2dly. Begin with the firft Course S. S. W. 2 Points, under which in the Tables, and oppofite to the Distance 54 Miles, ftands 49.9 for the Difference of Latitude, and 20.7 for the Departure; and as the Course is between the South and Weft, I fet the Difference of Latitude under the Column marked S. and the Departure under that marked Weft; in like Manner proceed with each Course and Distance, which, being found as above, will ftand as in the following Traverse Table: Diff. of Lat. Northerly 69,5 Dep. Wefterly 46,7 Having placed them as above, add up all the Weftings, Eaftings, Northings, and Southings feparately, and fet down their respective Sums at the Bottom of each Column; and as the Wefting is greater than the Eafting, fubtract the one from the other, and the Difference 46.7 fhews that the Ship's Departure is fo much Weft of her firft Meridian. Again, the Northing being greater than the Southing, fubtract the Lefs from the Greater, and the Remainder 69.5 fhews how far the Ship is to the Northward of her firft Place. Now having the Difference of Latitude and Departure made good upon the feveral Courses, feek in the Tables until they are found standing together in their refpective Columns, the nearest to which is 69.6 and 47, under 34 Degrees, against them ftands 84 for the Distance; confequently the Courfe, made good upon the feveral Courses, is N. 34 W. Diftance 84 Miles. To find the direct Courfe and Distance to the intended Port. To the Latitude left 49° 57' N. add the Difference 69 equal 1° 9* gives 51° 6' the Latitude in: Then From the Latitude of Cork Subtract the Latitude in The Diff. of Latitude between the Ship and Cork is 51,49 51, 6 43 Miles The Departure between the two Ports is The Departure between the Ship and Cork is With this Difference of Latitude 43, and Departure 115.3, feek in the Tables till they are found ftanding together in their respective Columns, the nearest to which will be found over 69° and 70° being added is 139, half that Sum 69° 30' is the Courfe, and half the Dif tance to these is 123 Miles. Hence the Ship's direct Course to Cork is N. 69° 30′ W. and Distance 123 Miles. The fame may be done By CALCULATION. To find the direct Courfe and Distance between the Lizard and Cork by Cafe VI. it will be, To the Tan. Cou. 55°20′ 10.16029 To the Distance 197 9.91512 2.29439 Hence the direct Course and Distance between the Lizard and Cork is N. 55.20 W. or N. W. by W. nearly, Distance 197 Miles, Then, For the first Courfe S. S. W. 2 Points, Distance 54 Miles. In like Manner proceed to find the Difference of Latitude and Departure for the other Courses and Diftance; which being found and fet down in their respective Columns, will ftand as in the foregoing Table. Having found the Difference of Latitude and Departure made upon the feveral Courfes, and alfo the Latitude in, with the Dif ference of Latitude and Departure between the Ship and Cork, as before, the direct Courfe by Cafe VI. will be found N. 69° 33′ W. and Distance 123 Miles. All the preceding may be found by Gunter's Scale, but fhall leave the working of them to exercife the Learner, who ought to be well acquainted with Traverse Sailing; and for that purpose it has been thought proper to fubjoin the following, which is the most general and useful that well can be, and may be worked by any of the foregoing Methods. A Ship being at Sea in Latitude 37° 10' N. is bound to a Port in Latitude 33° 0' N. the Departure between the Ship and the Place is 180 Miles, confequently by Cafe VI. the Courfe will be S. W. by S. 2 Degrees Wefterly, and Distance 308 Miles, but the Wind being variable, is obliged to ply upon these feveral Courses, the Distance run upon each, being obtained by the Log; and firft fhe fails (with her Larboard Tacks on Board) S. W. by W. 27 Miles, W. S. W. half W. 30 Miles, W. by S. 25 Miles, W. by N. 18 Miles. (Starboard Tacks on Board Wind shifting) S. S. E. 32 Miles, S. S. E. three quarters E. 27 Miles, S. by E. 25 Miles, S. 31 Miles, S. S. E. 39 Miles. Required the Latitude the Ship is in and her Departure from the Meridian, upon what Course the muft fteer if poffible, and how fär fhe muft fail to gain her intended Port? The Difference of Latitude and Departure being found by the preceeding Directions, will stand as in the following Table: The Ship is in Latitude 34° 20' N. the Departure is 47.4. W The Course to the intended Port is S. 58° 41′ W. or S. W. by W. one quarter Weft nearly, Distance 155.2. NOTE. The Teacher may put the Pupil upon MERCATOR'S SAILING immediately, if his Time be fhort (which is the Cafe with many who go to School purely to learn Navigation only) without going through MIDDLE LATITUDE SAILING, as the former is fully fufficient for the Seaman's Purpose, provided he be fhewn how to reduce Miles of Eafting or Wefting into Difference of Longitude, which must be done by Middle Latitude Sailing. MIDDLE LATITUDE SAILING. IN N PLANE SAILING the Earth was confidered as a Plane, reprefenting a Bowling Green, having the Meridians parallel to each other, and confequently the Degrees of Longitude equal in all Places; but this cannot be true, as the Earth is a Globe or Sphere; for As the Meridians are Circles on the Terraqueous Globe, meeting in the Poles, (as may be feen in the following Figure) it is obvious, that any two of these Circles must recede more at greater Diftances from the Poles; and at equal Distances from each Pole, or at the Equator, the Distance between the Meridians is greatest. The true Place of a Ship at Sea depends upon its Distance from the Equator, and fome noted Meridian; and fince the Meridional Diftance, that is, the Distance between any two Meridians, varies in every Latitude, it is therefore convenient this Distance should be reckoned in a fixed Latitude; and where the Degrees are of the fame Magnitude with thofe of the Meridian, which can be no where but on the Equator, where 60 Geographical Miles make a Degree. of The Circumference of all Circles are in direct Proportion to each other, as their Radii ; and fince the Earth turns once round its Axis in 24 Hours, every Point upon its Surface muft defcribe Circles parallel to the Equator: Hence it follows, that the Circumference any Parallel of Latitude in Miles, is to the Circumference of the Equator in Miles, as the Co-Sine of that Latitude is to Radius; and, that the Breadth of a Degree in any Parallel of Latitude, is to the Breadth of a Degree upon the Equator, as the Sine Complement of that Latitude is to Radius. By the laft Proportion was the following Table calculated, which fhews the Breadth of a Degree of Longitude in every Latitude; and may be made to answer for any Degrees and Minutes by taking pro s. D.L.) Miles. D.L. Miles. 79 76 14 52 5 59 77 23 55 23 41 45 28 59 30 90 77 13 501 62 95 58 31 659 67 24 54 81 42 44 59 38 43 43 7 59 56 25 54 8 59 42 26 53 93 44 43 9 59 26 27 53 56 45 42 43 63 27 TO 159 08 28 52 97 46 41 68 64 26 11 58 89 29 52 47 47 40 92 65 25 12 58 68 30 51 96 48 40 3 46 31 51 43 49 39 4 58 22 32 50 88 50 38 57 95 33 50 32 51 37 57 67 34 49 74 52 36 17 57 37 35 49 15 53 36 18 57 06 36 48 54 54 135 The above Table fhews how many Miles answer to a Degree of Lon 60 30 88 61 29 00 78 12 16 62 28 17 80 10 42 24 81 36 83 15 66 24 41 84 36 67 23 45 85 57 68 22 4 48 86 87 88 4444 48 45 38 35 32 28 23 18 14 09 11 71 19 54 89 05 gitude at every Degree of Latitude. |