First, D

107.00 deg.

RAW

The Geometrical Construction.

a Right-line at pleasure, as B A D, and upon any point thereof, as A, protract an Angle of

Secondly, The Distance of the two Head-lands being 356.00 Miles enter them between the two fides, at B and C, and joyn BC, making the Triangle B A С.

Thirdly, Make A D equal to AC, and joyn CD, so have you conftituted another Triangle ACD.

Now in the Triangle A B C, is Given. (1) The Side BC, 356 Co. (2) The Angle BAC 107. 00 deg: And in the Triangle ACD, the Angle BAC being 107. 00 de. the Angle DAC must be 73.00 de. And the Sides A C and A D, being equal (by conftruction) the Angles ADC and ACD, must be also equal, siz. (each of them) 53. 50 deg. And being thus far prepared,

you may proceed to find the Angle ACB.

By Trigonometrical Calculation.

Fig. LXVIII.

To a fourth Sine, 73 06 d.

9.980729

This 73. 06 d. should be the quantity of the Angle DCB, but (by the construction) the Angle you fee is Obtuse; and therefore the Complement of 73. 06 deg. to 180, viz. 106. 94 deg. is the quantity of the whole Angle DCB. From which if you

substract the Angle ACD, 53. 50 deg. there will remain 53. 44

deg. for the Angle ACB.

To the Side B A, 299.00

2.475672

And fo much did the Ship from B, fail to A, and that substracted from 424. 12 there remains 175. 12, and so much did

the Ship from C to A Sail.

II. Of MERCATOR's Sailing, by the True Sea-Chart.

1

LL. the foregoing Problems are performed by that kind of

A Navigation Commonly called Plain Sailing,

or Sailing by the Plain Sea-Chart; in which Chart, the Degrees of Longitude and La-titude, in all Places, are supposed to be equal'; which is Erroneous, though most practifed: But there are two other ways of Sailing, both more exact than the former, the one called Mercator's, the other, Sailing by the Middle Latitude.

That of Mercator's requires that the Degrees of Latitude in that Chart be inlarged as they go farther from the Equinoctial towards either of the Poles, which is done by Reducing them into Meridional Parts: but the Degrees of Longitudes into Miles and Centesms, as in Plain Sailing: And for the Reducing of Degrees and Minutes of Latitude into Meridional Parts, I have here inferted a Table for the ready performance thereof, to every Degree and Quarter, or 25 Centesms of a Degree.

A

II.

A

Plai

titu

tho

botl

othe

1

Cha

eith

nal

as in

of 1

the

25.6

:

Degrees