Here the Weftings being greater than the Eafting, the Difference fhews how far the Ship has got to the Weftward; and the Southings being greater than the Northing, fhew how far fhe has got to the Southward of the Place fhe fet out from.

Now the Difference of Lat. 26.4 and Dep. 7.1 being looked for in the Tables, will be found nearly standing together under 15° and against Dift. 27. Hence the Courfe made good upon the feveral Courfes is S. 15° W. and the Dift. 27 Miles.

In heaving the Log, one Man holds the Reel upon which the LogLine is wound, and another holds the Half-Minute Glafs; an Officer of the Watch heaves the Log over the Stern on the Lee-fide, and when he obferves the ftray Line is run off the Reel (to denote which there is fixed a red Rag) he cries turn! the Glafs-holder anfwers done! who, watching the Glafs, the Moment it is run out, eries ftop! the Reel being immediately stopped, the Knots, or Knots and Fathoms run off, how the Ship's Rate of Sailing per Hour, if the Wind happens to have been conftant.

EXAMPLE. I.

Yesterday at Noon we were in Lat. 24° 32′ N. and have till this Day at Noon run the following Courfes and Diftances per Log. viz. 3. W. by W. 45 Miles, E. S. E. 50 Miles, S. W. 30 Miles, S. E. by E 60 Miles. Required the Lat. come to, and the direct Courfe and Distance failed?

By PROJECTION.

With the Chord of 60° describe a Circle to reprefent the Compafs; and through the Centre C draw the Meridian S. N. and the Parallel, or East and Weft Line W. E.

Take, from the Line of Rhumbs on the Plane Scale, each Course, and lay it off from the Meridian on the Circumference, marking it with its proper Number, 1, 2, 3, 4, and draw the obfcure Lines € 1, c2, c 3, € 4.

The first Courfe fet off is 1 = S. W. by W. 5 Points, produce c 1, if neceffary, and lay off on it the first Distance 45 Miles from cto D; then will D represent the Ship's Place at the End of her firft Course.

Next draw DL parallel to the E. S. E. Line c2, which make equal to the fecond Distance 50 Miles-L q parallel to the S. W. . Line c 330 Miles; and qQ parallel to the S. E. by E. Line c4= 60 Miles; then will Qreprefent the Ship's Place at the End of her feveral Courses.

Produce the Meridian cS to P, draw the Line P Q parallel to W. E. and join c and Q; then will c P be the Difference of Lat. 98.6, PQ the Departure 37.5, Q the Distance 105.5 Miles, and the Angle Pc Q the Courie 20° 50'.

Hence the direct Courfe, or Courses made good, is S. 20° 50′, E. and the Distance 105.5 Miles.

To Work the fame by INSPECTION.

Complete the Traverfe Table as before directed, and write down the feveral Courses and Distances run upon each.

Begin with the first Course S. W, by W. 5 Points, Distance 45 Miles.

Over 5 Points, in the Table of Points, and against Distance 45, ftand 25,0 in the Column marked Diff. of Lat. at the Bottom, and 37,4 in the Column marked Departure. And as the Course is between the South and Weft, fet the Difference of Latitude under S, and the Departure under W.

In like Manner proceed with the feveral Courses and Distances; which, when found, will stand as in the following Traverse Table.

Having placed them as above, add up the Weftings, Eaftings, Southings, and Northings, and fet down their respective Sums at the Bottom of each Column; and as the Eaftings are greater than the Weftings, fubtract the lefs from the greater, and the Difference 37.5 fhews how far the Ship has gone to the Eastward of her first Place; and as there are no Northings, the Sum 98.6, in the Column marked S. fhews how far fhe has gone to the Southward of her first Place.

To find the Course and Diftance made good.

With the Difference of Latitude 98.6, and Departure 37.5, enter the Table, and you will find the neareft Number to thele itanding together are 98.1 and 37.6 under 21°, and against Distance 105; hence the direct Courfe is S. 21° E. the Distance 105 Miles, and the Lat. in is 22° 53' N. The fame may be found by Calculation.

Hence the Courfe is S. 20° 50' E. and the Distance 105.5 Miles nearly as before.

Suppofe a Ship from the Lizard in Latitude 49° 57' is bound to Cork in the Latitude 51° 49′ N. whofe Departure from the Meridian is 162 Miles Weft, but by Reason of contrary Winds is obliged to fail on the following Courses, viz. S. S. W. 54 Miles; W. by S. 39 Miles; N. W. by N. 40 Miles; N. E. by E, 69 Miles; N. N. W 60 Miles; I demand the direct Courfe, Diftance, Difference of Latitude and Departure made good upon the feveral Courfes, with the Latitude the Ship is in, and what Course she must afterwards steer, and how far, to gain her intended Port?

By PROJECTION,

I 52 112 Miles, the Dep. 162 M.

+

With the Difference of Latitude 112, and the Departure 162, between the Lizard and Cork by the last Cafe, the Courfe will be found nearly N. W. by W. and the Distance 197 Miles.

With the Chord of 60° defcribe a Circle, through which draw the Meridian, North and South, and, croffing that at Right Angles, draw the Eaft and Weft Points. The Centre reprefents the Lizard; then fet off two Points from the South Wefterly, through which draw a Line to the Centre for the first Course S. S. W. upon that fet off the first Distance run 54 Miles, which is the Ship's Place at the End of her firft Courfe; draw the W. by S. Rhumb, and, parallel to it, a Line paffing through the Ship's laft Place, and upon that fet off 39 for the fecond Distance; draw the N. W. by N. Rhumb, and parallel to it, as before, draw a Line paffing through the Ship's last Place, upon which fet off 40, and that will be the Place of the Ship at the End of her third Courfe; then draw the N. E. by E. Rhumb, and parallel to it, a Line paffing through the Ship's laft Place, and upon that fet off 69 for the fourth Distance; then draw a N. N. W. Rhumb, and Parallel to it, draw a Line, as before, through the Ship's laft Place; upon that fet off the laft Distance 60 which is the Place of the Ship at the End of her feveral Courses; from which draw a Line, parallel to the East and Weft Line, until it cuts the Meridian, for the whole Departure; from this to the Centre, being measured on the fame Scale, will give her Difference of Latitude made good upon the feveral Courses; and a Line drawn from the Ship's laft Place to her firft, will give the whole Distance;

and

N. B. The above Latitude is that which Cork was formerly laid down in, but in thefe Tables it lies 51° 41'. I could not alter the

1

and the Angle which this Line makes with the Meridian will be the Ship's Courfe.

Now to find what Courfe fhe muft fteer, and how far fhe muft ftill draw a Line from the Ship's laft Place to her intended Port for her go, Distance; and alfo draw a Line from the Ship's laft Place, parallel to the Meridian, for a new Meridian; and the Angle which this Line makes with the Distance, will be the Courfe fhe muft fteer to the intended Port; which may be easily understood by looking at the following Figure;

By the above Method any Traverse may be conftruded, and ale the Ship's Way pricked off on the Plane Chart.

But it being rather tedious, and not fufficiently accurate, we generally work at Sea

By INSPECTION.

Firft, to find the Course and Distance between the two Ports. In the Table it will be found, that the Numbers ftanding together nearest to 112 the Difference of Latitude, and 162 the Departure, are 113 and 161.3 over 55°, the Distance answering to these is 197, confequently the direct Courfe is N. 55 W. or nearly N. W. by W. Distance 197 Miles.