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. V. How to find the just Quantity or Content of any Piece of Ground in any Form.

VVE have shewed in the fore-going Chap. how to Measure the Geometrical Square, the Parallelogram, the Triangle, Trapezium, the Circle, and the like. Now we will shew you how to cast up the Contents thereof more fully. Sup∣pose the fore-going Figure A, B, C, D, E, F, G, H, K, be a Plott drawn or Protracted by a Scale of 10 Perch in an Inch, and the exact Contents thereof is required. Now because it is an Angular Plott, neither in the form of a Square, Parallelogram, Trapezium, nor Triangle; therefore all such Plotts must be reduced into some of these forms: which to effect, I reduce the main Body of the Field into the Trapezium ACEK, and the residue of it into 5 Tri∣angles, as ABC, and CDE, and EFK, FHK, and FGH.

Now to know the just Quantity of Acres, Roods, and Perches the Field contains, I first measure the Trapezium ACEK, I measure with my Compasses the length of the perpendicular CO, and apply it to my Scale of 10 Perch in an Inch, and find it 14 Perch 88/100 parts; and likewise the perpendicular KP, and find it 10 Perches, 50 parts, which I add together, and they make 25 Perches 38 parts, which I Multiply in half the Base AE 16:43, and the Product is 416:99:34: Therefore if you cut off 4 Figures to the right-hand, you will have the Contents of the Trapezium 416 Perch, and cut off 2 Figures of the 4, and before the Comma is 99 parts of 100 of a Perch and 34/1••0 remains, which is not to be taken notice of.

In like manner for the Triangle ABC, I multiply half the perpendicular: 4∷75 by the whole Base 25 Perch 26 parts, or the whole perpendicular by half the Base, as be∣fore; it is all one, and the Product is the Content of the Triangle ABC 119 Perch 98 parts: and so likewise for the Triangle CDE, multiply half the base 9 Perch 52 by 12 Perch, and 20 DY the perpendicular, and the Product is 116 Perch 14: is the Contents of that Triangle. Likewise in the Triangle EFK, the length of the perpen∣dicular FR is 7 Perch: 00 and the half length of the base EK is 14 Perch 70, multi∣plyed as one whole Number, the Product is 102 Perch 90 parts 00: the Contents of that Triangle EFK: the 4 Triangle FHK perpendicular: 6 P. 10: H q base FK 11 P. 50 the Contents is 70 Perch: 15: the first Triangle FGH the perpendicular GS is 7 P. 92 and the base FH, the half thereof is 6 P. 50: multiplyed together, and the Product is 51 P. 48 parts for the Triangle FGH.

Lastly, I add the several sums together, and they give the Content of the whole Figure in Perches and 100 parts.

The Area or Con∣tent of the ☞	1 Trapezium	ACEK	416:99
2 Triangle	ABC	119:98
3 The Triangle	CDE	116:14
4 Triangle	EFK	102:90
5 Triangle	FHK	70:15
6 Triangle	FGH	51:48
The Area or Content of the whole Field or Wood is	877 P. 64

Which if you will reduce into Acres, Roods and Perches,* 1.1 you must note, that 16 Foot and ½ Square is a Perch, and 160 of these Perches makes an Acre; therefore Di∣vide 877 Perch by 160, the Quotient shews the Acres to be 5; that which remains above 40 divide by 40, and the Quotient will be Roods 1: and that which remains will be 37 Perch. This is a General Rule for reducing of Perches; so that the whole Plott of Ground yieldeth the Content of the said Field 5 Acres, 1 Rood, 37 Perch and 64/109 of a Perch.

This is the way to cast up the Content of any Irregular Field, by reducing it into Trapeziums and Triangles, and adding their several Products into one Sum, which ought heedfully to be regarded, it being one of the most material works belonging to the Pra∣ctice of a Surveyor; for unless he be perfect herein, he can never perform any Work of that nature aright. I have been brief and plain in shewing the Art of Surveying by the Sea Compass; I might have been longer, but to avoid Prolixity, I think what is right is sufficient: If any desire a larger Discourse, he may make use of Mr. Leybourn's Com∣pleat Surveyor, or Mr. Wing's Art of Surveying, and others that have writ at large of the Use of the Plain Table, which is the most easy and useful Instrument in the Art of Sur∣veying of small Inclosures. But the Compass fitted as before, will with a little labour do any thing as exact as the Plain Table, Theodolite, Circumferentor, Protractor, or any other Instrument; especially large places, as Woods; Parks, Forrests, or Planta∣tions or the like: and what Direction I have given in Use of the Sea-Compass will serve for an Introduction to all other sorts of Instruments for Surveying of Land.

Notes

• * 1.1

  Reduce Perches into Acres, Roods, and Perches.