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.

To make a Scale for Fortification by the Tables.

[illustration] geometrical diagram

THis may be performed Geometrically by observing the former Instructions, whereby you may gain the length of every Line: but it will be sooner done, and more easie, by these Tables following.

First Table, for 12 Sides.

Numb. of Sides	4	5	6	7	8	9	10	11	12
Semi. Out. Pol.	1000	1000	1000	1000	1000	1000	1000	1000	1000
Semi. Inn. Pol.	661	700	731	756	777	795	810	823	834
The Front	412	347	299	261	232	209	190	174	160
The Gorge	158	151	141	132	123	115	108	101	96
The Flank	133	127	119	111	103	97	90	85	80

Second Table for 8 Sides.

Number of Sides	4	5	6	7	8
Semi. Outer Polyg.	1000	1000	1000	1000	1000
Semi. Inner Polyg.	661	706	740	766	787
The Front	412	346	296	259	229
The Gorge	158	156	148	138	130
The Flank	133	131	124	116	109

Make your Scale of a sufficient length, that may hold both Lines, the one for 12 Sides, and the other for 8. Make choice within the breadth of the Scale, between the Borders, any sufficient breadth, as CD; from whence draw Parallels to the Sides, and divide CD into ••0 Equal parts, and begin your Account from C with 45: so shall the end at D be 75 degr.

Now make choice of the length of the outer Po∣lygon, which here I make three Inches; and di∣vide a Line by the Side thereof, equal thereto, in 100 equal parts, and suppose each part into 10; so have you 1000 parts, agreeable to the Tables. The next thing is to draw Parallels to CE, ac∣cording to the Polygon half Angles, as you may see in the Tables under the Pentagon Fort, being the second Figure: So ••••om the Scale CD you have for the half Angle of a Pentagon 54 Degrees, whereby you may draw the Pentagon parallel FG; and so in the lower Scale of 8 Bastions. In the like manner you may do for all the rest.

Now to draw the cross Lines for the Semidiame∣ters of the Inner Polygons, as also the Lines for the Fronts, Gorges, and Flanks, you shall work thus. First, you must note, That the Semidiameter of the Outer Polygon is the Radius or whole Line of 1000

equal parts, and that is drawn at Right Angles, or a cross at F: But for the Semi∣diameter of the Inner Polygon, look in the Table of 12 Sides in the second Co∣lumn under 4, you have 661. Take the same Number off your Scale of Equal Parts, and lay it from E to H: Then in the third Column under 5 you have 700 parts; lay the same down from G to I, and make there a prick or point: Do the like for the Hexagon and Heptagon, as at I and K; proceeding along with all the rest, unto the Dodecagon. And lastly, draw a Line through all those Points: So have you the Arch Line HM for the Semidiameters of the Inner Polygon. In the same manner work for the Front, Gorge, and Flank Lines. The Scale of 8 Sides is the same Method.

I have also inserted on the left side of the Scale a Line of Chords, whose Radius (or Arch of 60 Degrees) is three Inches; and on the left side, a Line for the Sides of the Polygons. The Hexagon, or six Sides, is equal to the Radius: And for the Tetragon, or four Sides, it is equal to the Chord of 90 Degrees. So having described a whole Circle with the Chord of 60 Degrees, you shall find, that if you take from the Center N unto 5, it shall divide the Circle into 5 equal parts, for drawing the Figure of a Pentagon, which in the second Figure of a Pentagon Fort will reach from A to B, and so to X, Y, Z, and A. Now DA in the same se∣cond Figure you shall find to be the Semidiameter of the Outer Polygon, which in the Scale is GF; and taking GI off the Scale for 12 Bastions, or GO on the Scale of 8 Bastions, it will give the Semidiameter of the Inner Polygon, as DE in the same Figure. So likewise GP on the Scale will be equal to the Front AK in the Pentagon Fort. The like you may understand for laying down the Gorge and the Flank. And for the Curtain, as before, you must make RS 1 ½ the length of the Front AK.

This Scale will also be of good Use in Irregular Fortification. As for Instance. In the Irregular Fort, the seventh Figure, you shall find the half Bastion Angle GAF to be 58 Degrees, which falls on the Scale between the Pentagon and Hexagon, from whence you may draw a Bastion on some spare place, and from thence proportionate the same unto the outer side of the seventh Figure AB. The rest I leave to your own practice.