The mariners magazine, or, Sturmy's mathematical and practical arts containing the description and use of the scale of scales, it being a mathematical ruler, that resolves most mathematical conclusions, and likewise the making and use of the crostaff, quadrant, and the quadrat, nocturnals, and other most useful instruments for all artists and navigators : the art of navigation, resolved geometrically, instrumentally, and by calculation, and by that late excellent invention of logarithms, in the three principal kinds of sailing : with new tables of the longitude and latitude of the most eminent places ... : together with a discourse of the practick part of navigation ..., a new way of surveying land ..., the art of gauging all sorts of vessels ..., the art of dialling by a gnomical scale ... : whereunto is annexed, an abridgment of the penalties and forfeitures, by acts of parliaments appointed, relating to the customs and navigation : also a compendium of fortification, both geometrically and instrumentally / by Capt. Samuel Sturmy.

FIrst, If any two Places being proposed, the one under the Aequinoctial, the other may be in any other Latitude given, either North or South, and the Difference of Longitude of the Places being known; you may find the three things before spoken of in any Question, by the following Directions. We call the

Angle that the Rhomb leading from one Place to another, makes with the Meridians, the Position of these Places: But in regard the Arch of a Great Circle, drawn between two Places, is the most neer distance from the one Place to the other; therefore the Angles which that Arch makes with the Meridian of those Places, we call the An∣gles of Direct Position: or direct way of two Places one from the other.

* 1.1Now in the following Diagram, let A be the Entrance of the great River of Ama∣zones, under the Aequator; AQ the Arch of the Aequator, or Difference of Longi∣tude; and let C represent the Island of Lundy, lying in Latitude 51 deg. 22 min. Northerly, and CQ the Meridian thereof: and suppose the Difference of Longitude AQ to be 41 deg. 22 min.

[illustration] geometrical diagram

How to do these Questions Geographically.

FIrst, With an Arch of 60 Degrees describe the outward Meridian AEECQIF.

Secondly, Draw AEQ the Aequinoctial Line. Thirdly, Take 51 deg. 22 min. of the Line of Chords, and lay it from Q to C; and draw the Line CD through the Center, and the Line EF at Right Angles thereunto. Fourthly, Take off your Scale of ½ Tangents, counting from 90,-41 deg. 22 min. and lay from Q to A, for A re∣presents the River of Amazones. Now draw the Circle CAD through A, the Hori∣zon thereof is EF; then measure FK, and apply it to the Line of ½ Tangents, as before directed: and you will find the Angle of Direct Position to be 48 deg. 25 min. Take that Number out of your Line of ½ Tangents, from 1 Degree forwards towards 90, and lay it from H to L for the Pole, and draw a Line from L through A, it will cut the Line in I; so measuring CI on the Line of Chords, it will be 61 deg. 57 min. for the Distance, which is 1237 ⅓ Leagues and 3712 Miles.

By the Tables.

THen in this Triangle CAQ, Right-Angled at Q, there is required CA the nearest Distance of the two Places in the Arch of a Great Circle; and the Angle ACQ of Direct Position from the Island Lundy to the Amazones: and the Angle

CQO being the Complement of the Angle of the Direct Position of the Island of Lundy.

For the nearest Distance CA,

As Radius, is to Co-sine of Difference of Longitude 41 d. 22 m.	987534
So is Co-sine of the Latitude or Difference 51 deg. 22 min.	979699
To the Co-sine of the Distance 61 deg. 57 min.	967233

which 61 deg. 57 min. converted into Leagues, is 1237 ⅓ as before, the nearest Di∣stance between those two Places.

For the Angle of Direct Position from the Amazones toward Lundy, NAER,

As the Radius, to the Sine of the Differ. of Longitude 41 d. 22 m.	982011
So is the Co-tangent of Difference of Latitude 51 deg. 22 min.	990267
To the Co-tangent of the Angle of Position 27 d. 50 m. NAER	972278

For the Angle of Position ACQ,* 1.2

As Radius 90, is to Co-sine of Differ. of Lat. 51 d. 22 m. QC	989273
So is Co-tangent of Differ. of Longitude 41 deg. 22 m. AQ	1005522
To the Co-tang. of the Angle of Direct Position 48 d. 25 m. ACQ	994795

The same Proportions will hold by the Artificial Lines on the Scale.

And thus you see, he which will sail the nearest way from the Amazones to the Lizard, shall at first shape his Course 27 deg. 50 min. from the Meridian to the Eastward; that is, N. N. E. almost ½ a Point Easterly. Now if the Wind should serve that you might sail this Course, it is to be understood, that in this kind of sail∣ing he is not to continue this Course long; but to shift it, and incline more and more to the Eastward, as often as occasion requires: which how it may be done, shall be shewed in the following Discourse.

Notes

• * 1.1

  To draw a Great Circle from the Ama∣zones over Lun∣dy, put the Dif∣ference of Lon∣gitude on the West Side from AE to G; and draw the prickt Line NS, N for the North, and S for the South Pole: and through G draw the Azimuth Circle NGS, and draw the Parrallel of Latitude CZC; and through Z draw the Arch AEZRVQ, for the Circle which passeth from AE Amazones to Z Lundy.
• * 1.2

  Measure NR on the half Tan∣gents, and the Angle of Posi∣tion, and the Distance is all one as before.