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. III. The Mensurations of Solid Bodies of Timber and Stone, and first of Squared-Timber.

VVHatsoever hath length, breadth and thickness, is called a Solid-body; as Tim∣ber, and Stone, and the like, which are usually measured by the foot: and therefore you are to observe that a foot of Timber or Stone is accounted a foot square every way in the Form of a Die; whereby it plainly appears that a foot of Timber is 12 times more than a foot of Board, which it 144 Inches; but a foot of Timber must be 1728 Inches.

* 1.1For Timber that is squared you may find the Contents thereof on this wise; First find a Mean betwixt the two Sides at the End. Admit the height at the End be AC 16 Inches, the breadth thereof AB 25 Inches the half Sum.

By the Tables	120412
Add together	139794
Sum.	260206
The half Sum.	130103
	is the Square.

Root and Mean-proportion between 16 and 25 which is 20.

By the Line of Numbers.

Divide, and take the middle between 16 and 25, and you will find the Mean 20 as before; Then to know how many foot of Timber is in a Square of 16 Inches in height, 25 Inches broad, and 14 foot long.

Extend the Compasses always from 12 Inches unto the Mean-proportion or side of the Square 20 Inches; the same will reach from the length 14 foot turned twice over to 38 9/10 foot of Timber.

The Arithmetical way.

Thus. AB × AC. × AD / 144 = to the Contents in feet. 38 128/144

Or thus. AB × ACAD / 1728 = reduced into inches 168 in 14 foot 38 1536/1728 feet, as before found.

Yet it is common with the Carpenters to add the broad and narrow side together,* 1.2 and to take the ha•••• thereof; the true Square that way is very erroneous, especially when the difference between the side is much.

[illustration] geometrical diagram

In the former Example one side is 25, the other 16, the Sum 41, the half 20 50/100 inches; that is, half an inch too much, as was proved by the former Rules; that is just 20 for the Mean or true Square: so that by taking ½ the 2 sides 20 ½, it makes the piece of Timber 40 foot 4/10, when indeed it is but 38 9/10 feet, which is 1 foot and half too much.

Now if a Piece of Timber that is tapering, the Common Rule is to take the Mean betwixt both ends; and so to Work as in the last Form, but it is not absolute true.

For Example.

Admit a Piece of Timber were Square at one end 25 inch. and at the other 15 inches, and 14 foot long.

This is the absolute Arithmetical way.

ZAB, DE + AE. XAD / 432 = Contents 39:7/••••.

Notes

• * 1.1

  To find the Square-Root by the Tables.
• * 1.2

  A common Er∣ro•• amongst most Carpen∣ters.