zdly. Extend from rad. to 5 points, that extent will reach from the dep. 406 to the dift. 449 miles.' By INSPECTION. Find the cou. either among the points or degrees, and the dep. in its column; right against which ftands the dift. and diff. of lat. in their respective columns. Thus, with the cou. 5 points, and half the dep. I find 224,5 for the dift. and 95,8 for the diff. of lat, which being doubled, gives the dift. 449, and the diff of lat. 191,6 nearly as before. CASE IV. Distance and Difference of Latitude given, to find the Course and Departure. Suppofe a fhip fails 488 miles, between the fouth and the eaft, from a port in 2° 52' fouth latitude, and then by obfervation is in 7°23' fouth latitude; what courfe has fhe fteered, and what departure has she made ? From the latitude by obfervation 7° 23′ take 2° 52' the latitude left, the remainder 4° 31' multiply by 60=271 miles or minutes of difference of latitude. The extent, from the dift. 488 to the diff. of lat. 271, on the line of numb. will reach from rad. or 90°, to 33° 44′ the co-cou. on the line of fines. 'And the extent, from rad. to 56° 16′ on the line of fines, will reach from the dift. 488 to the dep. 405,8 on the line of numbers.' By INSPECTION. Seck in the Tables till against the dift. taken in its column be found the given diff. of lat. in one of the following columns; and adjoining to it stands the dep. which, if less than the diff of lat. the cou. is found at the top; but, if greater, the cou. is found at the bottom. Now, with half the dift. 244, and half the diff. of lat. 135,5 look in the Tables till they are found to agree in their respective columns, which they do nearly over 5 points; against them ftands 202,8 for the dep. which, being doubled, gives 405,6 nearly, as before. CASE V. Distance and Departure given, to find the Courfe and Difference of Latitude. Admit a fhip fails 488 miles between the north and weft from the island of Bermuda, in lat. 32° 35' north, until her dep. is 405 miles; what courfe has the fteered, and what lat is the in? To the fine of cou. 56° 6' 9.91904 To the diff. of lat. 272,2 2.43486 Hence the courfe is N. 56° 6' W. or N. W. by W. nearly. To the lat. failed from 32o 35' add the diff. of lat. 272, or 4° 32', gives 37° 07', the lat. the fhip is in. By GUNTER. • Extend from the dift. 488 to the dep. 405 on the line of numbers, that extent will reach from rad, to the cou. 56° 6' on the line of fines. 2dly. • Extend from rad. to the comp. of the cou. 33° 54' on the line of fines, that extent will reach from the dift. 488 to the diff. of lat. 272 on the line of numbers. By INSPECTION. Seek in the Tables till against the dift. taken in its column, be found the given dep. in one of the following columns; and ad joining joining to it ftands the diff. of lat. which, if greater than the dep. the cou. is found at the top; but if lefs, the cou. is found at the bottom. Now, with half the dift. 244, and half the dep. 202,5, I look in the Tables, and find them to agree in their columns, nearly over 5 points, against which is lat. 135,5, which being doubled, is 271, the diff. of lat. nearly, as before. CASE VI. Difference of Latitude and Departure given, to find the Courfe and Distance. A fhip fails between the north and weft till her difference of latitude is 271 miles, and her dep. is 406 miles; I demand her courfe and distance? Constructed as Problem XII. in Geo metry. Draw AB 271, and perp. to it BC 406; join C and A; then will the angle CAB be the cou. 56° 17', and AC the dift. =488 miles. Dep. 406. C33.43 ه و 56.17 Cou. Dist 488./ To find the Course. To find the Distance. As the diff.oflat. 271 co ar. 7.56703 As fin.-cou 56° 17'co ar. 0.07998 Is to rad. So is the dep. 406 10.00000 : Dep. 406 To the tan.of cou. 56°17' 10.17556: Dift. 488.1 2.60873 10.00000 2.6885L Hence her cou. is N. 56° 17′ W. or N. W. by W. and the dift. failed 488,1 miles. By GUNTER. Extend from the diff. of lat. 271 to the dep. 406 on the line of num. that extent will reach from rad, to 56° 17′ the cou. on the line of tan. 2dly. "For the dift. we must confider it as rad. (there being no line of fec. on the scale) and extend from rad. or 90° to the cou. 5 points on the line of fines, that extent will reach from the dep. 406, to the dift. 488 on the line of numbers. By INSPECTION. Seek in the Tables till half the given diff. of lat. 135,5, and dep. 203 are found together in their respective columns; then right against them will be found half the dift. 244, in its column, and the cou. ftand in degrees either at the top or bottom of the column where the diff. of lat. and dep, was found, which in this cafe is over 56° 15', or 5 points the cou. required. The fix foregoing Problems are the common cafe of Plane Sail ing, ing, 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: Question I. A fhip in 2° 10' fouth lat. fails N. by E. 89 leagues : what lat. is fhe in, and what is her dep. ? Anfwer. Lat. in 2° 12' N. and dep. 17.36 leagues. Question II. A fhip fails S. S. W. from a port in 41° 30′ north lat. and then by observation the faid fhip is in 35° 57' north lat. I demand the dift. run and dep. ? Anfwer. Dift. run 98,5 leagues, dep. 37,7 leagues. Question III. A fhip fails S. S. W. half W. from a port 2° 30' fouth lat. until her dep. be 59 leagues; I demand her dift. run and lat. in? Anfwer. Dift. run 125,2 leagues, lat. in 8° 1' fouth. Question IV. If a fhip fails 360 miles fouth weftward from 21° 59' fouth lat. until by observation fhe be in 24° 49' fouth lat. what is her cou. and dep. ? Anfwer. The cou. is S. W. by W. half W. or S. 61° 47′ W. and her dep. from the mer. is 317,3 miles. Question V. Suppofe a fhip fails 354 miles north eastward from 2° 9' fouth lat. until her dep. be 150 miles; what is her cou. and lat. in? Anfwer. Her cou. is N. 25° 4' E. or N. N. E. half E. nearly, and the is in lat. 3° 11' North. Question VI. Sailing between the north and the west, from a port in 1° 59' fouth lat. and then arriving at another port in 4° 8' north lat. which is 209 miles to the weftward of the first port; I demand the cou, and dift. from the first port to the second? Anfwer. The cou. is N. 29° 40′ W. or N. N.W. W. nearly; and the dift. of the ports is 422,3 miles, or 140,7 leagues. TRAVERSE SAILING. AVING learned thofe neceffary problems concerning a Single H Coure, the next is a Compound Course, commonly calle Traverse; in order to the right understanding of which, obferve the following definitions: A Traverfe is when a ship, meeting with contrary winds, fails on feveral courses. When the wind is directly or partly against a ship's direct courfe to the place fhe is bound to, fhe reaches her port by a kind of Z like course; which is made by failing with the wind, first on one fide of the ship, and then on the other fide. In a ship, when looking towards the ftem, head, or fore-part; Starboard fignifies the right-hand side; Larboard or Port the left-hand fide; Aft Aft or abaft is towards the hinder part, or stern ; The Beam fignifies athwart or across the middle of the ship. When the fhip fails the fame way the wind blows, the is faid to fail or run before the wind; and the wind is right aft, or right aftern; and her courfe is then 16 points from the wind. When a ship fails with the wind blowing directly across her, fhe is faid to have the wind on the beam; and her courfe is eight points from the wind. When the wind blows obliquely across the fhip, the wind is faid to be abaft the beam, or afore the beam, according as her course is more or less than 8 points from the wind. When a fhip endeavours to fail towards that part of the compass from whence the wind blows, fhe is faid to fail on a wind, or to ply to windward, or clofe hauled, or on a bowling. A veffel failing as near as the can to the point from whence the wind blows, is faid to be clofe hauled. The generality of ships will lie within about 6 points of the wind, but floops and other veffels will lie much nearer. The Windward, or Weather-fide, is that fide of the ship on which the wind blows; and the other is called the Leeward or Leefide. Tacks and fheets are large ropes made faft to the lower corners of the fore and main fails, by which either of these corners are hauled fore and aft. When a fhip fails by or on a wind, the windward tacks are always hauled forwards, and leeward, or lee-fheets aft. The starboard tacks are aboard when the ftarboard fide is to windward, and the larboard to leeward; and the larboard tacks are aboard when the larboard fide is to windward, and the starboard to leeward, either tacks the yards are braced up. To know how near the wind a fhip will lie, observe the course fhe goes on each tack when fhe is clofe hauled, then half the number of points between the two courfes will fhew how near the wind that fhip will lie. The most common cafes, in turning to windward, may ftructed by the following precepts: Having drawn the meridian, or north and fouth, and parallel of latitude (or eaft and weft line) in a circle, reprefenting the horizon of the place, mark, in the circumference, the place of the wind; draw the rhumb, paffing through the place bound to, and lay thereon the diftance of that place from the centre. On each fide of the wind lay off in the circumference the points or degrees fhewing how near the wind the ship can lie, and draw the rhumbs. Now, the first courfe will be on one of those rhumbs, according to the tack the ship leads with; draw a line through the place bound to, parallel to the other point, to meet with the firft, and this will thew the courfe and distance on the other tack. To |