This Right-Angle Triangle ABC, (Plate 2. Fig. 9.) may be made by Prob. 10, of Geometry; in which Note, 1. The Hypocenufe AC represents (the Point of the Compass the Ship hath fteered and) the Ship's Distance run. 2. The Leg AB, (the Meridian, that is, the North or South Direction of the Compals) the Difference of Latitude. 3. The Leg BC, (the Eaft or Weft Direction of the Compass, and a Parallel of Latitude) the Departure from the Meridian. 4. The Angle BAC, (the Angle of) the Ship's Course. 5. The Angle ACB, (the Angle of) the Complement of the Ship's Courfe. Note, The Angle which the Point of the Compafs (fteered by, or upon) maketh with the Meridian, or North, and South Point of the Compafs, is called the Angle of the Ship's Course, and the Angle it maketh with the Eaft or Weft Point, is the Complement of the Course. The Courfe, in this Example being SW. by W. is 5 Points from the South, or Meridian, and makes 56d. 15m. The Complement of the Courte is 3 Points; that is 33d. 45m, as may be feen in the Table, intitled, A Table of the Angles which every Rumb (or Point of the Compass) maketh with the Meridian, at the End of this Book. The Things thus explained, the Proportion (by Chapter 2. Section 2. Axiom I. and Cafe 1. of Plane Right-Angles-Triangles in Pages 36 and 37.) is as follows. For the Difference of Latitude, thefe three Proportions, viz. Radius Sec. Courfe Sec. c. Courfe } T.c.Courfe All these three Proportions may be wrought by the Logarithms, but I only work the firft. Subtract, giveth Latitude the Ship is in, 45d. 21m. North. Radius For the Departure, these three Proportions, viz. Sec. Courfe Sec. c. Courfe .. } The first of thefe by Gunter's Scale. Radius Distance: : S. Courfe.. Depart. from the Meridian, S. 8 Points 496 Min. :: S. 5 Points Minutes 412.4 Tenths, So that the Departure from the Meridian is Minutes 412.4 Tenths, which makes 6d. 52m. Meridian Diflance West. Problem, or Cafe 2. Courfe and Difference of Latitude given, to find the Distance run, and the Departure from the Meridian. Example. If a.Ship runneth SE. by E. from 1d. 45m. North Latitude, and then (by Observation) is in 2d. 50m. South Latitude. What is her Diftance and Departure? Plate 2. Fig. 10. This Triangle ABC may be made by Prob. 12. of Geometry. In this Example, having Latitude the Ship failed from, and La titude the is in by Obfervation, there are the Latitudes of two Places given; and by the fecond General Rule, in Page 58, the Difference of Latitude is found, as followeth : Latitude failed from Latitude by Obfervation, is The Difference of Latitude, is id. 45m. North 2d. 50m. South 4d. 35m. or 275 Minutes, found by multiplying by 60, the Minutes in a Degree. ift. For the Distance, the Proportions may be this ; S. c. Courfe.. Diff. Lat. :: Radius :: Distance. S. 3 Points.. 275 Min. :: S. 8 Points 495 Minutes. 2d. For the Departure, this ; Departure. S. c. Courfe.. Diff. Lat. : : S. Course Problem, or Cafe 3. Courfe, and Departure from the Meridian given; to find the Distance and Difference of Latitude. Examp. If a Ship fails NE. by E. from a Port in 3d. 15m. South Latitude, until the depart her firft Meridian 412 Min. I demand her Distance, and what Latitude he is in? Plate 2. Fig. 1k This Triangle may be made by Prob. 12. of Geometry. S. Course ift, For the Distance, the Proportion is this : : S. Courfe 412 Min. :: S. 3 Points 275 Minutes, which Difference of Latitude, is 275.3 Min. or - Subtract, giveth the Latitude the Ship is in having cross'd the Equator. 3d. 15m. South. 4d. 35m. North. d. 20m. North. Problem, or Cafe 4. Diftance and Difference of Latitude given ; to find the Course, and Departure. Example. Suppofe a Ship fails 496 Min. between the South and the West, from a Port in 2d. 48m. South Latitude; and then by Obfervation is in 7d. 23m. South Latitude: What Course hath fhe fteered, and what Departure hath the made? Plate 2. Fig. 12. This Triangle may be made by Prob. 11. of Geometry. By the two Latitudes mentioned in this Example, find the Difference of Latitude, as followeth, Latitude failed from, is - Latitude by Obfervation, is 2d. 48m. South. 7d. 23m. South. Subtract, gives the Diff. of Latitude 46. 35m. or 275 M. ft, For the Courfe, the Proportion is, Distance. Radius:: Diff. Lat... S. c. Course. 496 Min. S. 9od.: 275 Min. S. 33d. 40m. Which fubtract from god. the Remainder 56d. 20m. is the Course, which makes 5 Points neareft; SW. by W. is then the Ship's Course. 2d. The Proportion for the Departure is, Radius Distance S. Course Departure. §. 9od... : : 496 Min. S. 56d. 20m... 412 Minutes. Problem, or Cafe 5. Diftance and Departure given; to find the Courfe and Difference of Latitude. Examp. Admit a Ship fails 496 Minutes between the North and the Weft, from the Ifland Bermudas, in Latitude 32d. 25m. North, until her Departure is 412 Minutes; what Course hath the fteered? And what Latitude is the in? Plate 2. Fig. 13. This Triangle may be made by Prob. 11. of Geometry. ft, For the Courfe, take this Proportion. Distance.. Radius: : Departure.... S. Course. 496 min... S. 9cd.:: 412 min... S. 56d. 10m. N. Westerly. That is, 5 Points, which makes the Courfe to be N.W. by W. 2d, For the Difference of Latitude. Radius. Distance: : S. c. Courfe .. Difference of Latitude. d. m. Problem, or Case 6. Difference of Latitude and Departure given; to find the Course, and Distance. Examp. If a Ship's Southing be 275 Minutes, and her Eafting 412 Minutes, What is her Courfe and Distance? Plate 2. Fig. 14. This Triangle may be made by Prob. 13. of Geometry. 1ft, For the Courfe, take this Proportion. Diff. Lat... Departure:: Radius.. T. Course. 275 Min. 412 Min. T. 45d. ..T. 56d. 17m. SouthEafterly, or 5 Points, which makes the Courfe to be SE. by E. neareft. S. Course 2d, For the Distance, this Proportion. .. Departure: Radius .. Distance. S. 56d. 17m. 412 Min. :: S. 9od... 495.3 Min. The fix preceding Problems are the common Cafes of PlaneSailing; which the Learner ought to be well acquainted with; and for that End I here add fix more for Practice, whofe Answers may be found by the foregoing Rules. Queftion 1. A Ship in 2d. 10m. South Latitude, fails N. by E. 89 Leagues: What Latitude is fhe in; and what is her Departure? Anfwer. Latitude 2d. 12m. North, and Departure Leagues 17 and 36 Parts of a Hundred. Question 2. A Ship fails SSW. from a Port in 41d. 30m. North Latitude; and then by Obfervation, the faid Ship is in 36d. 57m. North Latitude: I demand the Distance run, and Departure? Anfwer. Distance run 98 Leagues 5 Tenths, Departure Leagues 37-7 Tenths. Question 3. A Ship fails SSW. half W. from 2d. 30m. South Latitude, until the Departure be 59 Leagues: I demand her Distance Run, and the Latitude she is in? Anf. Distance Run 125.2 Leagues, Latitude 8d. orm. South. Queft. 4. If a Ship failed 360m. South Westward, from 218. 59m. South Latitude, until (by Obfervation) fhe be in 24d. 49m. South Latitude: What is her Courfe and Departure? Anfw. Courfe is SW. by W. half W. and Departure from the Meridian is 317.3 Minutes. Queft. 5. Suppofe a Ship faileth 354 min. North Eastward, from 20. 9m. South Latitude, until her Departure be 150 min. What is her Courfe and Latitude he is in? Anfw. Courfe is NNE. a quarter East nearest, and Latitude the Ship is in, is 3d. 12m. North. Queft. 6. Sailing between the North and the Weft, from a Port in id. 59m. South Latitude, and then arriving at another Port in 4d. 8m. North Latitude, which is 209m. to the Weftward of the firfi Port: I demand the Course, and Distance from the firft Port to the fecond. Anfw. Courfe is NNW. half W. and Distance of the Ports is 422.3 min or 140.7 Leagues. So much for the firft Part of Plane Sailing, Traverfe is next in order. Sect. IV. Plane-Sailing, the fecond Part; fhewing how to refolue a Traverfe, or bring feveral Courfes into one. AVING learn'd thofe neceffary Problems concerning a single H Course, the next in order is a Compound Course, commonly called a Trauerfe; in order to the right Understanding whereof, obferve the following Definitions. 1. A Traverfe, is when a Ship (meeting with a contrary Wind) faileth on feveral Courses in 24 Hours. 2. To refolve a Traverfe, is to reduce or bring feveral Courses into one; the Courfes are known by the Compafs, and the Distance by the Log, which in common Voyages is heav'd once in two Hours, but in Ships of War, or to the East-Indies, every Hour. 3. The Log, is a Piece of Wood about feven Inches long, in Form like a Flounder, with the Head cut off, and fo faftened to a fmall Chard (or Line called the Log-line) at one End, with fo much Lead at the other, that when it is put into the Sea, it may fwim upright, or endwife, The Lag-line, is divided into equal Spaces, called 'Knots, |
