Degrees

A Table of Meridional Parts.

The Ufe of the Table of Meridional Parts. What Meridional Parts do answer to 26 deg. of Latitude:

Latitude 26. oo Deg

24. 25 Deg47. 50 Deg63.00 Deg

2. What Degrees and Cetefims do anfwer to.

11. 25 Deg.

679 Merid. Parts.Anfwer5c. 50 Deg.

3522 M. P.

9488 M. P.

283.75 Dég.

For the Refolving of the following Problems, which (in kind) Fig. will be the fame with thofe in Plain Sailing as to the Trigonometri. LXIX. sal Work. But in the performance of them, I will fet the places propofed down upon a Sea-Chart, made according to the Projection of Mercator, where the Degrees of Latitude are enlarged according as they tend nearer and nearer to the Pole: And on the out-fide of fuch a Chart, I have defcribed a Plain Sea-Chart alfo,where the Meridians and Parallels of Latitude are every where of an equal distance; and fo wrought the Questions according to both Charts, by which the difference will more plainly appear: And the Chart which I have here made to work the following Examples upon, begins (at the bottom of it) at about 49.50 deg. of Latitude, and extends upwards to 55. 50 deg. of Latitude; and at the Top and Bottom to Six Degrees Difference of Longitude: But the Parallels of Latitude in the Plain Chart, (which are diftinguifhed by Pricked Lines) ex-~ tend to above 59 deg. of Latitude within the fame Bounds.

PROB. I.

The Latitudes of two Places, and their difference of Longitude being known; To find, (1) The Rumb leading from one to the other: And (2) Their. Diftance upon that Rumb: according to Mercators Chart.

By Trigonometrical Calculation

L
ET one Place be at A in the Latitude of 50 deg. and the other
at C, in the Latitude of 55 deg. but differing in Longitude
Eaftward from B, 6. 50 deg. which two places thus fet downin

the

Fig. the Chart, draw the Line A C, which is the Rumb (or Course) LXIX. from A to C: And thus have you upon your Chart conftituted a Right-angled Plain Triangle ABC, in which you have given, (1) B C, the Difference of Longitude 6.50 deg. which you muft Reduce into Miles (or Minutes) of Longitude by multiplying them by 60, (as in Plain Sailing) and they make 330. 00 Miles.- (2) A B, the Difference of Latitude 5. co deg. which must be Reduced into Meridional Parts thus:

The Meridional Parts for 50. 00 d. are

For 55.00

Their Difference

3475

2968

493

Which are the Meridional Parts anfwering to the 5. co deg. Diffe rence of Latitude of the two Places A and C: And by thefe you may find;

(1.) The Rumb BAC.

(2) The Meridional Diftance upon the Rumb A C.

By Trigonometrical Calculation.
(1.) For the Rumb BAC

As the Merid. Dif. of Latitude A B, 493 M. P.

Is to the Dif. of Longitude B C 330 Miles

So is the Radius, Tangent 45 deg.

To the Tangent of BA C, 33. 80 degrees.

2.692847

12.518514

IO.

9.825667

Which is the Rumb, leading from A to C: whofe Complement 56.

20 deg. is the Angle B C A, or the Complement of the Rumb:

(2.) For the Meridional Diftance on the Rumb A C.

As the Co-fine of the Rumb: B CA, 56. 20 d.

9.919592

Is to the Merid. Differ. of Latitude AB 493 M. R. 12.692847 So is Radius Sine 90 deg.

IO.

To the Merid. Diftance A C, 593.27 M. P. 2.773255 Now to find the Meridional Degrees anfwerable to thefe Meridi onal Parts, you must

Firft, Subftract the MPO of AB, from the M P of A C, their Difference is Ico. 27 M.P. the half whereof is 50.13 M. P.

Secondly, Add this half Difference 50. 13, to the Meridional Parts of the Greater Latitude 55. co deg. viz. 3968, and it makes 4018. 13, which are the Merid. Parts anfwering to 55. 50 deg. of Alfo, fubftract this half Difference 50. 13, from the Merid. Parts of the Leffer Latitude 50.co deg. viz. 3475, and the Remainder

Latitude.

--

Remainder will be 3424. 87, which are the Merid. Parts anfwering Fig. to 49.38 deg. of Latitude.

Thirdly, The Difference of thefe two Latitudes laft found, viza, 55. 50 de. and 49. 38 deg. is 6. 12 deg. And that is the trie Distance upon the Rumb between A and C, in Degrees.

And according to this Method, may all the other Problems (before wrought by the Plain Sea-Chart) be performed by Tri. Calculation; by the fame Canons: Only remember, to Reduce the Difference of Latitudes and Diftance on the Rumb, înto Meridional Parts, but the Difference of Longitude into Miles, as in the

other.

Now that you may fee the Difference between thefe two ways; See the Figure of the Chart, wherein the two Places are laid down by the Plain Chart; as in the Triangle AOS, which Triangle be ing refolved (as is before fhewed) you will find

(1) The Rumb OAS, to be 47. 73 deg.

Differing from the truth 13. 93 deg..

(2) The Distance upon the Rumb AS, to be 7. 43 de.

Differing from the other

I. 31.

And let thus much fuffice for Sailing according to Mercator..

There is a third way of Sailing, which differs not much from this way of Mercator's, but may be performed without Reductien or ufe of Meridional Parts; which is called Sailing by the Middle Latitude: of which a little.

L.XIX..

I

III. Of Sailing by the Middle Latitude.

Shall exemplefie this way of Sailing by Four of the moft ufual Problems in Navigation: And they fhall be the fame as in the foregoing whereby the Difference will the better appear...

PROB. I

The Longitude and Latitude of two Places, A and C, Given
to find,

(1) The Rumb BA C.

(2) The Distance upon the Rumb: AC.

LET