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. V. How to Measure Round-Timber five several ways.

ADmit you were to Measure a Piece of Round-Timber, as a Tree whose Diameter or thickness at the end is 20 inches; I desire to know how many inches in length will make one foot of Timber.

By the Line of Numbers.

Extend the Compasses from the Diameter AB 20 inches unto the constant Number 13, the same distance will reach from the same 13 turned twice over unto 5 ½ inches for one foot, as AD.

The Arithmetical way. 2220/ABq = AD 5 50/100 inches for one foot.

Having the Diameter of a Piece of Timber, as admit it to be 20 inches, and the length suppose 15 foot; To find the Contents in feet.

By the Line of Numbers.

Extend the Compasses always from 13 54/100 to the Diameter AB 20 inches, the same distance will reach from 15 the length turned twice over unto the Contents 32 7/10 feet in the tree.

[illustration] geometrical diagram

The Arithmetical way.

Square the Diameter AB 20, and it is 400; treble it by 3, and it is 1200, mul∣tiply it by the length 15, and the Product is 18000, that divide by 550, and the con∣tents is 32 717/1000 feet of timber in a round piece or tree, which is 32 foot, and about ¾ quar.

Here is likewise another brief Rule, Arithmetically thus.

Square the Diameter AB 20, and it will be 400; Multiply that by 11, and it is 4400, divide it by 14, and the Quotient is 314, and 4 remains, which multiplyed by the length 15, the Product is 4714; that divide by 144, and the Quotient is 32 7/10 as before.

Or else you may find the Contents of the Circle by this Rule, as 7 is to 22, so is the Diameter to the Circumference; or multiply half the Diameter by half the Circumfe∣rence, and the Product is the Content of the Circle; that Multiply by the length, and divide by 144, gives the Content of the Timber or Tree in feet or parts.

Now the common way used by Artificers, is to measure round a Piece of Timber or Tree, and to take the one fourth part for the Square, which is very erroneous and false.

For Example.

The measure of the Compass or Circumference by the Rule before-going is 62 9/10 inch. of the round piece of timber or tree the ¼ thereof is 15 70/100 inches, which they take to be the Square; which Multiplyed into it self, produceth 243:66 for the Area of the Base; which Multiplyed by the length 15 foot, the Product is 365490, the Contents in feet and parts; that divided by 144, the Quotient is 25 371/1000 that is differing from the Truth no less then 7. 356/1000, that is, 7 foot and about a quarter too much: the Buyer hath then his due; but I conceive they agree in the Price to stand to that measure, by reason of the wast in Chips before it is brought into Squares; but the best way will be to mea∣sure the tree right, and afterwards allow for the Wast; or else in time the Error will be taken for Truth, and Truth will be accounted Error, as it is by too many this day.

How to Measure a Round piece of Tapering Timber.

Admit the Diameter of the Great End of a piece of tapering timber be AB 20 Inches, and the Lesser End CD 16 Inches, and the length EF 15 foot. To find the Contents, add both the Diameters 20 and 16, the Sum is 36, the half is 18 for the Mean.

Then, Extend the Compasses always from 13 54/100 to the Mean-diameter 18, the same will reach from the length 15 foot turned twice over unto 26 51/190 foot. Or by Arith∣metick, Square 18 the Mean-diameter, and it makes 324; that treble by 3, the Product is 972; that Multiply by the length 16, the Product is 14586, that divide by 550, and the Quotient is 26 51/100 foot, the Contents of the taper-piece of timber is 26 foot and half.