Now in this Cafe, as the Ship has croffed the Equator, therefore the Latitude 1° 45′ N. added to 2° 50′ S. is 4° 35', which multiplied by 60 gives 275 Miles for the Difference of Latitude, By making the Distance A B Radius it will be, Hence the Ship's Distance run is 495 Miles, and her Departure from the Meridian is 411.6 Easterly. By GUN TER, Extend from 3 to 5 Points on the Line marked S R, that Extent will reach from the Difference of Latitude 275 to the Departure 411.6 on the Line of Numbers.' 2dly.Extend from Radius or 8 Points to 3 Points, that Extent will reach from the Difference of Latitude 275 to the Distance 495 on the Line of Numbers,' By INSPECTION, Find the Course among the Points or Degrees, and the Difference of Latitude in its Column, right against which stand the Dif tance and Departure in their Columns. Now as the Difference of Latitude 275 is too great to be found in the Tables, I divide it by 5, and that gives 55, which I find over 5 Points in the Latitude Column; againft that ftands 99 for the Distance, and 82.3 for the Departure, which being multiplied by 5 is 495 the Distance, and 411.5 the Departure, nearly as before. CA S E III. Courfe and Departure from the Meridian given, to find the Distance and Difference of Latitude. If a Ship fails N. E. by E. 2 E. from a Port in 3° 15' South Latitude, until the depart from her firft Meridian 412 Miles, I demand her Distance, and what Latitude she is in? parallel to A B to cut A Cin C; through the Point C draw B C parallel to A D to cut the Meridian A B; then will A C be the Dif tance 456, and A B the Diff. of Lat. 195, nearly. By making the Distance A C Radius it will be, The Course 5 Points 64° 41' The Complement 2 Pts. 25° 19 To find the Diff. of Lat. To find the Distance. As S. Course 53 Pts. 9.95616 As S. Courfe 5 Points 52 Is to the Departure 412 2.61490 Is to the Departure 412: 9.95616 2.61490 So is Co-Sine Cou. 53 Pts. 9.63099 So is Radius 10.00000 From the Latitude left To the Diff. of Lat. 194.8 2.28973 To the Distance 455.8 Subtract the Difference of Latitude 195 Miles, or The Rem. being nothing, fhews the Ship is on the Equator. Extend from 5 Points to 2 on the Line marked S R, that Extent will reach from the Departure 412 to the Difference of Latitude 194.8 on the Line of Numbers." 2dly. Extend from Radius to 5 Points, that Extent will reach from the Departure 412 to the Distance 455.8 Miles.' By INSPECTION. Find the Courfe either among the Points or Degrees, and the De parture in its Column, right against which stand the Distance and Difference of Latitude in their refpective Columns. Thus, with the Course 5 Points, and the Departure, I find 228 for the Distance, and 97.5 for the Difference of Latitude, which being doubled, gives the Distance 456, and the Difference of Latitude 195, as before. CASE IV. Distance and Difference of Latitude given, to find the Courfe and De parture. Suppofe à Ship fails 496 Miles, between the South and the Eaft, from a Port in 2° 48 South Latitude, and then by Obfervation is in 7° 23′ South Latitude; what Courfe has the fteered, and what Departure has the made; From the Latitude by Obfervation 7° 23′, left, the Remainder 4° 35' multiply by 60 nutes of Difference of Latitude. Conftructed as Problem VIII. in Geo metry. A take 2° 48′ the Latitude 275, the Miles or Mi Draw the Meridian A B 275; upon B erect the Perpendicular B C; take 496 in your Compafles, and with one Foot on A, lay the other on the Line, B C; join A and C; then will B C be the Departure 412, and the Angle B BAC the Course = 56° 10′, or 5 Points nearly. To find the Course. To find the Departure. As the Diftance 496 2.69548 As Radius 10.00000 Is to Radius 10.00000 Is to the Distance 496 So is the Diff. of Lat. 275 2.43933 So is S. Course 56° 20′ 2.69548 9.92027 12.43933 To Co-fine Cou. 56° 20′ 12.61575 10,00000 9-74385 To the Departure 412.8 Hence the Courfe is S. E. by E. and the Dep. 412.8 Miles. 2.61575 By GUNTER. The Extent, from the Distance 496 to the Difference of Latitude 275 on the Line of Numbers, will reach from Radius or 90° to 33° 40' the Co-Course on the Line of Sines.' And the Extent, from Radius to 56° 20' on the Line of Sines, will reach from the Distance 496 to the Departure 412.8 cn the Line of Numbers,' By INSPECTION. Seek in the Tables till against the Distance, taken in its Column, be found the given Difference of Latitude in one of the following Columns; and adjoining to it ftands the Departure; which, if less than the Difference of Latitude, the Courfe is found at the Top; but if greater, the Courfe is found at the Bottom. Now with half the Distance 248, and half the Difference of Latitude 137.5, look in the Tables till they are found to agree in their refpective Columns, which they do nearly over 5 Points, againft, them stands 206.2 for the Departure, which being doubled, gives 412.4, nearly as before. Distance and Departure given, to find the Courfe and Difference of Latitude. Admit a Ship fails 496 Minutes between the North and Weft from the Ifland Bermudas in Lat. 32° 25' North, until her Dep. is 412 Miles; what Courfe has the fteered, and what Lat. is the in? Note. This Cafe is conftructed much the fame as the laft. To the S. of Cou. 56° 10′ 9.91942 To the Diff. of Lat: 276.1 2.44116 1 Hence the Course is N. 56° 10' W. or N. W. by W: To the Latitude failed from 32° 25' add the Difference of Latitude 276, or 4° 36', gives 37° 1′, the Latitude the Ship is in. By GUN T E R. Extend from the Distance 496 to the Departure 412 on the Line. of Numbers, that Extent will reach from Radius to the Course 56° 10' on the Line of Sines.' 2dly. Extend from Radius to the Complement of the Course 33° 50' on the Line of Sines, that Extent will reach from the Distance 496 to the Diff. of Lat. 276 on the Line of Numbers." By INSPECTION. Seek in the Tables till against the Distance, taken in its Column, be found the given Departure in one of the following Columns; and adjoining to it ftands the Difference of Latitude; which, if greater than the Departure, the Courfe is found at the Top; but if lefs, the Course is found at the Bottom. Now with half the Distance 248, and half the Departure 206, I look in the Tables, and find them to agree in their Columns, nearly over 5 Points, against which is Latitude 137.8, which being doubled is 275.6, the Difference of Latitude nearly as before. Difference of Latitude and Departure given, to find the Courfe and Distance. A Ship fails between the North and Weft till her Difference of Latitude is 184 Miles, and her Departure is 115 Miles; I demand her Courfe and Distance? Conftructed as Problem IX. in Geometry: Draw A B 184, and Perpendicular to it B C = 115 join C and A; then will the Angle C AB be the Courfe 32°, and A C the Distance 217 Miles. A |