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.

CHAP. XII. How to describe the Globe in Plano, by the Mathematical Scale.

THese, and all other Questions of this nature, concerning the Resolution of any Spherical Triangle, may very easily be performed by the Globe: But be∣cause the Globe is a chargeable Instrument, and so every one cannot have it, therefore several Men, have for several Uses, invented several ways to Project the Globe upon a Plain, as Mr. Gunter hath them in his Book of the Sector. The fittest for this purpose will be that of Gemma Frisius, which is most used in the Great Maps of the World, the Projection whereof is as followeth.

First, By the Chord of 60 deg. describe the Circle AENES, and by the Chord of 90 deg. divide it into four parts, as AEE a Cross Diameter for the Aequator, and NS for the great Meridian: Then by taking off every 10 deg. of the Chord, you may divide each Quadrant into 90 deg. and number them as in the Figure: Then if you take off your Line of ½ Tangents in your Scale every 10 deg. and 5 deg. and lay them from the Center C on the four Sides of the Quadrants, as you see the Figure, and number them as they are in the Figure; so shall you divide the Diameters into his parts AEE the Aequinoctial, NS the Meridian, which are half Tangents. You may do it also with∣out

the Scale, by your Ruler, if you stop one end of your Ruler at N, and turn the other end about to the several Degrees in the lower Semicircle ESAE: And also if you keep one end of your Ruler fixed in the Point AE, and lay the other end about to the se∣veral Degrees in the Semicircle NES; so have you the Meridian-diam ter divided into half Tangents likewise.

Now you have divided the Diameters, they must guide you in the drawing of the Meridians from Pole N to Pole S, which are perfect Circles; as likewise are the Parallels of Latitude.* 1.1 You may find the Centers in the Diameter AE, if you extend the Compasses from the first Degree on the half Tangents, to the Secants of every 10 Degrees, and with that Distance put one Point at 10 deg. in the Semidiameter AEC, and in EC will the other Point be the Center of the Meridian of the first 10 deg. from AE: and do the like from E in the same manner, for any other Degree. To draw the Meridian of 50 deg. Longitude, take the Secant of 50 deg. off the Scale, and one Point will stand in the Semidiameter AEC, at 50 deg. and the other will stand in the Center at East, and likewise at West for 50 deg. on the other side: And so do for the rest; and so you may find the Center of any Circle whatsoever, upon the Cross Semidiameter belonging to it, which you must continue beyond the Great Cir∣cle,* 1.2 where the Center will be in many Questions. For the Parallels of Latitude, it is thus: Take the Complement-number of Degrees off your Line of Tangents, put one Point in the Degree of Latitude, the other will stand in the Center.

[illustration] geometrical diagram

The GLOBE in PLANO. The Globe in Plaino.

For Example. If you will draw the Parallel of Latitude for 60 deg. take off the Tangent-line of your Scale 30 deg. the Compl. of 60 Latitude, and the other will fall upon V the Center of the Parallel of 60 deg. in the Semidiameter NS continued be∣yond the Circle.

So, Take the Tangent of 40 deg. and it will draw the Parallel of 50 deg. whose Center is at ♓: and so do in drawing all Parallels of Latitude. You may draw them also by making several Trials, until your three Points be in a Circle, and also draw the Parallels of Latitude: with the same Distance find their Centers; but if you can, by the Scale is the surest way.

The Four Scituations that are in the Globe.

The First Scituation.

AE is a Point of Intersection for the Mouth of the River of Amazones, Z Lundy, CRV the Obliquity 62 deg. 16 min. E the other Point of Intersection with the Aequa∣tor, NRV the measure of the Angle of Position. which applied to the Aequator from AE inwards, shews you 27 deg 50 min. from Amazones to Lundy. Now if you will know the Distance in such Questions, measure it in the Meridian that agrees with the Angle of Position; as namely, for this Distance AEZ, you must measure from N in the Meridian-line of 27 deg. 50 min. and you will find it 61 deg. 57 min. And so do for to measure any other Distance.

The Second Scituation.

I is the first Places Latitude, ♈ is the Difference of Longitude 52 deg. 55 min. ♈ is likewise the second Places Latitude; and ♍ H is the measure of the Angle of Position, which measured in the Semidiameter AEC, will be found 68 deg. 46 min. In that Meridian measure l r the Distance, and you will find it from N towards C, to reach 32 deg. 18 min. Remember to measure the Distances from the Poles in the same Meri∣dian, of the Number of Degrees of the Angle of Position: The greatest Obliquity of that Circle N r l is at W 54 deg. 25 min. Intersection of the Aequator at Y, W is a Meridian of greatest Obliquity.

The Third Scituation.

L is the first Places Latitude 51 deg. 22 min. North; E p is the Difference of Lon∣gitude 45 deg. 55 min. R is the second Places Latitude, or Rio de Plata, ▵ the greatest Olliquity 68 deg. 22 min. m n the Measure of the Angle of Direct Position: applied to EC will be found 36 deg. 02 min. in that Meridian: from the Pole measure the Di∣stance LR, and you will find it 95 deg. 18 min. P the Intersection of the Great Circle, passing over the two Places in the Aequator.

The Fourth Scituation.

The first Latitude is at L Lundy 51 deg. 22 min. Difference of Longitude counted from E 52 deg. 55 min. that Meridian will cut the Latitude of Barbadoes 13 deg. 10 min. at b: M ♓ the Measure of the Angle of Direct Position 67 deg. 51 min. and b L measured in that Meridian is 57 deg. 00 min. the Distance. Now to know the Angle of Position from Barbadoes, being Westward from Lundy, set it on the West side of the Figure, as at B; and likewise if the first Place be to the Eastward, put his Latitude to the East side of the Meridian.

Now to know the Angle of Position from Barbadoes, and Distance, and Obliquity, B □ O is the Arch of the Great Circle that passeth over these two Places; □ is Lundy, q h is the Measure of the Angle of Position 36 deg. 26 min. B □ measured in that

Line, you will find the Distance 57 deg. O is the greatest Obliquity 54 deg. 40 min. NO ☉ S a Meridian of the greatest Obliquity: d is the Intersection with the Aequator.

Notes

• * 1.1

  How to find the Centers of the Meridian-cir∣cles.
• * 1.2

  How to find the Centers of the Parallels of Latitude.