CAS E II.

Coafting along the Shore, I faw two Head-lands, the first bore N. N. W. the fecond N. N..E. Eafterly, then ftanding away E. by N. Northerly 16 Miles, the firft bore from me W. N. W. the fecond N. W. by N. Wefterly.

I demand the Distance of each of thefe Head-Lands from the firft Place, as alfo their Bearing and Distance from each other?

W. N. W. Line, W

and B C parallel to the N. W. by N. 1 W. Line, meeting the two firft Lines in the Points C and D, then D will be

N

E

B.

the firft, and C the fecond Head-land; join the Points D and C, and DC will be their Diftance afunder. Then draw a Line parallel to DC thro the Centre of the Compafs, and that will fhew their Bearings from each other; to find which

By CALCULATION.

To find the Distance of the firft Head-land.

Points
Points =

In the Triangle D A B are given the Angle D A B 8 95° 37', the Angle contained between the N. N. W. Line A D, and E. by N. N. Line A B, and the Angle A B D 3 39° 22' the Angle contained

and W. N. W. Line B D,

fecond, it will be,

between the E. by N. N. Line A B, and A B 16 Miles, whence by Axiom

So is Sine ABD

1,20412

39°22/

9,80228

11,00640. 9,84961

To the Side A D 14.35 the Dift. of the firft Head-land

1,15679 To

To find the Distance of the fecond Head-land.

=

In the Triangle A B C, are given the Angle B A C 342° 11', the Angle contained between the N. N. E. E. Line AC, and the É. by N. N. Line A B, and the Angle A B C 6 Points 70° 19', the Angle contained between the E. by N. N. Line A B, and the N. W. by N. W. Line B C, and the Side A B 16 Miles, whence by Axiom fecond, it will be,

2

To the Side A C 16.31 the Dift. of the fecond Head-land 1,21236

To find the Bearing and Distance of the Head-lands.

In the Triangle D A C are given the Side A C 16.31, the Side AD 14.35, and the Angle DAC 44 Points = 53° 26', tne Angles' contained between the N. N. W. Line A D, and the N. N. E. E.. Line A C, whence to find the Angles AD C, or A C D.

0,29226

So is T. of the Sum of Angles ADC and ACD 63°17. ́ ́

10,29816

10,59042

1,48657

To the Tangent of half their Difference

7° 14'

9,10385

Then 63° 17 added to 7° 31' is 70° 3, the greater Angle ADC, and 63° 17'-7° 14′ 56° 3′ the Angle A C D.

Now the Angle ADC 70° 14' added to 22° 30′, the Angle contained between the N. N. W. Line A D, and the Meridian, gives 93° 1′, which being more than a Right Angle, fhews that D bears from C, W. 3° 1' Southerly, and confequently C bears from D East 3° 1' Northerly.

7

To the Side DC 13.9 the Dift. between the Head-lands

1,14286

All the above Proportions may be worked by Gunter's Scale, but they are more readily done by Projection.

After this Manner may the mutual Bearings and Distances of any Number of Head-lands be found; as alfo the Maps of Harbours, Bea Coafts, &c, which are of excellent Ufe in reconnoitering the Enemy's Coafts, Towns, &c. without venturing too near their Forts. Many more Examples might be produced, which are not of fo much Ufe at Sea, and therefore are omitted.

There is a Method of afcertaining the Distances of Places by Sound, which is as follows: Fix a Pendulum of 38.2 Inches upon a Peg or Nail, and giving it a Swing, every time it paffes the Centre will give Seconds; and as it is found by many Experiments, that Sound travels 1142 Feet in one Second; therefore the Difference of Time between feeing the Flash and hearing the Sound being meafured by the Pendulum, the Distance may be eafily found by allowing 1142 Feet for every Second, or allowing 9. Half Seconds to. travel an English Mile, or five Seconds three Tenths to travel a Geographical Mile. If a Stop Watch is at Hand it will answer the Purpole better.

EXAMPLE.

Being at Sea, I counted 50 Seconds between the Time of seeing the Flash of a Gun and hearing the Report. I demand the Distance ?

If 50 Seconds be divided by 5,3, the Quotient 9,3 Miles, will be the Distance required; or if the fame Number of Seconds, viz. 50, be divided by 16, the Quotient 3 one eighth Leagues, will give the Leagues of Diftance, fo that the Gun, when it was fired, was 9,4 Miles, or 3 Leagues, and one eighth from the Obferver.

Hadley's Quadrant or a Sextant will be found more convenient for taking the Angular Distances of Objects in running along a Coast, when the Angles do not exceed 90° or 120, as they can be more accurately and expeditiously taken, and the Draught of a Sea Coaft or Harbour, as well as the Distances of Objects, be determined with fufficient Exactness: For having a Bafe or Stationary. Line, accurately measured, and the Angles taken from different Parts of it, the Interfections of the Line, including thefe Angles, will determine

the feveral Points of the Coaft or Harbour, and Sketches may be drawn to reprefent the Appearance of the Land, &c. If Time will permit, the Soundings, Rocks, &c. may be taken in a Boat, and the Bearings of the whole afterwards laid down by the Compafs. Even fuch a rough Draught as the above will be of great Ufe in giving an Idea of Coasts and Harbours of any Country we chance to fall in with, and if the Mariner has a Tafte for Drawing he may give a pretty good Defcription of the Parts he has been at, a Thing but too much neglected by our English Seamen.

CURRENT SAILING.

C

URRENTS are certain Settings of the Stream, by the Means of which all Bodies moving therein, are compelled to alter their Course, and fubmit to the Motion impreffed upon them by it. Whence, if a Current fets with the Courfe of the Ship, it augments her Motion by as much as the Drift or Rate of driving it.

Thus, if a Ship fails N. N. E. 20 Miles in a Current that fets N. N. E.8 Miles in the fame Time, her true Courfe will be N. N. E. 28 Miles in that Time; but if a Current fets againft the Ship, it leffens her Velocity by juft fo much as the Current's Drift is.

So that if a Ship fails N. E. 49 Miles'; in a Current' that fets S. W. 10 Miles in the fame Time, then her true Course will be N. E. 39 Miles;. and if, in the fame Time that the Ship fails N. E. 49 Miles, in a Current that fets S. W. 59, then the Ship will fall' a-ftern, and her true Course will be S. W. 10 Miles; but if the Ship thwarts the Current, it not only leffens or augments her Velocity, but gives her a new Motion compounded of that of the Ship and Current; that is,

A

DL

B

C

If a Body be agitated by two Motions at the fame Time, the one with a certain Velocity, that will carry it according to the Direction of the Line A B, the Length A Bin a certain Space of Time; the other according to the Direction of the Line AD, with a Velocity that will carry it to the Distance A D in the fame Time; then the Body will defcribe the Diagonal A C, and at the End of that" Time will be found in the Point C.

The Setting and Drift of the most remarkable Tides and Currents are pretty well known; but if in unknown Currents, the ufual Way to find the Setting and Drift, is thus:

Let three or four Men take a Boat a little Way from the Ship, and by a Rope fastened to the Boat's Stem, let down a heavy Iron Pot,

or

or loaded Kettle, into the Sea to the Depth of 80 or 100 Fathoms, when it can be, whereby the Boat will ride almost as steady as at Anchor; then heave the Log, and the Number of Knots run out in Half a Minute, will give the Miles which the Current runs per Hour, and the Bearing of the Log fhews the Setting of the Current.

If a Ship fals N. E. 110 Miles in a Curent that fets S. S. W. 30 Miles in the fame Time, and her true Course and Distance be required?

By CALCULATION.

In the Triangle ABC are given the Side A C.110, the Side B C 30 Miles, and the Angle A C B 22° 30', by Axiom III.

The Sum of the Sides 140 the Sum of Angs. A & B 157 30 opp. these Sides

Their Difference

80% the Sum of the Ang.

78 45 CAB and ABC