37°, the Course; and in the Latitude Column, find half the Meridian Difference of Latitude 154.5, the nearest to it is 154.1; against which, in the Departure Column, ftands 116.1, doubled is 232.2, the Difference of Longitude nearly as before. CASE VI. One Latitude, Courfe, and Departure given, to find the Distance, Difference of Latitude, and Difference of Longitude. ift. The Extent from 6 Points, to Radius on the Line marked SR, will reach from the Departure 957, to the Distance 1036, on the Line of Numbers.' ، 2dly. The Extent from 6 Points to 2 Points, on the Line marked SR, will reach from the Departure 957, to the Difference of Latitude 396, on the Line of Numbers. 3dly. The Extent from 6 Points to 2 Points, on the Line marked S R, will reach from the Meridian Difference of Latitude 667, to the Difference of Longitude 1610, on the Line of Numbers,' By INSPECTION. Over the Course 6 Points, and against a fifth of the Departure 191.4, ftands 79.2 and 207, which, multiplied by 5, gives 396, the Difference of Latitude, and 1035 for the Distance. Then in the Latitude Column find a Tenth of the Meridian Difference of Latitude 66.7, the nearest to that is 66.6; against which, in the Departure Column, ftands 160.8, which, multiplied by 10, is 1608, the Difference of Longitude. CASE VII. One Latitude, Distance failed, and Departure from the Meridian given to find the Courfe, Difference of Latitude, and Difference of Longitude. To Sine Course 50° 50′ 9,88941 To Diff. Lat. 407,3 =6° 47' Lat. left 49 30 N. M. Pts. 3428 Lat. in 42 43 N. M. Pts. 2840 To find the Diff. of Long. it will be, 9,80043 2,76938 5,46835 14 40 2,6099z 2 38 W. Hence the Ship's Courfe is S. 50° 50' E. or S. E, East nearly, and is in the Latitude of 42° 43′ N. and Long. 2° 38′ W. By GUN TE R. Ift. The Extent from the Distance 645, to the Departure 500 on the Line of Numbers, will reach from Radius to 50° 50', on the Line of Sines.' 2dly. The Extent from 50° 50' to 39° 10', on the Line of Sines, will reach from the Departure 500, to the Difference of Latitude 407, on the Line of Numbers.' 3dly. The Extent from 50° 50' to 39° 10′, on the Line of Sines, will reach from the Meridian Difference of Latitude 588, to the Difference of Longitude 722, on the Line of Numbers.' By INSPECTION. Now a Fifth of the Distance and Departure are 129 and 100, and are found together over 51°; and in the Latitude Column ftands 81.2, which multiplied by 5 is 406, the Difference of Latitude.' Then in the Latitude Column, feek of the Meridional Difference of Latitude 147, the nearest is 146,6; against which, in the Departure Column, ftands 181,1, multiplied by 4, is 724,4, the Dif ference of Longitude. Haying in the preceding Parts fhewn how to work the most ufeful Problems in Middle Latitude and Mercator's Sailing; fhall now work the four following Cafes both by Middle Latitude and Mercator's Sailings, in the Manner I generally teach Perfons who are of Age, and Youth of good Abilities; especially if they are limited to a fhort Time; and believe they are all that can well happen at Sea. The following four Cafes are worked by Middle Latitude and Mercator's Sailing. Required the Bearing and Distance between the Lizard in Lati tude 49° 57' N. and Longitude 5° 14 W. the Ifland of St. Mary's, one of the Western Islands, in Latitude 37° 00′ N. and Longitude 25° 6' Weft. By Mercator's Sailing. Draw the Meridian M T = 1077 the Merid. Diff. of Lat. and MT 777 the Prop. Diff. of Lat. perpendicular to MT draw TH and T O. Make TH1192 Miles, the Dif. of Long. Join H and M, TMH will be the Courfe S. 47° 54′ N. and O M the Dift. 1159 Miles. By Mid. Lat. Sailing. Draw the Meridian A B, with the Chord of 60° describe the Arch PS, upon which fet off 46° 32′ the Com. of Mid. Lat, from Q to S; through S draw the Line A N 1192 Miles the Diff. of Long. Let fall the Perpend. N B, which will be the Depar ture 865. Upon A B fet off A C 777, Miles, the Difference of Latitude, and apon C erect the Perpendicular C D, and upon it fet off the Dep. 865. Join D and A, and it is done, for DA will be the Distance 1168 Miles, and the Angle CAD the Course S. 48° 4' W. The CALCULATION. To the Departure 865,1 2,93708 To Tan. of Cou. 47° 54′ 10,04406 To Tan. of Cou. 48° 4′ 10,04666 To the Dift. in Miles 1159 3,06407 3 BY MIDDLE LATITUDE SAILING. 1ft. Extend from Radius or 90°, to 46° 32′ the Comp. Mid. Lat. on the Line of Sines, that Extent will reach from the Diff. of Long1192, to the Dep. 865, on the Line of Numbers." 777 2dly. Extend from the Dep. 865, to the Diff. of Lat. the Line of Numbers, that Extent will reach from Radius or 45°, to the Course 48° 4', on the Line of Tangents.' 3dly. Extend from Radius or 90°, to the Courfe 48° 4′, on the Line of Sines, that Extent will reach from the Dep. 865, to the Dift. 1163 Miles, on the Line of Numbers." BY MERCATOR. Ift.Extend from Merid. Diff. of Lat. 1077, to Diff. of Longitude 1192 on the Line of Numbers, that Extent will reach from Radius or 45°, to the Courfe 47° 54', on the Line of Tangents.' 2dly. Extend from Radius or 90°, to the Comp. of 42° 6′ on the Line of Sines, that Extent will reach from the Prop. Diff. of Lat. 777, to the Dift. 1159, on the Line of Numbers.' By INSPECTION. BY MIDDLE LATITUDE SAILING. Look for the Comp. of Mid. Lat. as if it was a Courfe in Plane Sailing, and Difference of Longitude in the Distance Column, oppofite to which will ftand the Departure in its Column. Having the Difference of Latitude and Departure, the Courfe and Distance is found in Cafe VI. in Plane Sailing.. Thus, taking of the Difference of Longitude 1192 = 298, and as the Comp. of Middle Latitude is 46° 32' or nearly 46; I took over 46° and 47°, and against Distance 298 ftands 214,4 and 218 in the Departure Columns; which added together, gives 432,4, half is 216,2, this multiplied by 4, because the Difference of Longitude was divided by 4, gives 864-8 the Departure: ́Again, taking of the Difference of Latitude, and of the Departure 1942 and 214.2, the nearest Numbers to these standing together are 216.2 |