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. 144, 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 Course 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 course and diftance?

Conftructed as Problem XII. in Geo

Dep. 406.

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
2.60853: Rad.

To the tan. of cou. 56°17' 10.17556: Dift. 488.1

2.60873

10.00000

2.68851

Hence her cou. is N. 56° 17′ W. or N. W. by W. and the dist. 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 case is over 56° 15', or 5 points the cou. required.

The fix foregoing Problems are the common case of Plane Sail

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:

Queftion I. A fhip in 2° 10' fouth lat. fails N. by E. 89 leagues: what lat. is the 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 obfervation the faid fhip is in 36° 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 westward 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 weft, 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 dist. 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.

H

TRAVERSE SAILING.

AVING learned thofe neceffary problems concerning a Single Course, the next is a Compound Courfe, commonly called a Traverse; in order to the right understanding of which, obferve the following definitions:

A Traverfe is when a fhip, meeting with contrary winds, fails on feveral courses.

When the wind is directly or partly against a ship's direct course 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, firft on one fide of the fhip, and then on the other fide.

In a fhip, when looking towards the ftem, head, or fore-part; Starboard fignifies the right-hand fide;

Larboard or Port the left-hand fide;

Aft or abaft is towards the hinder part, or stern;

The Beam fignifies athwart or across the middle of the ship. When the ship fails the fame way the wind blows, fhe is faid to fail or run before the wind; and the wind is right aft, or right aftern; and her course is then 16 points from the wind.

When a fhip fails with the wind blowing directly across her, she 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 ship, the wind is faid to be abaft the beam, or afore the beam, according as her courfe is more or less than 8 points from the wind.

When a fhip endeavours to fail towards that part of the compafs from whence the wind blows, the is faid to fail on a wind, or to ply to windward, or close-hauled, or on a bowling.

A veffel failing as near as fhe can to the point from whence the wind blows, is faid to be close hauled. The generality of fhips 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 ftarboard tacks are aboard when the starboard 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, obferve the course fhe goes on each tack when she is close hauled, then half the number of points between the two courses will fhew how near the wind that ship will lie.

The most common cafes, in turning to windward, may be conftructed 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 thofe rhumbs, according to the tack the fhip 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 course and distance on the other tack.

To

To refolve a Traverse, is to reduce and bring several courses into one; the courses are known by the compafs, and the distance by the log, which in common voyages is hove once in two hours, but in fhips of war, or in Eaft-Indiamen, every hour.

In the fteerage, or fome convenient place in the ship, there is generally kept a table, called the log-board, divided into feven columns; in the first is written the hours of the day, in the fecond, the knots the fhip runs during half a minute; each of these knots bear the fame proportion to a sea mile that half a minute does to an hour; confequently, fo many knots as the ship runs in half a minute, (the time allowed for trying the experiment) fo many miles the runs in an hour. In the third the fathoms, 10 of which ought to make a knot; in the fourth the courfes fteered by the compass; in the fifth the winds; in the fixth the lee-way, or how far the ship is drove to the leeward of the course fteered by the compass; in the seventh the transactions of the day, as in the following Table. Every day at noon the contents are tranfcribed into the log-book, which is divided into columns, exactly like the log-board, and the feveral courses being corrected by allowing for the lee-way and variations, and the distance run upon each being fet down in a Traverse-table, fhews what difference of latitude and departure the fhip has made during the laft 24 hours; and from thence is found. the latitude and longitude the fhip is in, &c. This operation is called doing a day's work.

Having placed the feveral courfes and diftances run upon each, begin with the firft courfe S. W. by S. which is 3 points, and the distance run upon it being fummed up, is 21,5, or an half, which being doubled (because the log is hove every two hours) is 43. In

like manner proceed with the other courfes, and then find the diff. of lat. and dep. for each cou. and dift.

When the cou. is to the fouthward, the diff of lat. must be fet in the column marked S, but if to the northward, in that marked N; likewise, when the course is to the eastward, the dep. must be fet in the column marked E; but if to the weftward, in that marked W. Thus the first courfe being S. W. by S. 3 points, the diff. of lat. belonging to it is fet under S. and the dep. under W. as in the following table :

Here the weftings being greater than the eaftings, the diff. fhews how far the ship has got to the weftward; and the fouthings being greater than the northings fhew how far fhe is got to the fouthward of the place she set out from.

Now the diff. of lat. 26,4 and dep. 7,1 being looked for in the Tables, will be found nearly ftanding together under 15° and againft dift. 27. Hence the courfe made good upon the feveral courfes is S. 15° W, and the dift 27 miles.