Queft. 5th. Suppose a Ship from the Latitude of 45° 40′ N. fails between the S. and E. 600 Miles, and then her Departure is computed to be 308 Miles. Required the Courfe, Lat. and Diff. of Lon. Courfe S. 30° 53' E. Lat. in 37° 5' N. Diff. of Long. 411.5, by Mercator. Anf. Courfe S. 30° 53' E. Lat. in 37° 5 N. Diff. of Lon. 410.49 by Middle Latitude. Queft. 6th. A Ship from the Latitude of 45° 30' S. fails N. N. W. until her Difference of Longitude be 7° 40'. Required the Latitude she is in, and her Distance failed? NOTE. This must be worked by Mercator's Sailing, thus: As Tang. Course 22° 30': Radius or 90° :: the Difference of Longitude to the Mer. Diff. of Latitude 1110 Miles. Now, from the Meridian Parts of the Lat. left 3072, take the Meridian Diff. of Latitude 1110, the Remainder 1962 is the Meridian Parts of the Latitude, come to 31° 4' S. having the Course and Proper Difference of Latitude, the rest is found by Cafe II. in Plane Sailing. The Ship is in Latitude 31° 4' S. Distance 937.4 Anf. {The Sailing, as Miles. Queft. 7th. A Ship in Latitude 51° 15' N. and Longitude 22° W. fails between the S. and W. until fhe has made 564 Miles of Departure, and 786 Miles of Difference of Longitude. Required her Courfe, Distance and Latitude and Long. in? NOTE. This must be worked by Middle Latitude thus: As Diff. of Lat. 786 Radius :: the Departure 564 Co-Sine of Middle Latitude 44° 9', +44° 9' 88° 18' the Sum Lat. and 88° 18′51° 15'Lat. left 37° 3'N. Having the Difference of Latitude and Departure, the Courfe is found to be S. 33° 30′ W. and the Distance 1021,7 Miles. It may now be fuppofed that the Learner is capable of working any fingle Course, either by Middle Latitude or Mercator's Sailing, we fhall now proceed to compound Courses, commonly called Traverfe Sailing, which may be worked by Middle Latitude and Mercator's Sailing; either by Projection, Calculation, Gunter's Scale, or Inspection. How to folve compound Courfes or a Traverse, has already been fhewn in Plane Sailing; but it is neceffary alfo to fhow, how proper Allowances for the Longitude fhould be introduced into fuch Accounts, which is easily done by any of the following Methods. Ift. Complete the Traverse Table to each Course and Distance as in Plane Sailing, and find the whole Difference of Latitude, Departure and Latitude in. 2d. With the whole Difference of Latitude and Departure, find the direct Courfe and Dittance. 3d. With the Latitude left and Latitude in, find the Complement of the Middle Latitude; with which, and the Departure. find the Difference of Longitude, by Middle Latitude Sailing. Or, with the Courfe and Meridional Difference of Latitude, find the Difference of Longitude by Mercator's Sailing. Thefe Methods are generally used in working a Day's-Work at Sea, but thofe that want a greater Degree of Accuracy, may work by the following Methods, efpecially in high Latitudes. By the feveral Differences of Latitudes and Departures, found in the Tables of Difference of Latitude and Departure, find the Latitudes come to, Middle Latitudes, and Complements of Middle Latitudes: With each Complement of Middle Latitude and corref ponding Departure, find the Difference of Longitude to each Course and Diftance, and fet them down in the two additional Columns. marked Difference of Longitude, Eaft and Weft, according to the Departure used; add up the Eaft and Weft Columns, and their Difference will be the whole Difference of Longitude, by Middle Latitude Sailing. But if you work by Mercator's Sailing, find the Meridional Difference of Latitude for each Courfe and Distance; with each Course and Meridional Difference of Latitude, find the Difference of Longitude; which fet down as above directed, and the Difference between the East and Weft Columns, will be the Difference of Longitude by Mercator's Sailing. By this Method the Ship's Place may be found at the End of each Courfe and Distance run, and pricked off on a Mercator's Chart. Suppofe a Ship from the Land's End in Latitude 50° 6' N. and Longitude 5° 55' W. is bound to the Island of St. Mary's in Latitude 37° c'N. and Longitude 25° 6' W. but by Reafon of contrary Winds is obliged to fteer the following Courfes; viz. S. by W. 24 Miles W. S. W. 32 N. W. W. 41, S. S. E. E 49, É. N: E. 2 E. 19, W. 21, N. E. I E. 36, S. 41, S. S. W. 92, and N. 36 Miles. And it be required the Latitude and Longitude fhe is in, with the direct Course and Distance to her intended Port? With the feveral Courfes and Diftances, find their Differences of Latitude and Departure, and set them down as in the following TRAVERSE It is plain by the Traverse Table, that the Ship has made 116.6 Miles of Southing and 55 Miles of Southing, and 55 Miles of Westing. Whence to find the Difference of Longitude it will be, By INSPECTION. Taking the Complement of Middle Latitude 41° as a Course, and the Departure 55 in its Column, the nearest is 55.1, against which ftands 84 in the Distance Column, the Difference of Longitude by Middle Latitude Sailing. And With the Proper Difference of Latitude and Departure, the Course found nearly 25°, and Distance 129 under the Course; in the Latitude Column look for the Meridian Difference of Latitude 179. the neareft is 180.4, against this ftands 84.1 in the Departure Column, which is the Difference of Longitude by Mercator's Sailing. To find the direct Course and Distance to St. Mary's. Diff. Sum Lat. 48° 9' N. Merid. Pts. 3305 Lon. of Ship 7° 19′ W. 6 W. 11 9 669 Ms. Diff. 912 Diff. of Long. 17 47=1067 2)859 42 34 By Middle Latitude Sailing. Is to Diff. of Lon. As the Diff. of Lat. 669 2.82543 As Co-fi. Course 49°35′ 9.81328 1067 3.02816 Is to Prop. Dif. of Lat. 669 2.82543 So is Co-fi. Mid. Lat. 42° 30 9.16717 So is Radius 90° 10.00000 To Tang. Course 49°35′ 10.06990 To the Dift. By Mercator's Sailing. 90€ 10.00000 2.82543 As Merid. Dif. of Lat. 912 2.95999 As Radius To Tan. Courfe 49° 29′ 10.06817 To the Distance 1030 3.01274 Hence the direct Cou. from the Ship to St. Mary's is S. 49° 35′ W. and Distance 1028 Miles by Middle Latitude Sailing; and S. 49° 29' W. and Distance 1030 Miles by Mercator's Sailing. The fame may be found By INSPECTION in the Tables. Take of the Diff. of 1067, viz. 267 nearly, and look for that in the Dift. Column over the Complement of Middle 47° nearly, and in the Departure Column ftands 195.3 of the Departure. Then look for 167.2, and of Departure 195.3, until they are found standing together in their refpective Columns, the neareft are found over 49° and 50°, viz. 195.5, 169.9, and 195.3, 163.9; the Distances correfponding to thefe are 259 and 255, their Sum is 514, half is 257, this multiplied by 4, gives 1028 Miles. Hence the Courfe is S. 49° 30' W. Dift. 1028 Miles, by Mid. Lat. Sailing. Again, taking of the Meridional Difference, and of the Diff. of Longitude, viz. 91.2 and 106.7, the nearest Numbers to these are 106.4, 92.5, and 106.5; 89.4 ftanding over 49° and 50° in the Latitude Columns, belonging to the above Degrees; look for of the Proper Difference of Latitude, viz. 66.9, the nearest is 66.9 and 66.8, the Distances to these are 102 and 104, their Sum is 206, half is 103, which being multiplied by 10, gives 1030 Miles. Hence the Courie is S. 49° 30' W. and Distance 1030 Miles by Mercator's Sailing, the fame as by Calculation. Here to have gone to Geometrical Strictnefs, the Difference of Longitude fhould have been found to every Courfe and Distance run, by Middle Latitude or Mercator's Sailing, which would have given the Ship's true Place at the End of each Courfe and Dift, but fhall leave the doing of that to the Reader; and as all Traverses are worked in the Manner fhown above, which is fufficiently exact for a Ship's Run in 24 Hours, I fhall therefore only add a few Queftions for the Learner's Exercife. Suppofe a Ship from the Latitude 68° 38' N. and Longitude 8° 40' E. is bound to the North Cape in 71° 10' N. and Longitude 26° 3' E. fails as in the following Table. Required the Latitude and Lon. fhe is in, and her direct Course and Distance to the Cape? |