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. VII. How to take the Distance of divers places one from the other, remote from you, according their true Situation in Plano, and to rotract (as it were) a Mapp thereof by the Compass and Pplain-Scale.

THe Problem serveth chiefly to describe upon Paper or Parchment all the most Eminent and Remarkable places in a Country, Town, or City, whereby a Mapp thereof may be exactly made by help of a Table of Observations following, as with a little Practice you may soon per∣ceive.

Upon some high Piece of Ground make choice of 2 Stations as A and P, from whence you may plainly discern all the Principal Places which you intend to describe in your Mapp; then at A Plant or set your Compass fixed, and turn the Index about to P; and let A and P bear one of the other North and South, as you see marked with the Letters N and S: and then direct your Sights to the several Marks from A to B, C D E F G H I K L M observing what degr. the Index cutteth. As suppose your Instrument fixed at A, and the Sights directed to B, the Index cutteth N E 83 degr. 50 min. and like∣wise the Index directed to C, cuts 82 degr. 5 min. and so in like manner take the rest of the Angles, as you see them in the Table following, which were noted down by you in a Paper-Book when they were taken.

The Stationary Distance 730 Perch, or 2 miles 90 Perch.
Places	Angles	deg.	min.
A B	N E	83:	50
A C	S E	82:	05
A D	S E	64:	50
A E	S E	56:	20
A F	S E	45:	26
A G	S E	41:	30
A H	S E	24:	40
A I	S E	09:	00
A K	S W	11:	00
A L	S W	16:	00
A M	S W	23:	00

Next measure the Stationary distance A P, which was found 730 Perch, which you must Note down likewise in your Book; then plant your Compass, and fix him at P, that the Chard may stand North and South on the Stationary-Line P A, then turn the Index to your first Mark K, the Index cuts N W 24 degrees; Likewise turn the sights to L, and mark the Inclination to the Meridian, and put it down N W 17 degr. and so do by all the rest of the former Marks or Points; and Note them down as you see in this Table P K: P L: P M: P I: P D: P B: P C: P E: P G: P F: P H: and where the Lines Intersect each other, drawn from the two Places A and P, there must you de∣scribe the several Places, to which you made Observation, where you may Write the Name of the Places.* 1.1

[illustration] geometrical diagrams

Book V: p.24.25.

Places	Angles	Deg.	Min.
PK	NW	24:	00
PL	NW	17:	00
PM	NW	12:	00
PI	NE	9:	00
PD	NE	21:	00
PB	NE	33:	50
PC	NE	43:	40
PE	NE	54:	10
PG	NE	64:	00
PF	NE	73:	20
PH	NE	87:	15

Lastly, If you would know the Distance of any of the Places thus described,* 1.2 one from another, you have no more to do, but open your Compasses to the two Places on the Paper; and then apply it to the same Scale, by which you laid down the stationary Dist∣ance AP, which in this Figure was laid down by a Scale of 20 Perch to an Inch: the like is to be understood of Fathoms, Yards, or Feet; and so applyed, it will without farther trouble effect your desire.

And you may Protract it by help of your Line of Chords, and Line of equal parts, as this you see is done; or by the help of your Protractor, as before directed: and if there is any other Notable Castle, or Tower, or Place, lying in a right-Line with your Ob∣servation upon any Hill, you must remember always in taking of Inaccessible Heights and Distances; as also in Plotting Unpassable Distances, by reason of Water, that you take these two stationary distances as far asunder as may be. And if at any time you require the Altitude of a Church, Castle, or Tree, standing upon a Hill, you must perform it at two Operations; first by taking the Altitude of the Church, or Castle, or Tree to∣gether as one Altitude; and secondly by taking the Altitude of the Hill alone; then by substracting the height of the Hill from the whole height, the remainder shall be the height of the Castle, or the like.

And here Note also, That in the taking of all manner of Altitudes, whether acces∣sible or inaccessible, you must always add the height of your Instrument from the Ground to the height found, the total is the true height. And thus much briefly touching this Matter.

Notes

• * 1.1

  See Figure 110 ☞
• * 1.2

  See Figure 101 ☜