9.46303 1.65260

the diftance the Ship must fail on each Tack.

There is a great Variety of useful Questions of this Nature that may be propos'd, but the Nature of them being better understood by practice at Sea, we shall leave them and go on to Current Sailing.

SECT. XII.

Concerning Currents, and how to make proper Allowances for them.

I.

•CUR

URRENTS are certain fettings of the Stream, by which all Bodies (as Ships, &c.) moving therein, are compell'd to alter their Courfe or Velocity, or both; and fubmit to the Motion impreffed upon them by the Current.

If the Current fets juft with the Courfe of the Ship, (i. e.) moves on the fame Rumb with it; then the Motion of the Ship is increas'd, by as much as is the Drift or Velocity of the Current.

Example.

Suppofe a Ship fails SEbS at the rate of 6 Miles an Hour, in a Current that fets SEbS 2 Miles an Hour. Requir'd her true Rate of Sailing.

Here it is evident that the Ship's true rate of -Sailing, will be 8 Miles an Hour.

CASE

If the Current fets directly against the Ship's Courfe, then the motion of the Ship is leffen'd by as much as is the Velocity of the Current,

Suppose a Ship fails SSW at the rate of 10 Miles an Hour, in a Current that fets NNE 6 Miles an Hour. Requir'd the Ship's true rate of Sailing.

Here it is evident that the Ship's true rate of Sailing will be 4 Miles an Hour. Hence it is plain,

Cor. 1. If the Velocity of the Current be less than the Velocity of the Ship, then the Ship will get fo much a Head as is the difference of these Velocities.

Cor. 2. If the Velocity of the Current be greater than that of the Ship, then the Ship will fall fo much a Stern as is the difference of thefe Velocities.

Cor. 3. Laftly, If the Velocity of the Current be equal to that of the Ship, then the Ship will ftand still; the one Velocity destroying the other.

CASE

If the Current thwarts the Courfe of the Ship, then it not only leffens or augments her Velocity, but gives her a new direction compounded of the Course the steers, and the fetting of the Current as is manifest from the following

Lemma..

Ifa Body at A be impell'd by two Forces at the fame time, the one in the direction AB cá

B

pable to carry that Body from A to B in a certain
fpace of Time, and the other in the Direction AD
capable to carry it from A to D
A
in the fame Time: Compleat the
Parallelogram ABCD, and draw
the Diagonal AC; then the Bo-
dy at A agitated by these two
Forces together will move along
the Line AC, and will be in the
Point C at the end of the Time.
in which it would have mov'd-a- D

C

long AD or AB with the Forces feparately applied. Hence the Solution of the following Examples will be evident.

Example 1.

Suppofe a Ship fails (by the Compafs) directly South 96 Miles in 24 Hours, in a Current that fets Eaft 45 Miles in the fame time. Requir'd the Ship's true Course and Distance.

Geometrically.

Draw A D (fee the last Scheme) to represent the South and North line of the Ship at A, which make equal to 96; from D draw DC perpendicular to AD equal to 45, and join A C. Then C will be the Ship's true place, AC her true distance, and the Angle CAD the true Courfe. To find which

By Calculation.

First, For the true Course D A C, it will be, by Cafe 4. of Ret-angular Trigonometry.

confequently the Ship's true Courfe is S 25°, 07/E or SSE 2o, 37', Easterly.

Then for the true distance A C, it will be, by Cafe 2. of Ret-angular Trigonometry,

As the Sine of the Course A is to the Departure DC fo is Radius

to the true Distance AC

25°, 07!

9.62784

45

1.65321

106

Example 2.

10.00000

2.02537

Suppofe a Ship fails SE 120 Miles in 20 Hours, in a Current that fets WbN at the rate of 2 Miles an Hour. Requir'd the Ship's true Course and Diftance fail'd in that time.,

Geometrically.

Having drawn the Compass NESW, let C reprefent the place the Ship fail'd from; draw the SE

Line CA, which make equal to 120; then will A

be the place the Ship caped at.

From A draw AB parallel to the WbN Line CD, equal to 40, the motion of the Current in 20 Hours, and join CB; then B will be the Ship's true place at the end of 20 Hours, CB her true diftance and the Angle SCB her true Courfe. To find which

By Calculation.

In the Triangle ABC, are given CA 120, AB 40, and the Angle CAB equal to 34°, 45', the distance between the EbS and SE Lines, to find the Angles B and C, and the Side CB.

First, For the Angles C and B it will be, by Cafe 4. of Oblique Trigonometry,

80

As the Sum of the Sides CA and AB 160
is to their Difference
fo is the Tang. of half the
Sum of the Angles B and C
to the Tang. of half their Diff.

}

73°, 07', 10.51783

59, 45′

10.21680 confequently the Angle B will be 131°, 52', and the Angle A CB 14°, 23'. Hence the true Course is S 30°, 37! E, or SSE 2°, 07 Easterly.

Then for the true diftance CB, it will be, by Cafe 2. of Oblique Trigonometry,:

Suppofe a Ship coming out from Sea in the Night, has fight of Scilly Light, bearing NEbN diftance 4 Leagues, it being then Flood Tide fetting ENE 2 Miles an Hour, and the Ship running after the rate of 5 Miles an Hour. Requir'd upon what Pp 2 Course