To the logarithm secant of the course S. 14° 03' E. add the logarithm of the proper difference of latitude 363.5, which gives the logarithm of the distance 374'.7. When the places under consideration lie so near the equator, it is not necessary to use Mercator sailing unless requested to do so at an examination, as plain sailing, in which the degrees of latitude and longitude are supposed to be equal, will give a result practically the same. EXAMPLE NUMBER 9 Find the course and distance from Sandy Hook light in latitude 40° 27' 42" N., and longitude 74° 00' 09" W. to Cape of Good Hope light in latitude 34° 21' 12" S., and 18° 29' 26" E. sec. Co. S. 48° 59' E. .18291 4488'.9 +3.65215 6840.0= 3.83506 EXPLANATION Find the difference of latitude by adding the latitude of Cape of Good Hope to that of Sandy Hook, convert it into miles and name it south, because Cape of Good Hope is south of the latitude of Sandy Hook. From Table 3 take the meridional parts for latitudes to the nearest mile and find their difference by adding, which is the meridional difference of latitude and takes the same name as the proper difference of latitude. Find the difference of longitude by adding the longitude of Cape of Good Hope to that of Sandy Hook, convert it into miles and name it east, because Cape of Good Hope is east of the longitude of Sandy Hook. From the logarithm of the difference of longitude 5549'.6 subtract the logarithm of the meridional difference of latitude 4827'.9, which gives the logarithm tangent of the course S. 48° 59' E. To the logarithm secant of the course S. 48° 59' E. add the logarithm of the proper difference of latitude 4488.9 and the result will be the logarithm of the distance 6840'.o. EXAMPLE NUMBER IO Find the course and distance from Cape Horn in latitude 55° 58' 41" S. and longitude 67° 16' 15" W. to Cape of Good Hope in latitude 34° 21' 12" S. and longitude 18° 29' 26" E. Find the difference of latitude by subtracting the latitude of Cape of Good Hope from that of Cape Horn, convert it into miles and name it north, because Cape of Good Hope is north of the latitude of Cape Horn. From Table 3 take the meridional parts for the latitudes to the nearest mile and find their difference, which is the meridional difference of latitude and takes the same name as the proper difference of latitude. Find the difference of longitude by adding the longitude of Cape of Good Hope to that of Cape Horn, convert it into miles and name it east, because Cape of Good Hope is east of the longitude of Cape Horn. From the logarithm of the difference of longitude 5145'.7 E. subtract the logarithm of the meridional difference of latitude 1869'.0 N., which gives the logarithm tangent of the course N. 70° 02' E. To the logarithm secant of the course N. 70° 02' E. add the logarithm of the proper difference of latitude 1297'.5 and the result will be the logarithm of the distance 3799'.7. EXAMPLE NUMBER II Find the course and distance from Cape Horn in latitude 55° 58' 41" S. and longitude 67° 16' 15" W. to Sydney, Australia, in latitude 33° 51' 41" S. and longitude 151° 12' 23" E. Find the difference of latitude by subtracting the latitude of Sydney from that of Cape Horn, convert it into miles and name it north, because Sydney is north of Cape Horn. From Table 3 take the meridional parts for the latitudes to the nearest mile and find their difference, which is the meridional difference of latitude and takes the same name as the proper difference of latitude. To the longitude of Cape Horn add the longitude of Sydney, because they are of different name and the result will be the difference of longitude east and as it is greater than 180° it is subtracted from 360° and gives the difference of longitude 8491'.4 W. From the logarithm of the difference of longitude 8491'.4 subtract the logarithm of the meridional difference of latitude 1903.9, which gives the logarithm tangent of the course N. 77° 22' W. To the logarithm secant of the course N. 77° 22' W. add the logarithm of the proper difference of latitude 1327'.o and the result will be the logarithm of the distance 6067'.4. DAY'S WORK Example 1.-A ship had Cape Henry light bearing N. W.72 W. distant 9 miles, ship's head S. 1/2 E. Deviations as per table on page 16. Throughout the 24 hours a current set N. N. E. magnetic 18 miles per hour. Variation 6° W. The ship was sailed as follows: 9.8 COURSE WIND DISTANCE S. by E. 1/2 E. W. 14 pt. 50'.4 S. by E. 34 E. W. S. W. 0 47.3 S. E. by E. S. 34 pt. S. W. S. S. E. 20.3 W. N. W. S. S. E. 10.7 S. W. S. S. E. 12.4 Find the course and distance made good and the ship's position. From that point find the course and distance to Diamond Shoal lightship. CAPE HENRY DIAMOND SHOAL 35° 05' 08" N. |