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. IV. How to Measure any Piece of Ground be it never so Irregular; And how to reduce the Sides into Triangles or Trapezias, and to cast up the Content thereof in Acres and Perches.

SUppose you were to Measure a Piece of Ground, or Wood, or Marsh, or any place whatsoever, by your Compass and a Line marked as the 4 Pole-Chain before described in the first Chapter; and if you cannot see all the Angles by reason of the bigness thereof, then you must measure round about by the sides thereof, as in this Figure following; and the Observations made in the Field are set down in the Field-Book following, so plain, that it need no further precept.

Suppose you made your first Observation at A in the Field in the following Figure, (the Compass being rectifyed as before directed) you direct your Sights along the hedge to the Mark in the corner at B, and the Index cutts 54 degr. from the South Westwards, and the distance is 5 Chain 12 Links, which set down in your Field-Book thus, A B bears S W 54 degr. 00 min. distance 5 Chain 12 Links; Then make your second Station at B, and direct your Sights to C, the Index cuts N W 45 deg. 00 min. distance 2 Chain 89 Links, which note down in your Field-Book, as you did before in the se∣cond place; and so do by all the rest. From C to D N W 76 degr. distance 3 Chains 35 Links, from D to E N E 31 degr. distance 4 Chains 55 Links, from E to F N E 56 degr. distance 2 Chains 57 Links, from F to G NE 21 degr. distance 2 Chains 24 Links, from G to H S E 51 degr. 00 min. 2 Chains 95 Links, from H to K S E 34 degr. 3 Chains 25 Links, from K to A SW 4 degr. 2 Chains 95 Links; Thus you see all the Observations plainly set down in the Field-Book, you may proceed to Protracting your places of Observation and Marks in the Field, and your degrees and length of Lines orderly placed in your Field-Book; We proceed two ways to examine the truth: Thus the Rule is.* 1.1

First,

As the Radius or Sine of 90 degr. is to the length of the side of the Field in Chains and Links, or Perches and 100 parts; so is the Sine of the degree cut by the Index to the length of the Parallel of East and West in Chains and Links, or Perches and 100 parts.

Therefore by your Scale extend the Compasses from the Sine of 90 to the length of the side of the Field in the Line of Numbers, the same distance will reach from the degrees cut by the Index to the length in the Parallel of East or West.

Secondly,

As the Radius or Sine of 90 degrees to the length of the side of the Field in Chains and Links: or Perch and 100 parts; so is the Complement Sine of the degrees cut by the Index to the length of the Meridian of North or South in Chains, or Links, or Perch, or 100 parts.

Wherefore Extend the Compasses from the Sine of 90 degrees to the length of the side of the Field in the line of Numbers; the same distance will reach from the Sine Com∣plement of degrees cut by the Index to the length of North or South in the Meridian.

So that you see the 4 last Columns in the Field-Book are noted North and South, East and West.

Now to know by the Chains and Links, the first Observation from A to B, is S W 54 degr. and the distance A B is 5 Chains 12 Links; therefore by the last Rule extend the Compasses from 90 degr. to 5 Chains 12 Links in the Line of Numbers, that distance

will reach from 54 degr. cut by the Index to 4 Chains 14 Links in the line of Num∣bers, which is the distance in the Parallel of West, and also the same extent will reach from the Complement of 54 degr. which is 36 degr. to 2 chains 97 links in the line of Numbers, which is the distance in the Meridian South, and put it in the South Column of your Field-Book, as you did 4 chains 14 links in the Column of West; and so you may do with the rest of the Observations.

But the most sure way and least Errour, is, to convert your chain and links into Perches and 100 parts of a Perch, and then you can Protract in Perch and 100 parts the better.

Thus if you Multiply the number of chains found in the side by 4, by reason 4 Perches are in every chain; and if there be above 25 links in the place of links, divide by 25, and the Quotient will shew the odd Perch to be added; and what remains is links: that Multiply by 4 likewise, the Product will be 100 parts of a Perch.

As for Example.

The first side AB his distance is 5 chains 12 links, multiplyed by 4, makes 20 Perch,* 1.2 48/100 parts, which put in the next Column to it; Now if you extend the Compasses from 90 degr. to 20 Perch 48/100 parts, the same distance will reach from the Sine of 54 degr. cut by the Index to 16 Perch 56 parts, which is in the West Column, and the same extent will reach from the Complement 54 degr. which is 36 degr. to 11 Perch — 88 parts,* 1.3 which I put in the South Column; and by the same Rule I work in like manner by the rest of the Observations. The second side BC is 2 chains 89 links, reduced as before, makes 11 Perch 56/100 parts; and so work by them, as before directed, you shall have all your Numbers stand as in the following Figure of the Field-Book.

Houses name.		Angle with Merid.	Cha. Lin.	Pol. 100 pts.	North.	South.	East.	West.
	AB	S W 54 00	5 12	20 48	P. pts.	11 88		16 56	1
	BC	N W 45 00	2 89	11 56	8 16			8 16	2
	GD	N W 76 00	3 35	13 40	3 32			13 00	3
	DE	N E 31 00	4 55	18 20	15 72		09 40		4
	EF	N E 56 00	2 67	10 68	6 00		8 88		5
	FG	N E 21 00	2 24	8 96	8 40		3 20		6
	GH	S E 51 00	2 95	11 80		7 32	9 20		7
	HK	S E 34 00	3 25	13 00		10 72	7 28		8
	KA	S W 4 00	2 95	11 80		11 68		0 24	9
				The Sum	41 60	41 60	37 96	37 96

Under the line are the distances in the East Column; and likewise the Figures on the inside the Meridian, are the points of North, as 1, 2, 3, 4, 5, 6 Column; and the Figures on the outside are 7, 8 to A, and are taken out of the South Column, and working as directed in the two first sides, you may find all the rest. The Figure makes all plain to the meanest Capacity; and so you will have the true Plott of your Ground, or Park, or Wood-land, or Plantation, or place whatsoever, drawn on Paper or Parchment. Now if there be any Houses by the hedge-side, made a mark in your Field-Book in that Angle, and how many Chains or Perch from the place you observe, and by it insert it into your Plott.

[illustration] geometrical diagram

As for Example.

* 1.4There is a House in the first side and Angle AB, SW 54 degr. about 2 Chains 42 Links, or 9 Perch 21 parts, and reckon 1 Chain 24 Links, or about 5 Perch; there∣fore put it down in your Book, with the Man's Name that ows the House, as I have done, (John Cooke) or the like; and if any House, Church, or Castle, be in the middle, take the Angle thereof from any Point, and measure the distance, and note it in your Book, and enter it into your Plott, as I have done this House. By these rules you may compleatly take a whole Parish, Plantation, or Island: Now if you draw a Plott by the Protractor described in the Book of Instruments, You must rule your Paper or Parchment with an obscure plummet Merid. Lines, and Parallel Lines about 1 inch and ½ asunder; and put the Pin, the Center and Rivet upon any Point, and turn the side of the Protractor on the Meridians, and look in the Field-Book for the Angle, and put the Edge of the Index to the degrees, and count the Perch on the Index-side, there make a Mark with your Pin for the second place, and draw a Line from that place by the Edge of the Ruler to the Centers for the side of the Hedge or Field.

As for Example.

Suppose you were to draw the side AB in the Plott with your Protractor, lay the Pro∣tractor on the out-side of the Meridian-Line, and the Diameter-Edge thereof to the Meridian-Line; then in the opposite Degree and Quarter as in this Example is NE: I put the Foot of the Index to 54 degrees, and from the Center, the Edge points SW 54 degr. Number the Chains, or Links, or 20 Perch 42 parts, and from that Number to the Center draw a Line by the Edge thereof, and you have the Side AB; by this Rule you may gain all the rest. There is no Man that understands any thing in these Arts, but knows readily how to Plott a Field by the Rule before-going without more Directi∣o••s, for they will be all the same.

Notes

• * 1.1

  How to know if the Sides be rightly measu∣red before you go out of the Field, and Pro∣tract the Plat∣form thereof.
• * 1.2

  〈 math 〉〈 math 〉
• * 1.3

  〈 math 〉〈 math 〉
• * 1.4

  How to draw the Plott by the Protractor.