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.

PROBL. I.

FOrasmuch as it is very requisite for a Compleat Artist to know how to Mea∣sure all manner of Buildings, as Walls, Timber-work, Tyling, and such like; I shall in the following Example make Illustration thereof.

Note this, that Walls and Tyling are measured by the Rod of 18 Feet, Wainscot by the Yard or Feet, and Board and Glass by the Foot only. There∣fore measuring any of these things, consideration must be had to the just Form and Figure thereof: Then by the following Rules you will soon have the Area Content thereof.

As for Example.

Suppose there be a Wall in the Form of the Figure, and it is required to know how many Perch, or Rods, Yards, and Feet are contained therein.

The Arithmetical way for Perch.

ABXAD, or thus, ABXAD.ZX2/16 ½ = 76 Perch.

Extend the Compasses always from 16 ½ to the length 66, the same Extent will reach from the height 19 Foot unto the true Contents of the Wall 76 Perch.

[illustration] geometrical diagram

Then to bring it into Rods, and Feet, and Yards, Work as before. Multiply 66 by 19, the Product is 1254 Feet; which Divide by 324 (because there is so many Square Feet in a Rod,) and the Quotient is 3 Rods, and 282 remains, which divide by 9 (for so many Feet is contained in a Yard,) and the Quotient is 31 Yards, and 3 remains which is Feet; so this Wall being 66 Foot long, 19 Foot high, there contains 3 Rods ¾ Yard, 4 Feet (for as 81 Feet or 9 Yards is a quarter of a Rod.

But suppose ABC be a Govel Dormant Pike, such you must measure them as Triangles, to bring it into Feet. Multiply 16 the Perpendicular by half the Base AC, the Product is 160, the Contents in Feet double it: divide by 33 half Feet, the Quo∣tient is 9 Perch, 11 ½ Feet remains. Work by the Line of Numbers as in the last Rule, and it will be 9 Perch 7/10, (or divide 160 by the Quotient 17 Yards and 7 Feet, remains the true Contents of the Dormant Pike, that is 1 Rod, 8 Yards, 7 Feet.

[illustration] geometrical diagram

But in Measuring of Chimneys which require more Workmanship then other ordi∣nary Walls, they are usually accounted at double measure. First measure them as single-measure. Take the length of the brast Wall EF, and the 2 side Angles DE, and FC, which Multiplyed into the height CB the Product of that Multiplication doubled, yieldeth the Content.

According to the Customary measure allowed for Chimneys that stand in a Govel or Side-wall, (but if the Chimney stand by himself, the Back is to be measured with the rest of the Chimney; but the Back standing against a Govel or Wall is accounted part of the Wall, and must not be measured with the Chimney.

[illustration] geometrical diagram

Admit this Figure LIK. GH. AB. DC be a Chimney to be measured, and according to double measure, the Content is required.

First measure the Base CF the Brast-wall DC, and FC the side Angles, which together makes 24 Feet; next take the height of the Square CB 18 15/100 Feet, which Multiplyed together, the Product is 435:60 Feet for the Content of the Figure ABDC. Then for the □ and Brast-Wall GH, and side Angles is 15 Feet, height n H 6:26 Feet: X as before, makes 93:90 Feet, for the Content of the Square GH m:n.

In like manner of Working, you will have the Contents of the Square IK:RV:92:16; like∣wise the Chimney-S••aft in compass is 9 Feet, and 8 Foot high. × together as before, is 72 Feet for the Contents: add these 4 Sums together, the Sum is 693:66 Feet doubled is 1387 Feet•• 32/100 Feet the Content of the Chimney according to Customary measure.

	Feet. Parts.
The Squares. ABDC:	435:60
The Squares. GHmn:	93:90
The Squares. IKRV:	92:16
The Shaft IL:	72:00
The Sum	693:66
doubled.	693:66
The Total Sum.	1387:32

Which reduced into Perches as before, is 5 Perch 26 Foot 07/100 Parts; or into Rods, is 4 Rods 10 Yards 1 Foot 12/100 according to these Measures: But it is fit the Master-Workman should Measure it, and should have so much Arithmetick, as to Multiply and Divide, or else he cannot be a Compleat Workman in every part.

Note that after the same order Slate-work and Tyling are measured either by Perch or Rods of 18 Foot square. Note that Roofs of Houses, and Timber-work, Partition-Floors, and the like, are reckoned by the Square of 10 Foot, but Worked by the same Rule, as have been already delivered in this Problem; therefore it needs no other pre∣cept.