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Mid. lat. (as a course)

' Departure (in lat. column) ..... 109“ give diff. long. (in dist. column) 183 Longitude left

21° 45' W.
Diff. long. 183
Longitude in

18 42 W.


3 E.


Course N. 421° E. (as a course)
Mer. diff. lat. 200-55 in lat. column)

} give diff. long. (in depart. column) 183-85 Longitude left

21° 45' W. Diff. long. 184

3 Longitude in

18 41 W.

4 E.

The above method is that generally practised at sea in estimating the difference of longitude made good in a day's run, being considered sufficiently exact for the distance sailed by a ship in that time.

Example.—A ship from Table Bay (C. Good Hope), in lat. 33° 54' S., long. 18° 24' E., makes good the following true courses, viz. : (I) S.W. by W. 47 miles; (2) S.W. 1 S. 80 miles ; (3) W. 1 S. 87 miles ; (4) S.W. by S. 140 miles ; (5) S.W. by S. 1 S. 118 miles ; (6) S.E. 124 miles; () W. by N. 130 miles; and (8) W.S.W. 140 miles. Required the latitude and longitude arrived at ; and also the true course and distance thence to Port Stanley (Falkland Is.) in lat. 51° 41' S., long. 57° 51' W

Ans. Diff. lat. 429-9 and dep. 484 give course S. 48° 23' W. and dist. 647.4 miles. Lat. in is 41° 4' S. ; long. in (by mid. lat., using Workman's Table) is 8° 13' E., and the same by Mercator's sajling.

Thence the course is S. 76° 50' W. and dist. 2797 miles, by both sailings, using Workman's Table in mid. lat. sailing ; neglecting this Table, the course by mid. lat. is S. 76° 53' W., and dist. 2809 miles

CURRENT SAILING A current is a running body of water flowing in some definite direction through the midst of the general waters of the ocean and its various seas; the effect of the progressive motion of the water is to cause all floating bodies to move more or less in the direction towards which the stream of current is directed; hence the setting of a current is that point of the compass towards which the water runs; and its drift is the rate at which it runs per hour, or in any other given time.

A not unusual method of ascertaining the set and drift of an unknown current is to take a boat, in calm weather, a small distance from the ship, being provided with a half-minute glass, a log, a heavy weight, or kedge, and a small boat-compass; then let down the weight by a rope fastened to the boat's stem, to the depth of about 100 fathoms, by which the boat will remain nearly as steady as at anchor; then the log being hove, its bearing will be the setting of the current, and the number of knots run out in half a minute will be its drift per hour. This method is, however, very uncertain, owing to the effect of submarine currents.

CURRENT SAILING is the method of determining the true course and distance of a ship, when the ship's motion is affected by and combined with that of a current.

The current being known, it remains to apply its effect on a ship's way, which will depend on the direction and velocity of both, with regard to each other. If a ship sail in the direction of the current, it is evident that the velocity of the current must be added to that of the vessel ; if her course be directly against the current, their difference will be the ship's true velocity. Example.—Ship’s course N.E., making by log 9 knots per hour; current

sets N.E. 2 miles per hour; hence, ship makes good 11

miles per hour = (9 + 2). Example.—Ship’s course E., making by log 8 knots per hour ; current

sets W. 3 miles per hour ; hence, ship makes good 5 miles

(8 — 3). If the current runs stronger than the ship’s rate, the ship, unable to make headway, is drifted to leeward by the current.

If a ship's course be oblique to the current, her direction by the compass will be compounded with that of the current; that is, she will proceed in the diagonal of the parallelogram formed according to the two lines of direction, and will describe or pass over that diagonal in the same time in which she would have described either of the sides by the separate velocities.

For, in diagrams 1, 2 and 3, let ABCD be a parallelogram, the diagonal of which is A D, then, by the composition of forces, if the wind alone would drive the ship from A to B in the same time that the current alone would drive it from A to C, then as the wind neither helps nor hinders the ship from coming towards the line C D, the current will bring it there in the

per hour =





same time as if the wind did not act; and as the current neither helps nor hinders the ship from coming towards the line BD, the wind will bring it there in the same time as if the current did not act. Therefore, the ship must, at the

Course end of that time, be found in both those lines, that is, in their meeting at D: consequently, the ship must have passed from A to D in the diagonal line A D. Hence the ship's true distance will be the third side of a triangle, whereof the other sides are the distance by the log and the drift of the current, and the true course will be the angle between that third side and the meridian.

But the usual method of solving the problem of the combined effect of the set and drift of the current with the course and distance made by the ship is by inspection, through the traverse table, as will be shown in the sequel.



Given the Course steered, and Distance run by Log, also the Set and Rate of a

Current, to find the Course and Distance made good Example 1.– A ship sails N.W. 60 miles, in a current that sets S.S.W. 25 miles in the same time. Required her course and distance made good.

NOTE.—The course and set must be both magnetic, or both true.

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BY CALCULATION In the plane triangle A B C are given the side A B 60', the side B C 25', and the included angle A B C (the difference between the direction of B A which is S.E. and the direction of B C which is S.S.W.) 6 points, or 67° 30'. To find the angle B A C and the side A C

Side A B orc
Side B C or a
Sum or ct a
Diff. or c-a.


180° oo'
LB .....

67 30
Sum of 48 A and C 112 30 = C+ A
Half sum

56 15 = }(C+ A)


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Hence the course made good, N A C, is N. 69° 36' W. or W.N.W. I W. nearly, and the distance A C 551 miles.


23:I S.


But the most usual, and the readiest way of allowing for the effects of a current, is to consider the setting and drift as a course and distance, and enter it accordingly in a Traverse Table ; then the whole difference of latitude and departure will give the true course and distance. By this method the preceding example is thus worked

Course N.W. 60 m. gives D. Lat. 42-4 N. ....Dep. 42-4 W.
Current S.S.W.
25 m.

193 N.

52.0 W. Then, the difference of latitude A D 19:3, and the departure C D 52, give the course DAC= N. 69° 38' W., and the distance AC = 55.46, by plane sailing ; or, preferentially because more simply and sufficiently accurate), by Traverse Table = N. 69° W., and distance = 55.5 miles.

Example II.-Suppose a ship in 24 hours sails as follows-S.W. 40 miles, W.S.W. 27 miles, and S. by E. 47 miles, being throughout the time in a current setting S.E. by S., at the rate of 1} miles per hour. Required her direct course, and distance made good.




S.W.40 m.



S. by E.47 m.


Diff. of Lat.

BY CONSTRUCTION Draw the compass, and lay off the several courses and distances, as in traverse sailing; then will D represent the place of the ship by the log. From D draw D C parallel to the

срер. В S.E. by S. line, and equal to 36 miles, for the set and drift of the current in 24 hours; then will be the ship's true place, the angle B A C the true course, measuring 11° 50', A C the distance 117, A B the difference of latitude 114:6, and B C the departure 24 miles.

OS.E.byS.36 m.

BY CALCULATION This process would be too tedious; the solution would be performed

BY INSPECTION Working the question by inspection, the set and drift of the current is taken into account in the Traverse Table after the courses and distances per log, and in the same manner.

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117.1 miles.

Then, by inspection, in Traverse Table difference of latitude 114:4, and departure 24:3 (the nearest), give course made good S. 12° W., and, distance 117 miles.

Or by plane sailing, difference of latitude A B 114-6, and departure BC 24.0, give the true course CAB = S. 11° 49' W., or about S. by W., and the distance AC Given the Course and Distance by Dead Reckoning, or by Log, and the True Position of the Ship (or the Position by Observation), to find the Set and Drift

of the Current Example I.-A ship sailing in a current has by dead reckoning run S. by E. 42 miles ; but by observations finds she has made 55 miles of southing, and 18 miles of westing. Required the set and drift of the current.


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BY CONSTRUCTION Having drawn the compass, set off 1 point from the south towards the east, and draw the S. by E. line A C, which make equal to 42 miles; through C draw the line C B parallel to the east and west, then will A B be the difference of latitude 41:19, and B C the departure 8-19, made by the log.

From A to G lay off 55, the difference of latitude, by observation, and through G draw a line parallel to the east and west ; from G towards F lay off 18, the true departure, and draw the line CF. From C


18 m.


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