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534 I 26 10.4 6 10 6% 9. 36 9.6 A Os 14 9.2 634 S53 8.9 7 S$ 34 8.6 7% S16 8.3. 7% 8 77 734 7 44 75 8 2 30 io 84 7 2-16 ZA 84 7 3 6.8 834 G = 35] 6.7 9 6 40 6.6 9% 6. 29 6.5 OY 6. 19 6.3 934 6 9 6.1 10 6 5 10% Sa 5.8 10% 5 43 a7 1034 S535 5.6 11 a ey 5.4 11% 52 20 ao 11% eee 52 1134 Ss Be 12 5 124% q $4 49 121% 4 48 4.8 1234 4. 42 4.7 3 An 7 4.6 134% ae 4.5 13% 4 26 4.44 1334 Ay 322 4.36 4 4.517 4.28 141% aS 4.2 1414 4 8 4.13 1434 4 4 4.06 iE ; 56 3.93 153 3 : ey 52 oe 12 3 43 : Pe 3. 45 375 16% 3. 41 3.69 164 3 2 a 163 343 : A 5 ee 303 173 S279 : ty 3-26 se 173 32.23 3 a 3 20 0.03 GET ACQUAINTED WITH SIMPLE PROPOR- . TION. The student should understand Sim- ple Proportion; he must already see its importance. A knowledge of it will facilitate the work of finding the distance from the time that the ship has run between bearings, and it will also do away with the long operations of ordinary Arithmetic. SOLUTIONS OF PLANE RIGHT-ANLED TRI- ANGLES, The following table shows. the length of the perpendicular and base for a given hypotenuse, or vice versa, for angles of from ™% point to 4 points of the compass. The length of the hypotenuse are given for from 5 to 20 miles, which will answer for the purposes intended: Angle of 1%4-Ft. Angle of %-Pt. Angle of 34-Pt. Hypo Perp Base Hypo Perp Base Hypo Perp Base D p.0 0:2 55.00; 5 24.9 0. 6 6.0. 0:3 6 6.0.0.6 6 765.9 0:9 170 0.3 7 TD 07 7 6,9 1,0 8 8.0 0.4 8. 8.02 0:8 8 7,9 2 9° 950-04 05. 970) 09 9. 8:9" 155 1p 610.0 0.5 210° 10.0. 10. 10. 9.9 15 at 120 05 Ue 90.900 Te 11 10.95 16 122-12,0 0.6212 11.9 1.2...12 3119 ste THE Marine REVIEW 13, 15:0 50,6 13.12.09" 13 315 12:9 1.9 14 414.0 OW 2. J4 139 14 2 Aa 13.8) 24 15: -E5:0% 07 = 15 1479 915 1 4 Re 2.0 16: 165025078) 16 15:9° 1.6 16. a8 23 LZ AZ0s0:8 17 169 7 AT 168 2.5 13;-.18.0 0:0 18. 17.9 18. 18 "178 26 191950) .009" 197 1859.61.99 19 18.8 28 20° 20:0: 150 < 20 19.9 20 20, 19:8 29 Angle of 1-Pt. Angle of 1%4-Pt. Angle of 1%4-Pt. Hypo Perp Base Hypo Perp Base Hypo Perp Base S10 5 49" 2 See Io 6. 53.9, 2 6 5:8. 15 6 be 7 20:9. Aca LOL a7, 7 0.7 200) 8 27.8 6116 O76 ako B ed Onis 9 3:5 1:8 9 8h. 22 9. 8:6 2.6 105 O08" 2.05 10 = 329.7 24 1 0.6 2 WiglQS 2a 31d e107 27) A 3 dA 23) 12 16. 2.9 1D 535 V3 12.82.50. 3182 712.6 8:2: 1S 24 238 1413-7, 2.7. 14 13/6) 3.4 214 (184 40 iS 14.7- 2.9 915 44:6 23,6 15, 14.4 ° 44 16; 19.7 -23.10, 46). 45.57.39. 16-458 odb d7 107 313.05 17 216.5 44 a7 tors ao 18 027 C8022 186175 4 418 17 oe 19. 18:6 3.7..,19 184.546 19 18:2 55 20° 7195672 8.9%) 20° °19.4" 4:0: 20 19.1 Angle of 2 Pts. Angle of 3-Pts. Angle of 4-Pts. Hypo Perp Base Hypo Perp Base Hypo Perp Base 5246.19. $ 420 29. 5 65 a5 6 85 235 6 80 83 6 43 ae 7 65 27. 74; SB Be oo 40 48 R74 Si 8 6e Ae 8 a by O° 8334 8 9S 50 864+ G4 10.92.38 10 83% 5:6 18 7.4 oa 11 10:0 42 iT 91 at Ay 7a oe 12 111 4.6< 12 A100 621m Be as 13.120 5.0 13 108, 22 13. 92. 90 14°29 $4 "14 116° 78 da Oe oO 18 13.9.°3,7 15 125 88.18 ie i096 16 148° 6.1 16413.8. 89 te wig. 404 17° 187 6.8 47> 144 94 AT Ae. 1 18 166 6.9 18 15.0. 10.0 18 127 127 19 17.6: 73°49 158 106 i 154 134 20 185° 79 20.166 114520 144. 18) THE TRAVERSE TABLES, The foregoing tables are nothing more than a portion of the data con- tained in the traverse tables, which by mere inspection the navigator, in sailing vessels on the ocean, employes for working out his dead reckoning. By such tables the solution of right- angled triangles is accomplished by mere inspection. In the regular tra- verse tables "Dist." (distance) is sub- stituted for Hypo (hypotenuse); "Lat." (meaning difference of latitude, north or south) for Perp (perpendicu- lar), and Dep. (departure eastings or westings) for base; that is, hypo rep- resents the distance; perp the merid- ian, and base a parallel on the chart. For example: DIFF, LAT, AND DEP. Supposing that you steered NE by N 15 miles, what is the diff. of lat. -and dep., that is, what distance has the vessel made north and east while sailing constantly on a NE. by N eourse . for 15. miles. .As NE by N is a 3-point course, look for angele of -3-points. in-. the. above table and sacamet: 15 An. Ryod column will be found 12.5 in perp. column and $3. in base. column, which means that to sail NE by N 15 miles the vessel changes her latitude 12.5 minutes or nautical miles, and her dep. 8.3 minutes or nautical miles; or she makes 12.5 nautical miles in the direction of north or 12.5 miles' 3i of northing and 83 in the direc- tion' .<of . east, or . $3 miles. of easting, -in sailing 15 miles NE by: Ne "This " Nelds geod = tar any 3-point course, and also for, the complement of a 3-point course, or a 5-point course, by assuming the base to be the perpendicular and the per- pendicular to be the base under angle of 3-points. For example: supposing the course was 15 miles NE by E, which is a 5-point course, the vessel would make 12.5 miles of easting and 8.3 miles of northing. This is plain for when the course is more than 4 points the dep. is greater than the diff of latitude, because we go more east or west than north or south. We can also see that the relations of the two elements are simply reversed. See diagrams. In a 5-point course, the diff. of lat. is the same as the dep. in a 3-point course, the complement of a 3-pt. course (3 from 8 is 5, 8 being the right angle, or 90°, and the com- plement of an. angle is what it lacks of being 8 points or 90°). Hence, in using the tables, as soon as you have a course of over 4 points, you begin at the bottom and read up, noting that while the dist. remains in the same place lat. and dep. are re- versed; but this has nothing to do particularly in the manner in which we employ them in off-shore distance finding. The following table will explain the system of the traverse tables. The above example is illustrated: 3-Point Course--NE by N. Dist. hat... Dép. 15 12S Dist. Dep. Lat, 5-Point Course--NE by E. SMALL SECTIONS OF THE EARTH FLAT. These tables are on the assump-- tion that small sections of the earth's - surface are flat. and so they are for Dep. 8.3 Miles Base Zz wn a ? oo a Gre a |S PAP 19 | 2 Ae 18 ey Sis oP ee mo VV all practical purposes of navigation. Then, it is plain to be seen that the