. or A. M.), and note the chronometer 
 time at instant of observation. From the time thus noted, 
 find the hour angle, H. A., which is equal to local apparent 
 time, and express it in degrees, minutes, and seconds. 
 Reduce the observed altitude to true, and correct the decli- 
 nation for G. M. T. From the data now at hand, calculate 
 two quantities that we will designate M and N. Find the 
 value of M by formula: 
 
 Tan M = sec H. A.Xtan Decl. 
 and that of A'^ by formula: 
 
 Cos A' = sin A/Xsin Alt.Xcosec Decl. 
 
 Name M the same as declination and N the same as 
 zenith distance. If they have the same name, take their 
 sum; if of different names, subtract the smaller from the 
 larger. The result is the latitude, which is named the same 
 as the larger quantity. 
 
 Example. — On June 8, 1904, in long. 60° 15' W. the sun 
 being obscured by clouds at noon, an altitude of the lower 
 limb, observed at about 12.40 p. m., was found to be 78° 
 33' 40", the observer facing south. At the instant of measur- 
 ing the altitude, the chronometer indicated 4^ 46™ 25', its 
 error on G. M. T. being 1" 55^ fast; index error= —3' 40"; 
 height of eye = 20 ft. Required the latitude. 
 
 Solution. — 
 
 Chron. = '^^ 46'° 25' 
 Error (fast) = - 1-^ 55' 
 
 G. D., June 8= 4b 44>" 30«
 
 134 
 
 CELESTIAL NAVIGATION 
 
 G. D., June 8= 4^ 44°> 30» 
 Long. (W) in time = 4»' I'" 0» 
 
 L. M. T.= 0»>43°>30« 
 Eq. ofT.= +1°' 13' 
 
 L. App. T.= Oh 44'° 43^ 
 Or. hour angle = 11° 10' 45" 
 
 Eq. of T. = l" 15.5' 
 Corr. for 4.7»'= - 2.2' 
 
 Eq. of T. = l'° 13.3' ( + ) 
 
 Change in lh = 0.47' 
 4.7h 
 
 2.209' 
 
 Decl. = N22°50'8.5" 
 Corr. for 4.7^= +1' 4.3" 
 
 Change in lh = 13.68" 
 4.7»> 
 
 Ded. = N22°51' 12.8" 
 
 9576 
 5472 
 
 Obs. Alt. = 78° 33' 40" 
 I. E.= -3' 40" 
 
 64.296" 
 
 Dip 
 
 78° 30' 
 = -4' 
 
 0" 
 23" 
 
 . D. 
 
 78° 25' 
 = +15' 
 
 37" 
 
 47" 
 
 Par. 
 
 78° 41' 
 = -0' 
 
 24" 
 10" 
 
 True Alt. = 78° 41' 14" 
 The true altitude being found, calculate the quantity M 
 and A^ according to formulas given; thus, 
 
 Tan M = Sec H. A. X tan Decl. 
 
 sec 11° 10' 45"= .00832 
 tan 22° 51' 12" = 9.62475 
 
 tan M = 9.63307 
 A/ = 23° 15' 
 
 CosA^ = sin MX sin Alt. 
 X cosec Decl. 
 
 sin 23° 15' = 9. 59632 
 
 sin 78° 41' 14" = 9. 99147 
 
 cosec 22° 51' 12"= .41075 
 
 Cos A/ = 9. 99854 
 
 A^ = 4°42' 
 
 Lat. = M + N = 23° 15' + 4° 42' = 27° 57' N. Ans.
 
 CELESTIAL NAVIGATION 135 
 
 LONGITUDE DETERMINATIONS 
 
 Time Sight of the Sun. — Measure an altitude of the sun in 
 the forenoon or afternoon when it bears nearly east or west, 
 and note the corresponding time, either directly on the 
 chronometer or by a watch previously compared with 
 the chronometer. The altitude should not be less than 15°. 
 
 Correct the chronometer time for error and accumulated 
 rate; the result will be the G. M. T., or G. D., at the instant 
 of observation. Reduce the observed altitude to true by 
 applying the usual corrections. Compute the latitude of 
 the ship by dead reckoning from the last observation up to 
 the time of taking the sight. Take out the equation of time 
 and correct it for the G. D. Similarly, correct the sun's 
 declination for the G. D., and find the polar distance {p) 
 as follows: If latitude and declination have the same name, 
 ^ = 90°-decl.; if of different name, ^ = 90° + decl. Then 
 calculate the hour angle by the formula 
 
 Sin i H. A. = "Vcosec p sec / cos 5 sin iS-d) 
 in which p = polar distance ; 
 / = latitude; 
 a = true altitude ; 
 5 = half sum of a, p, and /. 
 
 In other words, calciilate the hour angle by the given 
 formula, adding the log cosec p, log sec /, log cos S, and log 
 sin (S — a). The sum divided by 2 is the log sine for t-hour 
 angle. If" the observation is made in the forenoon, take out 
 the corresponding local apparent time from a. m. column in 
 the tables; if made in the afternoon, from the p. m. column. 
 
 The local apparent time having been determined, the 
 corresponding local mean time is found by applying the 
 equation of time according to its sign. The difference 
 between L. M. T. and the G. M. T., reduced to degrees, 
 minutes, and seconds, will be the required longitude. If 
 G. M. T. is greater than L. M. T., the longitude is west; if 
 the L. M. T. is greater than G. M. T., the longitude is east. 
 
 Example. — On Jan. 17, 1904, at about 3.50 in the after- 
 noon an altitude of the sun's lower limb measured 37° 7' 40"; 
 index error= —2' 30"; height of eye = 16ft.; at instant of 
 observation the chronometer indicated 7^ 26™ 478, its error
 
 136 CELESTIAL NAVIGATION 
 
 on G. M. T. being 2™ 43' slow; lat., by dead reckoning, is 
 46° 30' S. Find the longitude. 
 
 Solution.— Chron., Jan. 17 = 7'' 26" 47» 
 Error ( slow) = +2°> 43- 
 
 G. M. T. Jan. 17 = 7'' 29"' 30» p. m. 
 
 Decl. = S 20° 57' 42.9" Change in 1''= 28.51" 
 
 Corr.= -3' 33.8" X7.5'' 
 
 Decl. = S20°54' 9.1" 213.825 
 
 90° 0' 0" 3' 33.8" 
 
 P. D. = 69° 5' 51* 
 
 Eq. of T.= 9" 53.64' Change in li' = .86' 
 
 Corr.= +6.45' X7.5'' 
 
 Eq. of T. = 10°'0.09'+ 6.450* 
 
 Obs. Alt. = 37° r 40 
 I. E.= -2' 30" 
 
 37° 5' 10" 
 Dip= -3' 55" 
 
 37° 1' 15" 
 S. D.= +16' 17" 
 
 37° 17' 32" 
 
 . and Par. = - 1' 9" 
 
 
 a= 37° 16' 23" 
 
 
 p= 69° 5' 51" 
 
 cosec= .02956 
 
 /= 46° 30' 0" 
 
 sec= .16219 
 
 2)152° 52' 15" 
 
 
 5= 76° 26' 7" 
 
 cos= 9.37028 
 
 S-a= 39° 9' 44" 
 
 sin= 9.80039 
 
 2)19.36242 
 Sini H, A.= 9.68121 
 L. App. T.=3''49°'28» 
 •f lO-" 0' 
 L. M. T. Jan. 17 = 3"' 59'" 28' p. m. 
 G. M. T. Jan. 17 = 7" 29"" 30» p. m. 
 Diff. =3'' 30'» 2» 
 Long. = 52° 30' 30" W. Ans.
 
 CELESTIAL NAVIGATION 137 
 
 Time Sight of a Star. — Select a bright star bearing nearly- 
 east or west; measure its altitude and note the chronometer 
 time at instant of observation. Reduce the G. M. T. into 
 G. S. T. by adding the right ascension of the mean sun to 
 G. M. T., as shown in the example that follows: Correct 
 the altitude as usual and find, from the Nautical Almanac, 
 the star's right ascension and declination. Calculate the 
 hour angle in exactly the same way as for the sun, but use 
 only the p. m. column of the tables in finding the hour angle. 
 
 If the hour angle is east (or when the observed star is to 
 the east of the observer's meridian), subtract it from the 
 star's right ascension; if the hour angle is west (or the star 
 is west of the meridian), add it to the star's right ascension. 
 The resvilt will be the right ascension of the observer's 
 meridian, or the L. Sid. T. The difference between this 
 time and G. Sid. T., reduced to degrees, minutes, etc. is the 
 required longitude. 
 
 Example.— On Oct. 18, 1904, at about 2»' SO-" a. m.. the 
 observed altitude of the star Sirius (a Canis Majoris) when 
 east of the meridian was 53° 52' 40"; index error = +2' 43"; 
 height of eye = 22 ft. The time indicated by chronometer 
 was ll'' ?•" 21^ its error on G. M. T. being 3" 22^ fast; long, 
 estimated at 50° E; lat. = 15° 14' S. Find the longitude. 
 
 Solution. — First, find the approximate G. D.; thus, 
 Approx. L. M. T. Oct. 17= 14*' SO-" 
 Long. (E) in time = -3" 2 0" 
 Approx. G. D. Oct. 17= ll'' 10" 
 
 Then, from reading of chronometer get the G. M. T., or 
 
 G. D. and the corresponding sidereal time at Greenwich; thus, 
 
 Chron. = lli' 7" 2P S. T. G. M. N. = 13b 42™ 13.9, 
 
 Error (fast) = -3"22» 
 M.T.Oct. 17 = 11'^ 3" 59^ 
 
 ^ fforll" 
 C°"-|for4" 
 
 1™ 48.4« 
 .7* 
 
 R. A. M. S. = 13M4» 3« 
 S.T. Oct. 18= 0''48" 2» 
 *Decl. = Sl6°35' 5" 
 90° 0' 0" 
 
 R. A. M. S.= 
 
 = 13M4" 38 
 
 ♦P. D.= 73° 24' 5 
 *R. A. = 6" 40" 55»
 
 138 CELESTIAL NAVIGATION 
 
 Obs. Alt. = 53° 52' 40" 
 I. E.= +2' 43" 
 
 53° 55' 23" 
 
 
 
 Dip= -4' 36" 
 
 
 
 53° 50' 47" 
 
 
 
 Refraction = -0 42" 
 
 
 
 True Alt. or a= 53° 50' 5" 
 
 
 
 P= 73° 24' 55" 
 
 cosec = 
 
 .01845 
 
 /= 15° 14' 0" 
 
 sec = 
 
 .01553 
 
 2)142° 29' 0" 
 
 
 
 5= 71° 14' 30" 
 
 cos = 
 
 9.50729 
 
 S-a= 17° 24' 25" 
 
 sin = 
 
 9.47593 
 
 2)19.01720 
 sin i H. A.= 9.50860 
 *H. A. = 2b 30"' 32= E (Column p. m.) 
 *R. A. = 6h 40'"55 « 
 L. Sid. T. Oct. 18 = 4" 10"' 23» 
 G. Sid. T. Oct. 18 = Oh 48°' 2 ^ 
 Diflf. = 3h 22'" 2P 
 Long. = 50° 35' 15" E. Ans. 
 Equal Altitudes Near Noon. — Observe an altitude of the 
 sun shortly before noon (usually as many minutes as there 
 are degrees in the latitude in), clamp the sextant, and note 
 carefully the reading of the chronometer at instant of observ- 
 ing. After the sun has crossed the meridian and begins to 
 descend, watch by means of the clamped sextant the moment 
 when it attains the same altitude, and note the chronometer 
 at that instant. Find the mean of the two times by divid- 
 ing their sum by 2. Correct this time for whatever error 
 the chronometer may have. The result will be the G. M. T. 
 at apparent noon. Find, from the Nautical Almanac, the 
 equation of time; correct it for the G. M. T. and apply it to 
 the apparent time at noon (=0'' O"" 0'). The result will be 
 the L. M. T. at apparent noon. The difference between the 
 local and Greenwich time, converted into degrees, etc., 
 will be the approximate longitude of the ship at instant of 
 apparent noon.
 
 CELESTIAL NAVIGATION 139 
 
 If the vessel has sailed toward the sun, in the interval 
 between observations, the second altitude should be increased 
 by resetting the sextant as many minutes as there are miles 
 in the difference of latitude; if the vessel has sailed from 
 the sun, the second altitude should be decreased in the 
 same proportion. Thus, if the first altitude is 62° 24', and 
 the ship in the interval of time has changed her latitude 
 5' toward the sun, the sextant, when taking the second 
 observation, should be set to 62° 29'; if she has sailed from 
 the sun, the instrument should be set to 62° 19', before 
 measuring the second altitude. 
 
 Example. — On Aug. 16, 1904, in lat. 12° N, the sun was 
 observed to have equal altitudes when near the meridian 
 at the following times by the chronometer: Before noon, 
 4>^ 10"= 25^ after noon, 41^ 30'" 23«. Find the longitude of 
 the ship, the error of the chronometer on Greenwich mean 
 time being 2°^ 10' fast. 
 
 Solution. — Chron. before noon = 4h lO^^ 25' 
 Chron. after noon = 4b 30"" 23' 
 
 2)81^ 40°^ 48' 
 
 Mid. time = 411 20>" 24' 
 
 Error (fast) -2'" 10' 
 
 G. M. T. at noon = 4'' IS"' 14' 
 Eq. of T. Aug. 16 = 4" 11' Change in 1^ = 0.5' 
 
 Corr.= - 2.15' X4.3»' 
 
 Corr. Eq. of T.=4"" 8.85' ( + ) Corr.=2.15» 
 
 L. App. T. at noon = 0'^ 0" 0' 
 Eq. ofT.= +4-° 8.9' 
 L. M. T. at noon = 0h 4-" 8.9' 
 G. M. T. at noon = 4'> 18" 14 
 
 Diff. = 4'' 14°' 5.1' 
 Long. = 63° 31.3' W. Ans. 
 Sunrise and Sunset Sights. — When the sun's upper or 
 lower limb is exactly in contact with the sea horizon, either 
 at sunrise or sunset, note the chronometer and correct its 
 time for any error it may have. For the G. D. thus found, 
 find, from the Nautical Almanac, the equation of time,
 
 140 CELESTIAL NAVIGATION 
 
 the declination, and thence the polar distance. To the 
 polar distance, add the latitude at observation, and from 
 the sum subtract 21' if lower limb was observed, or 53' if 
 upper limb was used. Half the sum thus obtained is the 
 quantity S in the formula for hour angles. By adding to 
 5 the 21' or 53' previously subtracted, the quantity (S — a) 
 is had, whence the longitude is computed in the usual way. 
 as shown in the example that follows: 
 
 Example. — On Sept. 10, 1904, at sunset, the chronometer 
 indicated S^ 37"' 26^ when the sun's lower edge, or limb, 
 came into contact with the horizon; the chronometer s error 
 on G. M. T. was 5" 56« fast; lat. in, by dead reckoning, was 
 48° 10' N. Find the longitude. 
 
 Solution.— Chron. =8^ S?"" 26* 
 
 Error (fast) = - 5'' 5& 
 
 G. M. T. Sept. 10 = 8'' 31™ 30" 
 
 Eq. of T. =2'" 59.68 Change in li> = 0.86'' 
 
 Corr.= +7.38 X8.5»' 
 
 Corr. 
 
 Eq. of T. = S 
 
 m 
 
 6.9B 
 
 
 Decl. 
 
 = N 5° 
 
 0' 
 
 34" 
 
 
 Corr. 
 Decl. 
 
 = 
 
 8' 
 
 3" 
 
 Con- 
 
 = 4° 
 
 52' 
 
 31" 
 
 
 P. D. 
 
 90° 
 
 0' 
 
 0" 
 
 
 = 85° 
 
 7' 
 
 29" 
 
 
 Lat. 
 
 = 48° 
 
 10' 
 
 0" 
 
 
 133° 
 
 17' 
 
 29" 
 
 Co 
 
 nstant 
 
 = 
 
 21' 
 
 0" 
 
 
 2)132° 
 
 56' 
 
 29" 
 
 
 S 
 
 = 66° 
 
 28' 
 
 15" 
 
 Constant 
 
 + 21' 
 
 0" 
 
 ) Corr. = 7.310" 
 
 Change in 1^= 56.8" 
 
 X8.5»' 
 
 Corr. = 482.8" = 8' 3* 
 
 cosec= 0.00158 
 sec= 0.17590 
 
 cos= 9.60121 
 iS-a)= 66° 49' 15" sin = 9.96345 
 
 2)19.74214 
 sini H. A.= 9.87107
 
 CELESTIAL NAVIGATION 141 
 
 L. App. T. = 6»' 24'° 0« 
 Eq. of T.= -S"* 7« 
 
 L. M. T. Sept. 10 = 6b 20'" 53' p. m. 
 G. M. T. Sept. 10 = 8'' 31" 30« p. m. 
 
 Diff. = 2h 10"37« 
 Long. = 32°39.2' W. Ans. 
 
 The longitude thus found is approximate only. It is 
 evident that an abnormal refraction caused by unusual 
 atmospheric conditions at setting or rising often renders this 
 method unreliable. Its value lies in the fact that the obser- 
 vation can be made without the sextant, and hence, if that 
 instrument for some reason is rendered useless, the longitude 
 may be found simply by using a smoked glass to note the 
 contact .of the sun's limb with the horizon.
 
 142 CELESTIAL NAVIGATION 
 
 SUMNER'S METHOD 
 Sumner's method consists in fixing the position of a ship at 
 sea by means of astronomical cross-bearings or by the inter- 
 section of lines of position. A line of position, also called a 
 Sumner line, is a line drawn through a calculated position at 
 right angles to the observed body. Thus, a Sumner line 
 can be obtained whenever a sight of the sun or any other 
 celestial body is taken. For instance, in the morning, when 
 measuring the sun's altitude for a time sight, the observer 
 calculates the longitude, and uses the same data for calcu- 
 lating the true azimuth (or finds the azimuth directly from 
 tables). The azimuth is, of course, the sun's true bearing 
 at the moment that the altitude is measured. He then plots 
 the position on the chart, and through the longitude thus 
 found, and the latitude used in the computation, he draws 
 a line perpendicular to the sun's true bearing or azimuth. 
 This line is his Sumner line; he is somewhere on this line, 
 provided that his chronometer is not wrong and no errors 
 have been made in measuring the altitude or in the compu- 
 tations. His exact position on that line will depend on the 
 exactness of the latitude used; but, whatever the error in 
 the latitude, whether it is 10' or 20', the navigator will 
 have the great satisfaction of knowing that his vessel is 
 on that line. Now, having one line established, a second 
 line may be had by a similar observation, when the sun 
 has changed its azimuth enough to insure a defined point 
 of intersection between the two lines. Since the position 
 of the ship must be on each and both of these lines, it is 
 evident that its exact position must be at their point of 
 intersection. If, therefore, one observation for time sight 
 is made early in the morning and another some time later, 
 when the bearing of the sun has changed at least two points, 
 two Sumner lines are obtained whose point of intersection 
 will be the position of the ship, unless the ship has not moved 
 in the interval between the observations. But in case the 
 ship has changed its position in the interval, which is more 
 likely, the first Sumner line is carried forwards, parallel 
 to itself, according to the course and distance run, when 
 its intersection with the second Sumner line will be the
 
 CELESTIAL NAVIGATION 143 
 
 position of the ship at the time the second observation is 
 made. 
 
 This, in brief, is the whole theory of Sumner's method. 
 The- various forms of its utiUty in navigation is practically 
 unlimited, especially in approaching or navigating along 
 a coast line, when a Sumner line in combination with, for 
 instance, a chain of sounding or a single bearing of a distant 
 light, or other known object, will accurately fix the position 
 of a ship. (See Nautical Astronotry, Part 4, I. C. S. Ocean 
 Navigation Course.) It should be remembered that a 
 Sumner line may be had from any kind of observation, 
 whether it be for latitude or for longitude, provided that 
 the true bearing of the observed object is noted at instance 
 of measuring the altitude. Thus the Sumner line result- 
 ing from a meridian altitude of the sun will run true east 
 or west, and may be combined with a second line obtained 
 by a time sight taken 2 or 3 hr. later, or 2 or 3 hr. before 
 noon. Probably the most valuable Sumner line obtainable 
 is that from a star or planet at morning twilight crossed 
 by a subsequent line obtained from the sun; or one from 
 the sun in the latter part of the afternoon crossed by a sub- 
 sequent line from a star or planet at evening twilight. The 
 star or planet selected should, in each case, be situated so 
 that the resulting line will cross the line obtained from the 
 sun at right angles, or nearly so, in order to establish a good 
 point of intersection. 
 
 It is evident that if the bearing of the object is taken by 
 compass in order to get the true bearing, allowance must 
 be made for variation and deviation due to the direction of 
 the ship's head when observing. 
 
 In connection with th€ plotting of Sumner lines be careful 
 not to soil or deface the chart. If a regular chart is used, 
 draw very light pencil lines and avoid the common practice 
 of using the dividers in such manner as to punch holes at 
 every step. A good idea is not to use the chart for this 
 purpose at all. Simply construct a chart on a suitable 
 sheet of paper and on a sufficiently large scale according to 
 directions given on page 105. This will give more satisfac- 
 tion and will save the regular chart from being worn out too
 
 144 CELESTIAL NAVIGATION 
 
 soon. In fact, it is not always possible to plot lines on a 
 chart of small scale, and, moreover, a navigator may not 
 always have at his command sufficient table space to spread 
 out a good-sized chart. 
 
 Illustration. — Suppose that a time sight of the sun is taken 
 in the morning and that the resulting long, is 46° 50' W; 
 the lat., by dead reckoning is somewhat uncertain, but is 
 assumed to be 50° 45 N, and this value is therefore used 
 in computing the hour angle. At instance of observation, 
 the sun's true bearing was S 75° E, and hence the resulting 
 Sumner line runs N 15° E and S 15° W. This line a h, in 
 the appended diagram, is now laid down on the chart through 
 the position found and at right angles to the true bearing 
 of the sun. The ship's position is now somewhere on this 
 line, but on account of the uncertainty of the latitude used, 
 we cannot tell exactly where until a second line is established. 
 After making a run W S W 60 mi. another sight is taken, 
 and the position thus found is in lat. 50° 28' N and long. 
 48° 25' W. The true bearing of the sun at the second sight 
 is S 8° E, and hence the resulting Sumner line c d runs 
 S 82° W and N 82° E. In order to find the trxie position, we 
 proceed as follows: From any point x on the first Sumner 
 line, lay off the course and distance run in the interval 
 between sights, in this case W S W 60 mi., and at the extrem- 
 ity y of this line draw a h' parallel to the first Sumner line, 
 so that it will intersect c d, the second Sumner line. The 
 point z where a b' crosses c d will be the true position of 
 the ship at time of taking the second sight, its lat. and 
 long, being, respectively, 50° 29' N and 48° 15' W, To find 
 the true position of the ship at time of the first sight, we 
 draw a line from c, toward a h parallel to x y, the course 
 run; the point o where this line intersects a b was the position 
 of the ship at first observation. By inspection of the chart, 
 it will be noticed that the latitude assumed and used in the 
 first sight was nearly 8 miles in error
 
 CELESTIAL NAVIGATION 
 
 145 
 
 
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 146 
 
 SAILIXG DISTANCES 
 
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 00 ■>»' S! I- CO 
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 sBa9n«H a<i«0 « « »= » n. j 
 
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 SAILING DISTANCES 
 
 147 
 
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 ; f r; r< -c 00 
 
 I00dJ9AI1 
 
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 o;o«oxoino 
 
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 asr-tsu-j-ise-^c'dftt-xtfjt-aj
 
 ADDITIONAL SAILING DISTANCES, IN NAUTICAL MILES, 
 
 BETWEEN THE MOST FREQUENTED PORTS OF 
 
 THE WORLD 
 
 Bermudas to Nassau 
 
 Boston to Halifax 
 
 Boston to Liverpool (via Halifax) 
 
 Cape Bonavista to Cape Spear 
 
 Cape Spear to Cape Race 
 
 Cape Race to Liverpool 
 
 Cape Race to Halifax 
 
 Cape Race to Boston 
 
 Cape Race to New York 
 
 Cape Race to Philadelphia 
 
 Cape Race to Cape Pine 
 
 Colon to St. Thomas 
 
 Halifax to Liverpool 
 
 Honolulu to Apia 
 
 Honolulu to Dutch Harbor 
 
 Honolulu to Hong Kong '. . . 
 
 Honolulu to Numed 
 
 Honolulu to Panama 
 
 Honolulu to San Diego 
 
 Honolulu to San Francisco 
 
 Honolulu to Tahiti 
 
 Honolulu to Valparaiso 
 
 Honolulu to Vancouver 
 
 Honolulu to Wellington 
 
 Manila to Hong Kong 
 
 New Orleans to Colon . . 
 
 New Orleans to Havana 
 
 New Orleans to Minatitlan 
 
 New York to Barbados 
 
 New York to Colon 
 
 New York to Gibraltar 
 
 New York to Havre 
 
 New York to Bremerhaven 
 
 New York to Liverpool 
 
 New York to London 
 
 New York to Havana 
 
 New York to Panama (via Cape Horn) 
 
 New York to Pernambuco 
 
 New York to San Juan, Porto Rico. . . 
 
 New York to Minatitlan 
 
 New York to St. Thomas 
 
 New York to St. Vincent 
 
 • In<lloatc§ distance along the great-circle track.
 
 ADDITIONAL SAILING DISTANCES, IN NAUTICAL MILES, 
 BETWEEN THE MOST FREQUENTED PORTS OF 
 THE WORLD— {Continued) 
 
 Panama to Acapulco 
 
 Panama to David Chiriqui 
 
 Panama to Gulf of Fonseca 
 
 Panama to Manzanilla 
 
 Panama to Monterey 
 
 Panama to Punta Arenas 
 
 Panama to San Diego 
 
 Panama to Wellington 
 
 Quebec to Liverpool 
 
 Quebec to Plymouth 
 
 San Francisco to Apia 
 
 San Francisco to Acapulco 
 
 San Francisco to Columbia River Bar 
 
 San Francisco to Dutch Harbor 
 
 San Francisco to Honolulu 
 
 San Francisco to Humboldt 
 
 San Francisco to Manzanilla 
 
 San Francisco to Panama 
 
 San Francisco to Portland 
 
 San Francisco to Port Townsend 
 
 San Francisco to San Diego 
 
 San Francisco to San Juan del Sud. . . 
 
 San Francisco to Tahiti 
 
 San Francisco to Vancouver 
 
 San Francisco to Valparaiso 
 
 San Francisco to Yokohama 
 
 San Francisco to Victoria 
 
 St. Johns, N. F., to Quebec 
 
 St. Johns, N. F., to Boston 
 
 St. Johns, N. F., to Bristol 
 
 St. Johns, N. F., to Cape Bona vista. . 
 
 St. Johns, N. F., to Cape Spear 
 
 St. Johns, N. F., to Cape Race 
 
 St. Johns, N. F., to Galway 
 
 St. Johns, N. F., to Greenock 
 
 St. Tohns, N. F., to Liverpool 
 
 St. Johns, N. F., to St. Peter's Light. 
 
 Yokohama to Apia 
 
 Yokohama to Honolulu 
 
 Yokohama to Sydney 
 
 Yokohama to Vancouver 
 
 • Indicates distance along the great-circle track.
 
 150 UNITED STATES NAVY 
 
 UNITED STATES NAVY 
 
 ORGANIZATION OF THE NAVY 
 
 Administrative Bureaus. — By the Constitution of the 
 United States, the President is Commander-in-Chief of the 
 Navy, but in practice most of the administrative details 
 are left to the Secretary of the Navy, who is assisted by an 
 Assistant Secretary and by the chiefs of eight Bureaus, 
 between Which the work of the Navy Department is divided. 
 These Bureaus are: The Bureau of Yards and Docks, the 
 Bureau of Equipment, the Bureau of Navigation, the 
 Bureau of Ordnance, the Bureau of Construction and 
 Repair, the Bureau of Steam Engineering, the Bureau of 
 Supplies and Accounts, the Bureau of Medicine and Surgery. 
 
 In a general way, the above titles are descriptive of the 
 duties of the Bureaus, except in the case of the Bureau of 
 Navigation, which would be more accurately described as 
 the Bureau of Personnel, since it has nothing whatever to 
 do with navigation and has everything to do with the 
 enlistment and training of men, the assignment of officers 
 and crew to stations afloat and ashore, and, broadly speak- 
 ing, with all matters of organization, drill, and discipline. 
 
 A Chief of Bureau, while serving in that capacity, has the 
 rank and pay of a rear-admiral, no matter what his actual 
 rank may be on the Navy List. 
 
 Navy Yards. — Each navy yard is under the command of 
 a Commandant, who is either a rear-admiral or a captain; 
 but each of the Navy Department Bureaus has its repre- 
 sentative in charge of its own work at the yard, and main- 
 tains an intimate oversight and control of all such work. 
 
 The present navy yards are at Portsmouth, N. H.; Boston, 
 Mass.; Brooklyn, N. Y.; Philadelphia, Pa.; Norfolk, Va.; 
 Pensacola Fla.; Mare Island, Cal.; and Bremerton, Wash. 
 There are, also, naval stations at Newport, R. I.; New 
 London, Conn.; Washington, D. C. ; Port Royal and Charles- 
 ton, S. C. ; Key West, Fla.; Algiers, La.; San Francisco and 
 San Diego, Cal.
 
 UNITED STATES NAVY 151 
 
 Training stations for enlisted men are maintained at 
 Newport, R. I., Norfolk, Va., and San Francisco, Cal., and 
 an appropriation has been made for establishing one in the 
 Great Lakes. 
 
 Officers. — The officers of the Navy are divided into Line 
 officers and Staff officers; the Staff corps including medical 
 officers, pay officers, and chaplains, as sea-going officers; 
 and naval constructofs, civil engineers, and professors of 
 mathematics for service on shore only. 
 
 The grades in the Line, with the grades to which they 
 
 correspond in the Army, are as follows: 
 
 Admiral General 
 
 Vice-Admiral Lieutenant -General 
 
 T^ A 1 • 1 f Major-General 
 
 Rear- Admiral \ t, ■ ■,■ r- , 
 
 I Brigadier-General 
 
 Captain Colonel 
 
 Commander Lieutenant-Colonel 
 
 Lieutenant-Commander Major 
 
 Lieutenant Captain 
 
 Lieutenant, junior grade First Lieutenant 
 
 Ensign Second Lieutenant 
 
 Midshipman Cadet 
 
 Chief Boatswain Second Lieutenant 
 
 Chief Gunners Second Lieutenant 
 
 Chief Carpenters (are staff offi- 
 cers) Second Lieutenant 
 
 Chief Sailmakers (are staff offi- 
 cers) Second Lieutenant 
 
 The grades in the staff corps, with corresponding rank in 
 the Line, are as follows: 
 
 Medical Corps 
 
 Medical Directors With rank of Captain 
 
 Medical Inspectors With rank of Commander 
 
 Surgeons With rank of Lieutenant- 
 Commander 
 Passed Assistant Sur- 
 geons With rank of Lieutenant 
 
 Assistant Surgeon With rank of Lieutenant 
 
 junior grade
 
 152 UNITED STATES NAVY 
 
 Pay Corps 
 
 Pay Directors With rank of Captain 
 
 Pay Inspectors With rank of Commander 
 
 Paymasters With rank of Lieutenant- 
 Commander and Lieutenant 
 Passed Assistant Pay- With rank of Lieutenant, 
 masters junior grade 
 
 Assistant Paymaster With rank of Ensign 
 
 Chaplain With rank of Captain, Commander, 
 
 or Lieutenant 
 Professors of Mathe- f With rank of Captain, Commander, 
 
 mattes \ or Lieutenant 
 
 Naval Constructors and f With rank of Captain, Commander, 
 Assistant Naval Con-< Lieutenant, or Lieutenant, junior 
 
 structors L grade 
 
 Civil Engineers and f With rank of Captain, Commander, 
 Assistant Civil Engi-< Lieutenant, or Lieutenant, junior 
 
 neers I grade 
 
 The Warrant officers are the following: Boatswains, 
 gunners, carpenters, sailmakers, pharmacists, warrant 
 machinists. 
 
 Mates are officers, but have neither commissions nor 
 warrants. 
 
 The numbers of Line officers allowed by law in the different 
 grades are as follows: Admiral, 1; vice-admiral, — ; rear- 
 admirals, 18; captains, 70; commanders, 112; lieutenant- 
 commanders, 186; lieutenants, 324. In the grades below 
 lieutenant, the number is not at present limited by law. 
 
 Titles of OflBcers. — In conversation, admirals and captains 
 are addressed by their titles. A commander may be properly 
 addressed by his title, or as Captain. And any officer who 
 is actually in command of a ship is by courtesy addressed 
 as captain. All other Line officers are addressed as Mister. 
 Medical officers are commonly addressed as Doctor, but it is 
 not unusual to address a medical director, medical inspector, 
 or surgeon by his ranking title. Similarly, pay officers of high 
 rank are commonly addressed by their ranking titles, but those 
 below the actual rank of paymaster are called Paymaster.
 
 UNITED STATES NAVY 153 
 
 Insignia of Naval OflBcers. — The insignia of the various 
 grades are of two kinds, the first consisting of a device worn 
 on the collar, the shoulder strap, or the epaulet; the second, 
 of an arrangement of stripes on the sleeve. 
 
 The device for the collar or shoulder consists of two 
 parts, one indicating the branch of the service to which 
 the wearer belongs, the other, his rank in that branch. 
 
 Line officers wear a silver foul anchor. 
 
 Medical officers wear a gold oak leaf on which is embroid- 
 ered a silver acorn. 
 
 Pay officers wear a silver oak sprig. 
 
 Naval constructors wear a gold sprig of two live oak 
 leaves and "a silver acorn. 
 
 Professors wear a silver oak leaf and an acorn. 
 
 Civil engineers wear the letters C. E. in silver. 
 
 Chaplains wear a silver cross. 
 
 The insignia of rank in the Line and the various Staff 
 corps are as follows. These are worn in connection with 
 the preceding Corps marks. 
 
 Admiral Four silver stars 
 
 Rear- Admiral Two silver stars 
 
 Captain A silver spread eagle 
 
 Commander A silver oak leaf 
 
 Lieutenant-Commander.. . .A gold oak leaf 
 
 Lieutenant Two silver bars 
 
 Lieutenant, junior grade. . .One silver bar 
 
 Ensign A silver foul anchor 
 
 Midshipman A gold foul anchor 
 
 Chief Boatswain Two silver foul anchors crossed 
 
 Chief Gunners A flaming spherical shell in silver 
 
 Chief Carpenter A charm of silver 
 
 Chief Sailmaker A diamond in silver 
 
 The rank and corps are furtHer indicated by stripes on 
 the sleeves, as follows: 
 
 Admiral • Two stripes of 2-in. gold lace with 
 
 one stripe of 1-in. lace between 
 
 Rear-Admiral One stripe of 2-in. gold lace with 
 
 one stripe of ^-in. lace above 
 Captain Four stripes of ^-in. gold lace
 
 154 UNITED STATES NAVY 
 
 Commander Three .stripes of i-in. gold lace 
 
 Lieutenant-Commander. . .Two stripes of i-in. gold lace with 
 one stripe of J-in. lace between 
 
 Lieutenant Two stripes of ^-in. gold lace 
 
 Lieutenant, junior grade. .One stripe of -J-in. gold lace with 
 one stripe of J-in. lace above 
 
 Ensign One stripe of ^-in. gold lace 
 
 Midshipman One stripe of J-in. gold lace 
 
 All Line officers wear a gold star on the sleeve above 
 the stripes. 
 
 For Staff officers the stripes are the same as for Line 
 officers of corresponding grades, except that; first, staff 
 officers do not wear a star; and, second, each staff corps is 
 distinguished by colored cloth worn between the gold stripes, 
 thus, medical officers wear dark maroon; pay officers, white; 
 naval constructors, dark violet; professors, olive green; 
 civil engineers, light blue. In the case of chaplains, the 
 gold stripes on the sleeves are replaced by black. 
 
 Chief boatswains, chief gunners, chief carpenters, and 
 chief sailmakers wear one stripe of gold lace interrupted at 
 intervals of 2 in. by a break of i in. filled in with blue silk. 
 
 ENLISTMENT, CLASSIFICATION, AND PAY OF ENLISTED 
 MEN IN THE UNITED STATES NAVY 
 Recruiting Stations. — Men are enlisted at the following 
 recruiting stations and receiving ships" United States 
 Recruiting Station, 87 South Street, New York, N. Y.; 
 United States Recruiting Station, 22 Hanover Street, Boston, 
 Mass.; United States Recruiting Station, 1319 Market 
 Street, Philadelphia, Pa.; United States Recruiting Station, 
 207 North Calvert Street, Baltimore, Md. ; Seamen's Quarters, 
 U. S. Navy Yard, Washington, D. C; United States Recruit- 
 ing Station, Masonic Temple, Chicago, 111.; Receiving ship 
 Wabash, Navy Yard, Boston, Mass.; Receiving ship Hancock, 
 Navy Yard, New York, N. Y.; Receiving ship Lancaster, 
 Navy Yard, League Island, Pa.; Receiving ship Franklin: 
 Navy Yard, Norfolk, Va. ; Receiving ship Independence, Navy 
 Yard, Mare Island, Cal.; U. S. Navy Yard, Bremerton, 
 Wash.; U. S. Naval Recruiting Station, San Francisco, Cal.;
 
 UNITED STATES NAVY 155 
 
 U. S. Navy Yard, Pensacola, Fla.; U. S. Navy Yard, Ports- 
 mouth, N. H.; U. S. Naval Station, Port Royal, S. C; U. *S. 
 Naval Recruiting Station, Prudential Building, Buffalo, 
 N. Y.; also at any traveling recruiting station, information 
 regarding which will be furnished on application to the 
 Bureau of Navigation, Navy Department, Washington, D. C. 
 
 Applicants for enlistment in the United States Navy must 
 be over 18 years of age, of American citizenship and capable 
 of reading and writing English. The term of enlistment is 
 4 years, but no person will be accepted until he has passed 
 the medical examination prescribed by the regulations. 
 
 No minor under the age of 18 years will be accepted with- 
 out the consent of parent or guardian, and any such minor 
 claiming to be more than 18 years of age, in order to secure 
 enlistment, is liable to punishment. 
 
 Caution. — Applicants residing at. a distance should, in 
 all cases, communicate with the nearest recruiting station 
 for a list of qualifications before reporting for examination, 
 and on receipt of same should consult a physician and 
 ascertain the probabilities of their being able to conform 
 to the requirements. If favorably advised, the recruiting 
 office should be immediately informed, and request made 
 that the applicant's name be entered on the list to be noti- 
 fied, after which complete instructions will be given as t6 
 the proper time to report for examination. This course is 
 suggested, as no allowance is made for traveling expenses 
 of applicants, and they should be as certain as possible of 
 their ability to pass the examination before incurring any 
 expense. 
 
 Transportation is furnished only to accepted applicants 
 from the recruiting station to the point of assignment. 
 
 Age Limits. — First enlistment may be made in the follow- 
 ing ratings of men within the limits of age indicated in 
 Table following.
 
 156 
 
 UNITED STATES NAVY 
 
 Rating 
 
 Seamen 
 
 Ordinary seamen 
 
 Landsmen 
 
 Shipwrights 
 
 Blacksmiths 
 
 Plumbers and fitters 
 
 Machinists, first class 
 
 Machinists, second class 
 
 Sailmakers' mates 
 
 Electricians, third class 
 
 Boilermakers 
 
 Coppersmiths 
 
 Firemen, first class 
 
 Firemen, second class 
 
 Landsmen, for yeomen 
 
 Coal passers 
 
 Hospital stewards 
 
 Hospital apprentices, first class 
 
 Hospital apprentices 
 
 Officers' stewards 
 
 Officers' cooks 
 
 Mess attendants 
 
 Ships' cooks, fourth class 
 
 Musicians, first class 
 
 Musicians, second class 
 
 Buglers 
 
 Painters 
 
 Bakers, second class 
 
 Shipfitters, first class 
 
 Shipfitters, second class 
 
 Years 
 
 of Age 
 
 21 to 35 
 
 18 to 30 
 
 18 to 25 
 
 21 to 35 
 
 21 to 35 
 
 21 to 35 
 
 21 to 35 
 
 21 to 35 
 
 21 to 35 
 
 21 to 35 
 
 21 to 35 
 
 21 to 35 
 
 21 to 35 
 
 21 to 35 
 
 18 to 25 
 
 21 to 35 
 
 21 to 30 
 
 21 to 28 
 
 18 to 25 
 
 21 to 35 
 
 21 to 35 
 
 18 to 30 
 
 18 to 30 
 
 21 to 35 
 
 21 to 35 
 
 21 to 35 
 
 21 to 35 
 
 21 to 35 
 
 21 to 35 
 
 21 to 35 
 
 Ratings and Monthly Pay. — In the following table are 
 given the monthly pay for the various ratings in the Navy: 
 
 SEAMEN BRANCH 
 
 Chief Petty Officers: 
 
 Chief masters at arms $65 
 
 Chief boatswains' mates 50 
 
 Chief gunners' mates 50 
 
 Chief gun captains 50 
 
 Chief turret captains 60 
 
 Chief quartermasters 50 
 
 Petty Officers, First Class: 
 
 Masters at arms, first class $40 
 
 Boatswains' mates, first class 40 
 
 Gunners' mates, first class ; 40
 
 UNITED STATES NAVY 157 
 
 Gun captains, first class $40 
 
 Turret captains, first class 50 
 
 Quartermasters, first class 40 
 
 Petty Officers, Second Class: 
 
 Masters at arms, second class $35 
 
 Boatswains' mates, second class 35 
 
 Gunners' mates, second class 35 
 
 Gun captains, second class 35 
 
 Quartermasters, second class 35 
 
 Petty Officers, Third Class: 
 
 Masters at arms, third class $30 
 
 Coxswains 30 
 
 Gunners' mates, third class 30 
 
 Quartermasters, third class 30 
 
 Seamen, First Class: 
 
 Seamen gunners $26 
 
 Seamen 24 
 
 Apprentices, first class 21 
 
 Seamen, Second Class: 
 
 Ordinary seamen $19 
 
 Apprentices, second class 15 
 
 Seamen, Third Class: 
 
 Landsmen $16 
 
 Apprentices, third class 9 
 
 ARTIFICER BRANCH 
 
 Chief Petty Officers: 
 
 Chief machinists $70 
 
 Chief electricians 60 
 
 Chief carpenters' mates 50 
 
 Chief water tenders 50 
 
 Petty Officers, First Class: 
 
 Boilermakers $65 
 
 Machinists, first class 55 
 
 Coppersmiths 55 
 
 Shipfitters, first class 55 
 
 Electricians, first class 50 
 
 Blacksmiths 50 
 
 Plumbers and fitters 45 
 
 Sailmakers' mates 40 
 
 Carpenters' mates, first class 40 
 
 Water tenders 40 
 
 Painters, first class 40 
 
 Petty Officers, Second Class: 
 
 Machinists, second class $40 
 
 Electricians, second class 40 
 
 Shipfitters, second class 40 
 
 Oilers 37 
 
 Carpenter's mates, second class 35 
 
 Printers 35 
 
 Painters, second class 35
 
 15S UNITED STATES NAVY 
 
 Petty Officers. Third Class: 
 
 Electricians, third class : $30 
 
 Carpenters' mates, third class 30 
 
 Painters, third class 30 
 
 Seamen, First Class: 
 
 Firemen, first class S3o 
 
 Seamen, Second Class: 
 
 Firemen, second class $30 
 
 Shipwrights / 25 
 
 Seamen, Third Class: 
 
 Coal passers $22 
 
 SPECIAL BRANCH 
 
 Chief Petty Officers: 
 
 Chief commissary steward $70 
 
 Chief yeoman 60 
 
 Hospital stewards 60 
 
 Bandmasters 52 
 
 Commissary steward 60 
 
 Petty Officers, First Class: 
 
 Yeoman, first class $40 
 
 First musicians 36 
 
 Petty Officers, Second Class: 
 
 Yeoman, second class $35 
 
 Petty Officers, Third Class: 
 
 Yeomen, third class $30 
 
 Hospital apprentices, first class 30 
 
 Seamen, First Class: 
 
 Musicians first class $32 
 
 Seamen, Second Class: 
 
 Musicians, second class $30 
 
 Buglers 30 
 
 Hospital apprentices 20 
 
 MESSMEN BRANCH 
 
 Stewards to commanders in chief $60 
 
 Cooks to commanders in chief 50 
 
 Stewards to commandants 60 
 
 Cooks to commandants 50 
 
 Cabin stewards 50 
 
 Cabin cooks 45 
 
 Wardroom stewards 50 
 
 Wardroom cooks 45 
 
 Steerage stewards 35 
 
 Steerage cooks 30 
 
 Warrant officers' stewards 35 
 
 Warrant ofl^cers' cooks 30 
 
 Ship's cooks, first class 55 
 
 Ship's cooks, second class 40 
 
 Ship's cooks, third class 30 
 
 Ship's cooks, fourth class 25
 
 UNITED STATES NAVY 159 
 
 Bakers, first class %Ab 
 
 Bakers, second class 35 
 
 Mess attendants, first class 24 
 
 Mess attendants, second class 20 
 
 Mess attendants, third class 16 
 
 Special Pay and Privileges. — Every enlisted man and 
 apprentice who has been rated a seaman gunner, or holds 
 a gun captain's certificate, or a certificate of graduation 
 from one or more classes of the Petty Officers' School of 
 Instruction, receives S2 a mo. in addition to the pay of 
 his rating for each such certificate. 
 
 Each enlisted man of the Xavy receives 75 ct. per mo. in 
 addition to the pay of his rating for each rating, for each 
 good-conduct medal, pin, or bar which he may be awarded. 
 
 Coxswains detailed as coxwains of boats propelled by 
 machinery, or as coxswains to commanders in chief, receive 
 $5 per mo. in addition to their pay. 
 
 All enlisted men of the Navy receive $5 per mo. in 
 addition to their pay while serving on board of submarine 
 vessels of the Navy. 
 
 Seamen in charge of holds receive S5 per mo. in 
 addition to their pay. 
 
 Landsmen assigned to duty as jacks-of-the-dust, or as 
 lamplighters, receive $5 per mo. in addition to their pay. 
 
 Enlisted men detailed as crew messmen while so acting, 
 except when assigned as reliefs during the temporary 
 absence of the regular crew messmen, receive extra com- 
 pensation at the rate of So per mo. 
 
 Enlisted men of the naval ser\ace regularly detailed as 
 signalmen receive the following extra compensation in 
 addition to the monthly pay of their rating: Signalmen, 
 first class, $3; signalmen, second class, $2; signalmen, third 
 class, $1. 
 
 All enlisted men of the navy, after having qualified as 
 gun pointers, and who are regularly detailed as gun 
 pointers by the commanding officer of the vessel, receive 
 monthly, in addition to the pay of their respective ratings, 
 extra pay as follows: Heavy gun pointers of the first class, 
 SlO: heavy gun pointers of the second class $6; inter- 
 mediate gun pointers of the first class, $8; intermediate
 
 160 UNITED STATES NAVY 
 
 gun pointers of the second class, $4; secondary gun pointers 
 of the first class, $4; secondary gun pointers of the second 
 class, $2. 
 
 Enlisted men of the Navy regularly detailed by the com- 
 manding officer of a vessel as gun captains, except of second- 
 ary batlery guns, receive, in addition to the pay of their 
 respective ratings, $5 per mo., which in the case of men hold- 
 ing certificates as gun captains, or of graduation from the 
 gun captain class. Petty Officers' School, shall include the $2 
 per mo. to which such certificate entitles them. 
 
 Additional Rewards. — The pay of the various grades may 
 not seem large, but it must be remembered that it is nearly 
 all clear. The ship constitutes a comfortable home and the 
 government supplies an excellent ration. An outfit of cloth- 
 ing is issued free at the beginning of an enlistment. 
 Medical and hospital attendance are free. Thus, the only 
 real demand on the pay is for keeping up the outfit of 
 clothing. Men can and do save very large sums of money, 
 and these sums they have the privilege of depositing with 
 the government, which allows interest at the rate of 4% 
 compounded. There are, moreover, many additions to the 
 pay for special details of duty and special excellencies of 
 various kinds. A man distinguished in marksmanship and 
 serving as pointer of a turret gun receives $10 per mo. in 
 .addition to his regular pay. An expert signalman gets $5 
 additional; and so with many other cases, as indicated in the 
 pages that follow. 
 
 A man having served one term of enlistment and having 
 been honorably discharged, if he reenlists within 4 mo., 
 receives a bonus of 4 mo. pay. This amounts in the higher 
 ratings to as much as $280. Moreover, for each reenlistment 
 his monthly pay is slightly increased. 
 
 In case of disability from illness or accident, not only is 
 a man fully cared for without charge but his full pay goes 
 on, no matter how long the disability may continue; and 
 in the case of permanent disability resulting from causes 
 incident to the service, he receives a pension for life, pro- 
 vided that lie has served 10 yr. Even though he may be 
 in perfect health, lie has the privilege on reaching 50 yr.
 
 UNITED STATES NAVY 161 
 
 of age, provided that he has served for 30 yr., of being 
 placed on. the retired list for the remainder of his life with 
 three-quarters of the full pay of his grade. If he is a chief 
 petty officer, and any reasonably deserving man would 
 surely be this after 30 yr. service, this retired pay is $52.50 
 per mo., and for this he is not called upon to make any 
 return whatever. 
 
 Although, in general, a man must expect in the Navy, as 
 elsewhere, to begin at the bottom and work his way up, 
 there are many well-paid positions for which competent men 
 are enlisted directly. Thus, a man who is already a com- 
 petent seaman is gladly taken in as such, and, owing to 
 the great demand for coxswains, quartermasters, etc., he 
 may reasonably expect almost immediate advancement to 
 one of these ratings. So, in the artificer branch, a man who 
 is qualified for machinist, water tender, fireman, boilermaker, 
 electrician, plumber, painter, etc. is enlisted directly as such. 
 
 Naval Apprentices. — Boys between the age of 17 and 18 yr. 
 may, with the consent of their parents or guardians, be 
 enlisted to serve as apprentices in the Navy until they 
 reach the age of 21 yr. They are trained to fill the positions 
 of seamen, petty officers, and warrant officers, and from 
 these positions they can be advanced to be commissioned 
 officers in the Navy. Their pay as apprentices begins at 
 $9 per mo and increases to $21. 
 
 BRIEF OUTLINE OF DUTIES 
 Master at Arms. — The chief master at arms is the chief of 
 police of the ship. He has from one to three or four assist- 
 ants, according to the size of the ship. It is the duty of 
 these men to suppress disorder, to arrest offenders where 
 physical restraint is needed, and to confine any one .if ordered 
 to do so by proper authority. They have charge of the 
 cleanliness of the ship on the lower decks and are responsible 
 for the eating arrangements of the men, so far as regards 
 the condition of the tables and the table service. The 
 actual preparation of the food is in charge of the ship's 
 cooks, under the supervision of the commissary steward; 
 but the food is served by the berth-deck cooks, or crew
 
 162 UNITED STATES NAVY 
 
 messmen, and these messmen are subject to the direction 
 of the master at arms. 
 
 Boatswain's Mates. — The boatswain's mates are the 
 assistants to the officer of the deck in carrying on the work 
 of the ship. All orders given are repeated by them, and 
 they are expected to make sure, not only that the orders 
 are heard in all parts of the ship, but that they are obeyed. 
 If a boat is to be hoisted, they "pass the word" and then 
 make sure that the boat is properly hooked on, that the 
 deck force "man the falls," and that the boat is safely 
 hoisted and secured. They bear much the same relation 
 to affairs on the upper deck that the masters at arms bear 
 to those on the lower decks, except that, while they are 
 expected to maintain order, they have none of the police 
 functions that belong to the masters at arms. They call 
 attention by blowing a silver whistle, or boatswain's call. 
 
 Coxswains. — Coxswains have charge of boats, their outfits 
 and their crews. When a boat is absent from the ship 
 without an officer, the authority of the coxswain is absolute. 
 
 Machinists. — Machinists, when on duty, have charge of 
 the engine room and fire-room, have full authority there 
 and full responsibility for work and discipline. Thus, the 
 masters at arms, boatswain's mates, coxswains, and machin- 
 ists are directly charged with responsibility for the main- 
 tenance of discipline, and their orders are entitled to the 
 same weight as those of commissioned officers. Other 
 petty officers have no such general authority as this, though 
 many of them may be placed in positions of authority by 
 reason of special detail. An oiler or a fireman, for example, 
 may do a machinist's duty in the engine room; a gunner's 
 mate may be sent in charge of a party to bring off ammu- 
 nition, etc. 
 
 Quartermasters. — The quartermasters have charge of the 
 steering of the ship and everything connected with it, of 
 the making and reading of signals, and of the hourly record 
 of weather, etc. as entered in the ship's log. In port, they 
 stand watch on the bridge and are responsible for the 
 "lookout," reporting to the officer of the deck everything 
 of importance that goes on within sight of the ship.
 
 UNITED STATES NAVY 163 
 
 Yeomen. — Yeomen are writers or accountants; their 
 duties are purely clerical. One yeoman is usually allowed 
 for the commanding officers, two for the executive officer, 
 one for the engineer's department, one for the navigator, 
 and two or more for the pay department. 
 
 Commissary Steward. — The commissary steward has 
 charge of the purchase and preparation of provisions for 
 the men's messes. 
 
 The duties of other petty officers and rated men are 
 indicated with sufficient exactness by their titles. 
 
 PROMOTION OF ENLISTED MEN TO OFFICERS 
 
 Mates. — These are officers, although not commissioned, 
 their salary being S900 a yr. 
 
 "As a reward for long and faithful service in the navy, 
 the Department will in the future appoint ten mates annually 
 from the enlisted men of the service, appointments to be 
 made on or about July 1 of each year. No man will be 
 appointed who is not recommended for appointment by his 
 commanding officer and who does not come within the 
 following provisions: He must be a chief petty officer of 
 the seaman branch, at least 35 yr. of age, serving under 
 continuous service, who ^as had 15 yr. service in a sea- 
 going ship, with an average of 85% taken from all his 
 enlistment records, and there must be on file in the Bureau 
 of Navigation letters of recommendation from his command- 
 ing officers." 
 
 Warrant Officers. — Warrant officers rank next below 
 commissioned officers in the service; they are officers in 
 every sense of the word. Enlisted men who serve contin- 
 uously and reach the grade of chief petty officer or first- 
 class petty officer are eligible for appointment as warrant 
 officers. The warrant officers are boatswains, gunners, 
 carpenters, sailmakers, warrant machinists, and pharma- 
 cists. The pay of a warrant officer is from $1,200 to $1,800 
 a yr., and he may retire at 62 yr. of age on three-quarter pay. 
 
 Commissioned Officers. — Warrant officers after 10 yr. 
 service are given a commission and rank with ensigns of 
 the Line. A warrant officer who can pass the requisite
 
 164 UNITED STATES NAVY " 
 
 examination may be regularly commissioned as an ensign 
 in the Line of the Navy and advance through all the grades 
 of the service up to admiral, exactly as if he had graduated 
 at the Naval Academy. A number of such appointments 
 have already been made, the majority of appointees being 
 I. C. S. nautical students. 
 
 Educational Facilities in the Navy. — The earnestness with 
 which the Navy endeavors to help those who wish to fit 
 themselves for advancement in the service is evidenced by 
 the following statement of facilities provided for the purpose : 
 
 Elaborately equipped training stations for apprentices are 
 maintained at Newport. R. I., and San Francisco, Cal., where 
 from 1,000 to 2,000 young men are kept under instruction. 
 
 Similar stations for the training of recruits other than 
 apprentices are maintained at Brooklyn, N. Y., and at 
 Norfolk. Va., and a third will shortly be established at some 
 point on the Great Lakes. 
 
 Nine large and comfortable vessels are kept in cruising 
 commission for the training afloat of recruits of all branches. 
 The cruises of these ships are varied as much as possible with 
 a view to making the duty interesting as well as instructive. 
 
 The following special schools of instruction are maintained, 
 and any man whose abilities and conduct justify the privilege 
 can take a course in one or more of them : A school for the 
 training of petty officers, at Newport; a school for the train- 
 ing of torpedo specialists, at Newport; a school for the train- 
 ing of electricians, at Brooklyn; a school for the training of 
 wireless telegraphers, at Brooklyn; a school for the training 
 of yeomen, at Brooklyn; a school for the training of gunners, 
 at Washington; a school for the training of gunners, at New- 
 port; a school for the training of cooks, at Brooklyn. 
 
 It should be explained that the cooks for whom the 
 cooking school exists are those who cook for the enlisted 
 men, not for the officers. The attention that is given to 
 the question of food for the men is further illustrated by 
 the fact that a board of oflficers recently spent several 
 months in studying the most desirable articles to be pro- 
 vided for the rations of the men, and that the recommenda- 
 »i,.n^ ,.f these officers have resulted in the adoption on board
 
 THE ORGANIZA TION OF A MAN OF WAR 165 
 
 United States men of war of what is unquestionably the most 
 liberal and most appetizing ration allowed by any military or 
 naval service in the world. On the large ships of the Navy, 
 cold-storage rooms are fitted which admit of carrying consid- 
 erable quantities of fresh meat and vegetables and of furnish- 
 ing cool drinking water in the tropics. Moreover, the Navy 
 Department has, within the last few years, adopted the policy 
 of keeping refrigerating ships in company with all large 
 squadrons serving on tropical waters, and these ships carry 
 abundant supplies of fresh meats and vegetables, which are 
 distributed daily to all ships within reach. 
 
 THE ORGANIZATION OF A MAN OF WAR 
 
 OFFICERS AND THEIR DUTIES 
 
 The commanding oflficer, whatever his actual rank and 
 title on the Navy List, is the captain of the ship, and as such 
 is responsible for her safety, discipline, and efficiency. He is 
 assisted by a number of subordinate officers, each of whom 
 is charged with special duties, but this does not lessen his 
 responsibility, which extends to every detail throughout the 
 ship. Even when a pilot is taken for entering and leaving 
 port, the captain cannot, as in the case of a merchant vessel, 
 relinquish his responsibility for the navigation of the ship, 
 but must regard the pilot as merely an adviser. 
 
 The discipline of the ship is, subject to the captain, in 
 the hands of a certain number of Line officers, associated 
 with whom are the Staff officers of various corps; the medical 
 officers in charge of the health, hygiene, and sanitation of 
 the ship; the pay officer, in charge of accounts, money, 
 stores, and purchases; and, on large ships, chaplains. 
 
 The line officer ne.xt in rank to the captain is the 
 executive, who may be a lieutenant-com.mander, a lieutenant, 
 or on a small ship even an ensign. He attends to the details 
 of all matters of organization and discipline, directs the drills, 
 keeps the ship in good condition, transmits the orders of the 
 captain, and sees that they are executed — hence his title. 
 
 In immediate charge of the ship at any given time, and 
 responsible for the execution of the orders of the captain
 
 1 66 THE ORG AX IZ A TION OF A MAN OF \V A R 
 
 and executive, is the officer of the deck. There are usually 
 three or four officers who take this duty in turn, "standirig 
 watch," as it is called, for 4 hr. at a time. As these officers 
 also have charge of the divisions into which the crew is 
 divided for drills and for battle, they are called watch and 
 division officers. At sea, the officer of the deck is always on 
 the bridge to see that the proper course is steered, to look out 
 for and avoid dangers, and to carry on the routine of work. 
 In port, he is on the alert to maintain order, supervise all 
 work that may be in progress, receive visiting officials, etc. 
 In his capacity as division officer, he has command of a divi- 
 sion of men to whom he stands in the relation of the captain 
 of a company in a military organization. The watch and 
 division officers are always Line officers, usually lieutenants 
 or ensigns. They are assisted in all of their duties by such 
 junior officers as may be assigned to the ships. 
 
 The navigator is usually the Line officer next in rank to the 
 executive. He assists the captain in the navigation, deter- 
 mines the position of the ship as often as may be necessary, 
 and has charge of all the instruments used for this purpi ise. 
 
 The engineer officers were formerly a corps of specialists, 
 but the Personnel Bill of 1899 merged them in the Line, 
 and under the present system a certain number of Line 
 officers are detailed for duty in charge of the engineering 
 department of the ship, the actual standing of watches in 
 charge of the engines and boilers being entrusted to machinists. 
 
 ORGANIZATION OF THE CREW 
 The crew of a ship is first of all divided into two parts, 
 V r watches, the starboard and the port. Each watch is 
 subdivided into two parts, the first and the second. Thus, 
 a man's position on board is fixed in one way by the state- 
 ment that he belongs to the first part of the starboard 
 watch, to the second part of the port watch, etc. 
 
 A more important assignment is that to a division, as 
 this not only fixes his station in battle, but indicates the 
 j>art of the ship that he assists to keep in order, and in 
 which his most important duties are localized. The arrange- 
 ment of divisions is determined largely by the arrangement
 
 THE ORGAXIZA TION OF A MAN OF WAR 167 
 
 of the battery. The first division, for example, is usually 
 composed of the men stationed at the guns on or near the 
 forecastle; or, in a turret ship, of those stationed in the for- 
 ward turret. The ship is divided into parts corresponding 
 with the guns, so that each division keeps that part of the 
 ship in the order in which its guns are situated. 
 
 In addition to the gun divisions which are designated by 
 numbers, there is the powder division which supplies ammuni- 
 tion, passing it from the magazines to the guns. This is 
 usually the largest division in the ship, and is made up 
 chiefly of men whose regular duties keep them below decks, 
 such as cooks, stewards, mess-attendants, waiters, etc. With 
 these men, however, are associated many of the leading men 
 of the ship: gunners, mates, masters-at-arms, etc., charged 
 with the safety of the magazines and with an oversight of 
 the rapid and uninterrupted supply of ammunition. 
 
 The engineers' force constitutes a division by itself, but 
 sends a detail of firemen and coal passers to assist the 
 powder division in action. 
 
 In addition to his station for routine ship's work and 
 for battle, every man of the deck force is assigned to a 
 boat in which he takes his place when that particular boat 
 is engaged either in the ordinary boating that is incident 
 to necessary communication with other ships and with 
 the shore, or in the cases where the boats take part in opera- 
 tions against an enemy. Every officer and man on the 
 ship, moreover, has his station in a boat for abandoning 
 ship, in the event of collision or wreck. 
 
 In every ship, there is an organization of the crew as a 
 military force of infantry and field artillery for operations 
 on shore in case the occasion arises for landing such a force. 
 Hardly a year passes without the necessity for operations 
 of this kind in some part of the world. 
 
 Drilling. — Each dixnsion on the ship has its specified duties 
 in the case of fire, and -each man in the division knows his 
 station, whether this be to lead out a hose, to flood a maga- 
 zine with water, to close certain water-tight doors so that the 
 fire shall not spread, or to close air ports or hatches to prevent 
 a draft from fanning the flames; and all these duties become
 
 1 68 THE ORGANIZA TION OF A MAN OF WAR 
 
 so familiar by frequent drills that an actual fire on board 
 a man of war is rarely accompanied by any indication of 
 excitement, even though it may be near the magazine. 
 Similarly in case of collision; every man knows his station, 
 whether it be to get the collision mat over the side in hope 
 of stopping a leak, to close the water-tight doors, to start 
 the wrecking pump, or only to fall in ranks with his divi- 
 sion and keep silence while awaiting instructions. Natur- 
 ally, the most important drill of all is the battle drill, or, as 
 it is called, general quarters; and when the call for this is 
 sounded, whether at the regular morning hour for drill or 
 unexpectedly in the middle of the night, every man makes 
 his way quickly and silently to his station, the magazines 
 are opened and ammunition rushed to the guns; the guns 
 are loaded and swung until they bear upon the enemy, 
 either real or imaginary; the torpedoes are adjusted and 
 the tubes trained; switches are thrown on for searchlights 
 and signals; and, often within a minute, the ship is trans- 
 formed from tranquility and apparent inertness into a 
 state of alert and vigorous aggressiveness. 
 
 Constant drilling is carried on with devices for training 
 the gun's crews in loading, pointing, and firing the guns. 
 These drills have resulted, within a few years, in an extra- 
 ordinary increase in rapidity and accuracy of fire. Other 
 drills have for their object to familiarize the men with the 
 use of rifles, revolvers, broadswords, etc.; and others still 
 aim largely at physical development, being in the nature 
 of gymnastics. With the same end in view, coupled with 
 the further thought of affording recreation, athletic sports 
 are encouraged, and outfits for boxing, baseball, and foot- 
 ball are supplied by the government to all ships, and com- 
 manding officers are directed to afford all reasonable facilities 
 for the use of these and for competition between different 
 ships. All large ships have their athletic teams, many of 
 them with records of which they have a right to be proud. 
 Most ships also have racing boat crews; and races, both 
 rowing and sailing, are frequent when ships are in company. 
 
 The stations of the crew for all the drills that have been 
 outlined above are laid down in a book known as the Watch
 
 THE ORGANIZA TION OF A MAN OF WAR 169 
 
 Quarter and Station Book, which is prepared by the executive 
 officer and kept in his oflfice. Each man is furnished with 
 a slip of paper called the station billet, giving his number, 
 station to which he is asssigned, and full information as to 
 all his duties. 
 
 The office of the executive officer is presided over by the 
 ship's writer, who is one of the most important men in 
 the ship. In addition to keeping track of the stations of the 
 men, he keeps all records and makes out all details that 
 have to do with the crew. For each man on the ship, 
 there is kept an enlistment record, which is begun wher> 
 he enters the service and gives his history continuously 
 until his discharge, showing the various ratings that he 
 has filled and his proficiency in them, his ability in sea- 
 manship, ordnance, signals, etc., his conduct and his health. 
 This record is transferred with the man from ship to ship, 
 and at the end becomes a part of the permanent files of 
 the Navy Department. 
 
 The following is a sample of the daily and weekly routine 
 of a man of war, many small details being omitted: 
 
 DAILY ROUTINE IN PORT 
 
 5.30 A. M. Reveille. All hands turn out except those who 
 
 have had night watches. 30 min. allowed 
 
 for stowing hammocks, for coffee, and for 
 
 smoking. 
 6.00 Turn to (viz., begin work). Scrub clothes and. 
 
 clean ship. Time and opportunity allowed 
 
 for bathing, etc. 
 6.30 Send market boat ashore for provisions. 
 
 7.00 All hands. Men who have been sleeping-in, 
 
 turn out. 
 7.20 Spread mess gear (viz., make preparation for 
 
 breakfast). 
 7.30 Breakfast. Crew dress in prescribed uniform. 
 
 8.00 Colors (viz., hoist the ensign, band playing 
 
 National Anthem). 
 8.15 Turn to (viz., resume work).^ Clean bright 
 
 work (brass and steel) of ship and guns.
 
 170 THE ORGANIZATION OF A MAN OF WAR 
 
 8.45 Sick call (viz., all sick report to surgeon). 
 
 9.00 Knock-off bright work. Clear up the decks 
 
 and make everything shipshape, etc. 
 
 9.30 Quarters (viz., all hands go to stations at guns 
 
 or elsewhere, for muster, inspection, and 
 drill). Divisions are mustered and inspected 
 by their officers and report made to the 
 executive officer whether all are present. 
 
 9.40 1st drill period. Drills as prescribed. 
 
 10.30 2d drill period. Drills as prescribed. 
 
 11.00 End of forenoon drills. 
 
 11.20 Stand by scrubbed clothes (clothes lines are 
 
 lowered and clothes removed from lines). 
 Sweep decks. 
 11.50 Spread mess gear (prepare for dinner). 
 
 12.00 Dinner. 
 
 1.00 P. M. Turn to. 
 
 1.30 Afternoon drill period. 
 
 2.00 End of drill period. Sweep decks. 
 
 4.00 Knock-off work; artificers, carpenters, black- 
 
 smiths, etc., quit work. 
 
 4.30 Sweep and clean up decks. 
 
 5.00 Quarters (muster, followed by setting-up drill 
 
 for 10 min.). 
 
 5.30 Spread mess gear. 
 
 6.00 Supper. 
 
 6.30 Turn to. 
 
 Sunset Retreat. Ensign lowered, band playing National 
 
 Anthem. Hoist boats; make all secure for 
 the night. 
 
 7.30 Pipe down hammocks. Hammocks are taken 
 
 from place where stored and slung ready 
 for use. 
 
 8.00 Chief engineer, warrant officers, master at arms, 
 
 captain of hold, etc. report to e.xecutive 
 officer that their respective parts of the ship 
 are secure. Master at arms reports that the 
 galley fires and certain lights on lower decks 
 are out.
 
 THE ORGANIZA TlON OF A MAN OF WAR 171 
 
 8.55 Bugle call, preliminary to tattoo. 
 
 9.00 Tattoo (bugle). Pipe down for the night. 
 
 Turn in and keep silence. Muster anchor 
 watch. Taps. 
 Division of Time on Shipboard. — The day on shipboard is 
 divided into watches which are of 4 hr. each, except that the 
 period from 4 to 8 P. m. is divided into two watches of 2 hr. 
 each, called dog watches. The object of this is to make an odd 
 number of watches during the 24 hr. so that the starboard 
 and port watches of the crew will not be on duty at the same 
 time every day. The watches are designated as follows: 
 
 12 noon to 4 p. m Afternoon watch 
 
 4 to 6 p. M First dog watch 
 
 6 to 8 P. M Second dog watch 
 
 8 P. M. to midnight First watch 
 
 Midnight to 4 a. m Mid watch 
 
 4 to 8 A. M Morning watch 
 
 8 A. M. to 12, noon Forenoon watch 
 
 "the time on shipboard is marked by strokes on the ship's 
 bell, and is expressed by the number of bells (strokes) that 
 have been struck; thus, 1 bell is one stroke of the bell, 
 6 bells is six strokes of the bell, and so on. Counting from 
 12 o'clock, noon, which is 8 bells, the half hours through 
 the day and night run as follows: 
 
 12..30 P. M 1 bell 7.30 p. m 7 bells 
 
 1.00 P. M 2 bells . 8.00 p. M Shells 
 
 1.30 P. M 3 bells 8.30 p. m 1 bell 
 
 2.00 P. M 4 bells 9.00 p. m 2 bells 
 
 2.30 P. M 5 bells 9.30 p. m 3 bells 
 
 3.00 p. M 6 bells 10.00 p. m 4 bells 
 
 3.30 P. M 7 bells 10.30 p. m 5 bells 
 
 4.00 p. M 8 bells 11.00 p. m 6 bells 
 
 4.30 P. M 1 bell 11.30 p. m 7 bells 
 
 5.00 P. M '. . .2 bells 12 midnight 8 bells 
 
 5.30 p. M 3 bells 12.30 a. m 1 bell 
 
 6.00 p. M 4 bells 1.00 a. m 2 bells 
 
 6.30 p. M 5 bells 1.30 a. m 3 bells 
 
 7.00 p. M 6 bells and so on as before
 
 172 THE ORGAXIZA TION OF A MAN OF WAR 
 
 BRIEF NOTES AS TO ETIQUETTE OF A MAN OF WAR 
 
 The following brief notes will be of value to a recruit 
 unfamiliar with the customs of the Navy, and may be of 
 interest to others: 
 
 1. In saluting an officer, an enlisted man should stand 
 at attention and touch his cap. Attention is an erect posi- 
 tion with both heels together. 
 
 2. He should always salute when addressing an officer 
 and when addressed by him. Also when meeting him on 
 shipboard or on shore, and this whether he is in uniform 
 or not. 
 
 3. When an officer is moving about the ship in the per- 
 formance of his duty, it is not required that men shall 
 salute him every time he passes, nor are men who are them- 
 selves actually at work expected to stop their work to salute. 
 But it is always better to show an excess of courtesy in this 
 matter than a lack of it. 
 
 4. When the commanding officer passes along the deck, 
 all men near whom he passes should stand at attention 
 and salute. 
 
 5. When the commanding officer leaves the ship or 
 comes on board, in uniform, the signal for "silence" is 
 sounded on the bugle and everybody on deck stands at 
 attention. 
 
 6. The same ceremony is observed for an officer from 
 another ship making an official visit. 
 
 7. When the ensign (national flag) is hoisted at 8 A. M. 
 or hauled down at sunset, the band plays the "Star Spangled 
 Banner" and all officers and men face aft (toward the flag) 
 and stand at attention. As the flag reaches the peak, in 
 hoisting, or the rail, in lowering, all salute. The flag is 
 sometimes called the flag, sometimes the ensign, and some- 
 times the colors. 
 
 8. When one ship of war passes near another (of any 
 nationality), the call for "silence" is sounded by bugle, and 
 all men on deck face toward the side on which the other ship 
 is to be passed and stand at attention. 
 
 9. All officers and men coming on to the quarter deck 
 face toward the colors and salute.
 
 THE CLASSIFICATION OF WAR SHIPS 173 
 
 10. Men in a boat which is lying alongside the ship stand 
 up and salute as an officer passes in another boat. When 
 a boat is in charge of a coxswain only the coxswain salutes* 
 
 11. In the case of a squad of men in charge of one, only 
 the man in charge salutes. 
 
 12. Petty officers are entitled to be treated with respect^ 
 but are not saluted. 
 
 13. In cases where an accommodation ladder is shipped 
 on each side, enlisted men use the port side, the starboard 
 ladder being reserved for officers. 
 
 14. Except on duty, enlisted men shall keep clear of 
 the starboard side of the quarter deck, this being reserved 
 for the captain and the officers of the deck. 
 
 15. Men given an order by an officer, stand at attention,. 
 
 salute, and give "Aye, Aye, Sir!" and then execute the 
 
 order promptly. 
 
 Note. — The term "Aye, Aye'' is often used incorrectly in reply to a questioiiV 
 It is not at all the same thing as "Yes," but is au expression "of readiness to 
 obey. In other words, it is the response to an order, not to a question. 
 
 16. A man on shipboard wishing to see an officer, goes 
 to the place appointed for communicating with the officer 
 of the deck (this place, wherever it may be, is technically 
 called the mast) and states his wishes. If the officer of the 
 deck considers it proper to do so, he sends for the officer 
 who is wanted. The mast is the place for formal communi- 
 cation between officers and men, as for example, where a 
 man has a grievance and wishes to see the captain or execu- 
 tive. Similarly, men charged with offenses are brought to 
 the mast and their cases are investigated there". 
 
 THE CLASSIFICATION OF WAR SHIPS 
 
 General Considerations. — The weight that a ship of given 
 size will carry, and still float, is limited, while the amount 
 of weight that we would like to make her carry, in armor, 
 armament, engines, and coal supply, is practically unlimited. 
 This being the case, we are compelled to accept a compro- 
 mise, the nature of which will depend on the purpose for 
 which the particular ship in question is to be used. If we
 
 174 THE CLASSIFICATION OF WAR SHIPS 
 
 give her the heaviest guns and thickest armor, we shall 
 have comparatively little weight remaining for engines and 
 coal. "Very well," we say, "we want this ship for fighting, 
 not for running away. Let us give her first of all guns and 
 armor; and then do the best that can be done in the way 
 of speed and coal supply." Thus we get the battle ship. 
 But suppose that we want a ship not to oppose the fighting 
 ships of the enemy, but to avoid these and to chase and 
 capture her fleetest merchant steamers; such a ship must 
 carry nearly all her weight in powerful engines and large 
 coal supply. She needs few guns and no armor. This is 
 a commerce-destroying cruiser. Suppose, again, that we wish 
 to strike a mean between these two extremes, preserving in a 
 considerable measure the fighting qualities of the battle ship 
 and associating them with a speed and coal supply approxi- 
 mating to those of the fast cruiser; this gives us the armored 
 cruiser, powerful enough to give a good account of herself in 
 battle, even if obliged to fight a battle ship, but able, as a 
 rule, to avoid such odds by reason of her speed, and able, 
 also by reason of her speed, to overtake all but the fastest of 
 the enemy's cruisers and merchant steamers. 
 
 The following classes of ships are recognized bj"- the 
 great Naval Powers: 
 
 Battle ships are ships of large size, carrying the heaviest 
 guns and thickest armor, but with moderate speed and 
 rather small coal supply. They are designed to fight the 
 most powerful ships of an enemy, but not, as a rule, to go 
 far from a base. Such vessels can^' their heavy guns in 
 turrets. A representative type of this class is the new battle- 
 ship "Maine" shown in Fig. 1 (a), which has a displacement 
 of 12,500 T., and an average speed of 17 knots. Diagrams 
 {b) and (c) show, respectively, the armor protection and bat- 
 teries carried by the ship. 
 
 Armored cruisers are ships of large size carrying guns and 
 armor much lighter than those of a battle ship, but heavier 
 than those carried by any other class of ship (except moni- 
 tors). They have much higher speed than battle ships, and 
 earn*' sufficient coal for steaming long distances and opera- 
 ting at a distance from the base. They have a wider range
 
 THE CLASSIFICATION OF WAR SHIPS 175 
 
 
 
 
 
 Ml 
 
 "'"-'.Iris .'I 1 «i .
 
 176 THE CLASSIFICATION OF WAR SHIPS 
 
 lllll,
 
 THE CLASSIFICATION OF WAR SHIPS 177 
 
 of usefulness than any other class. The Russian cruiser 
 "Gromoboi," shown in Fig. 2, is a fair type of this class. 
 
 
 This ship has a displacement of 12,367 T., a speed of 20 knots, 
 and a coal-carrying capacity of 2,500 T. It will be noticed 
 that the distribution of armor on the '"Gromoboi" shown
 
 178 THE CLASSIFICATION OF WAR SHIPS 
 
 o| < 
 
 M-n^ 
 
 o] 
 
 M 
 
 o 
 
 L|
 
 THE CLASSIFICATION OF WAR SHIPS 179 
 
 in Fig. 2 (6) is about the same as on the "Maine," but that 
 the armor on the latter ship is much heavier. 
 
 Protected cruisers are ships of moderate size with no 
 side armor, but having their vital parts (engines, boilers, 
 and magazines) protected by a curved deck of steel from 
 2 to 4 in. thick. They have good speed and large coal 
 supply, with guns of moderate power, and are designed for 
 cruising on distant stations in time of peace and for block- 
 ading, scouting, and commerce destroying in time of war. 
 They are designed also for fighting, but not against armored 
 ships. The German cruiser "Kaiserin Augusta," diagrams 
 of which are shown in Fig. 3, belongs to this class of ships. 
 
 Cruisers and gunboats are ships of moderate and small 
 size, without armor or armored deck, with moderate speed 
 and light guns, b)ut often with ver^' large coal supply. They 
 are designed for cruising in time of peace and for blockading 
 and commerce destroying in time of war; also for fighting 
 against similar ships of an enemy. Ships of this class are 
 often sheathed; that is, their bottoms are covered with 
 wood, which in turn is covered with copper, to prevent 
 the fouling and pitting to which the bottom of a steel ship 
 is subjected, if not frequently docked. A sheathed ship 
 can remain out of dock for several years, if necessary. 
 They are often fitted with masts and sails. 
 
 Monitors are a special type, confined almost entirely to 
 the United States Navy, resembling battle ships in guns 
 and armor and in carr>-ing their large guns in turrets, but 
 differing from all other types of ships in that they are very 
 low in the water, and thus present a very small target. The 
 first monitor, designed by John Ericsson, was the forerunner 
 of the battle ship. They are effective fighters in smooth 
 water, but not in a rough sea, because the waves break 
 over their low decks and make it impossible to work their 
 guns, and because they have the further peculiarity of 
 rolling very rapidly. They are essentially harbor defense 
 ships. A type of this class of vessel, the U. S. S. "Wyoming," 
 is shown in Fig. 4 (a), (6), and (c). 
 
 Torpedo boats (Fig. 5) are light, low craft, very long 
 and narrow, of great speed, made as nearly invisible as
 
 180 THE CLASSIFICATION OF WAR SHIPS 
 
 iiii;
 
 THE CLASSIFICATIO.X OF WAR SHIPS 181 
 
 r 
 
 11(1 
 
 
 
 ilafc
 
 182 THE CLASSIFICATION OF WAR SHIPS 
 
 possible by their shape and color. They are armed with tor- 
 pedoes, and in some cases with a few light guns; they are 
 designed to attack larger ships with torpedoes, usually 
 under cover of darkness. Torpedo boats are, as a rule, 
 small vessels, their displacements varying from about 
 25 to 250 T., and are fitted with powerful engines to drive 
 them at the required high speed. Their interior space is 
 consequently ingeniously arranged and utilized in every 
 possible way to accommodate the crew, boilers, engines, 
 fuel, stores, and other equipments. In Fig. 6 is shown the 
 
 interior arrangement of a modern torpedo boat. The 
 several compartments designated by numbers are as follows. 
 1, chain locker; 2, tank; S, torpedo hoist; 4. spare torpedoes; 
 5, shaft for war heads; 6, crew's quarters; 7, magazine; 8, store- 
 room; 9, coal bunker; 10, boilers; 11, stoke hold; 12, main 
 engine;' 75, auxiliary engine; 14, magazine; 15, torpedo 
 tube; 16, wardroom and 'sick bay; 17, storeroom; 18, mess 
 room; 19, pantry; 20, 6 pdr. quick-firing gun; 21, 12 pdr. 
 quick-firing gun; 22, binnacle; 23, chart room; 24, bridge; 
 25, searchlight.
 
 184 THE CLASSIFICATION OF WAR SHIPS 
 
 Torpedo - boat destroyers 
 
 are greatly enlarged tor- 
 pedo boats, with higher 
 speed and better sea-going 
 qualities. Armed with tor- 
 pedoes, but carrying also 
 several guns of fair size, 
 this type was evolved with 
 a view to running down 
 and destroying the torpedo 
 boats of an enemy. Being 
 large enough to keep the 
 sea even in bad weather, 
 they can accompany a fleet 
 of battle ships and protect 
 them from torpedo boats, 
 while at the same time 
 themselves serving to at- 
 tack the enemy with tor- 
 pedoes. 
 
 Other ships that are es- 
 sential to a properly organ- 
 ized navy are scout ships 
 (large and fast), colliers, 
 supply ships, hospital 
 ships, distilling ships (to 
 supply the large amount 
 of fresh water needed by 
 modern boilers), repair 
 ships, and despatch boats. 
 
 A squadron is a small 
 number of ships under the 
 command of one officer. 
 
 A fleet is several squad- 
 rons grouped under the 
 command of an admiral. 
 
 A flotilla is a group of 
 small craft, torpedo boats, 
 etc.
 
 THE CLASSIFICATIOX OF WAR SHIPS 185 
 
 MAN-OF-WAR BOATS 
 
 Launches are large heavy boats designed primarily for 
 carrying cargo or for carrying large bodies of men in landing 
 operations. 
 
 Cutters are like launches, but much smaller, and are used 
 for both cargo and passenger boats; both launches and 
 cutters are fitted for carrying light field guns. 
 
 Whale boats are lighter than cutters and of a different 
 model, being sharp at the stem as well as at the bow; they 
 are used for miscellaneous work, being light and handy. 
 
 Dingies are small boats pulling usually four oars, used 
 for light work of any kind. 
 
 The barge, used only in a flagship, is the personal boat of 
 an admiral. 
 
 The gig is the personal boat of the captain; it is usually 
 a small whaleboat. 
 
 Steam launches and steam cutters are boats of fair size 
 run by steam and used for the general work of the ship. 
 
 In Fig. 7 are shown the various rigs of man-of-war boats 
 for sailing, of which (a) is the gaflf and boom rig used on 
 launches of the U. S. Navy; ib) is known as sprit rig; (c) 
 dipping lug foresail and standing lug mainsail; id) sljding 
 gunter; (e) balance lug; and (/) standing lug. 
 
 BUGLE CALLS 
 
 Signals for many of the events of daily routine are made by 
 bugle calls. Each class of boat has a call, and the indi- 
 vidual boats of the class are distinguished by one, two, or 
 more blasts after the call: thus, the signal for manning the 
 third cutter is the cutter call followed by three blasts. 
 
 Other bugle calls are: reveille, tattoo, taps mess-gear 
 quarters, retreat, assembly, silence.
 
 (e) (f) 
 
 Fig. 7
 
 A^4T^4L ORDXAXCE 187 
 
 NAVAL ORDNANCE 
 
 GUNS 
 
 The guns carried on shipboard as a part of the armament 
 of the ship (except shoulder pieces and revolvers, which 
 are technically known as small arms) are of great variety, 
 as regards both size and mechanical principles; ranging 
 from light automatic guns of musket caliber firing 500 shots 
 per min., to the monster 13-in. rifles of 60 T. weight, mounted 
 on a carriage of enormous strength, within a turret protected 
 by a hundred tons of armor, firing a projectile weighing 
 i T., and burning 500 lb. of powder at every round. 
 
 Classification of Guns. — All modern guns are built up of 
 steel, and all are rifled and breech-loading. 
 
 A built-up gun is one in which several layers of steel are 
 built up, one over another, on a principle to be hereafter 
 explained. 
 
 A rifled gun is one in which the barrel is grooved along 
 that part of its bore through which the projectile is to be 
 driven by the powder gases, the grooves running spirally 
 along and around the bore. 
 
 A breech-loading gun is one that is loaded from the 
 breech, the projectile being entered first and pushed for- 
 wards to the beginning of the rifled bore. The powder is 
 then entered, in the rear of the projectile, and the breech 
 closed by a heavy plug or block. The method of fitting 
 this plug, and the mechanical arrangement by which it 
 is opened and closed, constitute the essential features of 
 the various types of breech mechanism used with different 
 types of guns. Some of these breech mechanisms are 
 suitable only for small guns, others only for large ones, 
 while a few are adaptable to any caliber. The great object 
 of most inventors has been to obtain rapidity of action; and 
 in some types of mechanism, the operations of unlocking the 
 plug, withdrawing it from the gun, and swinging it out of the 
 way, are all done by a single sweep of a lever. These are 
 technically known as rapid-fire, or quick-fire, mechanisms. 
 They are confined to guns of 7-in. caliber and under.
 
 188 
 
 NAVAL ORDNANCE 
 
 In guns up to and including the 5-in. caliber, the powder 
 is commonly packed in a copper cartridge case, and the 
 base of the projectile is forced into the mouth of the case 
 and gripped there, forming a complete cartridge like that 
 for a musket or a revolver. Such ammunition, Fig. 1, is 
 technically known as fixed ammunition. The copper case 
 not only holds the powder, but also prevents the escape 
 of gas to the rear when the gun is discharged, thus doing 
 away with the necessity for a special arrangement for this 
 purpose (a gas check) , which wall be described in connection 
 
 Fig. 1 
 
 with guns that do not use cartridge cases. The breech 
 mechanism of a gun using a cartridge case must include 
 an extractor for withdrawing the case after firing. For 
 guns larger than 5-in. caliber, the powder is put up in bags 
 and loaded separately from the projectile. Guns using 
 fixed ammunition are called rapid-fire guns. 
 
 Other classes of guns are machine guns, which are fired 
 rapidly and continuously by turning a crank or lever, the 
 cartridges being fed in through a hopper; automatic guns 
 in which the shock of discharge of one cartridge extracts
 
 XAVAL ORDNANCE 1S9 
 
 the empty case and loads and fires the next cartridge, and 
 so on indefinitely as long as the supply of ammunition holds 
 out; and semiautomatic guns in which the shock of dis- 
 charge does a part of the work of the automatic guns, but 
 the loading is done by hand. 
 
 Principles of Gun Construction. — The power of guns has 
 been enormously increased within the last quarter century, 
 following upon the wonderful increase in the efficiency of 
 powders, and this has called for a corresponding increase 
 in the strength of guns. The old-style gun, whether smooth 
 bore or rifled, was made from a single piece of metal — cast 
 iron, wrought iron, bronze, or steel. There is a limit to the 
 possible strength of such a gun, since after a certain thick- 
 ness of wall has been reached, no increase in thickness adds 
 anything to the strength of the gun. This is easily explained. 
 When the powder inside the gun explodes, the pressure 
 developed is felt first by the inner layers of the metal. 
 These layers are expanded and transmit the strain to the 
 layers next outside them, which in their turn expand and 
 transmit the strain to the parts beyond, and so on. Thus 
 the successive layers into which we may imagine the walls 
 of the gun to be divided take up the strain, not all together, 
 but one after the other, from inside out, each one taking 
 a little less than the one inside. When the walls are 
 sufficiently thick for the extreme outer layer to feel the 
 strain just before the inner layer is ruptured, it will be use- 
 less to add more layers, because these would not take any 
 part in resisting the strain until the inner layers had been 
 stretched beyond the rupturing point. 
 
 In the modem system of gun making, the gun is built 
 up of hoops or bands of tempered steel shrunk one upon 
 another, on what is called the principle of initial tensions. 
 Suppose that we have two hoops of steel, one larger than 
 the other and of st:ch dimensions that the inner diameter 
 of the larger is slightly less than the outer diameter of the 
 smaller. If we expand the larger by heat, slip it over the 
 smaller one, and allow it to cool and set, the result will be 
 two-fold: first, the outer tube will be stretched and thus 
 put under an initial tension; and second, the inner tube
 
 ISO 
 
 NAVAL ORDNANCE
 
 NAVAL ORDNANCE 191 
 
 will be more or less compressed. In this condition, the 
 first effect of a pressure from the inside will be to expand 
 the inner tube, relieving the compression without putting 
 any strain upon the metal. By the time it has enlarged 
 sufficiently to begin to feel a strain, the outer tube will 
 feel the effect of the enlargement and will resist this by 
 reason of its own initial tension, and thus both tubes will 
 act together in resisting the pressure from within. The 
 laws that govern the beha\'ior of steel under these conditions 
 are so well known that it is possible to calculate the exact 
 amount of shrinkage required to make the various parts 
 of a gun act together to the best advantage, and instead 
 of using two layers only, we can use as many as we like and 
 put them together in such a way that all will act together 
 in resisting the pressure in the bore. Thus the gun is made 
 very much stronger than would be possible if it were in a 
 single part. 
 
 Another very great advantage of building up the guns 
 in this way is that all the parts, being small, can be more 
 perfectly tempered and annealed, and any defects in them 
 can be more easily detected, than if they were larger. 
 
 In practice, three layers are commonly used, as shown 
 in Fig. 2. The inner laj'er is a tube, running the whole 
 length of the gun and forming the bore and chamber. Over 
 the after part of this is shrunk the heavy jacket, and over 
 this, a layer of hoops. The hoops are continued forwards 
 of the jacket along the tube, only two layers being needed 
 at this part, as the pressure is lower here than it is toward 
 the breech. The dotted curve above the gun shows the 
 way in which the pressure varies throughout the bore. It 
 will be seen that the thickness of the wall of the guns corre- 
 sponds in a general way with the shape of this curve. 
 
 Gun Steel. — The steel of which guns are made is of the 
 very finest quality known, and a quality that, 25 yr. ago, 
 could not have been produced in the world. It is, indeed, 
 one of the most interesting facts in connection with the extra- 
 ordinary development of" our Navy that the demand for a 
 constantly improving quality of material has led to improve- 
 ments in the manufacture of steel far exceeding those that
 
 192 A'.4T'.4L ORDXAXCE 
 
 might have been expected from the demands of ordinary 
 industries. 
 
 Properties of Steel. — In the popular conception, the most 
 important characteristic of steel is its tensile strength; the 
 strength, that is to say, with which it resists rupture. In 
 gun steel, this is less important than its elastic strength, or 
 the strength with which it resists permanent deformation 
 or change of form. So long as a gun is exposed only to pres- 
 sures below its elastic strength, or "within its elastic limit," 
 it expands to the pressure and then returns to its original 
 shape, acting like a great spring; and it may be repeatedly 
 subjected to such pressures without being in the least weak- 
 ened or deformed. But if it is once subjected to pressure 
 beyond its elastic limit, it takes on a permanent enlargement, 
 which not only deforms it, but weakens the metal. 
 
 Other important qualities in gun steel are toughness, 
 ductility, and hardness, the last-named quality being espe- 
 cially important in the bore, which is called upon to resist 
 the wear arising from the motion of the projectile and the 
 friction of the powder gases as they rush down the bore. 
 The friction of these gases, combined no doubt with some 
 chemical action that is intensified by the high temperature, 
 produces a scoring of the bore that is technically known as 
 erosion, and which gradually enlarges the bore and thus 
 reduces the accuracy of the gun. The harder the steel of 
 the bore, the less it is eroded. 
 
 Ductility is the opposite of brittleness, and is that quality 
 which causes the steel to stretch before rupturing, instead 
 of flying apart suddenly and without warning, like glass and 
 similar substances. Steel is tested by breaking test pieces 
 in a testing machine under varying tensions and noting: 
 (a) the tension at which it ceases to spring back if the 
 tension is released, or the elastic limit; (b) the tension at 
 which it breaks, or the tensile strength; (c) the amount by 
 which it is stretched in breaking, or the elongation; (d) the 
 amount by which the cross-sectional area is reduced by 
 stretching, or the reduction of area. 
 
 Composition of Steel. — Steel, as known to metallurgists 
 until within quite recent years, was an alloy of iron and
 
 NAVAL ORDXAXCE 
 
 193 
 
 carbon, the percentage of the carbon varying considerably, 
 but being always less than 2%. Steel with .3% to .5% 
 is a low, soft, or mild steel; steel having from 1% to 2% is 
 high steel. Low steels approach wrought iron and high 
 steels cast iron, in their characteristics. 
 
 It has recently been found that other substances can be 
 advantageously added to the alloy of iron and carbon. 
 The most important of these substances for gun steel is 
 nickel, about 3% of which is used in the so-called nickel 
 
 Pi ^;i 
 
 ^ 
 
 ■f— =^' 
 
 
 Fig. 3 
 steel, which is now very generally used for guns and armor. 
 This amount of nickel takes the place of a part, but not the 
 whole, of the carbon. The nickel increases both the tensile 
 and the elastic strength. 
 
 The Treatment of Gun Steel. — Steel ingots for guns are 
 first cast, then forged under a hammer or press into the 
 right shape for which they are designed. Fig. 3 shows an
 
 194 NAVAL ORDNANCE 
 
 ingot in the 5,000-ton forging press of the Bethlehem Steel 
 Co. As in the forging irregular strains may be set up, 
 the next process is one of annealing; this consists in heating 
 the ingot to a red heat and allowing it to cool slowly. In 
 this process, the particles of the metal gradually readjust 
 themselves and settle into a condition of uniform crystal- 
 lization and of freedom from strain. The forging is then 
 tempered in oil; that is to say, it is heated to a high tem- 
 perature and plunged into a bath of oil, which cools it rapidly, 
 and, in the rearrangement of structure that results, modifies 
 all its characteristics, increasing very greatly the hardness, 
 toughness, and elasticity, but reducing the ductility; or, 
 in other words, rendering it brittle. To restore the ductility 
 and at the same time to relieve any internal strains that 
 may have been set up within the mass by uneven cooling 
 in the process of tempering, the ingot is now reannealed. 
 This final process, to a certain extent, undoes the effects 
 of the tempering; but whereas it reduces only a little the 
 elastic and tensile strength, it almost entirely restores the 
 ductility, and it also relieves the strains produced in tem- 
 pering. By reducing the hardness, it also prepares the 
 ingot for the machining to which it is next subjected. 
 
 Manufacture of the Guns. — Most of the guns for the Navy 
 are manufactured at the Washington gun factory, but con- 
 tracts have in some cases been made with private firms such 
 as the Bethlehem and Midvale Steel Companies for delivering 
 the guns complete. The various parts of the gun are received 
 at the factory in the shape of rough ingots for the tube, jacket, 
 and hoops. The first operation is to rough bore and turn 
 them, very caretul inspection being made during these and 
 subsequent operations for imperfections of any kind in the 
 metal. The shrinkage surfaces are then finished very care- 
 fully to dimensions that have been determined by calculations, 
 the calculations being based on the known characteristics of 
 the particular ingots to be used. The variations allowed in 
 dimensions of the shrinkage surfaces are never more than .001 
 or .002 in. The amount of shrinkage is greater for large than 
 for small guns, and greater for the outer parts (hoops over 
 jacket) than for the inner parts (jacket over tube).
 
 NAVAL ORDNAXCE 
 
 195 
 
 The outer surface of the tube and the inner surface of 
 the jacket having been accurately finished to the shrinkage 
 dimensions, the tube is placed in the shrinkage pit, muzzle 
 down, and the jacket in a hot-air furnace, where it is sub- 
 jected to a temperature of 600° F. for a length of time that 
 
 Fig. 4 
 
 experience has shown to be necessary. It is thus expanded 
 sufficiently to admit of slipping it over the tube. It is 
 then lifted by a crane and swung into position directly 
 above the end of the tube, Fig. 4, where it is carefully cen- 
 tered and then lowered into place. In the meantime a
 
 196 A^4F.4L ORDNANCE 
 
 stream of water has been started inside the tube; this keeps 
 the tube cool and causes the jacket to cool from the inside 
 out. As it cools it grips the tube, compressing it slightly, 
 as already explained, and at the same time taking on a 
 slight initial tension itself. When all parts are cool, the 
 tube and jacket, which now form one piece, are lifted and 
 placed in a lathe, where the outer surfaces are finished to 
 the proper dimensions for receiving the hoops. The hoops 
 are placed on in substantially the same manner as the jacket. 
 
 At certain points of the construction, locking bands, or 
 hoops, are used, so fitted, either with screw threads or with 
 shoulders, upon the other parts, as to lock all the various 
 parts together so that all shall help to resist longitudinal 
 strains, or strains in the direction of the axis of the gun. 
 These locking arrangements are shown in Fig. 2. 
 
 Rifling the Bore. — The final operation is that of cutting 
 the grooves of the rifling. This is done by a set of cutters 
 mounted on a long rifling bar connected with a mechanism 
 that moves the cutters down the bore and at the same 
 time revolves them, the motions of translation and rotation 
 being regulated automatically to give the required twist 
 to the grooves. Several grooves are cut at one time, and 
 the cutters are then revolved as much as necessary to cut 
 another set. 
 
 Star Gauging. — When the gun is finished, the bore is 
 carefully meastired by a star gauge. This is one of the 
 most important instruments used in connection with 
 ordnance, as it affords the only method of measuring the 
 diameter of the bore of a gun — a measurement that is often 
 wanted in service when it is thought that a gun may have 
 been injured by some accident; such, for example, as the 
 explosion of a shell in the bore. 
 
 The star gauge consists of a long brass sleeve made in 
 several sections that can be screwed together to give the 
 length required for working at any part of the bore. On 
 the end of tliis sleeve is a head carrying three radial points 
 of tempered steel, connected with a wedge inside the head 
 in such a way that as the wedge is moved forwards or 
 backwards, the points are forced out or drawn in. The
 
 NAVAL ORDNANCE 
 
 197 
 
 wedge is actuated by a long rod 
 running inside the sleeve and 
 having a handle at the outer end. 
 This handle has a pointer that 
 moves along a scale on the sleeve, 
 indicating how far the rod (and 
 hence the wedge) is moved in or 
 out. The bevel of the wedge 
 being known, this motion back 
 and forth gives the measure of 
 the motion of the points in and 
 out. For each caliber of gun, 
 there is a set of standard points; 
 and in preparing the star gauge 
 for use, these points are adjusted 
 so that they just fit the diameter 
 of a standard ring when the scale 
 on the rod is at zero. The gauge 
 is then put in the gun and care- 
 fully fixed at the point where the 
 measurement is desired. The 
 points are then forced out against 
 the bore, and the reading of the 
 scale (which is fitted with a ver- 
 nier) gives the diameter. In star 
 gauging a gun, a measurement is 
 usually made at every inch of its 
 length. 
 
 In Fig. 5 are shown the details 
 of a gun as loaded and ready for 
 firing. Although not shown in 
 the figure, the greater part of the 
 length of the gun is given up to 
 the rifled bore.' In rear of the 
 rifling, the bore is enlarged to 
 form the powder chamber, and in 
 rear of this comes the threaded 
 screw box, in which the breech 
 plug is held. At the rear end of
 
 198 
 
 .V.4F.4L ORDNANCE 
 
 the rifled bore is a slight slope against which the rotating 
 band of the projectile (to be described hereafter) brings up 
 when the projectile is pushed into its seat. This is the band 
 slope, and a little in rear of this is the chamber slope, carrying 
 the diameter up to that of the chamber. At the forward end 
 of the screw box is the gas-check slope, against which .the 
 gas check is seated when the bore is closed. 
 
 BREECH MECHANISMS OF GUNS 
 
 Breech Blocks. — In all guns of and above the 3-in. caliber the 
 same general system is used for closing the breech; this is the 
 French, or interrupted-thread, system shown in Fig. 1 (a) and 
 
 (6). On the outside of 
 the cylindrical block, is 
 a male screw thread en- 
 gaging a female thread 
 in the screw box of the 
 gun. If both of these 
 threads were continu- 
 ous, the block could 
 only be seated by 
 screwing it in with a 
 great number of turns. 
 To avoid this, the 
 threads are inter- 
 rupted, or slotted, 
 over several sections 
 of the circumference, 
 as shown in the fig- 
 ure. By bringing the 
 threaded parts of 
 the plug opposite the 
 blanks of the screw 
 box, the plug may be 
 pushed nearly into 
 its seat, where by 
 turning it through a part of a circle, the threads are engaged, 
 and the plug is forced home with considerable pressure, which
 
 NAVAL ORDNANCE 
 
 199 
 
 holds it up rigidly against the force of the powder gases when 
 
 the gun is fired. 
 
 Several modifications of the above general principle are 
 
 in use, having- for their object increased rapidity of action. 
 
 Thus, the Elswick breech plug, Fig. 2, is conical, this shape 
 
 giving the. advantage that the plug can be swung around 
 
 to the side at the 
 same time that it is 
 being withdrawn; 
 in other words, its 
 motion from the 
 first is on the arc of 
 a circle. 
 
 In the Welin 
 breechblock, Fig. 3, 
 the whole surface Is 
 divided into three 
 parts, and each 
 part is divided into 
 four steps, of which 
 
 three steps are threads of different lengths, and the fourth 
 
 step is blank. By placing the block as shown in the figure, it 
 
 can be pushed in, and to 
 
 lock it calls only for a 
 
 turn through one-twelfth 
 
 of the circumference. 
 
 With this arrangement, 
 
 the threads cover a much 
 
 larger proportion of the 
 
 surface of the block than 
 
 with other systems, and 
 
 therefore, for a given 
 
 strength a shorter and 
 
 lighter block can be used. 
 
 In the small calibers, moreover the use of a short block makes 
 
 it possible to swing the block around as in the Elswick sys- 
 tem, without hitting the opposite side of the screw box. 
 
 Other systems of breech closure are the Hotchkiss, in 
 
 which a block is thrown up across the breech for closing and
 
 200 .V.4I'.4L ORDXANCE 
 
 allowed to fall by its own weight for opening, and the 
 Driggs-Schroeder in w^hich a block is pivoted in rear of the 
 breech and turned up and down for closing and opening, 
 the last motion of closing bringing into play a beveled 
 surface that forces the cartridge home. 
 
 Breech Mechanisms. — In any mechanism using a slotted 
 screw block, there are certain operations that must be 
 performed. For opening, the block must be rotated suffi- 
 ciently to unlock the threads, withdrawn to the rear as far 
 as may be necessary for clearing the screw box, and swung 
 ofif to one side, leaving the breech of the gun clear for load- 
 ing. In closing the block, the operations are reversed. 
 In the earliest breech-loading guns, the block was rotated 
 by a lever, pulled to the rear by an entirely independent 
 motion, and swung to the side by a third motion. A 
 mechanism was soon devised by which the rotation and 
 withdrawal of the plug were so related to each other that 
 the continuous turning of a crank accomplished both, the 
 motion of the crank actuating a miter-wheel, which first 
 rotated and then withdrew the block without any change 
 to the crank-action. It was a simple step to add the third 
 motion, that of swinging the block; and the resulting 
 mechanism, in which the block is rotated, withdrawn, and 
 swung clear by the continuous turning of a crank, is in use 
 in most of our turret guns at present. 
 
 This system is not rapid enough for guns of smaller 
 caliber, and is replaced in such guns by various systems, 
 known by the names of their inventors, in which all the 
 operations of working the breech block are accomplished 
 by a single sweep of a lever. The systems used in the 
 United States Navy are the Haeseler, Dashiell, Fletcher, 
 Elswick, Vickers, and Maxim-Nordenfelt, for guns of 3-in. 
 caliber and above, and the Hotchkiss, Driggs-Schroeder, 
 and Maxim-Nordenfelt for small guns only. Space does not 
 permit an attempt at describing these, but it is not difficult 
 to understand that there are many combinations of gears, 
 cams, and levers by which a single movement of an arm 
 may first rotate a block, then withdraw it, and finally swing 
 it to the side.
 
 .V.4T'.4L ORDXAXCE 
 
 201 
 
 Gas Checking. — When a great gun is fired, the pressure 
 in the bore may be anywhere from 10 to 20 T. to the sq. in. 
 Under this pressure, the tendency of the heated gases to 
 escape is such that they seek any minute channel that 
 may be open to them and rush through this with tremendous 
 violence. The problem of sealing even^ such channel is 
 thus of great importance, and every system of breech 
 closure must provide for an absolutely tight joint around 
 the block, while at the same time leaving the block per- 
 fectly free to open. Where a cartridge case is used, the 
 
 case itself serves as a gas-check, the ^^— _- ^ 
 
 elastic metal of the case being set 
 out tightly against the walls of the 
 gun. 
 
 With guns that do not use fixed 
 ammunition, the De Bange system 
 of gas checking, or obturation, is 
 universally adopted. In this sys- 
 tem, Fig. 4, which is the invention 
 of a French officer, a tight joint is 
 made at the forward end of the 
 breech block B by a plastic pad a 
 composed of asbestos and tallow. 
 This pad is in the shape of a ring 
 and is carried on the stem c of the 
 mushroom w lying in the assembled 
 mechanism, between the after face 
 of the mushroom head and the for- 
 ward face of the breech plug. The pad is enclosed by two 
 steel rings, which help to keep it in shape. The surface of the 
 pad is slightly beveled, as is also the gas-check seat in the 
 gun; and the action of the threads on the block as the latter 
 is rotated in closing, jams the pad firmly up against the seat 
 forming a tight joint, which is made tighter when the gun is 
 fired by the pressure of the gases forcing back the mushroom 
 and squeezing the pad between the mushroom and the block. 
 
 Firing. — Guns are fired by primers, which are worked by 
 either electricity or percussion. Primers for fixed ammuni- 
 tion are inserted in a recess at the base of the cartridge 
 
 Fig. 4
 
 202 
 
 NAVAL ORDNANCE 
 
 case. For ordinary ammunition, they are inserted in a 
 lock that screws on to the rear end of the mushroom stem. 
 A vent running through the mushroom admits the flame 
 from the primer to the chamber, where it ignites the charge 
 (see Fig. 4) . As both brown powder and smokeless powder 
 are very slow of ignition, a considerable quantity of black 
 powder is used in the base of the charge. This is called 
 the ignition charge. All primers are vent-sealing; that is, 
 they are made of metal thin enough to be expanded against 
 the walls of the recess that contains them, and thus prevent 
 the escape of gas around them. 
 
 Figs. 5, 6, and 7 show the several forms of primers at 
 present used in the United States Navy. In Fig. 5 is repre- 
 sented the ordinary form of percussion primer used in 
 
 Fig. 5 
 
 cartridge cases of fixed ammunition. The striking of the 
 hammer on the primer explodes the fulminate of mercury 
 immediately under it, and the flame from this ignites the 
 black powder in the magazine. 
 
 The ordinary form of electric primer for fixed ammunition 
 is shown in Fig. 6. The electric circuit, open at the firing 
 key, is connected with a firing pin, which makes contact 
 at a when the breech is closed. From a, the circuit continues 
 through the insulated metal base plug to the ring c, thence 
 through the platinum wire bridge c to a second ring d, which 
 is in electrical contact with the cup that forms the base 
 of the powder pocket. This cup, in turn, communicates
 
 NAVAL ORDNANCE 203 
 
 with the walls of the primer and then with the walls of 
 the gun, and the gun is connected to the hull of the ship; 
 that is (electrically speaking) to earth. As the circuit is 
 grounded on the other side of the firing key, the closing 
 of this key completes the circuit, raises the wire of the 
 bridge e to incandescence, and ignites a wisp of guncotton 
 that is wrapped around the wire, thus firing the primer 
 and igniting the charge. 
 
 
 ■■....^.^■s,^,^,^.-,^^'.^,..,„„,^ ys \ V^'SSggg 
 
 l 
 
 Fig. 7 
 
 Fig. 7 shows a combination primer (percussion and electric), 
 the principle of which will be readily understood from what 
 has preceded. This primer is used for ordinary' breech-load- 
 ing guns where the flame has to make its way through a 
 long vent, and since this calls for a considerable quantity of 
 powder, the primer is necessarily much longer than the ordi- 
 nary. The combination primer for fixed ammunition is 
 identical with this in all respects except the length. 
 
 PROJECTILES 
 
 The projectiles for rifled guns are elongated and are held 
 point foremost, as they drive through the air, by the rapid 
 rotation about their axis, imparted to it from the twist of 
 the rifling. To make the projectile engage the rifling, it 
 is fitted with a rotating band c, c. Fig. 1, of soft copper a 
 little larger than the bore of the gun, the projectile itself 
 being a little smaLcr than the bore. When the projectile 
 is loaded, it passes freely through the enlarged powder 
 chamber and enters the bore, but the band brings up against 
 the band slope and prevents the projectile going farther. 
 When the gun is fired, the pressure of the gases drives the 
 soft band through the grooves, and sends it whirling down
 
 204 
 
 NAVAL ORDNANCE 
 
 the bore and out at the muzzle, spinning around its axis 100 
 times per sec. In Fig. 1 (a) and {b) is shown, respectively, 
 a projectile before and after firing at an armor plate; the 
 right-hand figure shows the effect of the rifling on the soft- 
 copper band. 
 
 The projectiles now commonly used in naval guns are 
 shown in Fig. 2, of which (a) is the armor-piercing shell, 
 (b) the common shell, and (c) shrapnel. Both armor-pierc- 
 ing shell and common shell are made of forged and tem- 
 pered steel. They differ 
 from each other chiefly in 
 the size of the interior cav- 
 ity, which carries the burst- 
 ing charge, and in the 
 thickness of the walls. In 
 order that they shall have 
 the same weight when 
 filled, the common shell is 
 considerably longer than 
 the armor piercer. 
 
 Armor-piercing shells are 
 intended, primarily, to pen- 
 etrate the heavy armor of 
 battle ships and armored 
 cruisers. It is very desir- 
 able that they should burst 
 after getting through; but 
 whether or not they can be 
 made to do this depends 
 on the kind of explosive with which they are loaded (black 
 powder, guncotton, lyddite etc.) and on the nature of the 
 fuse that is used to explode them. Both of these matters 
 will be considered later. A good armor-piercing shell should 
 penetrate a thickness of hard-faced armor equal to its own 
 caliber. Thus a 6-in. shell should penetrate G in. of armor 
 without breaking up. 
 
 Common shells are designed to penetrate the unarmored 
 parts o£ ships, and parts protected by comparatively thin 
 armor. As they carry a very large bursting charge, they 
 
 Fig. 1
 
 NAVAL ORDXAXCE 
 
 205 
 
 cannot fail to be very destructive to the interior of a ship 
 and to the personnel if they can be made to burst inside. 
 Here again the question of the bursting charge and the 
 fuse comes in, but this difference may be noted between 
 an armor-piercing and a common shell; that the former 
 accomplishes its principal purpose if it penetrates or breaks 
 up the enemy's armor, even if it does not explode; whereas 
 the latter fails of its principal purpose if it does not explode 
 inside the enemy's ship. 
 
 Shrapnel are used only against exposed masses of men, 
 whether on shore, on 
 the deck of a ship, or 
 in boats. This class 
 of projectiles is al- 
 ways fitted with 
 time fuses, set to ex- 
 plode at a certain 
 point of their flight, 
 the idea being that 
 they will explode 
 above and in front 
 of the body of men 
 against whom they 
 are fired. As a re- 
 sult of the explosion, 
 not only the frag- 
 ments of the shell, 
 but all the small 
 balls with which the 
 interior is filled, are 
 scattered over a wide 
 area. 
 
 Capped Projectiles. — The capped projectile, types of 
 which are shown in Fig. 3, is a development of the last few 
 years, and has increased the penetration, other things being 
 equal, by about 15%. The action of the cap has not been 
 satisfactorily explained, but the following indicates the 
 direction in which the explanation is to be found: When 
 a projectile strikes an armor plate, the plate springs back
 
 206 
 
 NAVAL ORDNANCE 
 
 more or less under the blow, and at the same time a con- 
 siderable part of its face is "dished" a little, the whole of 
 this action resulting from the elasticity of the plate and its 
 supporting structure. This spring of the plate is unfavor- 
 able to penetration; the point of the projectile would break 
 through the face of the plate more easily if the latter had 
 no spring to it. When a capped projectile strikes a plate, 
 the cap does the work of driving back the plate and dishing 
 it, and the point, when it breaks its way through the cap. 
 
 Fig. 3 
 
 finds the plate comparatively rigid. This is a favorable 
 condition for the action of the point, and it gets through 
 more easily than it would if the plate were yielding while 
 it (the point) was trying to get in. We must, of cour.se, 
 recognize that the total work done in the plate is no greater 
 in one case than in the other, but that the division of the 
 work into two parts — the elasticity being exhausted before 
 penetration begins — seems to make the penetration greater 
 than it would otherwise be. All armor-piercing shells are 
 now capped. 
 
 FUSES 
 
 Fuses are divided into two general classes — time and 
 percussion. 
 
 The time fuse is one that can be so arranged as to cause 
 the explosion of a shell at the end of a certain interval of
 
 A^4F.4L ORDNANCE 
 
 207 
 
 time. This is accomplished by means of a column of slow- 
 burning composition that is ignited in some way on the 
 firing of the gun, the length of the column being such that 
 it will bvirn for the desired interval of 
 time before communicating flame to 
 the bursting charge. The length of 
 the column can be adjusted for the 
 desired interval before the shell is fired. 
 Time fuses are used in the Navy for 
 shrapnel only, these being the only 
 projectiles that are exploded before 
 striking the target at which they are 
 fired. 
 
 A percussion fuse carries a percus- 
 sion cap that is exploded on striking a 
 target, provided that the shell meets sufficient resistance to 
 slow it down materially. The cap is exploded by a sharp- 
 pointed plunger, which drives forwards when the shell is sud- 
 denly slowed down or arrested. It is, of course, very impor- 
 tant to hold the plunger securely until the time of firing, so 
 
 that it cannot pos- 
 
 sibly strike the cap 
 and explode it by 
 a cc i d e n t . M a n >- 
 arrangements have 
 been devised for this 
 purpose; and it is the 
 nature of this device 
 that, to a great ex- 
 tent, determines the 
 individuality of the 
 many patented fuses 
 that are in common 
 use. Two characteristic devices are shown in Figs. 1 and 2. 
 In the Navy percussion fuse. Fig. 1, the plunger P is held in 
 place by a brittle wire that is strong enough to resist any 
 ordinary shock to which a projectile might be subjected in 
 handling, even if dropped from a considerable height. The 
 shock of discharge of the gun is sufficient to break the wire, 
 
 Fig. 2
 
 208 NAVAL ORDXANCE 
 
 and as the projectile moves forwards, the plunger is thrown 
 to the rear of the cavity in which it fits. When the shell 
 strikes, the plunger flies forwards and pierces the cap. The 
 flame from the explosion of the cap flashes through several 
 channels (not shown) to the interior of the shell, where it 
 ignites the bursting charge and explodes the shell. 
 
 In the Driggs fuse, Fig. 2 (a), the plunger is held in place 
 by two springs c, c\ that are thrown outward as in (6), 
 when the shell is fired from the gun, by the centrifugal 
 force due to the rotation of the shell. This releases the 
 plunger and leaves it free to act. This principle of a spring 
 or catch holding the plunger under ordinary circumstances, 
 but released by the spinning of the shell, has been applied 
 in a great variety of ways, some of them extremely ingenious. 
 
 Base Fuses. — All fuses are now used in the base of the 
 shell, leaving the point of full strength for penetration. 
 This makes it important to have a gas-tight joint where 
 the fuse screws in, as a leak of gas into the interior of the 
 shell will cause the shell to explode in the bore. 
 
 Delayed-Action Fuses. — A delayed-action fuse is one in 
 which the mechanism is so arranged that the explosion of the 
 shell, instead of taking place immediately upon impact against 
 armor, is delayed until the shell has had time to penetrate, 
 thus causing the explosion to take place inside the ship 
 instead of outside. Many very ingenious fuses of this kind 
 have been devised, but their mechanism, being somewhat 
 complicated, cannot be explained here for lack of space. 
 
 GUN MOUNTS 
 
 The structure on which a gun is carried, and by which it 
 is controlled in pointing and firing, is called a mount, or, 
 sometimes, a carriage. The requirements of a carriage are 
 that it shall admit of easy and rapid pointing, both in azimuth 
 and in elevation; that it shall lend itself to maximum rapidity 
 of fire; that it shall absorb the inevitable recoil of the gun 
 without undue strain; that it shall have sufficient strength 
 to withstand such strains as, under the most extreme condi- 
 tions, will result from the recoil; and that it shall return the 
 gun automatically to the firing position (technically, "to
 
 NAVAL ORDNANCE 209 
 
 battery") immediately after the recoil. As a rule, the mount 
 is in two parts, one of which can move in and out upon the 
 other. The gun is attached to the movable part, the top 
 carriage, and this top carriage recoils with the gun. In the 
 simplest style of mount, used only with the smallest guns, 
 the top carriage, carrying the gun, moves laterally around a 
 heavy pivot fitting into the lower part of the mount, but no 
 recoil is provided for, the shock of firing being absorbed by 
 the "give" of the mount. This puts a great strain on the 
 mount and the part of the ship to which it is secured, and 
 is not practicable with guns larger than the 6-pdr. 
 
 In a great majority of the mounts now in use, the recoil 
 is absorbed by a piston moving through a liquid in a cylinder. 
 This liquid is usually water, to which a certain percentage 
 of glycerine is added to prevent freezing. The piston rod 
 is attached to the top carriage, and the cylinder to the 
 lower carriage (or the reverse). To admit of a flow of 
 liquid past the piston, grooves are cut along the interior 
 surface of the cylinder, affording channels through which 
 the liquid makes its way from one side of the piston to the 
 other as the piston is forced through. Evidently, the 
 width of these grooves determines the freedom with which 
 the piston can move; that is to say, the freedom of recoil. 
 As it is desirable that the recoil should be very free at first, 
 and checked gradually, the grooves are made wide at that 
 part of their length which corresponds with the beginning of 
 motion, and are gradually "choked" down toward the oppo- 
 site end. The length, width, and depth of the grooves evi- 
 dently determine the length and velocity of recoil, and these 
 dimensions are carefully calculated for each class of gun. 
 
 For returning the gun to the firing position after recoil, 
 heavy spiral springs are used in the cylinders. These springs 
 are compressed by the recoil and must, of course, play an 
 important part in checking the recoil, their resistance 
 being added to that of the liquid. As soon as the recoil is 
 arrested, the springs run the gun out ready for another fire. 
 
 The gun is, whenever practicable, secured near its center 
 of gravity to the top carriage, so that it w^ll be balanced 
 perfectly, and its bearings are made so nearly frictionless
 
 210 NAVAL ORDNANCE 
 
 that very little power is needed to elevate or depress. The 
 little power required is furnished by a beveled gearing in 
 the hands of the pointer, who, with his eye ranging along 
 the sights, endeavors to keep the gun pointed on the target 
 in spite of the rolling and pitching of the ship. 
 
 The lateral training is done by another set of gear-wheels, 
 worked by another gun pointer, who also is provided with 
 a sight, and whose duty it is to keep the gun trained upon that 
 point of the enemy's length at which he is told to aim. 
 The pointer who has charge of the elevation controls the 
 firing key and fires the gun; his object should be to keep 
 his sight on the target at all times. This is called continuous 
 aim, and has only recently been made possible by the improve- 
 ment in gun mounts and sights. The "importance of it in 
 the case of a single shot may be explained as follows: There 
 is a perceptible interval between the instant when the 
 pointer decides to fire and the instant when the projectile 
 actually leaves the muzzle of the gun. This interval for 
 an 8-in. gun of 50 calibers is found to be, roughly, -^ sec. 
 Suppose the ship to be rolling 10 times per min., through 
 6° on each side of the vertical. The muzzle of the gun will 
 sweep through 12' of arc in xV sec, and this at a range of 
 2,000 yd. corresponds to an error in height on the target 
 of 21 ft. Thus, if the pointer decides to fire at a given 
 instant, his sights being exactly on the point of the target 
 which he wishes to hit, his aim may be thrown off by 21 ft. 
 by the time the projectile leaves the muzzle of the gun, 
 unless he continues to keep the sights on the target during 
 the actual discharge of the gun. Where a string of shots 
 is to be fired, the advantage of continuous aim is greatly 
 increased. Assuming that the system can be carried out 
 ideally, and assuming also that the lateral aim is main- 
 tained perfectly, as it easily can be, it should be possible 
 to fire as rapidly as the gun can be loaded, and to make a 
 hit every time. 
 
 Turret Mounts. — In the case of large guns mounted in 
 turrets, the lower carriage is composed of heavy slides 
 bolted to the turret and turning with it. The gun rests 
 in a cradle that moves in and out on the lower carriare
 
 NAVAL ORDNANCE 211 
 
 exactly as in the mounts for lighter guns. The elevation is 
 done by very heavy rams, usually hydraulic. The lateral 
 training of the turret trains the guns also. A vertical 
 framework in the rear of the gun furnishes guide rods for 
 an ammunition car, which runs up and down like an elevator 
 bringing ammunition from the magazines below to the 
 loading position in the rear of the guns. A rammer worked 
 by hydraulic or electric power, and installed directly in the 
 rear of the gun, pushes the projectile and the powder charge 
 from the ammunition car into the gun. The rammer is 
 telescopic in its working; that is to say, when not in use it 
 shortens on itself. A description of a turret mount would 
 demand more space than can be given here; the attached 
 illustration, however, gives a general view of mount for the 
 13-in. gun of the U. S. S. "Oregon," and by referring to the 
 accompanying numbers the essential parts of the mechanism 
 are readily identified. 
 
 1, gun;^, saddle; ^, front straps; 7, rear straps; //.recoil 
 cylinder; 13, rear bonnet; IS, stuffingbox and gland; 14, 
 opening for pump pressure and check-valve; 15, pre.- sure 
 side; 16, reverse side; 17, spring valve; £0, piston rod, h«.^d, 
 and nut; 21, overflow chamber; S2, connection for waste 
 pipe; S3, lug for elevator connecting-rod; 24, slide; S7, turret 
 girders; S8, deckings; ;?5, collar for pressure pipe; S^, pivot 
 bolts; 33, elevator; 35, elevator connecting-rod; 36, elevator 
 valves; 37, elevator valve rods and levers; 38, elevator pres- 
 sure pipe; 39, elevator exhaust pipe; 40, hydraulic rammer 
 in loading position; 42, hydraulic rammer brackets; 43. 
 hydraulic rammer transom; 44, hydraulic rammer trun- 
 nions; 4o, hydraulic rammer valves; 46, hydraulic rammer 
 operating lever; 47, hydraulic rammer fulcrum for lever, and 
 guide for valve stem; 48, ammunition car; 49, ammunition 
 car motor run in; 51, ammunition car motor valves; 52, 
 ammunition car motor pressure pipe; 53, ammunition car 
 motor exhaust pipe; 54, ammunition car guide rails; 56, 
 ammunition car bracket and sheave; 58, pedestal for 
 central column; 59, central column; 60, water section; 
 61, pressure pipe; 62. exhaust pipe; 63, platform; 64, ladder 
 to turret; 65, sights; 67, rollers; 68, roller paths.
 
 212 
 
 NAVAL ORDNANCE 
 
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 p-' •*■ in -^ I- ri r- tc ci ■*" ■♦' ^" t-^ 00 
 
 qoni 
 
 qoui 
 'ajoaiomSnaTiBjoi 
 
 jaaj^ 'm3naT lujox 
 
 ^^■>i^,-m-*-*t~'sa-i' 
 
 ^^ sc >o O CO >o O — ^ 00 00 
 o^" r^ r-^ O o — ' o cc =' ec M 
 -r o «o o ■« 35 ■« t- 00 X — 
 
 ■ X5 « --O 00 — — >0 
 
 suox 'jq3ia^ 
 
 qoai 'iaqiiBO 
 
 «-*-*-crf5in>nX5cto»«o;oxi 
 
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 O irt o 
 
 'v_ 3- cr cr =• cr s-js ^ ^ jC js o- o* ; 
 c = =' = .5 =' = a d a 3 a a a ! 
 «•^■*■^»ftlnlOX(©!©cC!OX^o^
 
 NAVAL ORDXAXCE 
 
 213 
 
 1 
 
 c 
 
 1 
 
 BUOi 
 -JOOJ 
 
 aizznn 
 
 6,932 
 
 7,498 
 8,011 
 13,602 
 13,864 
 14,709 
 
 13,864 
 15,285 
 27,204 
 25,985 
 46,246 
 33,627 
 40,350 
 
 fs'?^:^ 
 
 2.000 1 
 2,000 / 
 
 2,080 
 2,150 
 2,800 
 2,000 
 
 2,060 
 2,000 
 2,100 
 2,800 
 2,100 
 2,800 
 2,100 
 2,300 
 
 spnnoj 
 'aipoafojjjOiqSiaji. 
 
 f250 
 
 250 
 250 
 250 
 500 
 
 500 
 
 500 
 500 
 500 
 850 
 8.50 
 1,100 
 1,100 
 
 o ~ 
 
 Is 
 
 spnnod 
 'japjAOj 
 
 SS8I85lOinS 
 
 3 i i. % 
 
 sptinoj 
 
 'WPAOJ 
 
 uiioja 
 
 105 to 115 
 225 to 240 
 
 425 
 550 
 
 qoni 
 'jsqniBqo jo ^^3a^^ 
 
 42.1 
 42.1 
 45.1 
 45.1 
 64.0 
 .57.2 
 57.2 
 
 .57.2 
 57.2 
 75.6 
 74.1 
 91.9 
 80.9 
 
 qoai 
 ■SnxBta JO qiSaaq 
 
 195.2 
 
 195.2 
 242.8 
 282.8 
 271.0 
 247.3 
 283.7 
 247.3 
 294.9 
 313.4 
 343.1 
 388.1 
 370.5 
 370.5 
 
 qoni 
 '8Jog JO qjsuai ibjox 
 
 239.9 
 2:i9.9 
 290.5 
 330.5 
 335.0 
 306.3 
 
 343.8 
 307.3 
 354.9 
 389.0 
 419.2 
 480.1 
 454.5 
 454.5 
 
 188 J 'qjSnsT iBjox 
 
 21.5 
 
 21.5 
 25.4 
 28.7 
 28.6 
 27 4 
 
 27.4 
 31.2 
 33.3 
 36.8 
 41.8 
 40.0 
 40.0 
 
 snox 'jqSiajv 
 
 13.0 
 13.1 
 15.2 
 180 
 25.7 
 
 25.1 
 
 27.6 
 
 33.4 
 
 46.2 
 
 52 
 
 60.5 
 
 60.5 
 
 qoni 'Jsqil^O 
 
 X xxxxo o 2222222 
 
 
 Nature of Gun 
 
 8-in. b. 1. r., mark I. . 
 
 8-iii. b. 1. r., mark II. 
 
 81n. b. 1. r., mark III, of 35 cals. 
 
 8-in. b. I.r., mark III., of 40 cals. 
 
 8-in. b. 1. r., mark V., of 45 cals. 
 10-in. b. 1. r., mark I., of 30 cals. 
 10-in. b. 1. r., mark I., of 35 cals. 
 
 10-in. b. 1. r., mark II., of 30 cals. 
 
 10-in. b. 1. r., mark II., of 35 cals. 
 
 10-in. b. 1. r., mark 111., of 40 cals. 
 
 12in. b. 1. r., mark I. 
 
 12-in b. 1. r.,mark III., of 40 cals. 
 
 13-in. b. 1. r., mark I. 
 
 13-in. b. I. r., mark II. . 
 
 ^2 
 
 ^ ". I
 
 214 EXPLOSIVES 
 
 EXPLOSIVES 
 
 An explosive ma-\' be defined as a substance that, existing 
 normally in a solid or liquid state, and occupying, in that 
 state, a comparatively small volume, is capable of being 
 suddenly converted into gas with very great increase of 
 volume; or if it is prevented from expanding freely, then 
 with very great increase of pressure. 
 
 There are great differences between explosives in the 
 suddenness with which their explosion is effected; some 
 substances, like nitroglycerine, being converted into gas 
 almost instantaneously, while others require an appreciable 
 time. This difference is of very great importance in the 
 application of explosives to military purposes. We are 
 accustomed to think of the explosion of powder in a gun 
 as taking place instantaneously. The time occupied is 
 extremely short, but it is many times as long as that required 
 for the explosion of nitroglycerine. To understand the 
 difference, we must recognize the fact that an explosion is, 
 after all, only a case of combustion — a case, that is to say, 
 of the combination of certain substances with oxygen. 
 In ordinary cases of combustion, as of burning, the sub- 
 stance that bums (usually some form of carbon) finds the 
 oxygen for its combustion in the air; and as this supply is 
 very diffuse, and diluted by large quantities of nitrogen, 
 the combustion takes place slowly. In the case of gun- 
 powder, the oxygen for the combustion of the carbon exists 
 in a concentrated form in one of the solid ingredients of 
 the powder, where it is in intimate contact with the carbon 
 and other substances that are to be burned. This results 
 in an enormous increase of rapidity in the combustion, the 
 gases being given off so rapidly as to constitute an explosion. 
 In gunpowder, we have an example of a mechanical mixture 
 between the substances that are to be oxidized and the 
 substances that supply the oxygen for the oxidation (com- 
 bustion). Evidently, there will be a much more intimate con- 
 tact, and an even more sudden combination, if we associate 
 the oxygen and the substance with which it is to combine 
 in a single substance. Nitroglycerine is a substance of this 
 kind. It contains carbon and nitrogen, both of Vhich are
 
 EXPLOSIVES 215 
 
 oxidizable substances, and it also contains the oxygen neces- 
 sary to oxidize them. In appearance nitroglycerine resem- 
 bles a heavy oily liquid. If this liquid receives a shock, the 
 original arrangement of its components is broken up, and the 
 oxygen instantly combines with the carbon and nitrogen to 
 form various gases, thus producing an explosion that is many 
 times as violent as that of gunpowder, because many times as 
 sudden. Such an explosion as this is called a detonation. 
 
 The volume of the gases resulting from an explosion or 
 detonation is many times that of the solid or liquid from 
 which they are derived, but their volume is still further 
 increased by the heat that is liberated by the combination 
 of the various parts. Such a liberation of heat always 
 occurs when substances combine chemically with each 
 other, as, for example, when the carbon that makes up a 
 large proportion of our wood and coal combines with 
 oxygen, or burns. It is evident that a detonating explosive, 
 like nitroglycerine, is unfit for use as a propellant, that is, 
 for propelling a projectile from a gun, because the suddenness 
 and violence of its e.xplosion would burst the gun before 
 the projectile was started from its seat. What is needed 
 for a propellant is a more gradual explosion, the force of 
 which will be exerted more as a push than as a blow. To 
 illustrate the difference, let us imagine that a heavy sphere 
 of iron is lying on a smooth table. Strike this a sharp blow 
 with the hand, and the hand will be bruised while the 
 sphere will be hardly moved; the force exerted does not 
 have time to overcome the inertia of the sphere. Place the 
 hand against the sphere and push it, at first with little 
 pressure then with much more, but with, upon the whole, 
 no greater expenditure of force than was contained in the 
 blow. The sphere will be moved slowly at first, then 
 rapidly, and the hand will not be bruised at all. This is 
 the difference between a force applied suddenly and the 
 same force applied gradually; the first resembles, in a general 
 way, the violence of nitroglycerine, the other, the (compara- 
 tively) gradual action of gunpowder. 
 
 The same characteristic that makes the various high 
 explosives unsuitable for use as propellants makes them
 
 216 EXPLOSIVES 
 
 admirable for use as bursting charges in shell, since here 
 their violence is exactly what is needed, provided that it 
 is possible to explode them at the right moment. Unfor- 
 tunately, they are nearly all extremely sensitive to shock 
 and friction, which makes them very dangerous to handle 
 and to store, and especially dangerous for use in a shell that 
 is to be fired from a gun, because of the possibility of their 
 being exploded by the shock of discharge of the gun. This 
 danger is much less with some explosives than with others, 
 and the whole progress of development along this line has, 
 for many years, been directed toward the discovery of 
 explosives that, while having a maximum of power, will be 
 insensitive to ordinary shock, to friction, and to flame, 
 but capable of detonation by a fuse whose action can be 
 controlled with entire certainty. This will make it clear 
 that the fuse is as important as the explosive itself. If the 
 fuse is liable to act prematurely, there is still danger, no 
 matter how trustworthy the explosive may be. As nearly 
 all fuses contain fulminate of mercury, which is extremely 
 sensitive to shock, the problem of designing a fuse that 
 will be sure to act when the shell strikes, and not at any 
 other time, is a difficult one. 
 
 Perhaps the best known of the high explosives is nitro- 
 glycerine, previously referred to; it is extremely sensitive, 
 and is not very generally used in liquid form. Dynamite is 
 nitroglycerine absorbed in a soft and spongy sand called 
 Kieselguhr; in this shape it is much less sensitive to shock, 
 and may be handled and transported with a reasonable 
 degree of safety. It is much too sensitive, however, for 
 military purposes, and its use is limited to blasting. 
 Dynamite No. 2, Lithofracteur, and carhodynamite are modi- 
 fications of ordinary dynamite, and contain nitroglycerine 
 associated with some substance that is supposed to render 
 it safe in handling and transportation. 
 
 Guncotton, formed by treating ordinary cotton with nitric 
 acid, is in many respects the most convenient of the high 
 explosives. When dry it is very sensitive, but when wet (with 
 from 15% to 30% of water) it is insensitive to all ordinary 
 shocks, but may be caused to detonate by detonating dry
 
 EXPLOSIVES 217 
 
 guncotton in contact with it. The dry cotton can be detona- 
 ted in a number of ways, but the surest and most convenient 
 way is by a fuse of fulminate of mercury. Guncotton is com- 
 monly used for the explosive charge in torpedoes, the bulk of 
 the charge being wet cotton, while the fuse is made up of dry 
 cotton with an exploder of fulminate. Guncotton is some- 
 times used in this way as a bursting charge for shells. 
 
 Blasting gelatine is a compound of guncotton and nitro- 
 glycerine, in which, singularly enough, the qualities of both 
 ingredients are so far modified that the resulting compound 
 while retaining nearly all the explosive power of its two 
 constituents, is made less sensitive than either. It is 
 probably the safest of the high explosives, with the excep- 
 tion of wet guncotton. Rackarock is a mixture of potassium 
 chlorate and mono-nitrobenzene, the latter being an easily 
 oxidizable form of carbon, and the former a substance rich in 
 oxygen. HellhoTfiie belongs to the same class of explosives. 
 
 Fulminate of mercury, which has already been mentioned, 
 is one of the most sensitive and violent explosives known, 
 and therefore one of the most dangerous. It is, in fact, 
 never handled except in verv' small quantities. It is, how- 
 ever, almost indispensable in work with other explosives, 
 because the shock resulting from its detonation has some 
 peculiar characteristic, not fully understood, by reason of 
 which it can detonate any high explosive with which it is 
 in contact. Moreover, the flame from its detonation ignites 
 (and so explodes) gunpowder. It is this substance that is 
 used in percussion caps and in the cartridges of muskets 
 and revolvers; it is also used in almost all fuses for exploding 
 large shells, when extreme care must be taken to place the 
 fulminate in such a way that it cannot be set ofT by the 
 shock of firing the gun. This is not as difficult as the same 
 problem is when connected with a large quantity of explosive, 
 such as that which must be used to fill the shell. If the shell 
 were filled with fulminate, nothing could prevent its instanta- 
 neous detonation in firing the gun, and as a result the gun 
 would be blown into fragm.ents. The few grains of fulminate 
 used in detonators can be disposed of in such a way that it 
 will not feel the shock with violence enough to explode.
 
 218 EXPLOSIVES 
 
 Among the most common of the high explosives in use for 
 military and other purposes are picric acid, and the various 
 derivatives of this acid known as picrates. These sub- 
 stances are all high explosives, and many of them are so 
 extremely sensitive that they cannot be used for military 
 purposes. Others are so little sensitiva that a very large 
 charge of fulminate is required to detonate them. The well- 
 known English explosive lyddite is picric acid, and melinite, 
 the French explosive, is derived from the same acid. Shimose 
 powder, used by the Japanese with great effect in their war 
 with Russia, is known to be one of the many picrates. 
 
 One of the dangers in connection with picric acid arises 
 from the fact that this substance, when brought in contact 
 with iron or steel, forms the picrate of iron, which is almost 
 as sensitive to shock and friction as is the fulminate of 
 mercury. It is therefore necessary to coat the inside of 
 the shells with lacquer or asphaltum, and to be very careful 
 that the acid does not at any stage of preparation or handling 
 come in contact with bare iron. 
 
 Gunpowder. — Ordinary gunpowder (black gunpowder, as 
 it is now called) was invented some 6 centuries ago, and, 
 strangely enough, remains today practically unchanged in 
 composition, although variations have been introduced 
 from time to time in the proportion of the ingredients, and 
 imporliant variations in the size and shape of the grains. 
 It is a mixture of charcoal, sulphur, and potassium nitrate 
 (commonly called saltpeter), in the following proportions: 
 charcoal, 15%; sulphur, 10%; potassium nitrate, 75%. 
 Here we have an easily oxidizable substance, charcoal 
 (carbon), and a substance rich in oxygen, potassium nitrate. 
 Broadly speaking, the explosion consists in the production 
 from these solid substances of three highly heated gases — 
 nitrogen, carbon-monoxide, and carbon-dioxide. The first 
 of these exists originally in the potassium nitrate, where it 
 is combined with the oxygen. When the nitrate breaks 
 up, the nitrogen is left free (as a gas), and the oxygen com- 
 bines with the carbon to form the two other gases that have 
 been named. The sulphur assists in the various chemical 
 changes, but does not itself form a gas. It appears at the
 
 EXPLOSIVES 219 
 
 end of the explosion in combination with the potassium, 
 forming certain solid products which are responsible for the 
 smoke and the deposit in the bore, both of which are objec- 
 tionable features. 
 
 For many years, chemists and artillerists have been in 
 search of a powder whose explosion would give only gaseous 
 products. There were many advantages to be anticipated 
 from such a powder. It would be more powerful, because 
 all its energy would go into the gas that propels the pro- 
 jectile. It would be smokeless, because the smoke of black 
 powder is due to solid particles. And it would leave no 
 residue to foul the bore of the gun. In all this, there was 
 reason enough for seeking a new explosive; but it is only 
 within quite recent years that it has been regarded as an 
 absolute necessity. With the introduction of rapid-firing 
 guns into the Navy, it became necessary to have a powder 
 giving little or no smoke, if these guns were to be of any use 
 for the objects for which they were intended. For instance, 
 in repelling the attack of torpedo boats, the use of black 
 powder would entirely defeat the purpose of the guns, as 
 after the first few shots the cloud of smoke would com- 
 pletely obscure the whereabouts of the attacking force and 
 render the guns useless. It would, in fact, play directly 
 into the hands of the enemy by creating a curtain behind 
 which they could push home their attack with impunity. 
 
 The fact that the smoke given by black -powder is due 
 entirely to the solid products resulting from the combinations 
 formed by the potassium of the potassium nitrate, after 
 that substance has given up its oxygen for the combustion 
 of the charcoal, naturally suggested the idea of using some 
 nitrate that would give up its oxygen in the same way, bi.t 
 whose further compounds would be gaseous. Ammonium 
 nitrate is a substance of this kind, but it has the faculty of 
 absorbing water from the atmosphere so rapidly that it 
 is totally unsuited for use in gunpowder. It has, neverthe- 
 less, been the basis of many formulas for smokeless powder, 
 but none of these have been successful. 
 
 About 1890, there was brought out in Germany a powder 
 that, from its peculiar color, came to be known as brown ox
 
 220 EXPLOSIVES 
 
 cocoa powder. The composition of this was kept secret, but 
 analysis showed it to contain a much smaller proportion of 
 sulphur than black powder, and a larger proportion of salt- 
 peter and of moisture. These peculiarities, however, were 
 not sufficient to account for its superiority over black 
 powder. Yet this superiority was very marked. It gave a 
 higher velocity to the projectile, with much less strain on 
 the gun, and the smoke was notably less than with black 
 powder. The secret of its manufacture was closely guarded, 
 but chemists recognized the fact that this secret lay in the 
 nature of the charcoal used, and that this charcoal was not 
 as fully charred as that which was used for black powder. 
 Starting from this point, several manufacturers developed^ 
 cocoa powders that equalled, and in some cases exceeded, 
 the original German article. It is now known that the 
 original powder was made from straw that was charred by 
 superheated steam which did not reduce it to pure carbon, 
 but left much of the natural structure of the straw. This 
 partially burned straw retained oxygen, hydrogen, and 
 other substances in proportions that proved favorable to 
 the performance of the powder. 
 
 Cocoa powder entirely drove out black powder for large 
 guns. Although a distinct reduction was made in the 
 amount of smoke, in addition to improvements in other 
 respects, it still left much to be desired, and the search 
 for a really smokeless powder was continued. 
 
 It was natural that attention should be turned to the high 
 explosives, since all the products of these explosives are 
 gases; and shortly after the discovery of nitroglycerine and 
 nitrocellulose (guncotton), near the middle of the 19th 
 century, efforts were made to temper the violence of these 
 explosives sufficiently to make them suitable for use as 
 propellants. Guncotton was much more promising for this 
 purpose than nitroglycerine, and many promising results 
 were obtained by the early experimenters with it, some of 
 whom wrapped threads of the cotton spirally around wooden 
 or other cores, while others reduced the cotton to a powder 
 and mixed with it certain inflammable but non-explosive 
 substances, hoping by this means to tame and control the
 
 EXPLOSIVES 221 
 
 burning of the mixture. These mixtures frequently gave 
 good results; but they were unreliable and occasionally 
 detonated with destructive violence. The most important 
 step in advance came with the discovery that certain sub- 
 stances would entirely dissolve guncotton, completely 
 destroying the cellular structure that makes up its fibers, 
 and reducing it to a gelatinous mass that, when allowed to 
 set, takes on a hard, horny, semitranslucent character, 
 such as is familiarly seen in celluloid. Any substance 
 existing in this form is called a colloid. It was found that 
 in the colloid form, nitrocellulose burned rapidly, but with- 
 out any disposition to detonate, and that its burning could 
 be as perfectly controlled as that of black or brown gun- 
 powder. Moreover, it lost nothing of its power, since its 
 chemical composition remained unchanged. Thus the great 
 problem of a smokeless powder was solved. Among the 
 substances that have the power to dissolve nitrocellulose, 
 one of the most convenient is acetone, an aromatic liquid 
 resembling alcohol. Another convenient solvent is a mixture 
 of ether and alcohol. 
 
 The nitrocellulose having been dissolved in either of the 
 above solvents, the excess of the solvent is removed as far 
 as possible by compression and evaporation, but a con- 
 siderable quantity remains in the powder after it is fully 
 dried and gives the characteristic odor that is always asso- 
 ciated with smokeless powder. 
 
 The colloid is pressed into grains of the desired size and 
 shape, after which it is dried. It is then ready for use. 
 The smokeless powders now used by the United States, 
 France, and Russia are produced as just described; that is 
 to say, they are nitrocellulose powders pure and simple. 
 
 There is a class of smokeless powders that are a combina- 
 tion of nitrocellulose with nitroclygerine. As these are 
 both violent explosives, it is rather surprising to find that 
 mixing them produces a substance whose action can be 
 perfectly controlled; a substance, in short, that makes an 
 almost ideal smokeless powder. The explanation is that 
 the nitroglycerine acts as a solvent for the nitrocellulose, 
 dissolving it as perfectly as does acetone, and forming a
 
 222 EXPLOSIVES 
 
 perfect colloid. Po-.vders of this class are distinguished 
 from those that contain nitrocellulose only by referring to 
 them as nitroglycerine powders; but it must be remembered 
 that only a small percentage of their composition is really 
 nitroglycerine. The well-known English powder cordite is 
 of this class. It is very effective as a propellant, giving 
 considerably better results than the nitrocellulose powders, 
 but it develops so much heat in burning that it wears away 
 the bore of the gun very rapidly, by what is called erosion. 
 This makes it less satisfactory, on the whole, than the nitro- 
 cellulose powders, and there is talk among English artillerists 
 of substituting one of these for the cordite at present in use. 
 Granulation of Powder. — With any composition of powder, 
 whether black, brown, or smokeless, the size and shape of 
 the grains have an important effect on the action of the 
 powder in the gun. Broadly speaking, a small grain is 
 favorable to rapid combustion, and a large grain to slower 
 and more gradual burning. A small granulation is adapted 
 to a small gun, and a large granulation to a large gun. There 
 are, however, many other considerations that enter into 
 the problems of the most suitable granulation for a given 
 gun. When the powder is ignited, it burns slowly at first, 
 developing a pressure that, while still low, starts the pro- 
 jectile moving down the bore. This motion o*f the projectile 
 increases the volume in which the gases can expand, and so 
 would lower the pressure if it were not that more and more 
 gas is given off, so that the pressure is not only maintained 
 but is rapidly increased for a time; after which, the powder 
 being nearly or quite consumed and the space continuing 
 to increase very rapidly, as the projectile is driven toward 
 the muzzle, the pressure falls off almost as rapidly as it at 
 first increased. In a powder that burns too rapidly for the 
 particular gun in which it is used, the pressure rises suddenly 
 to a maximum, which perhaps puts a dangerous strain on 
 the gun, then falls off so quickly that it communicates 
 only a low velocity to the projectile. An ideal powder will 
 give a low maximum pressure, but will sustain this pressure 
 well down the bore toward the muzzle of the gun. To do 
 this we need what is called a progressive powder, or one, that
 
 EXPLOSIVES 
 
 225
 
 224 TORPEDOES 
 
 will bum slowly at first, then more and more rapidly, 
 keeping up the pressure behind the projectile until it actu- 
 ally leaves the gun. For this purpose, we must have our 
 grain of such a shape that, as it bums, the burning surface 
 will increase. Evidently this cannot happen with any 
 grain that bums entirely from the outside, as the grain 
 would grow steadily smaller and the surface would be 
 reduced. If the grain is pierced with holes that allow it 
 to bum from the inside outwards, as well as from the outside 
 inwards, we will have a constantly increasing burning surface 
 and therefore a progressive powder. This is the object of the 
 holes with which many forms of powder grains are pierced. 
 Such a grain, if having one hole only, is called single perfo- 
 rated or tubular; if having several holes, multiperf orated. 
 Many powders are made in solid flat strips or in sticks. 
 
 Various forms of granulation are shown in the figure, page 
 223, each form being designated by a number, as follows: 
 2, 13-in. smokeless; S, flake musket; 4, 8-in. 35 cal. smoke- 
 less; 5, 6-pdr. smokeless; 6, 4-in. 50 cal. smokeless; 7, 5-in. 
 40 cal. smokeless; 8, black musket; 9, black cannon; 10, 
 black hexagonal; 11, black Schagticoke rifle; 12, brown 
 prismatic; IS, 7-in. 45 cal. strip, experimental smokeless; 
 14, 8-in, 35 cal. stick, multiperforated smokeless; 15, 12-in. 
 40 cal. single-perforated smokeless; 16, sphere hexagonal 
 smokeless. 
 
 TORPEDOES 
 
 The torpedoes of the present day are all automobile; that 
 is, they carry in themselves their own motive power. In 
 the Whitehead torpedo, which is in almost universal use, this 
 power is supplied by an engine run by compressed air, the 
 air being stored in a reservoir that occupies considerably 
 more than half the total volume of the torpedo. Fig. 1 
 shows a Whitehead torpedo in section. Reference to this 
 figure will make the following description clear so far as the 
 general principles of its mechanism are concerned. A 
 description of the details would call for many times the 
 «pace that can be given to it here.
 
 TORPEDOES 
 
 225 
 
 War Head. — The bursting charge 
 of high explosive (usually guncot- 
 ton) is contained in the war head H, 
 and is exploded, in case the torpedo 
 strikes a solid object, by the action 
 of the fuse, which, as will be seen, 
 projects beyond the head. A plun- 
 ger in this fuse is driven in, on stri- 
 king, and pierces a percussion cap 
 containing fulminate of mercury. 
 The explosion of this cap detonates 
 the high explosive in the war head 
 with tremendous force; a force 
 amply sufficient to blow a hole in 
 the plating of any ship, and also, in 
 most cases, to explode the magazines 
 of the ship herself. The bursting 
 charge, in the latest type of torpe- 
 does, is 132 lb. 
 
 Exercise Head. — In firing the tor- 
 pedo for drill, an exercise head is sub- 
 stituted for the war head. This 
 exercise head is of the same dimen- 
 sions and weight as the war head, but 
 contains no explosive. It is some- 
 times made of very thin and soft 
 metal so that it collapses on stri- 
 king, thus proving that a hit has 
 been made. 
 
 Air Flask. — Immediately abaft 
 the head is the air flask B, which is 
 charged with air under a pressure of 
 more than 2,000 lb. to the square 
 inch. In the figure, this air flask has 
 been omitted for lack of space; it 
 is equal in length to distanjce from 
 point X to tail of torpedo. In bat- 
 tle, the flask is always kept charged, 
 and so perfect are the fittings of the
 
 226 
 
 TORPEDOES 
 
 valves communicating with it that the leakage is nardly per- 
 ceptible. Sufficient air is carried for a run of 2 mi., and it 
 is required that the first 1,200 yd. of this distance shall be 
 made at a speed of 35 kn. 
 
 Immersion Chamber. — The compartment C next abaft the 
 air flask is the immersion chamber, containing the mecha- 
 nism called the hydrostatic piston, by means of which the 
 torpedo is made to run at any desired depth below the sur- 
 face of the water. The details of this mechanism are com- 
 plicated, but its general principle is perfectly simple. The 
 
 Wa/trPrtssure 
 
 hi>/fr/,^AfSu/Mta^ 
 
 FlO. 
 
 object is to steer the torpedo down if it rises too high, and 
 to steer it up if it sinks too low. The hydrostatic piston 
 is actuated by two, forces that oppose each other; one of 
 these is a spring, the tension of which can be regulated by 
 screwing up a nut; the other is the pressure of the water, 
 which, of course, varies with the depth. The piston is 
 connected by a series of levers with a horizontal rudder at 
 the tail of the torpedo, so that as the piston moves back- 
 wards or forwards it cants the rudder up or down, and so 
 steers the torpedo up or down. In Fig. 2 (which is diagram- 
 matic merely) o is a water-tight bulkhead separating the
 
 TORPEDOES 227 
 
 immersion chamber from the adjoining (engine room) com- 
 partment. (See also, Fig. 1.) The immersion chamber is 
 absolutely water-tight, but the engine-room compartment 
 is open to the sea. Thus the water-pressure is felt on one 
 side of the bulkhead a, but not on the other side. A round 
 hole is cut in the bulkhead and covered by a flexible rubber 
 diaphragm. Inside this immersion chamber, a piston 
 moving in a guide tube is held against the rubber diaphragm 
 by a spring, which opposes its own tension to the pressure 
 of the water on the other side of the diaphragm. If the 
 water pressure exceeds the tension of the spring, the dia- 
 phragm is buckled in slightly, compressing the spring and 
 forcing back the piston. If, on the other hand, the water 
 pressure is less than the tension of the spring, the spring 
 extends itself and forces the piston the other way, buckling 
 the rubber diaphragm outwards into the engine compartment. 
 
 Attached to the piston, and moving with it, is one end 
 of a rod g, pivoted at e and connected through a system of 
 levers with the horizontal rudder at the tail of the torpedo. 
 If this rudder is canted upwards, it steers the torpedo toward 
 the surface; if canted downwards, it steers the torpedo down. 
 
 By screwing up a nut (not shown in the diagram), the 
 tension of the spring can be varied according to the depth 
 at which it is desired to have the torpedo run. Suppose 
 that it is desired to have it run at 10 ft. below the surface 
 so that it will strike the enemy's ship 10 ft. below the water- 
 line. The adjusting nut of the spring is then screwed to 
 a mark (previously determined by experiment) that we know 
 will make the tension of the spring exactly equal to the 
 water pressure 10 ft. below the surface. Suppose that after 
 the torpedo is launched, it starts off 15 ft. below the surface. 
 The water pressure on the diaphragm is too strong for the 
 spring, the spring yields, the piston moves forwards, the 
 rudder is canted upwards and steers the torpedo toward 
 the surface. Perhaps it now rises a little too high, allowing 
 the spring to overcome the water pressure and force the 
 piston back; this cants the rudder the other way and steers 
 the torpedo downwards a little. After a few variations 
 up and down, each one less marked than the one preceding.
 
 228 TORPEDOES 
 
 the torpedo steadies itself at the proper depth and keeps 
 this throughout the run. The actual working of the rudder 
 is accomplished by a small steering engine, the valve of 
 which is controlled by the rod from the hydrostatic piston. 
 This, of course, does not change the fact that it is the hydro- 
 static piston that governs the steering. 
 
 Main Engine. — The engine is in the compartment D next 
 abaft the immersion chamber, which compartment, as 
 already explained, is open to the sea. The engine is con- 
 nected with the air flask by a pipe (not shown in figure) in 
 which are two valves. One of these, the stop valve, is 
 opened just before the torpedo is fired, the other opens 
 automatically as the torpedo passes out of the tube, being 
 governed by a lever that projects above the torpedo in such 
 a position that it strikes against a projection on the tube 
 and is thrown back, opening the valve. Even this, how- 
 ever, does not start the engine. If it did, the propellers 
 •would begin to spin with great violence (technically to 
 race) before the torpedo entered the water. Another lever 
 must be tripped before the air can reach the valve chest 
 of the engine; this is a small lever so placed that as the 
 torpedo enters the water, the resistance of the water throws 
 down the lever and allows the engines to start. 
 
 Propellers. — To insure the straight running of the torpedo, 
 two propellers p p\ are used, placed "tandem," one being 
 right-handed and the other left-handed. The after one is 
 keyed to the shaft and turns with it. The forward one is 
 keyed to a sleeve on the shaft and worked from the shaft 
 by a set of beveled gearing. The necessity for two pro- 
 pellers turning in opposite directions arises from the ten- 
 dency that a propeller always has to throw the stern to one 
 side or the other, according as it is right- or left-handed. 
 
 Steering. — It will be noted that the torpedo, as thus far 
 described, has no arrangement for steering to right or left. 
 Until quite recently no such arrangement has been considered 
 necessary or practicable. It has been assumed that the 
 torpedo will follow the course in which it is launched, and 
 great care is taken to insure this by making the body per- 
 fectly symmetrical and balancing the weights as exactly as
 
 TORPEDOES 229 
 
 possible. When a torpedo is completed, it is tested as to 
 accuracy in running, and any defect is corrected by moving 
 a small vertical vane on the tail-piece, which, once adjusted, 
 is clamped securely and never thereafter disturbed. It is 
 well known that, as a matter of fact, torpedoes, however 
 carefully tested and adjusted, behave very erratically in 
 service. Cases have been known in which, after running 
 a certain distance, they have turned and run straight back 
 toward the ship from which they were fired. 
 
 The Obry Gear. — A very ingenious device, known as the 
 Obry gear, has recently been introduced, which can either 
 be used to keep the torpedo true to the course on which it 
 is launched, or can cause it to change its course after running 
 
 a certain distance and take up a . 
 
 wholly different course, decided I ^^ 
 
 upon just before firing. Supposa '^ -^ — 
 
 that a torpedo boat having two 
 
 tubes, one on each broadside, is \ 
 
 running toward a battle ship that ^ J 
 
 she proposes to attack. Under i ^' 
 
 ordinary circumstances, she would ^^ /' 
 
 have to change her course before ^s^ / 
 
 firing, in order to bring one tube to 
 
 bear, and the chance of making a 
 
 hit while changing course would be F "^ 
 
 very slight. If the torpedoes are 
 
 fitted with the Obry gear, she can turn both tubes off on the 
 
 bow or broadside and launch both torpedoes at once, the Obry 
 
 gear having been set in such a way that each torpedo, after 
 
 running 50 yd., for example, will turn and head directly 
 
 toward the enemy, as shown in Fig. 3. 
 
 The essential part of the Obry gear is a gyroscope, or 
 flywheel, that is set spinning at a very high velocity. The 
 principle of the gyroscope is this: A fly wheel which is spin- 
 ning in a given plane has a very strong tendency to con- 
 tinue spinning in that plane, and to resist any effort to turn 
 it into another plane. 
 
 In Fig. 4 is shown a view of the Obr\' gear, a being the 
 gyroscope and b the sector containing the actuating spring.
 
 230 
 
 TORPEDOES 
 
 The axis of the gyroscopic wheel is placed in a fore-and-aft 
 direction in the torpedo, and no matter how the torpedo 
 turns to right or left the spinning gyroscope by its inherent 
 directive force will cause the torpedo to turn back to its 
 original direction. In torpedoes using the Obry gear, 
 vertical rudders are fitted for steering right and left, as in 
 the case of the rudder of a ship or boat, and these rudders 
 are connected with the gyroscope. If, then, it is desired 
 to fire the torpedo on a certain course and cause it to keep 
 that course, the gyroscope is set spinning in the plane of 
 
 Fig. 4 
 
 the course, and if the torpedo swerves to either side, the 
 resistance of the spinning gyroscope moves the rudders and 
 steers it back. If we wish to run the torpedo for a short 
 distance and then cause it to turn, as in Fig. 3, the gyro- 
 scope is turned into the plane of the final course that we 
 wish to make the torpedo take up, and connect the rudders 
 in such a way (by means of appropriate mechanism) that 
 the gyroscope will take control of the steering after a certain 
 length of run and swing the torpedo into the plane in which 
 it (the gyroscope) is already spinning.
 
 TORPEDOES 
 
 231 
 
 The details of the Obry 
 mechanism are secret and, 
 of course, complicated, and 
 the device is not yet en- 
 tirely perfected. There is 
 no doubt,, however, of its 
 entire practicability, and it 
 will probably be in use 
 within a very short time. 
 
 Sinlcing Gear. — If a 
 loaded torpedo misses its 
 mark and fails to explode, 
 it would be left floating, 
 a menace to friends and 
 foes alike. Arrangements, 
 therefore, are provided, 
 such that if it does not 
 strike after running a 
 certain distance, a valve 
 opens automatically and 
 causes it to fill with water 
 and sink. 
 
 Launching Tubes. — Tor- 
 pedoes are fire^ from long 
 tubes, or guns, which, how- 
 ever, differ from ordinary 
 guns in that the impulse 
 they give to the torpedo is 
 sufficient only to launch it 
 clear of the ship and into 
 the water, when its own 
 engines take charge and 
 drive it forw'ards. On tor- 
 pedo boats and torpedo- 
 boat destroyers oven\-ater 
 tubes are used ; these tubes 
 are on deck, and are en- 
 tirely exposed to the pro- 
 jectiles of an enemy's ship.
 
 232 
 
 TORPEDOES 
 
 If a projectile strikes the fuse, it may explode the torpedo and 
 so destroy the boat carr>-ing it. This is a risk that must 
 be taken by vessels of this class, but it is one that cannot 
 properly be taken by larger ships, and on such ships tor- 
 pedoes, if carried at all, are carried below the protective deck 
 and are fired from underwater tubes. Fig. 5 represents an 
 overwater launching tube containing a torpedo ready for 
 firing, and in Fig. 6 is shown the torpedo just clear of the tube. 
 
 An overwater tube can be trained and pointed like a gun, 
 so far as lateral aim is concerned, but underwater tubes are 
 fixed and can be pointed only by the steering of the ship. 
 In the case of an underwater tube, special arrangements are 
 required to keep water from entering the ship and also to 
 prevent the nose of the torpedo from being thrown oflf by the 
 motion of the ship through the water, thus spoiling the aim. 
 
 The Torpedo Director. — The aiming of a torpedo from a 
 n-joving ship to strike another moving ship calls for quick
 
 TORPEDOES 
 
 233 
 
 and accurate estimate of the speed, course, and distance of 
 the enemy, and accurate knowledge of the speed of the 
 torpedo; and the application of these data to the solutiori 
 
 PosilionofEnemi/ X 
 ea Instant offiririf/ \\A 
 
 •^ 
 
 9 
 
 l^ 
 
 0^' 
 
 DIRECTOR. 
 
 
 DIRECTOR ENLARGED. 
 
 Position ofEnemy\ 
 allnsUuit qfstriking\ 
 
 Fig. 
 
 of a triangle. To fire directly at a ship i mi. distant and 
 moving 15 kn. would result in missing the mark by hun- 
 dreds of yards. The torpedo must be aimed ahead of him 
 bv an amount at which it will not do to guess. To solve
 
 234 TORPEDOES 
 
 the problems graphically, the torpedo director. Fig. 7, has been 
 devised. In this instrument, three bars are clamped upon 
 each other with movable clamps that may be secured by 
 setscrews. One bar a a' is graduated for the speed of the 
 enemy and is laid parallel with his course. The second 
 bar h b' is graduated for the speed of the torpedo. The 
 third bar c c' is a sighting vane, and is directed toward the 
 enemy's ship. In the upper diagram of Fig. 7 the three 
 lines a a', b b', and c c' represent the torpedo director, A the 
 position of the enemy at instant of firing the torpedo, and 
 B the position of enemy at instant of striking. The only 
 unknown factor in connection with the use of this instrument 
 is the speed of the hostile ship; but if this is accurately 
 estimated (which is possible) the torpedo stands a fair 
 chance of striking the target. 
 
 Torpedo Boats. — There has been much discussion within 
 the last few years with regard to the advisability of fitting 
 battleships to carry torpedoes. The discussion has ended, 
 so far as the United States Navy is concerned, in the decision 
 to carry them, but to lise underwater tubes only. This 
 decision is undoubtedly wise, but it is none ^the less true 
 that the most important sphere of usefulness for the torpedo 
 is found when it is used by a torpedo boat against a battle 
 ship or fleet of battle ships. A ship attacked on a dark 
 night by a horde of these little crafts closing in upon her 
 from all directions without warning is perhaps in the most 
 dangerous position in which she could be placed. The 
 effective range of the torpedo is not less than 1,500 yd., 
 and at that distance there is little hope of seeing a torpedo 
 boat even with the aid of a searchlight. If the boat is seen, 
 the defense of the battle ship lies in the rapid fire of her 
 light guns, but the chance that they will hit so small and 
 indistinct an object at a range of nearly a mile and inflict such 
 damage as to render the torpedo boat ineffective, is very 
 slight; and where a large number of boats attack at once, 
 their success should be almost assured. The torpedo of the 
 present is a vastly more dangerous weapon than that of even 
 a few years ago; and in the naval warfare of the future its his- 
 tory will be very different from what it has been in the past.
 
 SHIP BUILDIXG 235 
 
 SHIP BUILDING 
 
 PRINCIPLES OF CONSTRUCTION 
 
 To design and build a floating structure that will afford 
 comfortable living accommodation for many hundreds of 
 persons, convenient storage, not only for the necessaries of 
 life for this community, but for great quantities of freight, 
 with space for engines and boilers powerful enough to 
 drive the whole mass through the water at two-thirds the 
 speed of an express train, as well as space for the fuel needed 
 to maintain this speed for long periods of time; to make 
 this structure strong enough to withstand the shocks of 
 the heaviest gales and to have a hope of living safely through 
 the heavier shock of grounding or collision; all this is a task 
 •whose magnitude can hardly be overstated. And if to these 
 requirements we add the manifold items demanded by the 
 offensive and defensive features of a man of war, we have 
 what may not unreasonably be regarded as the most com- 
 plex problem of creative work with which the human mind 
 is called upon to deal. 
 
 Preliminary Considerations. — In designing a ship, it is 
 necessarj' first of all to form some idea of the size and weight 
 that she will have; the weight to include not only the ship 
 proper, but the full load that she is to carry. It is a prin- 
 ciple of hydrostatics that any floating body will settle in 
 the water until the part of it which is immersed displaces 
 a volume of water exactly equal in weight to the whole 
 of the floating body. If, then, a ship is to weigh, complete, 
 10,000 T., the volume of that part which is to be below the 
 water line must be exactly equal to the volume of 10,000 T. 
 of water. Provided that this volume is kept constant, 
 the factors of it may be varied by making the immersed 
 body long and fine and deep, or short and broad and shallow. 
 In and upon the underbody thus fixed the weights are to 
 be distributed. In this distribution, if the ship is a man of 
 war, comes an inevitable conflict between the demands for 
 hea\T guns, for thick armor, for powerful engines, and for
 
 236 
 
 SHIP BUILDING 
 
 large coal supply, which must be settled by a compromise 
 dictated by considerations of the special duty for which the 
 ship is to be used. 
 
 Stability. — In the arrangement of the weights and the 
 dimensions of the hull, the first consideration is the stability 
 of the ship; or, in other words, its safety from the possi- 
 bility of capsizing. The stability depends on what is 
 called the metacentric height, which may be thus explained. 
 Suppose that the ship is lying at rest in the water and in an 
 upright position, as in Fig. 1 (a). The center of gravity is 
 
 Fig. 1 
 
 at G, and we may consider the whole weight of the ship to 
 be concentrated at this point and acting downwards. This 
 downward force is balanced by the buoyancy of the immersed 
 section, constituting an upward force that may be considered 
 as concentrated at B, the center of figure of the immersed 
 section. These forces being equal and opposite, and acting 
 along the same straight line, the body remains at rest. 
 If the ship is inclined — as she continually will be by the 
 action of winds and waves and many other causes — the 
 center of gravity remains where it was before (unless there 
 is some shifting of weights), but the center of buoyancy
 
 SHIP BUILDING 237 
 
 changes its position because the form of the immersed 
 section has been changed, Fig. 1 (6). Suppose that the 
 new position is at C; now, the weight of the ship is at G, 
 acting downwards as before, but the buoyancy acts upwards 
 through C, on one side or the other of G. The distance 
 G Z between the Hnes of action of G and (7 is a lever, at 
 the ends of which these forces act to turn the ship. In this 
 case, the line C Z M, along which the buoyancy acts, cuts 
 the original line of its action G B a.t the point M. This- 
 point is called the metacenter. Since it is above G, the 
 forces that act on the ship when inclined from the vertical 
 will tend to bring her back to an upright position, and the 
 ship will be stable; that is, when she is heeled or rolled ta 
 either side the forces called into action will bring her back 
 to an upright position. If the line CZM should cut the; 
 line G B at a. point below G, the force called into play when- 
 the ship was heeled or rolled would act to heel her still 
 farther, and she would capsize. As the center of gravity 
 of a given ship cannot be varied greatly in the design of 
 the hull (since we must assume an approximate distribution 
 of weights as decided upon), the position of G is fixed, and 
 the designer must shape his under-water hull so as to place 
 the center of buoyancy in such a position that the meta- 
 center will be far enough above the center of gravity to 
 give the ship a strong disposition to return to an upright 
 position when moved out of this position by any change 
 whatever. The height of the metacenter above the center 
 of gravity is called the metacentric height. 
 
 A ship that has a considerable metacentric height is stiff, 
 but not steady. She will not roll ver>^ deeply, but she will 
 roU very quickly. As quick rolling is unfavorable for gun 
 fire, men of war are usually given rather slight metacentric 
 height, and this has in some cases been carried so far as to 
 reduce the stability beyond the point of safety. It is sup- 
 posed to have been this defect of design that caused the 
 capsizing of the British battle ship "Captain," in the Bay 
 of Biscay on Sept. 1, 1870. This ship had a verj^ slight 
 metacentric height and rolled little and slowly; but when 
 she found herself in a seaway that rolled her in spite of
 
 238 
 
 SHIP BUILDING 
 
 her sluggishness, she had not s-afficient righting moment 
 (or righting leverage) to return to an upright position. 
 
 Strain. — It is clear that a structure designed to meet the 
 strains to which a ship is subjected must have great strength. 
 At one instant, the ship may be resting on the crest of a 
 wave, Fig. 2 (a), which supports her amidships, while the 
 ends hang altogether unsupported; an instant later, the ends 
 
 
 (b) 
 
 Fig. 2 
 
 may be buoyed up and the midship section unsupported, 
 as in Fig. 2 (&). And the strains created thus are only a 
 few of the total strains that will be felt by a ship rolling 
 and pitching in a sea, while being driven through it by her 
 powerful engines. 
 
 Composition of the Hull. — In the following brief descrip- 
 tion of the most important features of a ship, reference will 
 be made to Figs. 3 and 16, representing the midship section 
 of a small steamer of very simple construction. Following 
 the description of this, note will be made of departures 
 from this type in the more elaborate construction of large 
 merchant vessels and men of war. 
 
 The frame is built of three principal parts: two angle 
 bars, with their flanges facing each other, connected by a 
 vertical floor plate of iron or steel riveted along its edges 
 to the flanges of the angle bars, as shown in section at 
 B C, Fig. 3. The outer angle bar is technically the jrame 
 bar, the inner one the reverse bar. The space between
 
 SHIP BUILDIXG 
 
 239 
 
 the bars is greatest at the midship line, and is gradually 
 reduced toward the turn of the bilge, above which point 
 the bars come together and are riveted to each other, 
 flange to flange, the floor plate being dispensed with, 
 as shown in section taken at ^4 B. The frames are con- 
 tinuous from gunwale to gunwale, crossing the keel with- 
 out a break. (This is not true of ships having double- 
 
 Guriiva/e Bar ^ ^ 
 
 ,i/^perDeckS/rif^'r 
 
 , fieverse frame 
 
 Sec/tonaf 
 A-B 
 
 P///ar- 
 
 Dec/t S^r/»^er P/a/e 
 
 Peverse Pram. 
 
 B/^eAee/so/? 
 
 \ 
 
 Rei'erse Frame 
 
 ' Cg/fferMee/scn- 
 
 F/oorP/a/e^ 
 
 "iS/e/e /nfercos/a/ /^ee/s 
 
 Fig. 3 
 
 bottoms, as will be seen hereafter.) The keel, in this case 
 a har keel. Fig. 4, extends fore and aft throughout the 
 length of the ship, being made up of as long sections as 
 can be obtained. The frames are rigidly secured to it by 
 the first strake of the outside plating, known as the
 
 240 
 
 SHIP BUILDING 
 
 Cenfer Kee/son 
 
 garboard strake. This strake is bent like an angle iron, one 
 flange (narrow) being riveted to the sides of the keel, while 
 the other and much broader flange is riveted to the frame 
 and the adjoining strakes of plating as shown in detail in 
 Fig. 5 (a). In {h) and (c) of the same figure is shown a second 
 and third type of keel, known, respectively, as the side-bar keel 
 and flat-plate keel. Above the floor plates lies another longi- 
 tudinal girder, running the whole length of the ship. This 
 is the main or center keelson. It is secured to the frames, 
 binding them rigidly together, and forms, with the keel, 
 the backbone of the ship. The longitudinal framing further 
 includes a number of side keelsons and stringers, some 
 running the full length of the ship, others a part of the 
 length only. And here it may be noted that all longitudinal 
 girders on the bottom of the vessel 
 are called keelsons, and those on 
 the sides, above the hWga, stringers. 
 At some distance on each side of 
 the center line comes the side keel- 
 son, worked intcrcostally; that is, 
 in short lengths between the 
 frames — intercostally being thus 
 distinguished from continuous. 
 The sections of this keelson are 
 very firmly secured to the frames 
 and the bottom plating, and add 
 greatly to the longitudinal strength 
 of the ship, though less than if they 
 were continuous. The method of securing the side keelson 
 to the frames by angle bars is shown in Fig. 3. Outside the 
 side keelson comes the bilge keelson, which, being on top of 
 the floor, is continuous; and along the side above the bilge 
 is a side stringer. (In a larger ship there would be several 
 of these.) The legs of the frames are tied together across 
 the ship by beams, one of these being used for every second or 
 third frame. The beams connect with the frames by bracket 
 plates, or knees, riveted to both. As the beams not only 
 resist the tendency of the frames to open out but also keep 
 them from closing in, they serve as both ties and struts. 
 
 
 Fig. 4
 
 SHIP BUILD I XG 
 
 241 
 
 The decks are laid over the beams and add much to the 
 longitudinal stiffness. They are reenforced by a special 
 
 F/afP/afeKeef. 
 Fig. 5 
 string piece, broad and flat, laid along the beams through- 
 out the length of the ship, and known as a deck stringer . 
 This acts like the deck planking, but is heavier, and is,
 
 242 
 
 SHIP BUILDING 
 
 moreover, founo running along every tier of beams, even 
 if these beams do not carry a deck. At their forward ends, 
 the keel and center keelson are connected to the stem, 
 which is in fact a vertical continuation of these girders at 
 the bow of the ship. At the after end, they are secured 
 to the foot of the rudder post, as indicated in Fig. 6. At 
 both bow and stern, additional strength is given by heavy 
 triangular pieces called "breasthooks," Fig. 8, set into the 
 
 angle that terminates the 
 body of the ship, and con- 
 necting the ends of the 
 stringers already described. 
 Fig. 7 is a view of the stern 
 of a vessel, taken in dry- 
 dock, showing rudder, star- 
 board propeller, and the 
 plating riveted \o the stern 
 parts. 
 
 The construction that 
 has just been described is 
 that of a very simple mer- 
 chant vessel. In larger 
 vessels, there are wide 
 divergencies from this, but 
 the general principles are 
 not greatly different. One 
 of the most important 
 divergencies is the double- 
 bottom construction, used 
 with many merchant 
 steamers for carrying water or ballast, and in men of war 
 to give security in case of grounding and of damage by tor- 
 pedoes. Figs. 9 and 14 illustrate this construction. 
 
 In Fig. 9 we note that the keel is of the flat type, similar 
 to the one shown in Fig. 5 (c), and that the center keelson, 
 instead of standing on top of the floors, is directly above 
 the keiel and riveted to it; also, that it cuts through the 
 frames, being itself a continuous girder throughout the 
 length of the ship. The same is true of the five longitudinals 
 
 Cue^ee/f-
 
 SHIP BUILDING 
 
 243 
 
 that w Jl be seen between the center keelson and the armored 
 deck. It follows that the frames in this part of the ship 
 cannot be continuous, but must be worked intercostally 
 between the longitudinals. This detracts somewhat from 
 the transverse stiffness' of the ship, but is very favorable 
 to longitudinal strength. Moreover, extreme precautions 
 
 Fig. 7 
 are taken to make the joints as strong and rigid as possible. 
 This construction is confined to that part of the ship (about 
 two-thirds of the total length) that has a double-bottom 
 proper. Beyond this part, at both bow and stem, the 
 frames are made continuous, and the longitudinals (except
 
 244 SHIP BUILDING 
 
 the center keelson) are intercostal. A comparison of Fig. 14 
 with Fig. 15 will show other points of difference between the 
 framing along the midship portions and at the ends, which 
 cannot be described here for lack of space. In Fig. 10 is 
 shown a construction in which a water-tight platform run- 
 ning throughout the length of the ship forms a double 
 bottom. 
 
 In Fig. 9 the double bottom extends on each side of the keel 
 to the fourth longitudinal, which thus forms the side bound- 
 ary of the water-tight cellular construction. These longitudi- 
 nals are therefore made water-tight by very careful construc- 
 tion and by calking. The center keelson and the second 
 longitudinal on each side are also made water-tight, so that 
 
 the double bottom is 
 divided longitudinally 
 into four sections, two 
 on each side of the keel. 
 o^ • Of J ^ ^<^(^y^»>. The third longitudinal 
 
 \ Wi%%^hm^ 1^ g'&qvl side has open- 
 
 ings through which the 
 9reas/^oo^ water can pass and 
 through which a man 
 can crawl for purposes 
 of cleaning and inspec- 
 tion. Similarly, every 
 Fig. 8 fourth or fifth frame 
 
 throughout the double-bottom is made solid and water-tight, 
 the others having manholes like those in the longitudinals. 
 The actual construction of the open frames is shown in Fig. 1 1 . 
 where c is the frame bar, h the reverse bar, and a a bracket- 
 plates corresponding to the floor plates of Fig. 3. 
 
 In Fig. 12 is shown a ship in process of construction, giving 
 an excellent view of the framing and the double-bottom con- 
 struction. In this ship, the third longitudinal on each 
 side, very conspicuously shown, forms the boundary of the 
 double-bottom, and the first and second longitudinals do 
 not run throughout the whole length of the ship. 
 
 The outside plating is riveted to the frames, and adjoin- 
 it?g plates are riveted to each other. Several methods of
 
 SHIP BUILDING 
 
 245 
 
 bringing the edges of the plates together are shown in 
 Fig. 13. It will be clear that the plating must add very 
 much to the strength of the ship, both longitudinally and 
 transversely. 
 
 Compartments. — A ship is divided internally into com- 
 partments for various purposes by bulkheads (partitions), 
 some running longitudinally and others transversely. These, 
 being riveted solidly to the frames, beams, etc., add very 
 greatly to the strength and stiffness of the ship. 
 
 y^e /<ee/ 
 
 
 In all modem steamers, a certain number of the bulk- 
 heads are made water-tight, to prevent the flooding of the 
 whole ship from a leak in one compartment. In men of 
 war, the water-tight compartments are very numerous. 
 Communication is afforded by means of doors, also water- 
 tight, which in the most recent ships can be closed by an 
 electrically governed mechanism operated from the bridge.
 
 246 
 
 SHIP BUILDING 
 
 Well up toward the bow is a bulkhead of exceptional strength, 
 known as the "collision bulkhead," designed to afford security 
 in the event of a head-on collision. 
 
 It is important that the water-tight compartments 
 
 Fig. 10 
 
 should not be too large, and this is especially true of those 
 which are near the ends of the ship or which are confined 
 
 Fig. 11 
 to one side. The flooding of a single very large compart- 
 ment on the starboard bow of the British battleship 
 "Victoria" led to the capsizing of that ship when she was
 
 SHIP BUILDING 
 
 247 
 
 k 
 
 i 
 
 
 ^-W . ' 
 
 #-B' 
 
 Fig. 12
 
 248 
 
 SHIP BUILDING 
 
 rammed by the "Camperdown" in 1893. Had the "Victoria" 
 had no water-tight compartments at all, she would doubtless 
 have sunk, but the catastrophe would not have been so 
 sudden, and the loss of life much less. 
 
 The interior division of a man of war is necessarily more 
 complicated than that of a merchant steamer. This sub- 
 division, together with many other interesting details of 
 
 /nner S/ra/ees Oout/e^ 
 ro Secure /7us/> C>u/erSuf;fyee. 
 
 the structure of a man of war, is shown in Figs. 14, 15, and 
 16, which are reproduced from Knight's "Modern Seaman- 
 ship" by the courtesy of the D. Van Nostrand Company, pub- 
 lishers. The elaborate bracing shown in Fig. 15 is needed to 
 strengthen the bow for ramming.
 
 SHIP BUILDING 
 
 249 
 
 Lightening Holes 
 
 SVid Beams 
 
 Fig. 14
 
 250 SHIP BUILDING 
 
 Many men of war have heavily armored decks protecting 
 their vital parts — that is, their engines and boilers, ammuni- 
 tion rooms, etc. This deck is nearly flat amidship, but 
 curves down toward the side to meet the upper edge of the 
 side armor. Such a deck may be rather thin on the flat 
 part, but must be thicker on the slopes, as here a shell stri- 
 king it would have a more direct impact. 
 
 The side armor rests upon an armor shelf built into the 
 frames, which is shown in Figs. 9 and 14. The armor is 
 secured by heavy bolts running through a. thick backing of 
 teak, and screwed into the inner face of the armor plate. 
 
 Armor. — The armor of modem ships is invariably of steel, 
 and is subjected to special treatment to give it the qualities 
 that are found to be necessary for resisting the impact of 
 heavy shells. These qualities are, first, hardness, to resist 
 penetration, and second, toughness, to resist breaking up. 
 These qualities are antagonistic to each other; ordinarily, 
 a steel that is tough is rather soft, while one that is hard is 
 almost necessarily brittle. The armor primarily used for 
 ships was of wrought iron, which was toiigh but soft. 
 
 The first steel armor — introduced a quarter century ago — 
 was much like wrought iron, though inferior to it. There was 
 no difficulty about making hard steel, but this was too brittle. 
 The first move toward combining the two properties consisted 
 in welding a hard steel face on a tough wrought-iron back. 
 This compound armor, as it was called, gave good results, the 
 hard face resisting penetration, and the soft back holding the 
 plate together. In more recent years a better solution of 
 the problem has been found in making a homogeneous plate 
 of steel, and hardening the face of it by a special process 
 of tempering. Two such processes have been invented, the 
 Harvey and the Krupp. These processes give a plate in which 
 the hard face and the tough back are combined without the 
 weld, which was a plane of weakness in the old compound 
 plate. In comparing armor plates with each other, it is con- 
 venient to refer their resisting power to that of wrought iron, 
 since this is almost perfectly uniform, and its characteristics 
 do not change from year to year. Accordingly, we say that 
 Harveyized armor has a resisting power of 2 (or a figure of
 
 SHIP BUILDIXG 
 
 Wood Deck Plank. 
 Deck Plahng 
 
 Deck Plating 
 
 Fig. 15
 
 252 
 
 SHIP BUILDING 
 
 Hammoch Cloth 
 y — -Spar Deck ^ 
 
 f -Covering Plate- 
 / Hammock 
 Berthing 
 
 HammocH . 
 Berthinq 
 
 ••^"FJ^Sft^n^a 
 ■ 'aterWau 
 -Beam 
 Arm 
 
 Fig. 16
 
 SHIP BUILDING 253 
 
 merit of 2), meaning that a given thickness has a power of 
 resistance equal to twice that thickness of wrought iron. 
 
 The very latest and best armor made, which is treated 
 by the Krupp process, or Kruppized, has a resisting power 
 of 2.5, and the turrets of our latest battle ships, the "Con- 
 necticut" and " Louisiana," which carry 10 inches of this 
 armor, have the same resisting power as if they were cov- 
 ered with wrought iron 25 inches thick. 
 
 NOTES RELATING TO SPEED, TON- 
 NAGE, AND COAL CONSUMPTION 
 OF A STEAM VESSEL 
 
 SPEED OF VESSELS 
 
 The exact amount of power required to propel a vessel 
 at a given speed cannot be deduced very readily from the 
 elementary' principles of mechanics. Instead, we must relv 
 on empirical rules based on the actual performance of vessels. 
 The conditions that influence the relation between power 
 and speed are many, but only a few of the more important 
 ones will be enumerated here. For instance, the area of the 
 blades of the screw propeller may not be sufficient for high 
 speed, owing to a churning of the water when the propeller is 
 revolved beyond a certain number of revolutions. Although 
 the power expended in revolving the propeller faster may be 
 considerable, the increase of the speed may be very slight. 
 A similar state of affairs may occur if the area of the buckets 
 of a paddle wheel is too small. It may be large enough 
 for a low rate of speed, and still be entirely too small for 
 a higher rate, thus showing, probably, a high efficiency of 
 the propelling instrument at a low speed, and a very poor 
 one at a higher rate. Again, the efficiency of the engine 
 may vary greatly for different powers developed by the 
 same engine. 
 
 For these reasons no positive rule can be framed that 
 will express the relations between power and speed under
 
 254 SPEED, TOXXAGE, 
 
 all conditions. By the following rule, however, the approx- 
 imate number of horsepower (I. H. P.) required to propel a 
 vessel at a certain speed may be found: 
 
 Rule. — Multiply the cube of the speed by the cube root of 
 the square of the ship's displacement, in tons; divide the product 
 by the constant corresponding to the length, speed, and shape 
 of the vessel. 
 
 Let /. H. P. = indicated horsepower; 
 
 Z) = displacement of vessel, in tons; 
 X = constant referred to; 
 5 = speed, in knots per hour. 
 The above rule expressed algebraically is then as follows: 
 
 The terms used in this formula are explained in the order 
 in which they appear. 
 
 Indicated Horsepower. — An engine generally absorbs a 
 certain amount of the work done by the steam owing to 
 friction of pistons, rods, and wearing surfaces. The actual 
 useful or net work put ftut by the engine is for this reason 
 less than that done by the steam on the pistons. The pres- 
 sure acting on the pistons is ascertained by attaching to 
 the cylinder an instrument called the indicator, which 
 registers on a sheet of paper the variation of the steam 
 pressure. The amount of power calculated from the mean 
 effective pressure obtained from the indicator card by 
 means of the indicator is known as the indicated horse- 
 power of the engine. 
 
 Displacement. — In the technical sense in which this 
 teriTi is applied to ships or any other floating bodies, dis- 
 placement refers to the displacement of the water by the 
 total or partial immersion of any object placed in it. The 
 volume of water displaced may be measured in cubic feet 
 or in tons, and the weight of water displaced (which is equal 
 to the weight of the floating object) is called the displace- 
 ment. 
 
 Constant. — The constant employed in the formula is 
 found in the following table:
 
 AND FUEL CONSUMPTION 
 
 TABLE OF CONSTANTS 
 
 255 
 
 Description of Vessel 
 
 Speed 
 Knots 
 
 i- 
 
 Under 200 ft., fair . . 
 
 9-10 
 
 9-10 
 10-11 
 11-12 
 
 9-11 
 
 9-11 
 11-12 
 
 9-11 
 11-13 
 
 9-11 
 11-13 
 13-15 
 
 9-11 
 11-13 
 11-13 
 13-15 
 15-17 
 15-17 
 
 i 200 
 
 Under 200 ft., line 
 
 2SU 
 
 Under 200 ft., fine 
 
 210 
 
 Under 200 ft., fine \ . .. 
 
 200 
 
 From 200-250 ft fair. . . 
 
 220 
 
 From 200-250 ft., fine 
 
 240 
 
 From 200-250 ft fine. 
 
 1 220 
 
 From 250-300 ft., fair 
 
 1 250 
 
 From 250-300 ft., fair 
 
 220 
 
 From 250-300 ft. fine 
 
 260 
 
 From 250-300 ft., fine 
 
 240 
 
 From 250-300 ft., fine 
 
 200 
 
 From 300-400 ft., fair 
 
 260 
 
 From 300-400 ft fair 
 
 240 
 
 From 300-400 ft., fine 
 
 260 
 
 From 300-400 ft fine .... 
 
 240 
 
 From 300-400 ft., fine 
 
 190 
 
 Above 400 ft fine 
 
 240 
 
 
 
 To determine whether a vessel is fair or fine, it is usual 
 to compare its displacement, in cubic feet, with the volume 
 of a rectangular box having a length equal to the length 
 of the vessel on the water-line, a width equal to the beam, 
 and a depth equal to the draft of the vessel diminished by 
 the depth of the keel. If the displacement is .55 of the 
 volume of the box, or less, the vessel is fine; if above .55 and 
 less than .70, it is fair. The quotient obtained by dividing 
 the displacement by the contents of the imaginary box is 
 called the coefficient of fineness. 
 
 Illustration. — To illustrate the application of the given rule, 
 suppose that a vessel 260 ft. long and finely shaped is to have 
 a speed of 15 kn.; what should be the indicated horsepower 
 of the engine, assuming the vessel to have a displacement of 
 1,000 T? From the table, we find X = 200. Inverting values 
 in the given formula, we find the required horsepower to be 
 153xf'l,000"2 ^ 3,375X100 
 200 200 
 
 /. H. P. 
 
 1,687.5. Ans.
 
 256 SPEED, TONNAGE, 
 
 TONNAGE AND DISPLACEMENT 
 
 By the application of a simple method known as Simpson's 
 rules, the volume of the immersed portion of a ship can be 
 ascertained; which, if considered as water and divided by 35, 
 will give the displacement, in tons. But as vessels vary 
 considerably in form, the mere length, beam, and draft of 
 a ship cannot be utilized for finding the displacement; 
 hence, the coefficient of fineness previously mentioned must 
 be used in the computation of displacement. Knowing the 
 extreme dimensions of a vessel and its coefficient of fineness, 
 the exact displacement is readily found. For example, 
 take a vessel 100 ft. long, 20 ft. beam, and floating at 8 ft. 
 draft, the coefficient of fineness being .6, the displacement 
 
 ^.jj^^ 100X20 X8X_-6 = 274.3 T. 
 oo 
 
 Tonnage refers to the internal capacity, or volume, of a 
 ship. A glance at a tonnage certificate or a register of 
 shipping for any vessel shows two distinct classes of tonnage, 
 viz., gross and net tonnage. 
 
 Gross tonnage is the entire internal capacity measured 
 according to certain rules, as specified in the navigation laws 
 of the United States, and according to size and type of vessel. 
 
 Net tonnage is the remainder after having taken from the 
 gross tonnage allowances for crew space, engine and boiler- 
 room, shaft alley, etc. The net tonnage is supposed to 
 represent the earning capacity of the ship, and it is there- 
 fore made the basis for port and navigation charges. The 
 detailed rules for computing tonnage are quite complicated, 
 and do not come within the scope of this pocketbook. 
 They will be found, however, in the navigation laws of the 
 United States, or under the Revised Statutes, Chap. I, 
 Title XLVIII, Sec. 4.150 to 4.153, and Chap. 398. If it be 
 required to ascertain the tonnage of a vessel, the best thing 
 to do is to submit the drawings and plans to the nearest 
 local inspector of the United States Steamboat Inspec- 
 tion Service. 
 
 Displacement, which is often confused with tonnage, is, 
 as stated before, the weight of the water that the ship dis- 
 p!:..js, or, what is the same thing, the weight of the ship
 
 AXD FUEL CONSUMPTIOX 257 
 
 itself and everything on board. Hence, the displacement of 
 a vessel varies from day to day. or from one voyage to 
 another, according to the cargo, coal, stores, etc. on board, 
 while tonnage, being determined by the type and internal 
 dimensions of the ship, remains constant. When the 
 dimensions and capacity of a certain ship are required, it is 
 usual to give the displacement as well as the gross and net 
 tonnage of the ship. Thus, the internal capacity of the 
 steamship "Dakota," belonging to the Great Northern Steam- 
 ship Company, is given as follows: Gross tonnage, 21,000; 
 net tonnage, 13,500; displacement, 37,500 gross tons. The 
 port and navigation charges for this vessel are therefore 
 based on 13,500 net tonnage. 
 
 PROBLEMS ON SPEED 
 
 Very often the question as to the number of revolutions at 
 which the engine must be run to drive the vessel at a certain 
 speed comes up before those in charge of a steamer. If the 
 revolutions per minute of the engine for a certain speed of 
 the vessel are known, the question may be readily answered. 
 Assuming the percentage of slip to remain constant, doub- 
 ling the velocity of the stream projected by the propelling 
 instrument, that is, doubling the revolutions of the engine, 
 and hence of the screw propeller or paddle wheels, doubles 
 the speed of the vessel. In other words, the speed varies 
 directly as the revolutions of the engine. 
 
 By the term slip is understood the velocity of the stream 
 projected by any propelling instrument, in reference to the 
 surrounding water, in a direction opposite to that in which 
 the ship moves. Since the actual velocity of the stream 
 cannot be obtained by calculation, it has become a common 
 practice to consider the pitch of the propeller P multiplied 
 by the revolutions per minute R as the speed of the stream. 
 Under this assumption, slip may be defined as the difference 
 between the theoretical speed, P' expressed by the formula 
 _ PXJ?X 60 
 6,080 
 and the actual speed of the vessel, in knots per hour; or, the 
 difference between the speed of a vessel corresponding to
 
 258 SPEED. TOXXAGE, 
 
 the product of pitch of the propeller and the number of 
 revolutions in a given time, and the actual speed of the 
 vessel in the same time. 
 
 The slip is usually expressed in per cent, of the velocity 
 of the stream propelling the vessel. 
 
 In actual practice the percentage of slip varies some- 
 what at different speeds and under different conditions; 
 hence, the following rule, which is based on the assumption 
 of a constant percentage of slip, does not give the ciact 
 number of revolutions per minute required. This can be 
 found only by actual trial. However, it will give a very 
 fair approximation. 
 
 Rule. — To find the number of revolutions per minute at which 
 to run the engine in order to give the required speed, divide the 
 product of the revolutions producing any given speed and the 
 required speed by the given speed. 
 
 Let i^ = revolutions per m.inute for a given speed; 
 5 = given speed; 
 R\ = required revolutions; 
 5i = required speed; 
 then, the given rule, expressed algebraically, will be 
 
 Ri = -^ 
 
 Example. — If a vessel is propelled at a rate of 16 kn. 
 when the engine is making 32 rev. per min., what should 
 be the number of revolutions per minute to reduce the 
 speed to 14 kn.? 
 
 Solution. — Applying the above rule, we find 
 
 „ 32X14 __ . . 
 
 Ri = — Tp — =28 rev. per mm. Ans. 
 
 Number of Revolutions Propeller Should Make to Run at 
 Required Speed, the Pitch of Propeller Being Known. — In 
 order to solve this problem, the slip of the propeller for 
 the required speed must be known ; and if not known from 
 trial-trip records, must be assumed at a conservative figure. 
 The slip of well-designed propellers varies between 5 and 
 15%, the average being about 10%. Owing to the slip of 
 the propeller, it must be run at a higher number of revolu- 
 tions than would be the case otherwise.
 
 AND FUEL COXSUMPTION 259 
 
 Let P = pitch of propeller, in ft.; 
 X = required speed, in knots; 
 7? = re volutions per minute at required speed; 
 A^ = number of feet, in a knot (6,080); 
 5 = per cent, of slip, expressed as a decimal. 
 The number of revolutions for the required speed is then 
 found by the proportion QOX P:N = K:RX(.1—S); whence, 
 „ 6,080 XiC , ., 60XPXi?X(l-S) 
 
 ^ = 60XPX(l-5)'^"^^ 6:080 
 
 Example 1. — The pitch of a propeller is 16 ft.; how many 
 revolutions per minute must it make to drive the ship at 
 the rate of 10 kn. per hour, the slip being estimated at 10%? 
 Solution. — Applying the first formula given, and sub- 
 stituting values, we get 
 
 „ 6,080X10 __. . 1 A 
 
 ^^60X16X(l-.l) = '°' ''''■ P^^ "^^"- "^"^^^'- '^"'- 
 Example 2. — A propeller having a pitch of 20 ft. makes 
 70 rev. per min.; from a trial-trip record, the slip is known 
 to be 12% at that number of revolutions. What is the speed 
 of the ship ? 
 
 Solution. — Applying the second formula given, we get 
 ^ 60X20X70X<1-.12) ,^.^, , . 
 
 K = QQSO ^ ^^^ ' 
 
 FUEL CONSUMPTION AND SPEED 
 
 The fuel consumption may be said to vary directly as the 
 horsepower developed (this is not exactly true, but only 
 approximately). The horsepower varies directly as the cube 
 of the speed, whence it follows that the fuel consumption 
 will also vary as the cube of the speed (approximately). 
 Let S = certain speed of vessel; 
 
 C" = coal consumption at speed S; 
 5 = new speed; 
 c = coal consumption at speed 5. 
 
 Then, c = -^ , and -^ = A 7=^
 
 •260 FUEL CONSUMPTION AND SPEED 
 
 Example 1. — A steamer consumes 100 T. of coal per da. 
 at a speed of 10 kn.; what should be the speed in order to 
 cut the coal consumption down to 50 T. per da.? 
 
 Solution. — Using the second formula, we find 
 
 5 = -v/ — = f^ 500 = 7.9, or 8 kn., nearly. Ans. 
 
 Example ?. — A steamer consumes 80 T. of coal per da. at a 
 speed of 12 kn. per hr. ; suppose that the speed is to be reduced 
 to 10 kn. per hr. ; what would be the fuel consumption per 
 da. at that rate of speed? 
 
 Solution. — Using the first formula, we find 
 
 103X80 1,250 ■ . oT ^ ■ A 
 
 <: = ^^- = -2^=44.8T. per da. Ans. 
 
 Example 3. — If a steamer consumes 15 T. of coal per da. to 
 produce a speed of 9 kn. per hr., how many knots would she 
 steam if the coal consumption were reduced to 12 T. per da. ? 
 
 Solution. — In this case, c = 12, 5 = 9, and C=15. Inserting 
 these values in the second formula, we find the new speed, or 
 
 3/12x93 3/4X729 a,v^-i, 001 . 
 5 = -%/ — i-^ — =-%/ =-— = F 583.2 = 8.3 knots per hr., nearly. 
 
 Ans. 
 
 Example 4- — A steamer consumes 20 T. of coal per da. at 
 a normal speed of 10 kn. per hr. The distance to the nearest 
 port where coal can be had is 600 mi., and the estimated 
 quantity of coal in the bunkers is but 35 T. Find what 
 •speed should be maintained in order to reach the coaling 
 station with the coal supply on hand. 
 
 Solution. — The best way to proceed in a case of this kind 
 
 is to assume a lower speed, say 8 kn., and calculate the new 
 
 .- .u . A .u 83X20 256 
 
 ■coal consumption tor that speed; thus, c= „ — ~"o^ 
 
 = 10.24 T. per da., or .43 T per hr. The time required to 
 cover a distance of 600 mi. at a speed of 8 kn. per hr. is 
 '8*' = 75 hr., and at a coal consumption of .43 T per hr. the 
 total quantity of coal required at that speed is 75 X .43 
 
 = 32} T. Hence, if a speed of 8 kn. per hr. is maintained, 
 the supply of coal on hand (35 tons) will suffice to reach the 
 coaling station under ordinary weather conditions. Ans.
 
 ROPES 261 
 
 In practice it is advisable to have a good margin of coal 
 in excess of the calculated amount, for the reason that the 
 actual coal consumption at the reduced speed will, as a rule, 
 exceed the calculated consumption because of the decrease in 
 economy of the engine, induced by reducing the developed 
 horsepower. 
 
 ROPES 
 
 Ropes in general use on shipboard, in reference to the 
 material from which they are made, are of three kinds: 
 hemp, manila, and wire ropes. Although wire rope is rapidly 
 superseding all other kinds, even for certain running gears, 
 fiber ropes are still used very extensively, and for certain 
 purposes can never be replaced by steel ones. 
 
 Fiber Ropes. — The very best of the fibers used in the 
 manufacture of cordage is the so-called manila fiber, which 
 is obtained from the leaf stalks of the Musa textilis, or textile 
 banana, the entire supply of which comes from the Philip- 
 pine Islands. This fiber is very strong and durable, but not 
 ver>' flexible, and, therefore, is not well adapted to the man- 
 ufacture of small cordage, though it is ver>' satisfactory for 
 the larger sizes. When dry it contains 12% moisture, and 
 will absorb as much as 40% in a damp atmosphere; moist- 
 ure, however, does not tend to promote the decay of this 
 fiber. In fact, in hot, dry weather an occasional wetting of 
 the rope is thought to prolong its life. A freezing tempera- 
 ture renders the fiber brittle. The hardest and strongest 
 fiber is that from the outer layer of leaf stalks; that from 
 the inner layers is increasingly fine and weak. The butts 
 of the fibers are stronger than the tops. 
 
 Next in importance is the common hemp, which is the fiber 
 of the stalk of the plant of that name. It is grown through- 
 out Europe, in India, and in some parts of America. The 
 kind best adapted to the manufacture of cordage is that 
 grown in Russia. This fiber is more flexible than manila 
 fiber, but less strong and less durable. It decays very 
 rapidly if kept wet. A tarred hemp rope immersed in water 
 is stated to have lost, in 4 mo., nine-tenths of its strength.
 
 262 
 
 ROPES 
 
 Hemp rope used on shipboard is invariably tarred. The 
 tar acts as a preservative on the rope, but has a tendency to 
 slightly reduce its strength and flexibility; the use of tar 
 in standing rigging also serves to diminish contraction and 
 expansion due to wet and dry weather. It is advisable that 
 a tarred hemp rope should not be used until 6 mo., or even 
 1 yr., after its manufacture. This period of rest allows the 
 tar to become uniformly distributed throughout the fiber, 
 and the English Admiralty Board states that the rope has 
 10% greater durability than if it is used as soon as made. 
 Manila ropes are never tarred. Hemp rope when not tarred 
 is known as white rope. 
 
 Coir, the fiber of the outer husk of the cocoanut, is occa- 
 sionally used in cordage manufacture, it is quite strong, but 
 is short, stiff, coarse, and rough. On account of its buoy- 
 ancy, and because moisture does not affect it, rope made of 
 coir is particularly well adapted for tow ropes. 
 
 In manufacturing rope, the fibers are first spun into a 
 yam twisted right hand. From 20 to 80 of these yarns are 
 twisted together left hand to form a strand. Three or four 
 strands are then twisted right hand into a rope. Ropes 
 composed of four strands generally have a center, or core, 
 
 consisting of a small 
 rope about which the 
 strands are laid. (See 
 b. Fig. 1.) This cen- 
 ter rope is called the 
 Jteart. The primary 
 object of the twisting 
 is to hold the fibers 
 in place, so that each 
 may do its share of 
 the work. When the 
 strands are twisted up left hand, the yams are untwisted, 
 but when the rope is twisted up right hand the strands 
 are untwisted and the yarns again twisted up. There is 
 thus a certain degree of equilibrium that the rope maker 
 endeavors to attain, at which the tendencies of the rope 
 and the strands to untwist are equal in amount and 
 
 Fio. 1
 
 ROPES 263 
 
 opposite in direction. If the twist is great, the rope is 
 hard and stiff, and keeps its form well, but it is not so strong 
 as a rope with less twist. 
 
 Hawser and Cable. — A rope of 3 strands is called a hawser, 
 a. Fig. 1. A rope of 4 strands is said to be shroud laid, b, 
 Fig. 1. Very large ropes are made by twisting 3 hawsers 
 together to form a cable, as in c. Fig. 1. 
 
 As a rope bends over sheaves and drums, the fibers slide 
 on one another, and are thus worn out quite rapidly, espe- 
 cially near the heart of the rope; a rope will therefore last 
 much longer if it runs over large sheaves. Rope is desig- 
 nated by its circumference, expressed in inches, and is 
 issued in coils of about 113 fathoms each. 
 
 Small Stuff is the name given to various small ropes used 
 on shipboard; they are distinguished by the number of 
 strands and yams used in their make up. Thus, ratline, 
 used principally for seizings and rattling down the rigging, 
 is composed of 3 strands twisted right hand, each strand 
 containing from 4 to 8 yams. Spun yarn is spun left hand, 
 and consists usually of three yarns; it is used extensively 
 for various purposes, such as, seizings, mousings, to serve 
 ropes, etc. Rope yarns are mostly made from condemned 
 tarred hemp rope; this too is a, very much needed article 
 around deck and aloft. A man should never go aloft 
 without a supply of rope yams; he will find them very useful 
 in fixing up and strengthening worn-out mousings, stops, etc. 
 
 Wire Rope. — Wire from which ropes are manufactured is 
 commonly either of iron or of steel. Steel wire has nearly 
 displaced iron, as it has, for most purposes, many advantages. 
 Iron wire ropes are, however, stUl made and used. The 
 only iron suitable for this use is the best quality of charcoal 
 iron, and most manufacturers advertise that they use 
 Swedish charcoal iron, the malleable iron made from the 
 pure ores of Sweden having acquired an excellent reputation 
 throughout the world. 
 
 The greatest strength in a wire rope would be attained 
 by laying the component wires parallel, and the strength 
 of the cable would then be equal to the sum of the strengths 
 of the individual wires composing it. Suspension-bridge
 
 264 
 
 ROPES 
 
 cables are actually constructed in this way, but this system 
 of construction is not suitable for running ropes. Such a 
 cable is a mere bundle of wires; it has no stability of form 
 and would spread out laterally where it came in contact 
 with a sheave or drum. The wires would rub against one 
 another, wear rapidly, and probably be broken one at a 
 time by kinking or by catching on something. In order to 
 overcome these objections, wire ropes, other than those 
 for large suspension bridges, are made up somewhat after 
 the model of the hemp rope; i. e., by twisting together a 
 certain number of wires to form a strand, and a certain 
 number of strands to form the rope. In recent years, a num- 
 ber of special rope sections have been introduced. The 
 wires composing a rope are all circular and of the same 
 diameter, the prevailing geometrical form of the rope section 
 
 Fig. 2 
 
 being the hexagon. The simplest form of rope strand is 
 composed of 7 wires, arranged as in Fig. 2 (a); 6 of these 
 strands are commonly arranged around a core of tarred 
 hemp to form the rope. This rope is largely used for trans- 
 mission purposes in manufacturing establishments, and for 
 shrouds, stays, etc. of the standing rigging of a ship. 
 Fig. 2 (&) shows a rope consisting of 6 strands, each being 
 made up of 12 wires, laid around a hemp center; this con- 
 struction makes an extremely flexible and very light rope, 
 and is used almost exclusively for running gear on ship- 
 board. In (c) is shown the type of construction known as 
 the special flexible hoisting rope consisting of 6 strands of 
 37 wires each, laid about a hemp center, combining extreme 
 flexibility and high tensile strength. It is used largely on 
 cranes, derricks, and dredges, and when galvanized it is
 
 ROPES 265- 
 
 frequently employed with great success for towing hawsers. 
 Fig. 2 {d) shows the ordinary hoisting-rope construction. 
 The 6 strands consist of 19 wires each, laid around a hemp 
 center. This construction combines flexibility, needed for 
 the rope to pass over drums and sheaves, and high tensile 
 strength. It is probably the most universally applicable of 
 any form of rope. 
 
 In special types of wire ropes, the hemp heart is 
 replaced by a core of wire. Such ropes are much stiffer 
 than those with hemp cores, and are only adapted for use 
 as standing ropes. The substitution of the wire for the 
 hemp core adds about 10% to the weight of the rope, but 
 does not add materially to its strength. This is because 
 the wires in the central strand, making a smaller angle 
 with the axis of the rope than those in the outside strands, 
 are not able to accommodate themselves to the stretching of 
 the rope under load and, therefore, carry an undue pro- 
 portion of the load, breaking before the wires are fully 
 loaded. 
 
 Protection of "Wire Rope. — Ropes used on shipboard are 
 mostly made of galvanized wire, the purpose being to pre- 
 vent corrosion by protecting the iron or steel of the wire 
 against contact with air or water. Galvanizing accomplishes 
 this in the case of standing ropes, but is not effective for 
 running ropes. The friction of the rope against sheaves, 
 drums, or anything else with which it comes in contact, 
 soon wears off a portion of the zinc, and with both zinc 
 and iron exposed and in contact with water, corrosion 
 proceeds more rapidly than it would if the zinc were not 
 present. A further objection to the galvanizing process is 
 that the necessary heating of the wire has the effect of par- 
 tially annealing it and, consequently, reducing its strength. 
 
 Various preparations are used for coating wire rope to 
 prevent corrosion due to exposure to water and dampness. 
 The most easily applied, and as effective as any, while it 
 sticks, is raw linseed oil. The chief objection to its use 
 is that, being a liquid, it runs or is washed off the rope in a 
 short time, necessitating another treatment, in default of 
 which the wires are soon corroded. In order to partially
 
 266 
 
 ROPES 
 
 meet this objection, the oil is sometimes mixed with its 
 weight of lampblack, thus giving it more body. The liquid 
 condition of the pure oil is, however, a great advantage, as 
 the oil finds its way readily into the interior of the rope, 
 and the inside wires are thus effectively protected. 
 
 MANILA ROPE 
 
 Circum- 
 
 Weight 
 
 Breaking 
 
 Strain 
 
 ference in 
 
 per Foot 
 
 
 
 
 
 Inches 
 
 in Pounds 
 
 Tons 
 
 Pounds 
 
 1 
 
 .019 
 
 .28 
 
 560 
 
 1 
 
 .033 
 
 .39 
 
 784 
 
 li 
 
 .074 
 
 .78 
 
 1,568 
 
 2 
 
 .132 
 
 1.36 
 
 2,733 
 
 2i 
 
 .206 
 
 2.14 
 
 4,278 
 
 3 
 
 .297 
 
 3.06 
 
 6,115 
 
 3i 
 
 .404 
 
 4.27 
 
 8,534 
 
 4 
 
 .528 
 
 5.78 
 
 11,558 
 
 4i 
 
 .668 
 
 7.39 
 
 14,784 
 
 5 
 
 .825 
 
 9.18 
 
 18,368 
 
 5i 
 
 .998 
 
 10.97 
 
 21,952 
 
 6 
 
 1.190 
 
 12.77 
 
 25,536 
 
 6^ 
 
 1.390 
 
 14.50 
 
 29,120 
 
 7 
 
 1.620 
 
 16.35 
 
 32,704 
 
 7h 
 
 1.860 
 
 18.14 
 
 36,288 
 
 8 
 
 2.110 
 
 19.93 
 
 39,872 
 
 9 
 
 2.670 
 
 23.52 
 
 47,040 
 
 10 
 
 3.300 
 
 27.10 
 
 54,208 
 
 11 
 
 3.990 
 
 30.69 
 
 61,376 
 
 12 
 
 4.750 
 
 34.27 
 
 68,544 
 
 13 
 
 5.580 
 
 37.86 
 
 75,712 
 
 14 
 
 6.470 
 
 41.44 
 
 82,880 
 
 NoTB. — For safe-working load, allow from one-fifth to one-seventh of the 
 breaking strain. 
 
 Pine tar, applied hot, is sometimes used, and one appli- 
 cation will last a long time on account of the viscous, sticky 
 nature of the material. For the same reason, however, the 
 preservative does not so readily reach the interior of the 
 rope. Coal tar aLso is used for this purpose. In order to 
 neutralize any acid that may be contained in either pine
 
 ROPES 
 
 267 
 
 or coal tar, it is usual to add slacked lime, in the proportion 
 of about 1 bu. to 1 bar. of tar. The mixture is boiled thor- 
 oughly before application. Sawdust is sometimes added, to 
 give additional body. 
 
 GALVANIZED IRON WIRE ROPE 
 
 (Used for Shrouds and Stays) 
 
 Composed of 6 Straxds axd Hemp Cexter, With 7 or 12 
 
 Wires to the Strand 
 
 
 
 
 Circumference 
 
 Circum- 
 ference in 
 Inches 
 
 Weight 
 per Foot 
 in Pounds 
 
 Breaking 
 
 Strain 
 
 Tons of 
 
 2,000 lb. 
 
 of New 
 
 Manila Rope 
 
 of Equal 
 
 Strength 
 
 Inches 
 
 
 .16 
 
 1.4 
 
 2 
 
 u 
 
 .20 
 
 1.8 
 
 It 
 
 
 .25 
 
 2.3 
 
 
 .36 
 
 3.2 
 
 3 
 
 If 
 
 .49 
 
 4.4 
 
 31 
 
 2 
 
 .64 
 
 5.8 
 
 4i 
 4f 
 
 2i 
 
 .81 
 
 7.3 
 
 2i 
 
 1.00 
 
 9.0 
 
 5 
 
 2f 
 
 1.21 
 
 11.0 
 
 5i 
 
 3 
 
 1.44 
 
 13.0 
 
 51 
 
 3i 
 
 1.70 
 
 15.0 
 
 6 
 
 3i 
 
 1.95 
 
 18.0 
 
 n 
 
 3f 
 
 2.25 
 
 20.0 
 
 4 
 
 2.55 
 
 23.0 
 
 8 
 
 4i 
 
 2.90 
 
 26.0 
 
 8i 
 
 4i 
 
 3.25 
 
 29.0 
 
 9 
 
 4f 
 
 3.60 
 
 32.0 
 
 9* 
 
 5 
 
 4.00 
 
 36.0 
 
 10 
 
 5i 
 
 4.40 
 
 40.0 
 
 lOi 
 
 5i 
 
 4.85 
 
 44.0 
 
 11 
 
 XoTE. — For safe-working load, allow from one-fifth to one-seventh of the 
 breaking strain. 
 
 The preceding and following tabular statements relating 
 to the weight and breaking strain for different sizes of wire 
 ropes have been furnished by the makers, principally by 
 Messrs. John A. Roebling Sons, Trenton, N. J., and should 
 for this reason be considered comparatively trustworthy.
 
 268 . ROPES 
 
 GALVANIZED STEEL HAWSERS 
 
 (Used extensively for towing) 
 
 Composed of 6 Strands and a Hemp Center. Each 
 
 Strand Consisting of 12 Wires and a Hemp Core 
 
 
 
 
 Circumference 
 
 Circum- 
 
 Weight 
 
 Breaking 
 Strain 
 
 of New Manila 
 Hawser of 
 
 ference in 
 
 per Foot 
 
 
 Equal 
 Strength 
 
 Inches 
 
 in Pounds 
 
 Tons of 
 2,000 lb. 
 
 
 
 
 Inches 
 
 2i 
 
 .54 
 
 12.3 
 
 5* 
 
 2i 
 
 .67 
 
 14.4 
 
 6 
 
 21 
 
 .81 
 
 16.4 
 
 6i 
 
 3 
 
 .97 
 
 21.5 
 
 8 
 
 3i 
 
 1.14 
 
 24.0 
 
 8i 
 
 3 
 
 1.32 
 
 27.0 
 
 81 
 
 3 
 
 1.51 
 
 29.0 
 
 9i 
 
 4 
 
 1.72 
 
 32.0 
 
 10 
 
 4i 
 
 1.94 
 
 39.0 
 
 11 
 
 4i 
 
 2.18 
 
 42.0 
 
 IH 
 
 4| 
 
 2.42 
 
 45.0 
 
 12 
 
 5 
 
 2.70 
 
 53.0 
 
 12i 
 
 5i 
 
 2.95 
 
 57.0 
 
 13 
 
 5i 
 
 3.25 
 
 61.0 
 
 13i 
 
 STEEL HAWSERS FOR HEAVY TOWING 
 
 Composed of 6 Strands and a He.mp Center, 37 Wires 
 to the Strand 
 
 Circum- 
 
 Weight 
 per Foot 
 
 Breaking Strain, in Tons 
 
 ference in 
 
 
 
 
 
 Inches 
 
 in Pounds 
 
 Cast-Steel 
 
 Special 
 
 3 
 
 1.44 
 
 31 
 
 40 
 
 3i 
 
 1.95 
 
 42 
 
 55 
 
 4 
 
 2.55 
 
 55 
 
 72 
 
 n 
 
 2.90 
 
 62 
 
 81 
 
 3.60 
 
 76 
 
 99 
 
 5 
 
 4.00 
 
 84 
 
 109 
 
 tt 
 
 4.85 
 
 101 
 
 131 
 
 6.25 
 
 128 
 
 166 
 
 Note, — For safe-working load, allow from onc-flftli to one-seventh of the 
 breaking strain.
 
 GALVANIZED CAST-STEEL WIRE ROPE 269 
 
 (Used for Yacht Rigging) 
 Composed of 6 Straxds and Hemp Center, 7 or 19 Wires 
 
 TO THE StRAXD 
 
 
 
 
 Circumference 
 
 Circum- 
 
 Weight 
 
 Breaking 
 Strain 
 
 of New 
 Manila Rope 
 
 ference in 
 Inches 
 
 per Foot 
 in Pounds 
 
 Tons of 
 2,000 lb. 
 
 of Equal 
 
 Strength 
 
 Inches 
 
 
 .16 
 
 3.7 
 
 3 
 
 Is 
 
 .20 
 
 4.5 
 
 3i 
 
 
 .25 
 
 5.7 
 
 4^ 
 
 }! 
 
 .30 
 
 6.8 
 
 4. 
 
 .36 
 
 8.1 
 
 4J 
 5k 
 
 
 .49 
 
 10.8 
 
 2 
 
 .64 
 
 14.0 
 
 6 
 
 2i 
 
 .81 
 
 17.6 
 
 7 
 
 2i 
 
 1.00 
 
 22.0 
 
 8 
 
 2| 
 
 1.21 
 
 26.0 
 
 8i 
 
 3 
 
 1.44 
 
 31.0 
 
 9 
 
 3i 
 
 1.70 
 
 36.0 
 
 10 
 
 3^ 
 
 1.95 
 
 41.0 
 
 11 
 
 3f 
 
 2.25 
 
 47.0 
 
 12 
 
 4 
 
 2.55 
 
 53.0 
 
 13 
 
 GALVANIZED IRON AND CAST-STEEL WIRE ROPE 
 
 (Used for Running Gear) 
 Composed of 6 Strands and Hemp Center, Each Strand 
 
 Consisting of 12 W 
 
 res and a 
 
 Hemp 
 
 Core 
 
 Circum- 
 
 Weight 
 per Foot 
 in Pounds 
 
 Breaking Strain 
 
 ference in 
 Inches 
 
 
 
 
 Iron 
 
 
 Cast-Steel 
 
 
 .11 
 
 1.14 
 
 
 
 2.28 
 
 1| 
 
 .13 
 
 1.60 
 
 
 
 3.20 
 
 1* 
 
 .17 
 
 2.15 
 
 
 
 4:30 
 
 IX 
 
 .24 
 
 2.78 
 
 
 
 5.56 
 
 If 
 
 .33 
 
 3.47 
 
 
 
 6.94 
 
 2 
 
 .43 
 
 4.29 
 
 
 
 8.58 
 
 2{ 
 
 .54 
 
 6.13 
 
 
 
 12.30 
 
 2i 
 
 .67 
 
 7.20 
 
 
 
 14.40 
 
 2f 
 
 .81 
 
 8.21 
 
 
 
 16.40 
 
 3 
 
 .97 
 
 10.70 
 
 
 
 21.50 
 
 3i 
 
 1.14 
 
 12.00 
 
 
 
 24.00 
 
 NoT«. — For safe-working load, allow from one-fifth to one-seventh of the 
 breaking strain.
 
 270 ROPES 
 
 SPLICES AND BENDS 
 
 Splicing is the operation of joining two pieces of rope so 
 as to obtain one continuous piece with no appreciable 
 increase of diameter at the splice. There are several kinds 
 of splices but the principal ones are the short splice, the 
 long splice, and the eye splice. The principle of all splicing 
 consists of joining or "marrying" the strands, thinning 
 them out, and tapering them so that the diameter at the 
 
 Fig. 1 
 
 splice is the same or only slightly greater than that of the 
 rope itself. In the long splice, no increase in diameter is 
 allowed. The only tools necessary for splicing hemp or 
 manila ropes used for ordinary running gears are a marline- 
 spike and a knife. The marlinespike is made of either iron 
 or hardwood, is from 12 to 14 in. long, and about 1 in. in 
 diameter at the thick end, the other end being sharpened to 
 a blunt point about as shown in Fig. 1 ; it is always operated 
 by the right hand, while the left encircles the rope. After 
 pushing the extreme point through between the strands to 
 be separated, the thick end is placed against the body of
 
 ROPES 
 
 271 
 
 the operator; then, using both hands, the rope is twisted 
 so as to render the work of opening the strands easy. 
 
 The marh'nespike should be provided with a good laniard, 
 attached to the hole in its thick end, and when vised aloft it 
 should be slung around the operator's neck or -secured to the 
 rigging. 
 
 The Short Splice. — To make the short splice, unlay the 
 strands at the end of each rope for a distance about as shown 
 in Fig. 2; this distance depends entirely on the diameter 
 of the rope, but as the proportion will be the same for all 
 diameters, the illus- 
 tration serves as a 
 general guide ; be 
 sure to unlay enough ; 
 a few inches too 
 much is better than 
 too little as the ends 
 have t o b e cut ofif 
 anj^vay. Then, place 
 the two ends together 
 as shown at Fig. 2 (a) , 
 so that each strand 
 lies between two 
 strands of the other 
 rope. Hold the 
 strands x y z and the 
 rope .4 in your left 
 
 ^ssssssssssss 
 
 (c) 
 Fig. 2 
 
 hand; if the ^ o p e s ^^^g^^^^^^SSSSSSSSa 
 are too large to hold fc»=>*^^**"^ 
 
 thus, fasten them to- 
 gether with twine; 
 then take one of the strands, say «, pass it over strand y, 
 and, having made an opening, either wnth the thumb or with 
 a marlinespike, in the manner illustrated in Fig. 1, push this 
 strand n through under x and pull it taut; this operation is 
 known as tucking. Proceed similarly with strands m and o, 
 passing each over the immediately adjoining strand and 
 under the next one. Perform precisely the same operation 
 with the strands of the other rope, passing each strand over
 
 272 
 
 ROPES 
 
 the adjoining one and under the next, thus making the splice 
 appear as at Fig. 2 (b). In order to insure security and 
 strength, this tucking must be repeated by passing each 
 strand over the third and through under the fourth; then, 
 after subjecting the spHce to a good stout pull, cut off the 
 ends of the strands, and you have the finished splice as shown 
 at Fig. 2 (c). 
 
 In slings and straps used for heavy work, the strands 
 should be tucked twice each way, and over one-half of each 
 strand should be whipped, or bound, with twine to one-half 
 
 Fig. 3 
 
 of the rest, in order to prevent the strands from "creeping 
 through" when the splice is taxed to the full capacity of 
 its strength. 
 
 In the short splice, the diameter at the joint is greater 
 than that of the rope, for which reason it is not a suitable 
 splice where the rope is to be used in tackles and pulley 
 blocks, or in places that will not admit anything larger 
 than the rope itself. In such cases the long splice is used; 
 this, when properly made, the untrained eye can hardly 
 distinguish from the rest of the rope. 
 
 The Long Splice. — To make the long splice, unlay the 
 ends as before, but about three times as far, and place
 
 ROPES 
 
 273 
 
 them together, as shown at Fig. 3 (a), in the same manner 
 as for the short spUce. Then unlay one of the strands, 
 say X of the right-hand rope, and in the groove thus made 
 lay the strands n of the left-hand rope, taking good care to 
 give this strand the proper twist, so that it falls gracefully 
 into the groove previously occupied by strand x. Do like- 
 wise with strands y and m, unlaying y gradually and in ifts 
 place laying the strand m\ the result is shown at Fig. 3 (&). 
 Now, leaving the middle strands p and g in their original 
 positions, cut off all the strands as shown at (6) ; then 
 relieve strands n and x of about one-third of their yarns, 
 
 and with what is left cast an overhand knot as shown — 
 taking care that the knot is made so that the strands will 
 follow the lay of the rope, and not cross it. Pull this knot 
 taut and dispose of the ends as in the short splice, by passing 
 them over the adjoining strand and through under the 
 next, cutting off a few yams at each tuck. Proceed similarly 
 with strands p and g, and y and m. The splice, when it is 
 completed, appears as at Fig. 3 (c). Sometimes the over- 
 hand knot is made without first thinning the strands, and 
 then split, and the half strand put through as described; 
 but by doing so, the surface of the splice is never as smooth as
 
 274 
 
 ROPES 
 
 by the other method, which, for strength and neatness, is 
 second to none. 
 
 The Eye Splice. — To make an eye splice, unlay the strands 
 about as far as for the short splice, and bend into the required 
 size of eye, as shown at Fig. 4 (a). Then tuck the end of 
 the middle strand y under one of the strands of the stand- 
 ing part — having previously made the necessary opening 
 with the marlinespike — and pull taut, getting what is shown 
 at (6). Push the strand x from behind, and under the strand 
 on the standing part next above that under which the 
 middle strand y was passed, so that it will come out where 
 >' went in, getting what is shown at (c); then pass the third 
 strand z under the remaining free strand in the standing 
 part, next to the one under which y was passed, getting (d). 
 Pull the strands taut, and from each cut out one-third of 
 the yams; pass each remaining two-thirds over the adjoining 
 strand of the rope, and then through under the next, as in 
 the short splice; then cut off one half of the yarns, and tuck 
 the other half under its correspond- 
 ing strand for the third time ; give it 
 a good stretching, cut off the ends, 
 and thus complete the splice as 
 shown at {e) Fig. 4. 
 
 In four-stranded ropes, the short 
 and long splice are made essentially 
 the same; in the eye splice, the first 
 strand is tticked imder two strands 
 of the rope, the second tucking 
 being done exactly as in the three- 
 stranded rope. 
 
 The Chain Splice. — To make a 
 cliain splice, unlay the strands of the 
 rope and reeve two of them through 
 the end link; then unlay the third strand for about the dis- 
 tance shown, and in its place lay one of the other strands, the 
 same as in making the long splice; make an overhand knot 
 and dispose of the ends in the usual way; dispose of the third 
 strand x — one of the two reeved through the link — as when 
 making the eye splice, by "tucking" near the link; cut off the 
 
 Fig. 5
 
 ROPES 
 
 275 
 
 ends, and the splice is com- 
 plete as shown at Fig. 5 ib) . 
 This is a very neat and 
 strong splice, and can be 
 used with advantage in 
 connection with chains 
 that are tailed, or length- 
 ened, with a rope that has 
 to pass through sheaves or 
 places that do not allow 
 any increase of diameter in 
 the rope. 
 
 Splicing in Wire. — In 
 making a long splice in 
 wire rope, the same prin- 
 ciples are followed as in 
 splicing fiber ropes. The 
 strands are unlaid, inter- 
 ne laced, and each placed 
 snugly in the groove made 
 ^ by unlaying the opposing 
 strand whence the ends are 
 tucked away in such man- 
 ner as to follow the lay of 
 the rope. Before unlaying 
 the strands, it is advisable 
 always to put on a good 
 seizing at the extremities 
 of the intended splice in 
 order to prevent the rope 
 from untwisting farther 
 than is desired. The 
 length of the splice de- 
 pends, of course, on the size 
 of the rope. When unlay- 
 ing the strands, be sure to 
 do so without taking the 
 turn out. The strands may 
 also be unlaid in pairs and
 
 276 
 
 ROPES 
 
 singled up when married. The hemp heart is cut out close to 
 where seizings are applied. Before tucking away the ends, 
 each pair should be approximately at equal distances from 
 one another, as shown in Fig. 6 (a). The beginning of an 
 eye splice in wire is shown in Fig. 6 (b). When the size of 
 the eye is fixed, put on a seizing as shown; then open up the 
 standing part somewhat, at place where tucking is to be 
 done, by giving the rope a certain amount of twist. This 
 will render the tucking comparatively easy. When tuck- 
 ing, have 3 strands on top and 3 strands underneath the 
 
 Fig. 7 
 
 standing part (assuming that the splicing is done hori- 
 zontally), and dispose of them in such manner that each 
 strand will come out in consecutive order, or as shown in 
 Fig. 6 (c). It does not matter under how many strands 
 (one or two) on the main rope they pass as long as they 
 come out in their proper lay. The strands are now tucked 
 once or twice, taking care not to make the tucks too short, 
 in which case the splice will be a lumpy one. Then hammer 
 the splice with a wooden mallet and trim off the ends snugly. 
 The short splice is made in the same way as the eye splice.
 
 ROPES 277 
 
 Splicing in wire calls for special tools, such as are shown in 
 Fig. 7, and a certain amount of skill, which can be acquired 
 only by long practice, and proper training by a capable 
 instructor. 
 
 BENDS AND HITCHES 
 
 In Figs. 1, 2, and 3 are shown a number of bends and 
 hitches in common use on shipboard. The manner in 
 which these bends are made is evident on inspection of the 
 illustrations, and hence only a few explanatory- remarks 
 concerning the use to which some of them are put will be 
 needed. 
 
 The reef knot is the best, simplest, and most used method 
 of connecting the ends of two ropes, small-sized cordage; 
 the granny knot is undesirable and unprofessional in every 
 respect; it slips easily and is hard to untie. For the purpose 
 of attaching two ropes of different size, the single or double 
 sheet bend should be used. The double carrick bend is 
 sometimes used for bending two hawsers together. The 
 bowline is perhaps the most useful bend ever invented; 
 it can be applied in various ways, from hoisting a man 
 aloft to the bending together of two hawsers. To make it, 
 take the end of the rope in the right hand and the standing 
 part in the left and lay the end over the standing part; 
 then with the standing part make a turn or loop around the 
 end and pass the latter over and around the standing part 
 and back through the bight again, thus completing the 
 knot. The figure-of-eight knot turned in a rope will prevent 
 it from unreeving. In Fig. 2 are shown a few methods of 
 applying a rope to a hook. The cross-hitch is used for a 
 sling or strap when the rope spreads away to its load; this 
 hitch prevents the sling from slipping in the hook in case 
 the load comes in contact with some obstruction while being 
 hoisted. The Blackwall hitch should be made with the end 
 twice around the hook as shown, except for very light loads; 
 experience has proved this to be the safest way, since with 
 only one turn the end is liable to "creep" when subjected 
 to a heavy strain, especially in damp weather when the 
 moisture absorbed by the rope serves as a lubricant. The 
 sheepshank is useful for shortening up a rope. In this
 
 278 
 
 ROPES 
 
 Sfuareor 
 Reeff(not 
 
 GnmnyKhof 
 
 Snj/e Sheet Bemf 
 
 Ooi/UeS/jeefffent/ 
 
 Running Bow//ne
 
 ROPES 
 
 279 
 
 Correct anct IVron^ 
 
 to belay a sheef 
 o ckat 
 
 5/nf/e Spanish Runner ana 
 
 Burton. 7acAI& OouMe Spamsft 
 
 Burton. 
 
 Fig. 3
 
 ROPES 
 
 Oi^erhand Knot tia// Jiitch Halliard Bend Fishermans Bend 
 
 Timber Hitch Timber and Hal/ Hitch C/oire Hitch 
 
 fiolling Hitch Ttvo Hal/ Hitches Hound Turn & 2 Hal/ Hitches 
 
 Method o/ Doubting 
 C/inch Round Turn & Hal/ Hitch Up a t^oorinff 
 
 Fig. 3
 
 WIND AXD WEATHER 281 
 
 figure is shown also the correct and incorrect way of fasten- 
 ing a rope — say the sheet of a sail — to a cleat; it is evident 
 that if the sheet is belayed as shown on lower cleat, the 
 increased strain on the sail will jam the rope and render 
 it difficult, if not impossible, to ease off the sheet. The 
 bends and hitches shown in Fig. 3, do not, we believe, require 
 any explanation, and can be made by referring to the illus- 
 trations. 
 
 WIND AND WEATHER 
 
 Weather Indications by a Mercurial Barometer. — The use 
 
 of the barometer as a weather glass is common both on sea 
 and on land. But only those that have long watched and 
 carefully compared its indications with the prevailing 
 weather conditions are able to foretell more than that a 
 rising barometer indicates less wind or rain; a falling 
 barometer, more wind or rain, or both; a high barometer, 
 fine weather; and a low one, the reverse. But useful as are 
 these general conclusions in most cases, they are sometimes 
 erroneous. 
 
 By attending to the following brief observations, any one 
 not accustomed to the use of a barometer may do so with 
 less hesitation and with immediate advantage. 
 
 The column of mercury in a good barometer usually 
 stands, on an average, some tenths of an inch higher with 
 or before polar and easterly winds than it does with or 
 before equatorial and westerly winds <of equal strength and 
 dryness or moisture) in all parts of the oceans. The terms 
 polar and equatorial are here used with reference to winds 
 blowing from the nearest polar direction, or from the equa- 
 torial parts of the earth. 
 
 This peculiarity of the barometer causes many mistakes 
 to be made. The barometer is high, perhaps, but falling. 
 Wind or rain, or both, are expected in consequence, yet 
 neither follows to any decided extent. A change of wind 
 from one quarter to another only takes place. Reversely, 
 the barometer is low, but rising. Fine weather is expected; 
 yet, instead of that, a strong wind, accompanied perhaps by
 
 282 WIND AND WEATHER 
 
 rain, hail, or snow, rises from the polar direction. By such 
 changes as these, seamen are often misled, and calamity, 
 caused by unpreparedness, may sometimes occur as a 
 consequence. 
 
 There may be heavy rains or violent winds beyond the 
 horizon, and even within the view of an observer, by 
 which his instruments may be affected considerably, though 
 no particular change of weather occurs in his immediate 
 locality. Sometimes, severe weather from an equatorial 
 (southerly in north latitudes, northerly in the southern 
 hemisphere) direction, not lasting long, may cause no great 
 fall of the barometer, because followed by a period of wind 
 from polar regions; and at times the mercurial column may 
 fall considerably with polar winds and fine weather, appa- 
 rently against the rule, because a continuance of equatorial 
 winds is about to follow. 
 
 As a general rule, the barometer rises for northerly winds 
 (included between the northwest and northeast), for dry 
 or less wet weather, for less wind, or for more than one of 
 these changes, except on a few occasions, when rain, hail, 
 or snow, with a strong wind, comes from the north. 
 
 The barometer falls for southerly winds (included between 
 the southeast and southwest), for wet weather, for stronger 
 wind, or for more than one of these changes, except on a 
 few occasions, when moderate wind, with rain or show, 
 comes from the northward. 
 
 There is little variation of the barometer between the 
 tropics, because the wind blows generally in the same direc- 
 tion and with equal force, and no contending currents of air 
 cause any considerable change in the temperature or density 
 of the atmosphere. For violent storms or hurricanes, how- 
 ever, within the tropics, the barometer falls very low, but 
 soon returns to its usual state after the storm center has 
 passed. 
 
 It has been observed on some coasts that the barometer 
 is differently affected by the wind, according as it blows 
 from the sea or from the land, the mercury rising on the 
 approach of the sea breeze and falling previously to the 
 setting in of the land breeze.
 
 WIND AND WEATHER 283 
 
 Indications by Appearance of Sky. — Some young seamen 
 hardlj- appreciate sufficiently common rules about weather, 
 which are as true as they are trite; namely, that a red sky 
 at sunset presages fine weather; a red sky in the morning 
 bad weather or much wind, if not rain; a gray sky in the 
 morning, fine weather; that soft-looking or delicate clouds 
 foretell fine weather, with moderate or light breezes; hard- 
 edged, oily-looking clouds, wind; that a dark, gloomy blue 
 sky is windy, but a light, bright blue sky indicates fine 
 weather; that, generally, the softer the clouds look the less 
 wind, although rain may be expected; and the harder, more 
 "greasy," rolled, tufted, or ragged, the stronger the wind 
 will prove. Also, that a bright yellow sky at sunset pre- 
 sages wind; a pale yellow, wet; and that, by the preponder- 
 ance of red, yellow, or gray tints the coming weather may be 
 foretold very nearly — indeed, if aided by instruments, 
 almost accurately. 
 
 These indications of weather, afforded by the colors of 
 the sky, seem to deserve more critical study than has yet 
 been given to the subject. 
 
 Indications by the Aneroid Barometer. — A rapid rise 
 indicates unsettled weather. 
 
 A gradual rise indicates settled weather. 
 
 A rise, with dry air and cold increasing, in summer, indi- 
 cates wind from the northward in north latitudes, but from 
 the southward in south latitudes; and if rain has fallen, 
 better weather may be expected. 
 
 A rise, with moist air and a low temperature, indicates 
 wind and rain from the northward in north latitudes, but 
 from the southward in south latitudes. 
 
 A rise, with southerly winds, indicates fine weather in north 
 latitudes, the conditions being reversed in south latitudes. 
 
 A steady barometer, with dry and seasonable tempera- 
 ture, indicates a continuance of very fine weather. 
 
 A rapid fall indicates stormy weather. 
 
 A rapid fall,. with westerly winds, indicates stormy weather 
 from the northward. 
 
 A fall, with a northerly wind, indicates stormy weather, 
 with rain in summer and snow in winter.
 
 284 WIND AXD WEATHER 
 
 A fall, with increased moisture in the air and the tempera- 
 ture rising, indicates wind and rain from the southward. 
 
 A fall, with dry air and cold increasing, in winter, indicates 
 snow. 
 
 A fall, after very calm and warm weather, indicates rain 
 with squally weather. 
 
 All indications pertaining to the fall of the aneroid apply 
 to northern latitudes; in southern latitudes, wind directions 
 are reversed. 
 
 HURRICANES 
 
 Cyclones, or hurricanes, have a rotary motion around a 
 center, or focus, and a progressive, or for^vard, motion. 
 The peculiarity of the rotarj' motion is that in each hemis- 
 phere it invariably occurs in different directions. Thus, in 
 the northern hemisphere, the rotation is contrary to the 
 motion of the hands of a watch, that is, from right to left; 
 in the southern hemisphere, the rotation is with the hands 
 of a watch, that is, from left to right. From the rotary motion 
 of cyclones, it is evident that the wind in the front and 
 rear of the storm must be in a direction perpendicular to 
 the line of progression a 6, as shown in (x) of the appended 
 diagram, or nearly so; in other words, if the cyclone is moving 
 in a north north-easterly direction, the wind in its front 
 should be about east southeast and in its rear about west 
 northwest. From this, an important conclusion may be 
 drawn, namely, that if we assume the area of the cyclone to 
 be divided into two equal parts by the line of progression 
 a b, and that another line e d is drawn through the center c 
 perpendicular to ab, the front quadrant bed, in which the 
 wind blows toward the line of progression, or track of center, 
 is the most dangerous part of the cyclone, with the exception 
 of the center itself. The rear quadrant a c d may also be 
 considered as dangerous, because the direction of the wind 
 will tend to carry the vessel that may happen to be there 
 into the front quadrant and thence into the path of the 
 center. These two quadrants, or the semicircle a d b, are 
 therefore known as the dangerous semicircle, and the other
 
 WIND AND WEATHER 
 
 285v
 
 286 WIND AND WEATHER 
 
 half aeh a.s the navigable semicircle, since the wind in the 
 latter will blow away from in front of the storm center. 
 
 These semicircles change sides when the hemisphere is 
 changed, the dangerous semicircle always being to the right 
 of the line of progression in northern latitudes and to the 
 left in southern latitudes. 
 
 From the foregoing conclusions, rules have been drawn up 
 for the use of navigators to enable them to determine on 
 which tack a ship should be laid-to when confronted with a 
 storm of cyclonic character, the object of these rules being 
 to prevent the wind veering by the ship's head and to insure 
 its veering or shifting constantly farther aft so that she may 
 be constantly "coming up" to the wind, whereas in the 
 former case she would be "breaking off" from the wind, and, 
 -even with sails set, would, in so violent a gale, be in danger 
 of gathering stemboard. 
 
 SUGGESTIONS FOR THE HANDLING OF SHIPS IN OR 
 NEAR CYCLONES 
 
 As to the handling of ships in or near a cyclone, one should 
 bear in mind that the safety of his vessel will depend to 
 a great extent on his good judgment as well as on his knowl- 
 edge of the nature and peculiarities of revolving storms. 
 All positive rules are, of course, more or less defective, and 
 if blindly carried out may prove very dangerous; they are, 
 nevertheless, of great value when judiciously used in com- 
 bination with a good judgment of prevailing circumstances. 
 
 The first thing for a navigator to do when he has good 
 reason to believe that a hurricane is approaching is to find 
 the bearing of its center, and then to shape his course so as 
 to avoid it. 
 
 The early indications of an approaching hurricane are as 
 follows: Barometer above the normal, with cool, very clear, 
 pleasant weather; a long, low ocean swell from the direction 
 of the distant storm; light, feathery, cirrus clouds, radiating 
 from a point on the horizon where a whitish arc indicates 
 the bearing of the center. Later indications are a falling 
 barometer; halos about the sun and moon; increasing ocean 
 swell; hot, moist weather with light, variable winds; deep-red
 
 WIND AND WEATHER 287 
 
 and violet tints at dawn and sunset; a heavy mountainou 
 cloud bank on the distant horizon; barometer falling rapidly, 
 with passing rain squalls. The most timely and trusty 
 indication of a cyclone is often the rise of the thermometer 
 in connection with a reversal of the normal wind. Thus, 
 in the regions of the trade winds, a brisk westerly wind 
 suddenly springing up should at once arouse suspicion, 
 particularly in the hurricane season. Equally suspicious is 
 a strong easterly wind suddenly succeeding the normal 
 westerly winds prevailing between 40° and 45° N on the 
 routes between the United States and Europe. Scarcely any- 
 thing, except an approaching area of low atmospheric pres- 
 sure, can be supposed to cause the sudden change of the 
 East Indian monsoon in August and September. A cautious 
 navigator, therefore, may, by attending to the abnormal and 
 sudden change of wind direction, foresee that he is in front 
 of a revolving gale, though his barometer remains high, the 
 sea smooth, and none of the usual signs of hurricanes can be 
 distinguished overhead. 
 
 To Find the Bearing of the Center. — Being convinced that 
 the approaching storm is of a cyclonic character, the bear- 
 ing of its center is determined. This is done b^^ facing the 
 wind, in which position the center may be assumed to bear 
 10 or 11 points to the observer's right in northern latitudes 
 and 10 or 11 points to the left in southern latitudes. If, 
 however, the ship is well within the storm area, and the 
 barometer is falling steadily, the bearing of the center may 
 be less than 10 points; and if the barometer has fallen as- 
 much as § in., the bearing may be considered as 8 points. 
 
 To Determine Position of Ship in Relation to Storm Track. 
 Having the approximate bearing of the storm center, the 
 next thing to do is to find the position of the ship in relation 
 to the track, or line of progression, of the storm. This can 
 be determined by observing the shifting, or veering, of the 
 wind. In the northern hemisphere, if the wind shifts to 
 the right, the ship is to the right of the track, as at 5", in 
 diagram (x) of the preceding illustration, or in the dangerous, 
 semicircle; if it shifts to the left, the ship is to the left of 
 the track, as at Si, or in the navigable semicircle.
 
 :238 WIND AND WEATHER 
 
 These conditions are reversed in the southern hefnisphere. 
 There, if the wind shifts to the right, the ship is to the right 
 of the track, as at Si, (y), or in the navigable semicircle; 
 while, if the wind shifts to the left, the ship is at 5 (y), 
 or in the dangerous semicircle (in both cases the observer 
 is assumed to be looking in the direction toward which the 
 storm is advancing). But if the wind is "steady," shifting 
 but very slightly and increasing in velocity, it indicates 
 that the ship, whether in the north or south hemisphere, is 
 on the track and in front of the center, as at 52, (x) and (y) . 
 
 To Find Whether Center Is Approaching or Receding. 
 When a ship is well within the area of a hurricane the 
 approach of the center is indicated by a rapidly falling 
 barometer, increase of wind, heavy squalls, intense light- 
 ning and rain, heavy and confused sea, continued shifting 
 of the wind, except when on the track of the center. 
 
 The receding of the center is usually indicated by a rising 
 barometer, more steady wind decreasing in velocity, weather 
 clearing, but sea very confused and dangerous. 
 
 Brief Rules for Action to Avoid Center. — Having deter- 
 mined the bearing of the storm center and the position of 
 the ship in reference to the progressive motion of the storm, 
 the following rules for avoiding the storm center should be 
 adhered to as far as circumstances will permit: 
 
 Northern Hemisphere. — If on the track of the storm center 
 and in front of the advancing storm, run or steam before 
 the wind; keep a steady course until the wind shifts well 
 on starboard quarter. Then, if obliged to lie-to, do so on 
 the port tack. 
 
 If in the dangerous semicircle, steam or run off with the 
 wind on starboard quarter; if obliged to lie-to, do so on the 
 starboard tack. 
 
 If in the navigable semicircle, steam or run off with the 
 wind on starboard quarter; if obliged to lie-to, do so on 
 the port tack. 
 
 Southern Hemisphere. — If directly in front of the advancing 
 storm center, run or steam before the wind; keep a steady 
 ■course until the wind gradually shifts around to the port quar- 
 ter. Then, if obliged to lie-to, do so on the starboard tack.
 
 WIND AND WEATHER 289 
 
 If in the dangerous semicircle, steam or run off with the 
 wind on the port quarter; if obliged to lie-to, do so on the 
 port tack. 
 
 If in the navigable semicircle, steam or run off with the 
 wind on the port quarter; if obliged to lie-to, do so on the 
 starboard tack. 
 
 Vessels, especially steamships, sometimes overtake hurri- 
 canes because their speed is greater than the progression of 
 the storm center. In such cases, it is obvious that the ship's 
 course should be altered so as not to approach the center. 
 
 The Storm Center. — The foregoing rules apply to cases 
 when hurricanes are encountered in open sea. If, however, 
 the vessel is unable, from want of sea room, to perform the 
 necessarj^ maneuvers, her position becomes one of great 
 danger. Every precaution should then be taken to prepare 
 for the passage of the storm center over the ship. In 
 entering the center, which may be several miles in diameter, 
 the wind suddenly ceases and glimpses of clear sky can be 
 seen, now and then interrupted by puffy squalls. The sea 
 is enormous and very dangerous, apparently coming from 
 all directions of the compass. After the center has passed 
 over, the ship is again struck by a gale of renewed energy 
 and hurricane force, but from the opposite direction. This 
 constitutes one of the most critical dangers known to 
 seamen. Apparently, the best thing to do when caught in 
 the center of a hurricane is to try to get the vessel in such a 
 position as to best meet the opposite wind, which may be 
 expected to burst forth very quickly and violently, and 
 thereby prevent the ship gathering sternboard, or drifting 
 backwards in a helpless position with enormous seas break- 
 ing over her. Only strongly built vessels are able to with- 
 stand the heavy strain they are subjected to under such cir- 
 cumstances, and many ships whose names now figure on 
 the list of "missing" in all probability met their fate in 
 the center of a revolving storm. 
 
 The t3rphoon of the Western Pacific Ocean is, in many 
 respects, the counterpart of the West Indian hurricane of 
 the Atlantic. Both classes of storms have their origin in 
 the vicinity of tropical groups of islands, and .under similar
 
 290 WIXD AXD WEATHER 
 
 barometric conditions; both undergo the same slow develop- 
 ment and exhibit a similar tendency to recurve on reaching 
 the higher latitudes. 
 
 The first barometric indication of the approach of a 
 typhoon is the disturbance of the daily fluctuations of the 
 mercurial column. In the low latitudes where typhoons 
 originate, a good mercurial barometer during settled weather 
 should show a decided maximum about 10 a. m., the reading 
 at that hour standing between 29.85 and 29.95 in. (758.2 to 
 760.7 millimeters), while about 4 p. M. there should be a 
 corresponding minimum, the reading at that hour being 
 about tV in. (2.5 millimeters) less than at 10 a. m. The 
 same thing is repeated at 10 P. M. and at 4 A. m. If the fore- 
 noon maximum is appreciably below 29.85 in., or if the 
 descent between this and the afternoon minimum is markedly 
 greater than tV in., the weather should be watched with 
 great care. Several successive days of light, variable winds 
 and calms; a period of hot, sultry weather; increasing 
 moisture of the atmosphere; increasing amount of cloud and 
 an ominous heaving of the sea, are all conditions forerunning 
 the occurrence of the typhoon. 
 
 The average tracks of the various classes of typhoons, 
 together with the frequency and the season of appearance 
 of each class, are to be found on Pilot Charts of the Pacific 
 Ocean. For a more complete account of typhoons, consult 
 the North Pacific Pilot Chart for July, 1898. 
 
 Remarks. — It must be borne in mind that although the 
 region and season of the year would render the navigator 
 very cautious, yet every strong wind or gale met with, 
 particularly in the tropical regions, must not be treated as 
 a cyclone. When there is reason to stxspect the advance of 
 a cyclonic storm, the safest proceeding is to lie-to and 
 carefully watch the barometer, weather indications, and 
 shiftings of the wind. A decided drop of the atmospheric 
 pressure of at least i in., together with marked shiftings of 
 the wind, should be experienced before the storm can be 
 regarded as cyclonic. 
 
 Meteorological Observations at Sea. — The United States 
 Hydrographic Office is conducting an extensive system of
 
 WIND AXD WEATHER 291 
 
 ocean meteorological observations. It seeks the cooperation 
 of all navigators, requesting them to take one observation 
 every day at a prescribed moment, which is simultaneous 
 for every part of the globe. These simultaneous observa- 
 tions are charted and published by the Hydrographic Office 
 at Washington on its Monthly Pilot Charts and Hydro- 
 graphic Bulletins. By entering into this arrangement and 
 taking part in the observational work, every seaman may 
 contribute materially to this scientific enterprise and further 
 the elucidation of the law of storms, as well as secure for 
 his own use a large supply of valuable meteorological infor- 
 mation. 
 
 When about to sail, the master or navigating officer of 
 a vessel should call at the local branch hydrographic office 
 and request the officer in charge to furnish him with the 
 latest information in the shape of Lists of Lighls, Lists of 
 Beacons, Buoys, and Daymarks, Notices to Mariner?, 
 Hydrographic Bulletins, and Pilot Charts. All these pub- 
 lications are furnished free to masters who can satisfactorily 
 show that they are voluntary weather observers for the 
 United States Hydrographic Office, or that they are willing 
 to become such. He should also request a supply of blank 
 weather reports and envelopes sufficient to last until his 
 return to a United States port ; also of cards for barometer 
 comparisons, with instructions as to the manner of making 
 these comparisons, which are given in Hydrographic Office 
 publication No. 119. The comparison cards should be 
 filled out while the vessel is lying in port and should be 
 mailed before sailing. They require (if mailed in a United 
 States port) neither envelope nor postage. 
 
 For the convenience of those masters who rarely visit an 
 American port, a limited supply of blanks, pilot charts, etc. 
 is maintained at the U. S. consulate in each of the more 
 important shipping centers abroad. A list of those con- 
 sulates at which this is the case is published on the monthly 
 pilot charts. 
 
 Having arrived at his destination, the forms containing the 
 observations recorded during the voyage should be enclosed 
 in one or more of the envelopes furnished for that purpose.
 
 292 WIND AND WEATHER 
 
 If in a foreign port, this envelope should be addressed to 
 the United States Hydrographic Office, Navy Department, 
 Washington, D. C, and handed to the United States consul, 
 who is under instructions from the Secretary of State to 
 forward it with his official mail, free of all' expense. If 
 mailed at any port outside of the United States, postage 
 must be prepaid at letter rates. 
 
 In any United States port, the package should be addressed 
 to the nearest branch hydrographic office and mailed. The 
 franked envelope does not require any postage when mailed 
 within the United States, Hawaii, the Philippine Islands, 
 or Porto Rico. 
 
 The forms should be returned promptly at the close of 
 each voyage, or even at the first port of call. They should 
 not be held until the return of the vessel to the United 
 States. 
 
 . On the receipt of the completed forms, either at the 
 United States Hydrographic Office or at any of its branches, 
 a letter of acknowledgment is at once addressed to the 
 master of the vessel, thanking him and the officer charged 
 with the duty of taking the observations for their services, 
 and replying to any inquiry or request that the master or 
 the observer may have made on the pages alloted to that 
 purpose. These letters of acknowledgment should in all 
 cases be preserved, as they may prove of value in identify- 
 ing the bearer as an observer at the several branch hydro- 
 graphic offices, and as such entitled to the various official 
 publications. 
 
 The list of Atlantic and Pacific coast ports at which 
 branch hydrographic offices are established is at present 
 (March, 190-i) as follows: Boston, custom house; New 
 York, Maritime Exchange; Philadelphia, Bourse Building; 
 Baltimore, custom house; Norfolk, custom house; Savannah, 
 custom house; New Orleans, custom house; Galveston, Levy 
 Building; San Francisco, Merchants' Exchange; Portland, 
 Ore., custom house; Port Townsend, custom house.
 
 CODE FLAGS AND PENNANTS 
 INTERNATIONAL CODE OF SIGNALS 
 IHstinguishing 

 
 SIGNALS 293 
 
 SIGNALS 
 
 INTERNATIONAL CODE OF SIGNALS 
 
 The new International Code of Signals, shown in the 
 attached figure, and which came into use on January 1, 1901, 
 consists of 26 flags; viz., 2 burgees, 5 pennants, and 19 square 
 flags, besides the code flag, which is used also as the ans%ver- 
 ing pennant. Its object is to supply means of intercourse 
 between ships meeting at sea, as well as between ships and 
 established signal stations on land. It has been adopted 
 by all the important maritime powers of the world, and the 
 interpretation of the several thousand different signals 
 composing the system are translated into the language of 
 each nation. All ships, therefore, when meeting at sea 
 are enabled to communicate with one another, no matter 
 if one is an American and the other a Greek, or whether 
 the commander of one vessel is able to master the language 
 of the other in a verbal conversation. 
 
 Arrangement of Code Book. — The new Code Book pub- 
 lished by the Bureau of Equipment, U. S. Navy Department, 
 is divided into three parts, as follows: 
 
 Part I contains instructions on how to make and how to 
 answer a signal, accompanied by suitable examples; then 
 comes an alphabetical spelling table, numeral signals, urgent 
 and important signals, compass signals, signals appertaining 
 to money and all kinds of measurements, signals relating to 
 latitude, longitude, time, barometer, thermometer, phrase 
 signals formed with auxiliary verbs, and geographical signals. 
 Of these signals, only those coming under the heading of 
 "urgent and important" are made with 2 flags in a hoist; 
 all others are made with 3 flags, with the exception of 
 geographical signals, which are made with 4 flags in a hoist. 
 
 Part II contains an index of general vocabulary signals, 
 and a second list of geographical signals, in which the names, 
 of places are alphabetically arranged. The vocabulary sig- 
 nals are with few exceptions 3-flag signals.
 
 2»4 SIGNALS 
 
 Part III contains a list of storm-warning, display, life- 
 saving, and time-signal stations of the United States; also 
 Lloyd's signal stations of the world, and American, English, 
 and French semaphore, distance, and wigwag codes. 
 
 Since each of the 26 letters of the alphabet is represented 
 by a flag, it is evident that any word can be spelled by this 
 system, and if the word to be spelled consists of more than 
 4 letters, two or more hoists must be used, as no hoist is 
 to contain more than 4 flags. Explanations and instruc- 
 tions on this subject are to be found on pages 13 and 14 of 
 the code book. 
 
 CHARACTER OF SIGNALS AS INDICATED BY THE 
 NUMBER OF FLAGS IN A HOIST 
 
 One-Flag Signal. — The meaning of flags and pennants 
 hoisted singly and with the code flag is found on pages 7 
 and 35 of the code book. 
 
 Two-Flag Signals. — Signals composed of 2 flags are urgent 
 or important signals; they run from A B to Z Y. 
 
 Three-Flag Signals. — Signals composed of 3 flags are 
 either Compass, measurement, auxiliary phrases, or general 
 vocabulary signals. Compass signals run from A B C to 
 AST; signals relating to money, from A S U to AV J; 
 and those relating to weight and measures, from A V K 
 to B C N. Three-flag signals having the code flag upper- 
 most relate to latitude, longitude, time, barometer, or to 
 the thermometer. 
 
 Four-Flag Signals. — Signals composed of 4 flags are either 
 geographical or alphabetical signals. All geographical sig- 
 nals begin with the letter A or B and run from A B C D to 
 B F A U. Alphabetical signals commence with the letter C. 
 
 SELECTED SIGNALS 
 
 The following is a selection of signals for the use of vessels 
 meeting at sea, or vessels in sight of signal stations. By 
 committing these signals to memory, much delay in search- 
 ing for them in the code book is obviated.
 
 SIGNALS 295 
 
 Signals Meaning 
 
 E C— What ship is that ? 
 S I — Where are you from ? 
 S H — Where are you bound ? 
 5 G — When did you sail ? 
 U B — Do you wish to be reported? 
 U D — Report me, by telegraph, to Lloyd's. 
 U R Z— Report me all well. 
 
 U £— Report me, by telegraph, to owners. 
 U F — Report me, by telegraph, to "Shipping Gazette." 
 U G — Report me to Lloyd's (either by post or tele- 
 graph) . 
 U I — Report me to "New York Herald" office, London. 
 U J — Report me to "New York Herald" office. New York. 
 
 V J — I wish to signal ; will you come within easy signal 
 
 distance ? 
 VM — Cannot distinguish your flags; come nearer, or, 
 make distant signals. 
 
 V I — Repeat your signal. 
 
 5 W — I wish to obtain orders from my owner — (name) . 
 
 T D — There are no orders for you here. 
 
 T E — Wait for orders. 
 
 Q U — Will you forward my letters? 
 
 Q R- — Send your letters. 
 
 Y E — Want assistance. 
 
 Y L — Want immediate medical assistance. 
 
 N C — In distress; want immediate assistance. 
 
 D C — We are coming to your assistance. 
 
 C X — No assistance can be rendered; do the best you 
 
 can for yourselves. 
 F //—Send a boat. 
 E U — Boat is going to you. 
 E X — Cannot send boat. 
 B O — Have lost all my boats. 
 
 I — Come nearer. Stop, or heave to. I have some- 
 
 -- f thing important to communicate, 
 
 over H] 
 
 I F — Cannot stop to have any communications. 
 
 R Z — Where am I ? What is my present position ?
 
 296 SIGNALS 
 
 Q I B — What is your latitude brought up to the present 
 
 moment ? 
 Q Z K — What is your longitude brought up to the present 
 
 moment ? 
 Q H W — My latitude is . . . 
 Q Z F — My longitude by chronometer is . . . 
 XN — Will you show me your Greenwich time? 
 G U — Will you give me a comparison? Wish to get a 
 rate for my chronometer. 
 I Q H — I have no chronometer. 
 G Q — My chronometer has run down. 
 M R — Have broken main shaft. 
 M W — One screw disabled; can work the other. 
 MQ — Engines completely disabled. 
 M X — Passed disabled steamer at . . . 
 H M — Vessel seiiously damaged; wish to transfer 
 
 passengers. 
 G Y — Can you spare me coal? 
 H C — Indicate nearest place I can get coal. 
 B I — Damaged rudder, cannot steer. 
 J D — You are standing into danger. 
 S A — Are there any men of war about? 
 X O — Beware of torpedo boats. 
 X P — Beware of torpedoes; channel (or fairway) is 
 
 mined, 
 y P — Want a tug (if more than one, number to follow). 
 
 Y O — Want provisions immediately. 
 
 Y R — Want water immediately. 
 
 C", or code flag over C — Yes, or affirmative, 
 D, or code flag over D — No, or negative. 
 
 DISTANT SIGNALS 
 Distant Signals are used when, in consequence of distance 
 or the state of the atmosphere, it is impossible to distinguish 
 the colors of the flags of the International Code, and, there- 
 fore, to read a signal made by those flags; they also provide 
 an alternative system of making the signals in the Code, 
 which can be adopted when the system of flags cannot be 
 employed. Three methods of making distant signals are
 
 SIGNALS 
 
 297 
 
 used: (1) by cones, balls, and drums; (2) by balls, square 
 flags, pennants, and wafts; (3) by the fixed coast sema- 
 phore. 
 
 In calms, or when the wind is blowing toward or from the 
 observer, it is often difficult to distinguish with certainty 
 between a square flag, pennant, and waft, and as flags 
 when hanging up and down may hide one of the balls and 
 so prevent the signal being understood, the system of cones, 
 balls, and drums is preferable to that of flags, pennants, 
 and wafts. 
 
 The following special distant signals are made by a single 
 hoist followed by the "Stop" signal. They are arranged 
 numerically for reading off the signal. 
 
 
 SPECIAL DISTANT SIGNALS 
 
 2 — "Preparative," 
 "answering," or 
 "stop," after each 
 complete signal. 
 
 1. 2 — Aground; want 
 immediate assist- 
 ance. 
 
 1 — Fire or Leak; 
 want immediate 
 assistance. 
 
 !> 
 
 2 — A n n u 1 
 whole signal. 
 
 .3 — You are run- 
 ning into danger, 
 or. Your course is 
 dangerous. 
 
 2, 4 — Want water im- 
 mediately. 
 
 
 3, 2 — Short of provi- 
 sions; starving. 
 
 4, 2 — Annul the last 
 hoist; I will repeat 
 
 it. 
 
 1,1, 2 — I am on fire. 
 
 1,2, 1 — I am aground 
 
 2, 2— Yes, or af- 
 firmative. 
 
 2, 3, — No. or neg- 
 ative.
 
 298 
 
 SIGNALS 
 
 h 
 N 
 
 1.2.4— Send lifeboat. 
 
 1,3. 2 — Do not aban- 
 don the vessel. 
 
 1,4, 2 — Do not aban- 
 don the vessel until 
 the tide has ebbed. 
 
 2, 1, 1 — Assistance is 
 coming. 
 
 2, 1, 2 — Landing is 
 impossible. 
 
 2, 1, 3 — Bar or en- 
 trance is dangerous. 
 
 2, 1, 4— Ship dis- 
 abled; will you as- 
 sist ' me into port ? 
 
 2, 2. 1— Want a pilot. 
 
 2, 2, 3— Want a tug; 
 can I obtain one? 
 
 2, 2, 4— Want the 
 name of ship (or sig- 
 nal station)in sight, 
 or, Show your dis- 
 tinguishing signal. 
 
 IN 
 
 2, 3. 1 — Show your 
 ensign. 
 
 3, 2 — Have you any 
 dispatches (mes- 
 sages, orders, or 
 telegrams) for me? 
 
 3, 3— Stop, bring- 
 to, or. Come nearer; 
 I have something 
 important to com- 
 municate. 
 
 3. 4 — Repeat signal 
 or hoist it in a more 
 conspicuous posi- 
 tion. 
 
 , 4, 1-;— Cannot dis- 
 tinguish your flags; 
 come nearer or 
 make distant sig- 
 nals. 
 
 , 4, 2— Weigh, cut, 
 or slip; Wait for 
 nothing; Get an 
 offing. 
 
 2,4. 3 — Cyclone, hur- 
 ricane, or typhoon 
 expected. 
 
 3, 1. 2— Is war de- 
 clared, or. Has war 
 commenced? 
 
 3, 2. 1— War is de- 
 clared, or. War has 
 commenced. 
 
 3. 2, 2 — Beware of 
 torpedoes; channel 
 is mined.
 
 
 SIGXALS 2G9 
 
 3, 4, 2 — Keep a good 
 
 o o o -D^^r^^^ «f o lookout, as it is re- 
 
 '•toVd^Wr °' k P-^^<i that ene- 
 
 twipciiij uudi-o. 11^ my s men ot war are 
 
 going about dis- 
 guised as merchant 
 3. 2. '4— Enemy is in ships. 
 
 sight. 
 
 3, 3, 2 — Enemy is 
 closing with you, 
 or, You are closing 
 with the enemy. 
 
 4, 1, 2 — Proceed on 
 your voyage. 
 
 The following distant signals, made with flag and ball, or 
 pennant and ball, have the special signification, indicated 
 beneath them. Jupiter, Fla. [See following page]. 
 
 \um You are running P^^ 
 
 [W^lf into danger. V 
 
 jfv Fire, or leak; want Ir^^^ 
 
 ^^^^^ immediate assist- T' 
 
 1 ~ ^"^^- i k 
 
 Short of provisions 
 — starving. 
 
 Aground; want im- 
 mediate assist- 
 ance. 
 
 LIST OF WEATHER BUREAU STATIONS ON THE UNITED 
 STATES SEACOAST TELEGRAPHIC LINES 
 
 Atlantic Coast. — Nantucket, Mass.; Narragansett Pier, 
 R. I.; Block Island, R. I.; Norfolk, Va.; Cape Henry, Va.; 
 Currituck Inlet, N. C; Kitty Hawk, N. C; Hatteras, N. C; 
 Sand Key, Fla; 
 
 Pacific Coast. — Tatoosh Island, Wash.; Neah Bay, Wash.; 
 East Clallam. Wash.; Twin Rivers, Wash.; Port Crescent, 
 Wash.; North Head, Wash.; Point Reyes Light, Cal.; San 
 Francisco, Cal.; Southeast Farallone, Cal.; Jupiter, Fla. 
 
 Lake Huron. — Thunder Bay Island, Mich.; Middle Island, 
 Mich.; Alpena, Mich. 
 
 Of these stations, the following are equipped with Inter- 
 national Code signals, and communication can be had there- 
 with for the purpose of obtaining information concerning
 
 300 SIGXALS 
 
 the approach of storms, weather conditions in general, and 
 for the purpose of sending telegrams to points on commercial 
 lines: 
 
 Nantucket, Mass.: Block Island, R. I.; Cape Henry, Va.; 
 Hatteras, N. C; Kitty Hawk, X. C; Sand Key, Fla.; 
 Jupiter, Fla.; Tatoosh Island, Wash.; Neah Bay, Wash.; 
 Point Reyes Light, Cal.; Southeast Farallone, Cal. 
 
 Any message signaled by the International Code, as 
 adopted or used by England, France, America, Denmark, 
 Holland, Sweden, Norway, Russia, Greece, Italy, Germany, 
 Austria, Spain, Portugal, and Brazil, received at these 
 telegraphic signal stations, will be transmitted and delivered 
 to the address on payment at the receiving station of the 
 telegraphic charge. All messages received from or addressed 
 to the War, Navy, Treasury, State, Interior, or other official 
 department at Washington, are telegraphed without charge 
 over the Weather Bureau lines. 
 
 DISTRESS SIGNALS 
 
 When a vessel is in distress, and requires assistance from 
 other vessels or from the shore, the following are the signals 
 to be used by her, either together or separately: 
 
 Daytime. — 1. A gun or other explosive signal fired at 
 intervals of about a minute. 
 
 2. The International Code signal of distress indicated 
 by A^C. 
 
 3. The distant signal, consisting of a square flag, having 
 either above or below it a ball or anything resembling a ball. 
 
 4. The distant signal, consisting of a cone pointing 
 upwards, having either above or below it a ball or anything 
 resembling a ball. 
 
 5. A continuous sounding with any fog-signal apparatus. 
 At Night. — 1. A gun or other explosive signal fired at 
 
 intervals of about a minute. 
 
 2. Flames on the vessel (as from a burning tar barrel 
 oil barrel, etc.). 
 
 3. Rockets or shells, throwing stars of any color or 
 description, fired one at a time at short intervals. 
 
 4. A continuous sounding with any fog-signal apparatus.
 
 U. S, STORM SIGNALS 
 
 N.fF: s.w. 
 
 Winds Winds 
 
 Flags 8 feet square. 
 
 N. E. S. E. Hu rri ca ne" 
 Winds Winds Signal 
 
 Pennants 5 feet hoist, 12 feet fly. 
 
 U. S. WEATHER-BUREAU SIGNALS 
 
 Clear or 
 Fair WeafAer 
 
 11 
 
 3 
 
 y 
 
 ^Locatliai/v 
 II orS/iow 
 
 When number 4 is placed above number 1, 2, or S it indicates 
 warmer; when below, colder; when not displayed, the tempera- 
 ture ts expected to remain about stationary. Number 6 is used 
 also to indicate anticipated frosts.
 
 SIGMALS 301 
 
 Xot Under Control. — A vessel temporarily disabled at sea, 
 through the breaking down of her engines, etc., but not 
 requiring assistance, shovild, in daytime, hoist two black 
 balls, or shapes resembling balls, one above the other, and at 
 night two red lights in a similar position. Such signal 
 means *' I am not under control," and should be kept 
 hoisted until repairs are effected or until the vessel is in a 
 position to proceed on her voyage. 
 
 U. S. STORM SIGNALS 
 
 Storm Warning Flags. — A red flag with a black center 
 indicates that a stonn of marked violence is expected. 
 The pennants displayed with the flags indicate the direction 
 of the wind: red, easterly (from northeast to south); white, 
 westerly (from southwest to north). The pennant above 
 the flag indicates that the wind is expected to blow from 
 the northerly quadrants; below, from southerly quadrants. 
 By night, a red light indicates easterly winds, and a -white 
 light above a red light, westerly wnnds. 
 
 Hurricane Warning. — Two red flags, with black centers, 
 displayed one above the other, indicate the expected approach 
 of tropical hurricanes, and also of those extremely severe 
 and dangerous storms that occasionally move across the 
 lakes and northern Atlantic coast. Hurricane warnings are 
 not displayed at night. 
 
 Storm signals are displayed by the United States Weather 
 Bureau at 141 stations situated along the Atlantic and 
 Gulf coasts, and at 27 stations situated on the Pacific coast 
 of the United States. 
 
 SIGNALS FOR PILOT 
 
 The following signals, when used or displayed together or 
 separately, shall be deemed to be signals for a pilot: 
 
 Daytime. — 1. The Jack, or other national ensign, usually 
 worn by merchant ships, having around it a white border 
 one-fifth the breadth of the flag, to be hoisted at the foretop. 
 
 2. The International Code pilot signal indicated by P T. 
 
 3. The International Code flag S, with or without the 
 code pennant over it.
 
 S02 SIGNALS 
 
 4. The distant signal consisting of a cone, point upwards, 
 having above it two balls, or shapes resembling balls. 
 
 At Night. — 1, The pyrotechnic light, commonly known 
 as a "blue light," every 15 min. 
 
 2. A bright white light, flashed or shown at short or 
 frequent intervals, just above the bulwarks, for about a 
 minute at a time. 
 
 LIFE-SAVING SIGNALS 
 
 The following signals, recommended by the recent Inter- 
 national Marine Conference for adoption by all institutions 
 for saving life from wrecked vessels, have been adopted by 
 the Life-Saving Service of the United States: 
 
 1. Upon the discovery of a wreck by night, the life- 
 saving force will bum a red pyrotechnic light, or a red rocket, 
 to signify: "You are seen; assistance will be given as soon 
 as possible." 
 
 2. A red flag waved on shore by day, or a red light, red 
 rocket, or red Roman candle displayed at night, will signify: 
 "Haul away." 
 
 3. A white flag waved on shore by day, or a white light 
 slowly swung back and forth, or a white rocket or white 
 Roman candle fired by night, will signify: "Slack away." 
 
 4. Two flags, a. white and a red, waved at the same time 
 on shore by day, or two lights, a white and a red, slowly 
 swung at the same time, or a blue pyrotechnic light burned 
 by night, will signify: "Do not attempt to land in your own 
 boats; it is impossible." 
 
 5. A man on shore beckoning by day, or two torches 
 burning near together by night, will signify: "This is the 
 best place to land." 
 
 Any of these signals may be answered from the vessel 
 as follows: In the daytime, by waving a flag, a handker- 
 chief, a hat, or even the hand; at night, by firing a rocket, 
 a blue light, or a gun, or by showing a light over the ship's 
 gunwale for a short time and then concealing it. 
 
 NoTB. — It is important that all .signals from shore arc answered hy the ship 
 «t once, particularly so at niKht. It signals are not aiiswereil within a reason- 
 *ble time, the life-saving crew on thi; beach might infer that the crew of the 
 •trandeil vessel have perished, ami as a consequence they may abandon their 
 etlorts ut regcue.
 
 SIGXALS 303 
 
 USE OIL IN HEAVY SEA 
 
 Running before a gale, use oil from bags at the catheads, 
 or from forward waste pipes; if yawing badly and threaten- 
 ing to broach-to, use oil forwards and abaft the beam, on 
 both sides. Lying-to, distribute oil from the weather bow. 
 With a high beam sea, use oil bags at regular intervals along 
 the weather side. In a heavy cross sea, have bags along 
 both sides. Steaming into a heavy head sea, use oil through 
 forward closet pipes. There are many other cases where oil 
 may be used to advantage, such as lowering and hoisting 
 boats, riding to a sea anchor, crossing rollers or surf on a 
 bar, and from life boats and stranded vessels. Thick and 
 heavy oils are the best. Mineral oils are not so effective 
 as animal or vegetable oil. Raw petroleum has given 
 favorable results, but is not so good when refined. Certain 
 oils, like cocoanut oil and some kinds of fish oil, congeal in 
 cold weather, and are therefore useless, but may be mLxed 
 with mineral oils to advantage. As a general rule, probably 
 the best way to use oil is by filling the closet bowls forward 
 with oakum and oil, letting the oil drip out slowly through 
 the waste pipes. Another simple and easy way to distribute 
 oil is by means of-canvas bags about a foot long, filled with 
 oakum and oil, pierced with holes by means of a coarse 
 sail needle, and held by a lanyard.
 
 304 NAUTICAL MEMORANDA 
 
 NAUTICAL MEMORANDA 
 
 Progress of steam navigation from its inception to the 
 launching of the 'Great Eastern" in 1858: 
 1707 Denis Papin experimented on River Fulda with 
 
 paddle-wheel steamboat. 
 1736 Jonathan Hulls patented designs similar to modern 
 
 paddle boat. 
 
 1769 James Watt invented a double-acting side-lever 
 
 engine. 
 
 1770 Perier, in France, made experiments with steam as 
 
 motive power for vessels. 
 1785 James Ramsey, in America, propelled- a boat with 
 
 steam through a stern pipe. 
 17S6 John Fitch, in America, propelled a boat with 
 
 canoe paddles fixed to a moving beam. 
 
 1787 Robert Miller, of Edinburgh, experimented similarly. 
 
 1788 Miller and Symington produced a double-hull stern- 
 
 wheel steamboat. 
 1802 "Charlotte Dundas," the first practical steam tug, 
 
 designed by Symington. 
 1804 "Phoenix," screw boat designed by Stephens, in New 
 
 York; first steamer to make a sea voyage. 
 1807 "Clermont," first passenger steamer continuously 
 
 employed; designed and built by Robert Fulton; 
 
 machinery built by Boulton and Watt; made 
 
 regular trips between New York and Albany; 
 
 speed about 5 kn. 
 1811 "The Comet," first successful passenger steamer in 
 
 Europe; built by Henry Bell and made trips 
 
 between Glasgow and Greenock. 
 1816 "Witch," first steamboat built in Sweden; constructed 
 
 by S. Owen; had an 8-H. P. engine and a four- 
 
 bladed propeller. 
 
 1818 "Rob Roy," first merchant steamer in the world, 
 
 built at Glasgow. 
 
 1819 "Savannah," first auxiliary steamer to cross the 
 
 Atlantic; fitted with paddle wheels; made the trip 
 from Savannah to Liverpool in 22 da.
 
 XAUTICAL MEMORAXDA 305 
 
 1821 "Aaron Manby," first steamer — English canal boat — 
 
 built of iron. 
 1823 City of Dublin Steam Packet Co. was established. 
 1824: General Steam Navigation Co. was established at 
 
 London. 
 1825 "Enterprise" made the first steam passage to India. 
 1825 "William Fawcett," pioneer steamer of the P. & O. S. 
 
 N. Co. 
 1830 T. & J. Harrison (Harrison Line) established at Liver- 
 pool. 
 1832 "Elburkah," iron steamer, took a private exploring 
 
 party up the river Niger. 
 1834 Establishment of Lloyd's Register for British and 
 
 foreign shipping. 
 
 1836 Establishment, at Trieste, of the Atistrian Lloyd 
 
 Steam Navigation Co. 
 
 1837 "Francis B. Ogden," first successful screw tug; equip- 
 
 ped with Ericsson's propeller. 
 
 1838 "Archimedes" made the Dover-Calais passage in less 
 
 than 2 hr. ; fitted with Smith's propeller. 
 
 1838 "R. F. Stockton," built for a tug and fitted with 
 
 Ericsson's 'propeller; sailed to America; first iron 
 vessel to cross the Atlantic; first screw steamer 
 used in America. 
 
 1839 "Thames," pioneer steamer of the Royal Mail Steam 
 
 Packet Co. 
 
 1840 "Britannia," pioneer steamer of the Cunard Line. 
 1840 "Chile," pioneer steamer of the Pacific Steam Naviga- 
 tion Co. 
 
 1845 "Great Britain," first iron screw steamer, precursor of 
 
 modem transatlantic steamer. 
 1845 Wilson Line, Thos. Wilson, Sons & Co., Ltd.. estab-, 
 
 lished at Hull. 
 1847 Pacific Mail Steamship Co. established in America. 
 1850 Natal Line established at London. 
 1850 Messageries Maritimes de France established. 
 
 1850 Inman (now American) Line established at Liverpool. 
 
 1851 "Tiber," first steamer of the Bibby Line, established 
 
 in 1821, at Liverpool.
 
 306 
 
 AM UTICAL MEMORANDA 
 
 1852 "Forerunner," pioneer steamer of the African Steam- 
 
 ship Co. 
 
 1853 Union Steamship Co., now Union Castle Line, estab- 
 
 lished. 
 1853 "Borxissia," first steamer of the Hamburg-American 
 Packet Co., established in 1847. 
 
 UNITED STATES NAVY 
 
 {From Report of the Office of Naval Intelligence, United States 
 Navy Department, 1905) 
 
 Type of Vessel 
 
 Built 
 
 Tons 
 
 Build- 
 ing 
 
 Tons 
 
 Battle ships, first class. 
 
 Other battle ships and 
 coast defense iron- 
 clads 
 
 Armored cruisers 
 
 Protected cruisers, first 
 class (above 6,000 
 tons) 
 
 Protected cruisers, sec- 
 ond class (3,000 to 
 6,000 tons) 
 
 Other cruisers and 
 scouts (above 1,000 
 tons) . 
 
 12 
 
 12 
 2 
 
 2 
 
 15 
 
 23 
 
 137,329 
 
 47,945 
 17,415 
 
 14.750 
 
 56,393 
 
 32,773 
 
 13 
 
 8 
 3 
 4 
 2 
 
 192.700 
 
 111,800 
 
 28,800 
 
 12,400 
 
 2,170 
 
 Totals 
 
 66 
 
 306,605 
 
 30 
 
 347,870 
 
 
 
 Combined totals. . . .96 vessels of 654,475 tons 
 
 NoTK.— Gunboats and other vessels of less than 1,000 T. are not given in 
 the ta))le, nor are transports, dispatch vessels, converted merchant vessels or 
 jachts. or olisolete cruisers. Vessels not begun are not included in the table. 
 There are Ki torpetio-boat destroyers, 27 torpedo boats, 8 submarine boats 
 belonging to the Navy, and 6 torpedo boats under construction. 
 
 1854 "Canadian," first steamer of the Allan Line, estab- 
 
 lished in 1820. 
 
 1855 Establishment of the British India Steam Naviga- 
 
 tion Co. 
 
 1856 "Tempest," first steamer of the Anchor Line.
 
 NAUTICAL MEMORANDA 
 
 307 
 
 1858 "Bremen." first transatlantic steamer of the Xord- 
 deutscher Lloyd, established in 1856. 
 
 1858 "Great Eastern" launched on the Thames, Jan. 31; 
 commenced May 1, 1854. 
 
 MERCHANT MARINE 
 
 {From Report of the United States Commissioner of Naviga- 
 tion 1905) 
 
 Districts 
 
 Number 
 of Vessels 
 
 Gross 
 Tonnage 
 
 
 17,040 
 
 42 
 
 2,492 
 
 61 
 
 3,172 
 
 1,466 
 
 2,978,876 
 
 Porto Rico 
 
 6.180 
 
 Pacific Coast 
 
 741 825 
 
 
 32.386 
 
 Great Lakes 
 
 1,816 511 
 
 
 222,124 
 
 
 
 Total 
 
 24,273 
 
 5 797,902 
 
 
 
 Classification of 
 
 THE Above 
 
 
 Type of Vessel 
 
 Number 
 of Vessels 
 
 Gross 
 Tonnage 
 
 Sailing vessels 
 
 13,073 
 
 7.727 
 
 703 
 
 2.770 
 
 1,941.878 
 
 Steam vessels 
 
 Canal boats 
 
 3,176,874 
 79,408 
 
 Barges 
 
 599.742 
 
 Total 
 
 24,273 
 
 5,797,902
 
 NUMBER AND TONNAGE OF VESSELS BUILT IN THE 
 UNITED STATES DURING THE YEARS 1868 TO 
 1903, INCLUSIVE 
 
 {From Report of the Commissioner o 
 
 F Navigation) 
 
 
 Sailing Vessels 
 
 Steam Vessels 
 
 Year 
 
 
 
 
 
 
 Num- 
 
 Gross 
 
 Num- 
 
 Gross 
 
 
 ber 
 
 Tonnage 
 
 ber 
 
 Tonnage 
 
 1868 
 
 910 
 
 874 
 
 142,742 
 149,029 
 
 236 
 279 
 
 63,940 
 
 1869 
 
 65,066 
 
 1870 
 
 816 
 
 146,340 
 
 290 
 
 70,621 
 
 1871 
 
 756 
 
 97,176 
 
 302 
 
 87,842 
 
 1872 :... 
 
 645 
 
 76,291 
 
 292 
 
 62,210 
 
 1873 
 
 804 
 
 144,62© 
 
 402 
 
 88,010 
 
 1874 
 
 961 
 
 216,316 
 
 404 
 
 101,930 
 
 1875 
 
 798 
 
 206,884 
 
 323 
 
 62.460 
 
 1876 
 
 698 
 
 118,672 
 
 338 
 
 69,252 
 
 1877 
 
 581 
 
 106,331 
 
 265 
 
 47,514 
 
 1878 
 
 532 
 
 106,066 
 
 334 
 
 81,860 
 
 1879 
 
 468 
 
 66,867 
 
 335 
 
 86,361 
 
 1880 
 
 460 
 493 
 
 59,057 
 81,209 
 
 348 
 444 
 
 78 053 
 
 1881 
 
 118,070 
 
 1882 
 
 666 
 721 
 
 118,798 
 137.046 
 
 502 
 439 
 
 121 843 
 
 1883 
 
 107,229 
 
 1884 
 
 706 
 
 120,621 
 
 410 
 
 91,328 
 
 1885 
 
 533 
 
 65,362 
 
 338 
 
 84.332 
 
 1886 
 
 405 
 
 41,237 
 
 240 
 
 44,467 
 
 1887 
 
 447 
 
 34,633 
 
 299 
 
 100,074 
 
 1888 .... 
 
 423 
 489 
 505 
 733 
 
 48,590 
 
 50,570 
 
 102.873 
 
 144,290 
 
 430 
 440 
 410 
 
 488 
 
 142 006 
 
 1889 
 
 159 318 
 
 1890 
 
 159 045 
 
 1891 
 
 185,037 
 
 1892 
 
 846 
 493 
 
 83.217 
 49,348 
 
 438 
 380 
 
 92 531 
 
 1893 
 
 134,308 
 
 1894 
 
 477 
 397 
 
 37,827 
 34,900 
 
 293 
 248 
 
 83 720 
 
 1895 
 
 69,754 
 
 1896 
 
 369 
 
 65,236 
 
 286 
 
 138,028 
 
 1897 
 
 338 
 
 64,308 
 
 288 
 
 106,153 
 
 1898 
 
 359 
 
 34,416 
 
 394 
 
 105,838 
 
 1899 
 
 420 
 
 98,073 
 
 439 
 
 151,058 
 
 1900 
 
 504 
 
 116,460 
 
 422 
 
 202,528 
 
 1901 
 
 526 
 
 126,165 
 
 506 
 
 273,591 
 
 1902 
 
 581 
 
 97,698 
 
 579 
 
 308,178 
 
 1903 
 
 470 
 
 89,979 
 
 551 
 
 271,781 
 
 NoTB. — Cfnal boats and barges are not included In this table.
 
 NAUTICAL MEMORANDA 
 
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 310 
 
 NAUTICAL MEMORANDA 
 
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 NAUTICAL MEMORANDA 
 
 311 
 
 In the preceding tables, giving an estimate of the sea 
 strength of the principal naval powers in July, 1905, the 
 figures for Russia and Japan are revised to include changes 
 brought about by the gains and losses during the war. In 
 the classification of the ships the term protected cruiser has 
 been omitted, because all cruisers, except the smallest and 
 oldest, now have protective decks. Scouts are considered 
 as cruisers in which battery and protection have been 
 sacrificed to secure extreme speed. It should be further 
 noted that in this comparison the following vessels are not 
 included: Those over 20 yr. old, unless they have been 
 reconstructed and rearmed; those not actually completed; 
 gunboats and other vessels of less than 1,000 T.; and lastly, 
 torpedo craft of less than 50 T. displacement. 
 
 NUMBER AND TONNAGE OF THE MERCHANT MARINE 
 OWNED BY THE PRINCIPAL MARITIME NATIONS 
 
 {From Report by the Department of Commerce and Labor 1905) 
 
 Country 
 
 Sailing Vessels 
 50 T. and More 
 
 Steamers 
 100 T. and More 
 
 Num- 
 ber 
 
 Tonnage 
 
 Num- 
 ber 
 
 Tonnage 
 
 Great Britain 
 
 United States 
 
 6.839 
 
 3,751 
 
 1,740 
 
 3,006 
 
 1,449. 
 
 914 
 
 1,554 
 
 1,515 
 
 867 
 
 1,521 
 
 911 
 
 797 
 
 704 
 
 576 
 
 374 
 
 278 
 
 111 
 
 163 
 
 120 
 
 2,196,443 
 
 1,454.152 
 
 767.981 
 
 545,087 
 
 535,703 
 
 528,267 
 
 517,964 
 
 278,445 
 
 174,824 
 
 174,624 
 
 173,636 
 
 126,135 
 
 104,722 
 
 94,294 
 
 76.375 
 
 60.736 
 
 51,886 
 
 40.540 ' 
 
 29.118 j 
 
 5,929 
 
 846 
 
 844 
 
 533 
 
 556 
 
 1,193 
 
 351 
 
 594 
 
 99 
 
 373 
 
 180 
 
 341 
 
 304 
 
 403 
 
 186 
 
 26 
 
 38 
 
 93 
 
 224 
 
 13.966,972 
 
 1,610.466 
 
 925 683 
 
 Russia .... 
 
 593 742 
 
 
 1,139 575 
 
 Germany. . 
 
 2 767 463 
 
 Italv 
 
 714 .SS7 
 
 Sweden 
 
 473 051 
 
 Turkey 
 
 98 066 
 
 Japan 
 
 556 036 
 
 Greece . . 
 
 321 330 
 
 
 477 087 
 
 Holland 
 
 608 153 
 
 
 712 804 
 
 Brazil 
 
 Portugal. . . . 
 
 123.597 
 45 633 
 
 ChiH 
 
 62 742 
 
 Argentina 
 
 Austria 
 
 73,128 
 540,354
 
 312 
 
 NA UTICAL MEMORANDA 
 
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 rt tn ra 
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 NAUTICAL MEMORANDA 
 
 313 
 
 cr 6- 
 
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 314 
 
 NAUTICAL MEMORANDA 
 
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 TO PRODUCE BREATHIXG 315 
 
 The new White Star liner "Baltic," whose dimensions are 
 given in the preceding table, is probably better equipped 
 electrically than any other vessel, either afloat or building. In 
 addition to the usual electrical appliances to be found on 
 board present-day ocean liners, the "Baltic" is equipped with 
 an electrical device for preventing collisions with other 
 vessels. The moment another ship enters the magnetic 
 field of the "Baltic," the needle of the indicating instrument 
 points in the direction of the vessel approaching, or being 
 overtaken, and the officer in charge of the deck is thus in 
 a position to take the steps necessary to avoid a collision. 
 Even the rhythmic beats of an unseen steamer's screws are 
 registered by means of this delicate apparatus. Another 
 safeguard is an electric contrivance to show on the bridge 
 if the ship's lights are burning properly. An electric log 
 for ascertaining the speed of the ship is another acquisition, 
 and an electric lead for sounding is also on the list. There 
 is, further, an electric device for registering all signals, 
 including steam sirens. The "Baltic" is equipped with elec- 
 tric refrigerating as well as electric cooking apparatus. — 
 Scientific American. 
 
 TO RESTORE APPARENTLY DROWNED 
 PERSONS 
 
 TREATMENT WHEN SEVERAL ASSISTANTS ARE ON 
 HAND 
 
 As soon as the patient is taken from the water, expose 
 the face to the air, toward the wind if there be any, and 
 wipe dry the mouth and nostrils; rip the clothing so as to 
 expose the chest and waist, and give two or three quick, 
 smarting slaps on the chest with the open hand. If the 
 patient does not revive, proceed immediately to expel water 
 from the stomach and chest, as follows: Separate the jaws 
 and keep them apart by placing between the teeth a cork or 
 small bit of wood; turn the patient on his face, a large bundle 
 of tightly rolled clothing being placed beneath the stomach 
 (see Fig. 1) ; press heavily on the back over the stomach for 
 ^ min., or as long as fluids flow freely from the mouth.
 
 316 
 
 TO PRODUCE BREATHING 
 
 To Produce Breathing. — Clear the mouth and throat of 
 mucus by introducing into the throat the comer of a hand- 
 kerchief wrapped closely around the forefinger; turn the 
 
 Fig. 1 
 
 patient on the back, the roll of clothing being so placed as 
 to raise the pit of the stomach above the level of the rest of 
 
 Fig. 2 
 
 the body (see Fig. 2). Let an assistant, with a handkerchief 
 or piece of dry cloth, draw the tip of the tongue out of one 
 comer of the mouth (which prevents the tongue from falling
 
 TO PRODUCE BREATHING 
 
 317 
 
 back and choking the entrance to the windpipe), and keep 
 it projecting a little beyond the lips. Let another assistant 
 grasp the arms just below the elbows and draw them steadily 
 upwards by the side of the patient's head, and to the ground, 
 the hands nearly meeting (which enlarges the capacity of 
 the chest and induces inspiration). While this is being 
 done, let a third assistant take a position astride the patient's 
 hips, with his elbows resting on his own knees, his hands 
 extended ready for action. Next, let the assistant stand- 
 ing at the head turn down the patient's arms to the side of 
 the body (see Fig. 3), the assistant holding the tongue 
 
 7f "^v'^^''t^ 
 
 Fig. 3 
 
 changing hands, if necessary, to let the arm pass. Just 
 before the patient's hands reach the ground, the man astride 
 the body will grasp the body with his hands, the balls of 
 the thumbs resting on either side of the pit of the stomach, 
 the fingers falling into grooves between the short ribs. 
 Now, using his knees as a pivot, he will at the moment 
 the patient's hands touch the ground throw (not too sud- 
 denly) all his weight forwards on his hands, and at the 
 same time squeeze the waist between them, as if he wished 
 to force something in the chest upwards out of the mouth; 
 he will increase the pressure while he slowly counts one, 
 two, three, four (about 5 sec), then suddenly let go with
 
 318 TO PRODUCE BREATHING 
 
 a final push, which will spring him back to his first position. 
 This completes expiration. 
 
 At the instant the pressure is taken from the waist the 
 man at the patient's head will again steadily draw the arms 
 upwards to the sides of the patient's head, as before (the 
 assistant holding the tongue again changing hands to let 
 the arm pass, if necessary), holding them there while he 
 slowly counts one, two, three, four (about 5 sec). 
 
 Repeat these movements, deliberately and perseveringly, 
 12 to 15 times in every minute — thus imitating the natural 
 motions of breathing. 
 
 If natural breathing is not restored after a trial of the 
 bellows movement for the space of about 4 min., then 
 turn the patient a second time on the stomach, rolling the 
 body in the opposite direction from that in which it was 
 first turned, for the purpose of freeing the air passage 
 from any remaining water. Continue the artificial respi- 
 ration from 1 to 4 hr., or until the patient breathes, accord- 
 ing to the preceding instructions; and for a time, after the 
 appearance of returning life, carefully aid the short gasps 
 until deepened into full breaths. Continue the drying and 
 rubbing, which should have been unceasingly practiced 
 from the beginning by assistants, taking care not to interfere 
 with the means used to produce breathing. Thus the limbs 
 of the patient should be rubbed, always in an upward 
 direction toward the body with firm, grasping pressure 
 and energy, using the bare hands, dry flannels, or handker- 
 chiefs, and continuing the friction under the blankets or 
 over the dry clothing. The warmth of the body can also be 
 promoted by the application of hot flannels to the stomach 
 and armpits and bottles or bladders of hot water, heated 
 bricks, etc., to the limbs and soles of the feet. 
 
 After Treatment. — When breathing has been established, 
 let the patient be stripped of all wet clothing, wrapped in 
 blankets only, put to bed comfortably warm, but with free 
 circulation of fresh air. and left to perfect rest. Give 
 whisky, or brandy, and hot water in doses of a teaspoonful, 
 or a tablespoonful, according to the weight of the patient, 
 or any other stimulant at hand, every 10 or 15 min. for the
 
 TO PRODUCE BREATHING 
 
 319 
 
 first hour, and as often thereafter as may seem expedient. 
 After reaction is fully established, there is great danger of 
 congestion of the lungs, and if perfect rest is not maintained 
 for at least 48 hr., it sometimes occurs that the patient is 
 seized with great difficulty of breathing, and death is liable 
 to follow unless immediate relief is afforded. In such cases, 
 apply a large mustard plaster over the breast. If the patient 
 gasps for breath before the mustard takes effect, assist the 
 breathing by carefully repeating the artificial respiration. 
 
 The foregoing treatment should be persevered in for some 
 hours, as it is an erroneous opinion that persons are irrecover- 
 able because life does not soon make its appearance, persons 
 having been restored after persevering for many hours. 
 
 MODIFICATION OF TREATMENT IN CASE NO ASSIST- 
 ANT IS AT HAND 
 To Produce Respiration. — If no assistant is at hand and 
 one person must work alone, place the patient on his back 
 with the shoulders slightly raised on a folded article of 
 clothing; draw forward the tongue and keep it projecting 
 just beyond the lips; if the lower jaw be lifted, the teeth 
 
 Fig. 1 
 
 may be made to hold the tongue in place; it may be neces- 
 sary to retain the tongue by passing a handkerchief under 
 the chin and tying it over the head. Grasp the arms just 
 below the elbows and steadily draw them upwards by the 
 sides of the patient's head to the ground, the hands nearly
 
 320 
 
 U. S. NATURALIZATIOX LAWS 
 
 meeting as shown in Fig. 1. Next, lower the arms to the 
 sides and press firmly downwards and inwards on the sides 
 and front of the chest over the lower ribs, drawing toward 
 the patient's head, as shown in Fig. 2. Repeat these move- 
 ments 12 to 15 times every minute, etc. 
 
 Remarks. — In any operation for restoring to life an 
 apparently drowned person, remember the following: 
 
 Fig. 2 
 
 Prevent unnecessary crowding of persons round the body, 
 especially if in an apartment. 
 
 Avoid rough usage, and do not allow the body to remain 
 on the back unless the tongue is secured. 
 
 Under no circumstances hold the body up by the feet. 
 
 On no account place the body in a warm bath, unless 
 tinder medical direction, and even then it should only be 
 employed as a momentary excitant. 
 
 U. S. NATURALIZATION LAWS 
 
 The conditions and manner of admission of an alien to 
 the citizenship of the United States are prescribed by Sec- 
 tion 2, 165-74 of the Revised Statutes of the United States. 
 
 Declaration of Intentions. — The alien must declare on 
 oath before a circuit or district court of the United States, 
 or a district or supreme court of the territories, or a court of 
 record of any of the states having common-law jurisdiction
 
 U. S. NATURALIZATION LAWS 321 
 
 and a seal and clerk, 2 yr. at least prior to his admission, 
 that it is, bona fide, his intention to become a citizen of the 
 United States, and to renounce forever all allegiance and 
 fidelity to any foreign prince or state, and particularly to the 
 one of which he may be at the time a citizen or subject. 
 
 Oath on Application for Admission. — He must, at the time 
 of his application to be admitted, declare on oath, before some 
 one of the courts above specified, "that he will support the 
 constitution of the United States, and that he absolutely 
 and entirely renounces and abjures all allegiance and fidelity 
 to every foreign prince, potentate, state, or sovereignty of 
 which he was before a citizen or subject," which proceedings 
 must be recorded by the clerk of the court. 
 
 Conditions for Citizenship. — If it shall appear to the satis- 
 faction of the court to which the alien has applied that he 
 has made a declaration of intention to become a citizen 2 yr. 
 before applying for final papers, and has resided continuously 
 within the United States for at least 5 yr., and within the 
 state or territory where such court is at the time held 1 yr. 
 at least; and that during the time "he has behaved as a man 
 of good moral character, attached to the principles of the 
 constitution of the United States, and well disposed to the 
 good order and happiness of the same," he will be admitted 
 to citizenship. 
 
 Seamen. — Any seaman, who is a foreigner, who declares 
 his intention of becoming a citizen of the United States, in 
 any competent court, and has served 3 yr. on board a 
 merchant vessel of the United States subsequent to the date 
 of his declaration, may, on his application to any competent 
 court, and on the production of a certificate of discharge 
 and good conduct during that time, together with the cer- 
 tificate of his declaration of intention to become a citizen, 
 be admitted to citizenship in the United States. 
 
 Persons Discharged From United States Navy or Marine 
 Corps. — Any alien of the age of 21 yr. and upwards, who has 
 enlisted or may enlist in the United States Navy or Marine 
 Corps, and has served or may hereafter serve 5 consecutive 
 years in the United States Navy, or one enlistment in the 
 Marine Corps, and has been, or may hereafter be, honorably
 
 322 U. 5. XATURALIZATION LAWS 
 
 discharged, may be admitted to citizenship without a pre- 
 vious declaration of his intention to become a citizen. 
 
 Minors. — Any aHen under the age of 21 yr. who has 
 resided in the United States during the 3 yr. next prece- 
 ding his arriving at that age, and who has continued to 
 reside therein to the time of his application to be admitted 
 a citizen thereof, may, after he arrives at the age of 21 yr., 
 and after he has resided 5 yr. within the United States, 
 including the 3 yr. of his minority, be admitted a citizen, 
 but he must make a declaration on oath and prove to the 
 satisfaction of the court that for the 2 yr. next preceding, it 
 has been his bona fide intention to become a citizen. 
 
 Children of Naturalized Citizens. — The children of persons 
 who have been duly naturalized, being under the age of 21 yr. 
 at the time of the naturalization of their parents, shall, if 
 dwelling in the United States, be considered as citizens 
 thereof. 
 
 Chinese. — The naturalization of Chinamen is expressly 
 prohibited by Section 14, Chapter 126, Laws of 1882. 
 
 Protection Abroad to Naturalized Citizens. — Section 2,000 
 of the Revised Statutes of the United States declares that 
 "all naturalized citizens of the United States while in foreign 
 countries are entitled to and shall receive from this govern- 
 ment the same protection of persons and property which is 
 accorded to native-born citizens." 
 
 Right of Suffrage. — The right to vote comes from the state, 
 and is a state gift. Naturalization is a federal right, and is 
 a gift of the Union, not of any one state. In nearly one-half 
 of the Union, aliens (who have declared intentions) vote and 
 have the right to vote equally with naturalized or native- 
 born citizens. In the remaining states, only actual citizens 
 may vote. The federal naturalization laws apply to the 
 whole Union alike, and provide that no alien may be natu- 
 ralized until after 5 yr. residence. Even after 5 yr. resi- 
 dence and due naturalization, he is not entitled to vote 
 unless the laws of the state confer the privilege upon him; 
 but in several states he may vote 6 mo. after landing, if 
 he has declared his intention, under United States law, to 
 become a citizen.
 
 CUSTOM-HOUSE FEES 323 
 
 CUSTOM-HOUSE FEES 
 
 The following is a partial list of the custom-house fees and 
 other charges required by law to be paid by vessels at the 
 several custom houses in the United States: 
 Entry of vessel of 100 T. or more from foreign port ... .$2 .50 
 Clearance of vessel of 100 T. or more to foreign port. . . 2 .50 
 
 Entry of vessel under 100 T. from foreign port 1 .50 
 
 Clearance of vessel under 100 T. to foreign port 1 . 50 
 
 Post-entry 2 . 00 
 
 Permit to land or deliver goods 20 
 
 Bond taken officially 40 
 
 Debenture, or other official certificate 20 
 
 Bill of health 20 
 
 For recording bill of sale, mortgage, hypothecation or 
 
 conveyance of vessel, under Act of July 29, 1850. . . .50 
 For recording a certificate for discharging and cancel- 
 ling any such conveyance 50 
 
 For furnishing a certificate setting forth the names of 
 the owners of any registered or enrolled vessel, the 
 parts or proportions owned by each, and also the 
 material facts of any existing bill of sale, mortgage, 
 hypothecation or other encumbrance, the date, 
 amount of such encumbrance, and from and to whom 
 
 made 1.00 
 
 For furnishing copies of such records, for each bill of 
 
 sale, mortgage, or other conveyance 50 
 
 Certificate of registry, including bond and oath 2.25 
 
 Indorsement on certificate of registry of change of 
 
 master 1 . 00 
 
 For every bond under the Registry Act 25 
 
 Certificate of enrolment 50 
 
 Indorsement on certificate of enrolment, of change of 
 
 master, etc 20 
 
 License, and granting the same, including bond and 
 
 oath, if not over 100 T 70 
 
 License, and granting the same, over 100 T 1 .20 
 
 License, vessel not over 20 T., including bond and oath .45 
 Indorsement on a license of change of master, etc 20
 
 324 CUSTOM-HOUSE FEES 
 
 Certifying manifest, and granting permit for licensev^. 
 
 vessels to go from district to district $ .10 
 
 Receiving certified manifest, and granting permit on 
 arrival of such vessel 10 
 
 Certifying manifest, and granting permission to regis- 
 tered vessels to go from district to district 1 . 50 
 
 Receiving certified manifest, and granting permit on 
 arrival of such registered vessel 1 . 00 
 
 Granting permit to a vessel, not belonging to a citizen 
 of the United States, to go from district to district, 
 and receiving manifest 2 . 00 
 
 Receiving manifest and granting permit to unload, to a 
 vessel not belonging to an American citizen, on arrival 
 at one district from another 2 . 00 
 
 Services other than admeasurement to be performed by 
 the Surveyor in vessels of 100 T. or more, having 
 on board merchandise subject to duty 3 . 00 
 
 For like service in vessels under 100 T., having similar 
 merchandise 1 . 50 
 
 For like services in all vessels not having merchandise 
 
 subject to duty 67 
 
 Protection to American seamen 25 
 
 Crew list 25 
 
 General permit to land passengers' baggage 20
 
 NIENIOI^^NDA
 
 NIKMORANDA
 
 NIENIOR^NDA
 
 NIENIORANDA
 
 MiENlORANDA
 
 NIENIORANDA
 
 Promotion 
 y vancement in Salary 
 
 and 
 
 ' Business Success ^ 
 
 Secured 
 Through the 
 
 Marine Engineers' 
 and Ocean, Lake, and 
 Coastwise Navigation 
 
 COURSES OF INSTRUCTION 
 
 OF THE 
 
 International 
 Correspondence Sciiools 
 
 International Textbook 
 Company, Proprietors 
 
 SCRANTON, PA., U.S.A. 
 
 SEE FOLLOWING PAGES
 
 Passed Many Exam- 
 inations 
 
 I wish to say that your Schools are all O. K. 
 They have been instrumental in my being 
 able to pass the following examinations: 
 Assistant Engineer, U. S. N., Spanish Ameri- 
 can War; Warrant Machinist, U. S. N., Regular 
 Service; Chief Engineer, U. S. Coast Survey; 
 Chief Engineer, U. S. Quartermaster's Depart- 
 ment, U. S. Army; and I have just passed as 
 Local Inspector of Boilers, of Ocean Steamers 
 of 10,000 tons. I not only passed all of these 
 examinations, but have been appointed to all 
 but the Local Inspector of Boilers, and I hope 
 to be in it before the summer is over. I now 
 fill the position of Chief Engineer on board 
 one of the U. S. Quartermaster's Boats, U. S. 
 Army. I would have been unable to pass all 
 of these examinations, all of them being very 
 hard, if I had not studied in your Schools. 
 
 Any time I can do anything for you let me 
 know, as your School is a Godsend to practical 
 men, but I am sorry to say that a great many 
 do not see it. It was one of your circulars 
 that set me thinking. It was as follows: 
 "A man cannot stand still; he either goes 
 ahead or lags behind." 
 
 D. C. Young, 
 625 Apple ton St., Baltimore, Md.
 
 PROMOTED TO ENSIGN 
 
 W. D. Greetham, Ensign, U. S. N., Washington, D. C. 
 says he thinks very highly of the I. C. S. and is confident 
 he owes his recent advancement to the rank of ensign to 
 the information gained by studying the I. C. S. Navigation 
 Course. 
 
 FIREMAN BECOMES WARRANT MACHINIST 
 
 T. G. Sprengel. Warrant Machinist, U. S. N., U. S. S. 
 "Massachusetts," could not ship in the United States Navy 
 as a machinist because he didn't have sufficient knowledge. 
 He went as a fireman, second class. By studying the 
 I. C. S. Course he has now reached the position of warrant 
 machinist in the Navy. He says he would not take one 
 hundred times the cost of the Course for the benefit received 
 from it. 
 
 COAL PASSER BECOMES ELECTRICIAN 
 
 A. M. H.wiRiCK, Electrician, U, S. N., U. S. S. "Prince- 
 ton," enrolled in the I. C. S. while a coal passer in a boiler 
 room. At the present time he is electrician on board the 
 U. S. S. " Princeton," and his salary has been increased about 
 200 per cent. 
 
 OBTAINED UNLIMITED LICENSE 
 
 W. G. MiCHALSKi, 807 South Broadway, Baltim.ore, Md., 
 passed the examination for chief mate on ocean-going 
 steamers and has been given an unlimited license for that 
 position. He also has been promoted from second officer 
 to the position of chief officer. Mr. Michalski thanks the 
 I. C. S. for his success. 
 
 PASSED EXAMINATIONS EASILY 
 
 William J. Ryan*, 53 North Main St., W^oonsocket, R. I., 
 by studying the Ocean Navigation Course, has successfully 
 passed examination for the position of second mate on 
 ocean steam vessels. 
 
 EASILY UNDERSTOOD AND MOST INTERESTING 
 
 Charles Liess.m.»n, U. S. S. " Marblehead," in a letter to 
 the Schools says the Course has proved to be most interesting 
 and simple; that he cotild not help mastering the subjects. 
 
 IS PILOT ON GREAT LAKES NOW 
 
 Henry Ericksen, 670 Seventh St., Milwaukee, Wis., passed 
 the United States examination for pilot on the Great Lakes, 
 by means of his studies with the I. C. S. His salary has 
 been increased 130 per cent. 
 
 3
 
 The Course a Great 
 Benefit 
 
 I found the International Correspondence 
 Schools' Ocean Navigation Course of the 
 greatest benefit to me. And the Reference 
 Library Volumes not only have proved most 
 useful when preparing for examination and 
 as books of reference for actually working 
 navigation at sea, but they have been 
 admired by every officer in the service who 
 has seen them. 
 
 Henry B. Soulek, Lieutenant, U. S. N., 
 Bureau of Navigation, 
 
 Washington, D. C.
 
 PASSED AN EXAMINATION 
 
 William Santimo, Brechin, Ont., by studying the Lake 
 Navigation Course, has been able to pass an examination for 
 a mate's certificate. 
 
 PRAISE FROM GOVERNMENT OFFICERS 
 
 WiLHELM Weidlick, Puget Sound Harbor 16, Seattle, 
 Wash., prepared for a mate's certificate by studying the 
 1. C. S. Course in Ocean Navigation. He passed with flying 
 colors. Captain Pratt, of the United States Coast and 
 Geodetic Survey, and many other prominent ship masters, 
 declared, in this connection, that the Course is the most 
 complete work of its kind they ever have seen. 
 
 COXSWAIN BECOMES THIRD OFFICER 
 
 Andrew E. Knudson, New York, passed the Board of 
 Inspectors' examination and is now serving as third officer 
 on board of the " El Vail, " of New York. When he enrolled 
 in the I. C. S. he was a coxswain in the Navj'. 
 
 BECOMES FIRST-CLASS PILOT 
 
 R. R. WiLMOT, 948 Jefferson Ave., Brooklyn, N. Y.. was 
 an unlicensed man, acting as third mate on a steamship 
 when he began studying in the I. C. S. He has passed the 
 examination for master of ocean steam vessels and for fi.rst 
 chief pilot. He is now second officer of the S. S. "El Mar" 
 and a member of the American Masters, Mates, and Pilots' 
 Association. He says there never has arisen during his 
 service at sea a problem in nautical science that he has not 
 been able to solve by means of the knowledge gained from 
 his Course. 
 
 FROM DECKHAND TO BOATSWAIN 
 
 Bertolf Mathiesen, 815 Witherspoon Bldg., Phila- 
 delphia, Pa., took up the Ocean Navigation Course and in 
 a few months was promoted to the position of quarter- 
 master on the Government dredge "Delaware," which 
 carries 56 men. In 11 months from the time of his enrol- 
 ment he was made boatswain. He gives the I. C. S. entire 
 credit for his quick promotions. 
 
 SEAMAN TO COXSWAIN 
 Ferdinand Johansen, U. S. S. "Alliance," Culelera, 
 Porto Rico, says the I. C. S. Ocean Navigation Course is 
 excellent. He learned from it the rules of the road, safety 
 arrangements, and information about codes and steam 
 launches. He has advanced from ordinary seam^an in the 
 United States Navy to coxswain of a forty-foot steam 
 launch with corresponding increases in wages.
 
 Simple and Thorough 
 
 I take pleasure in saying that the Naviga- 
 tion Course of the International Correspond- 
 ence Schools is the most simple and thorough 
 method for a student to learn navigation. 
 Having but a limited common-school educa- 
 tion and having received a Diploma with no 
 assistance outside the School, is a voucher of 
 the School's gviarantee. You are at perfect 
 liberty to refer to me at any time that I can 
 be of service to you, and it will give me great 
 pleasure to recommend the Schools whenever 
 I have the opportunity. 
 
 With kind regards, I remain, 
 
 William Henry Caoss, 
 
 Bar Pilot, Charleston, S. C.
 
 FROM DECK HAND TO MATE 
 
 Henry E. Farrer, South Bend, Wash., holds a mate's 
 license that he was able to win by studying the Lake Naviga- 
 tion Course. At present he is n-.ate of a tug, earning 875 
 a month and board. When he enrolled he was deck hand 
 on a steamer, earning S45 a month. 
 
 FROM SEAMAN TO THIRD OFFICER 
 
 A. Frederiksex, 1310 Laguna St., San Francisco, Cal., 
 says he does not know of a school in the United States, 
 outside of the Naval Academy, so good as the I. C. S. 
 Ocean Navigation School. He says every subject per- 
 taining to ordinary practical navigation is fully treated and 
 that the Course gives an education far beyond any required 
 to pass the examinations for unlimited license as master or 
 mate of steam or sailing vessels. When he enrolled in the 
 I. C. S. he was a seaman in the United States Navy. At 
 present he is third officer of the steamship "City of Tara." 
 His salary has been increased 250 per cent. 
 
 COAL PASSER TO ENGINEER 
 
 W. H. Demeritt, U. S. S. "Mangrove." Key West, Fla., 
 has advanced from the position of coal passer, in the light- 
 house service, to second in charge of the engineering depart- 
 ment of one of the largest steamers in the United States 
 light-house service — the U. S. S. "Mangrove." It didn't 
 take Mr. Demeritt long to master the Course; and at the 
 examination he made the highest percentage on record in 
 his district. 
 
 FROM $18 A MONTH TO $1,000 A YEAR 
 
 Stanley S. Stevens, Delaware City, Del., enrolled in the 
 I. C. S. Marine Engineers' Course while earning about S18 
 a month. What he learned from, the Course enabled him 
 to pass the Government examination for marine engineers' 
 license. He is now earning SI, 000 a year and says he owes 
 his position entirely to I. C. S. instruction. 
 
 WATCHMAN PASSES PILOTS' EXAMINATION 
 
 R. C. LuDWiG, 162 Broadway, Benton Harbor, Mich., 
 enrolled for the Lake Navigation Course while holding a 
 position as watchman on a lake steamer. With the knowl- 
 edge gained from his Course he passed the examination for 
 first-class pilot, of all tonnage for Lake Michigan, Green 
 Bay, and the Straits of Mackinaw. Last season he held a 
 position as second officer on a steamer and received commen- 
 dation from his superior officers. Mr. Ludwig is going to 
 continue his studies with us until he secures a first-class 
 license for all the Great Lakes and connecting waters. His 
 salary has increased 70 per cent.
 
 Commendation From a 
 Commander 
 
 I received the Volumes of your Course in 
 Navigation several weeks ago and have 
 examined them with much interest. They 
 seem to me admirably adapted both in plan 
 and in execution to the purpose for which 
 they are designed, and I am sure that the 
 Course of Instruction which they represent 
 cannot fail to be of great value to all who may 
 take it under your guidance. 
 
 The two features of the work which have 
 impressed me most forcibly are: first, the 
 happy balancing of theory and practice; and 
 second, the originality and helpfulness of the 
 illustrations. 
 
 Austin M. Knight, 
 
 Commander, U. S. Navy
 
 PASSED EXAMINATION FOR FIRST-CLASS PILOT 
 
 Thomas Wilmot, U. S. Steamer "Morrill," Milwaukee, 
 Wis., has been able to stand a stiflf examination for the 
 position of first-class pilot, on the Great Lakes. He pre- 
 pared for this by studying the L C. S. Lake Navigation 
 Course. 
 
 SALARY INCREASED 140 PER CENT 
 
 JOHAN WiLLADSEN, Sun Oil Co., Marcus Hook, Pa., by 
 studying the Marine Engineers' Course has advanced from 
 the position of fireman to second engineer, on board the 
 steamship "Paraguay." From the Course Mr. Willadsen 
 learned all about marine machinery and boilers and secured 
 sufficient technical knowledge to obtain a marine engineer's 
 license. His salary has been increased 140 per cent, since 
 he started studying the Course. 
 
 FIREMAN BECOMES ENGINEER 
 
 J. K. MuNSON, Shelton, Wash., a fireman when he enrolled 
 in the Marine Engineers' Course, is now engineer of the tug 
 "Victor" and his salary has been increased over 200 per 
 cent. He says he will be glad to hear from anybody that 
 wants to write to him regarding the I. C. S. 
 
 TUG-BOAT FIREMAN BECOMES MARINE ENGINEER 
 
 Joseph H. Pratt, 1349 Fifth Ave., Watervliet, N. Y., 
 was working as a tug-boat fireman when he began his Course 
 in the L C. S. He advanced to the position of assistant 
 engineer and then to that of marine engineer. His salary 
 has doubled as a result of studying the Course. 
 
 SALARY DOUBLED 
 
 Charles Fredrickson, Fairfield, Conn., by means of the 
 Marine Engineers' Course, has advanced from the position 
 of fireman to that of second engineer on an ocean-going tug 
 owned by the Lehigh Valley Railroad Company. His salary 
 has been doubled. 
 
 OILER BECOMES ASSISTANT ENGINEER AT $90 A MONTH 
 
 Emil Stolsen, Frankfort, Mich., was employed as an 
 oiler on one of the Ann Arbor Company's car ferries when 
 he started to study the L C. S. Marine Engineers' Course. 
 He is now assistant engineer for the same company. His 
 salarv has been advanced from ?37,.50 to S90 a month. Mr. 
 Stolsen says that if it was not for the I. C. S. he would have 
 been unable to pass the examination required for a marine 
 engineer's license.
 
 None Too Old to Learn 
 
 It gives me great pleasure to recommend 
 the I. C. S., especially to marine engineers. 
 I am the owner of several steamers and felt 
 my position very keenly, as I was not able to 
 pass the government examinations to secure 
 papers that Avould allow me to run my own 
 boats. Although no longer a young man, 
 I enrolled for the Marine Engineers' Course, 
 and, in a short time, was able to pass the 
 examination before the Government Inspec- 
 tors and obtain papers for ^OO-ton steamers 
 I am convinced that if employes would fit 
 themselves for their professions through the 
 Schools they would command more respect 
 from their, employers. 
 
 P. F. West. Bridgeport, Conn.
 
 FROM $90 A MONTH TO $150 A MONTH 
 
 George Gale, 310 Twenty-first St., West New York, 
 N. Y., began the Marine Engineers' Course in the I. C. S. 
 while employed as first assistant engineer on one of the 
 Southern Pacific Company's steamships. The salary paid 
 to first assistant engineers by this company is S90 a month. 
 At present Mr. Gale is chief engineer on one of the same 
 company's steamships, running between New York and 
 Galveston. His salary is ?150 a month. He says the knowl- 
 edge of electricity gained from the Course was specially 
 valuable to him and that the cost of the Course is one of 
 the best investments he ever made. 
 
 MACHINIST STUDIES THE COURSE 
 
 W. A. Buckley, U. S. S._ "Kentucky," care Postmaster, 
 New York, was a machinist's apprentice in a marine engine 
 shop when he enrolled for the Marine Engineers' Course. 
 He found the knowledge gained from the Course to be of 
 much value in connection with his shop work and, later, 
 with his work on board ship. He is now chief -machinist's 
 mate in the United States Navy. 
 
 PASSED EXAMINATION FOR LICENSE 
 
 John J. Crowley, S. S. "Larimer," Port Arthur, Tex., 
 had just left an English ship, where he was donkeyman, and 
 taken a position on an American steamer as fireman when 
 he enrolled in the I. C. S. Marine Engineers' Course. By 
 studying he soon passed the third assistants' examination 
 for license and immediately received an appointment. He 
 is going to take the examination for second assistant, then 
 first assistant, and then chief. 
 
 FIREMAN TO ENGINEER 
 
 S. Watson, 113 Christiana St., Samia, Canada, says he 
 considers the I. C. S. instruction the best obtainable in the 
 lines taught. He enrolled in the Marine Engineers' Course 
 and has advanced from the position of fireman to that of 
 engineer of a boat. 
 
 RUNS YACHT AND AUTOMOBILE ENGINES 
 
 Merrill W. Keister, Box 367, Lake Geneva, Wis., while 
 working as a fireman on the Great Lakes tried to get a license 
 as engineer, but failed. Then he enrolled for the I. C. S. 
 Marine Engineers' Course and secured the much-desired 
 license, together with a position as engineer on a private 
 yacht, at Lake Geneva, Wis. In the winter he runs an auto- 
 mobile. His salary has been advanced from S50 a month to 
 SI 15 a month. 
 
 11
 
 Ilnttrb ^tatrs Naual AraJirmg 
 Anitapnlta, Mb. 
 
 International Correspondence Schools, 
 Scrantott, Pa. 
 Gentlemen: At your request, I have care- 
 fully examined your textbooks on Ocean 
 Navigation and unhesitatingly pronounce 
 them an admirably arranged and compre- 
 hensive treatise, and one that should prove 
 a valuable aid to any person taking up the 
 study of Navigation. 
 
 You are to be congratulated on presenting 
 a subject, unfortunately an intricate one to 
 many, in a most clear and simple way. 
 W. C. P. MuiR, 
 Lieut. -Commander, U. S. N. 
 
 12
 
 EARNINGS GREATLY INCREASED 
 
 W. J. Dru.mmond, Act. Boatswain, U. S. N,, U. S. S. 
 "Siren," Navy Yard, Norfolk, Va., enrolled in the I. C. S. 
 while a third-class quartermaster, earning S31.36 a month. 
 His study with the I. C. S. enables him to hold the position 
 of boatswain with a salary of SI aO a month. Mr. Drummond 
 recently has passed the examination for warrant rank. 
 
 SEAMAN BECOMES MATE 
 J. H. A. Johnson, Boatswain's Mate, First Class, U. S. N., 
 Newport, R. I., is very proud of his I. C. S. Diploma, which 
 has helped him to advance. When he started to study in 
 the I. C. S. he was a seaman in the Navy. Now he is boat- 
 swain's mate, first class. 
 
 NOW SENIOR STEAM ENGINEER 
 
 R. E. Skeldox, Toledo, Ohio, is an example of am.bition 
 and I. C S. training combined to make success. Mr. Skeldon 
 was employed as engineer on a Government tug on the Great 
 Lakes when he enrolled in the Marine Engineers' Course. 
 He applied himself to his studies and now holds the position 
 of senior steam engineer on the floating plant engaged in 
 United States engineering work in the Cleveland district. 
 
 NEW YORK CLUBMAN COMMENDS COURSE 
 
 I have put a great deal of spare time, for the last few 
 years, into the self-study of navigation, having gone through 
 "Raper's" and "Node's" and many other textbooks; but J 
 have never mastered it, owing, first, to the failure of every- 
 body, until now, to make this subject sufficiently clear in 
 the explanation of its theory, and also to the fact that 
 none of them give sufficient examples for a student to 
 familiarize himself thoroughly with each step. I am learning 
 under your system. Your work, I think, is more perfect and 
 intelligible than anything that has heretofore been published. 
 
 A. J. MOXHAM, 
 
 Mem.ber, New York Yacht Club 
 THOROUGH AND ABLE INSTRUCTION 
 
 Having just completed a Course of study in Ocean Naviga- 
 tion and received my Diploma, I feel that a few words of 
 appreciation are due the International Correspondence Schools 
 for their efforts in my behalf as one of their pupils. 
 
 The fact that I was able to pass through this Course in 
 the comparatively short time of a little over 6 months I 
 attribute entirely to the thorough and able manner in which 
 all subjects are treated and to the earnest efforts on the 
 part of the Instructors to encourage, explain, and advise on 
 any deficiency they may note in the student's work. 
 J. S. Crogh.\n, 
 
 Boatswain, U. S. Navy 
 
 13
 
 Nrm fnrk Nautiral (EoUpg? 
 Npw fork, N. ^. 
 
 International Correspondence Schools, 
 Scranton, Pa. 
 Gentlemen: It has been my pleasure 
 during the past week to carefully read 
 thoroughly your three textbooks on "Navi- 
 gation and Nautical Astronomy." I feel it 
 obligatory to write to you for the purpose of 
 expressing my extremely high opinion of said 
 work. I cannot understand how it could be 
 improved. It is masterly in every detail, 
 yet is so clearly and concisely written that it 
 is within the comprehension and assimilation 
 of the average lay student. I take off my 
 hat to the author of the books, whoever he 
 may be. 
 
 Howard Patterson. Principal
 
 EXPLANATIONS FULL AND CLEAR 
 
 Your Ocean Navigation Course is an excellent one, all 
 explanations and statements being very full and clear. 
 * * * Before I took up this Course, I tried to study naviga- 
 tion from Bowditch's "Practical Navigator," but soon gave 
 it up on account of its confusing technicality to one not 
 having a mathematical foundation such as is provided in 
 your Course. Carl I. Ostrom, 
 
 Quartermaster, U. S. Navy 
 
 MOST SATISFACTORY TREATISE ON THE SUBJECT 
 
 I have gone over the Lake Navigation Course very care- 
 fully, and will say that, without doubt, it is the most satis- 
 factory treatise on the subject that could be compiled. 
 The work reveals a master hand, and, as a whole, furnishes 
 the most thorough and masterly education that could be 
 devised for the mariner on the Great Lakes, who stands 
 greatly in need of such an education, but to whom it has 
 heretofore been inaccessible. 
 
 Capt. Frank Henrich, Nautical Expert, 
 
 In charge Branch Hydrographic Office, 1001 Torry Bldg. 
 
 Duluth, Minn. 
 
 THOROUGH AND CONCISE 
 
 After thoroughly perusing the textbooks on Navigation 
 and Nautical Astronomy of the International Correspond- 
 ence Schools, I can conscientiously say that they are the 
 most thorough and comprehensive work on the subject I 
 have ever seen, and, therefore, I can and will recommend 
 them to all my friends who desire to take a Course in Naviga- 
 tion. E. Greths, 
 
 Chief Mate S. S. "Francis H. Legget," 
 Formerly Teacher of Navigation at San Francisco, Cal. 
 
 COULD NOT READ NOR WRITE ENGLISH 
 
 Sewerin Falk, U. S. S. ''Kentucky," care of Postmaster, 
 New York City, enrolled in the I. C. S. Ocean Navigation 
 Course while a seaman in the United States Navy and unable 
 to read nor write English. He studied the Course with the 
 aid of a dictionary. Now he not only can read and 
 write English but has had his salary doubled, in a better 
 position than when he enrolled. He holds a Diploma for the 
 Ocean Navigation Course. In a letter to the Schools, 
 Mr. Falk has written: "It is beyond mv power to express 
 my heartfelt gratitude toward the Schools for the thorough 
 instruction and careful corrections given to me ; and for the 
 interest they have taken in helping me along. It is with 
 great pleasure I recommend the I. C. S to every man and 
 woman that desire to better their position." 
 
 15
 
 REFERENCE VOLUMES OF GREAT VALUE 
 
 When 1 enrolled in the I. C. S., I had only a common -sc hoc 
 education, and was a carpenter's mate, third class; but no\ 
 I am carpenter's mate, second class. The instruction an 
 books supplied by the Schools are so thorough and clear tha 
 the student cannot fail to succeed in his studies, particular] 
 in the Navigation Courses. I therefore recommend the l.C.J- 
 to all seamen who wish to prepare themselves for a nautic;) 
 examination. The Reference Volumes are of great value t 
 me as a reference library. Sven J. Troin, 
 
 U.S. S. "Atlanta." 
 EASY TO LEARN NAVIGATION 
 Thomas Chantre, U. S. S. "Des Moines," North Atlant' 
 Squadron, Sixth Division, Cap Cod Bay, in a letter to i 
 Principal of the School of Navigation has written the follow 
 ing: "I take pleasure in saying that the Navigation Course 
 the I. C. S. is the most simple and thorough method for an; 
 ambitious seaman to learn navigation. Having but a liniit ■'< 
 common school education to start with, I have received th 
 I. C. S. Diploma with no help outside of the I. C. S. Instn 
 tion Papers. This is a voucher of the Schools' guarantee 
 teach any one that will study. It is my honest opinion tu^ 
 their Course in Navigation cannot be other than of grca 
 benefit to any sailor trying to lisc in his profession." 
 SALARY INCREASED 100 PER CENT. 
 Peter J. Milne, 164: Bagot St., Kingston, Ontario, cov 
 hardly work division, in Arithmetic, when he enrolled in 
 Marine Engineers' Course. Now he can master the n. 
 difficult problems and has advanced from the positior 
 stationary fireman to that of chief engineer for the Cen, 
 Company, Kingston. By means of the Course he h 
 ^•cured a first-class engineer's certificate. 
 
 PASSED INSPECTOR'S EXAMINATION 
 John H. Frkuenborg, 112 Seventh Ave., North, Scatt" 
 Wash., by studying the Lake Navigation Cor.rse, has be 
 :ihle to pass the inspector's examination in Seattle, for mat 
 ; iipers for steam vessels. When he enrolled he was a dev 
 and, soon securing a position as mate at a large increase i. 
 alary. 
 
 EDUCATION MUCH IMPROVED ' 
 
 J. S. Drarwooi), care of vStcamer "Masaha." Marine P. C 
 Detroit, Mich., began studying the Lake Navigation Cours 
 hile working as a laborer. As a result of the imrcnse 
 i.nowledge Mr. Dearwood has, his income has bten incrciseS. 
 i Ic says: "I was only in the fourth grade when I IcK 'dr. 
 md would not take for the I. C. S. Course twice wii: 
 ic. I ha\e much improved in my general ednca: 
 (crtainly would nrcnuncnil xunr Sdinols f o .-in\- < m. 
 an education.
 
 THE LIBRARY 
 UNIVERSITY OF CALIFORNIA 
 
 Santa Barbara 
 
 THIS BOOK IS Dl E ON THE LAST DATE 
 STAMPED BELOW.
 
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