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.

SECT. X. How by knowing what quantity of Powder will load one Piece of Ordnance; to know how much will load any other Piece whatsoever.

ADmit you have a Saker of three Inches three quarters at the bore diam. and it re∣quires 4 pound of Powder; what will a Demi-Canon of 6 ½ Inch. require? Work by these Rules always.

As the Logarithm of 3 75/190 diam.	257403
The Logarithm of 6 50/1••0 Inch. diam.	281291
the difference increasing,	23888
	(3
The triple of the difference added	71664
The Logarithm of 4 l. of Powder, 0 ounces.	160206
to the Logarithm of 20 8/10 or 20 84/199 l. of Pow.	231870

* 1.1So that the Demi-Canon must have 20 pound 13 ounces for her Charge of Powder; reduce the Fraction as before in the Margin into ounces.

By the Scale, extend the Compasses from 3 75/100 to 6 50/100 Inches diam. the same distance turned three times over from 4, will reach to 20 84/1••0 pound weight, as before.

The Arithmetical way.

C 6 50/100 ×4/3 75/100 C = 20 l. 13 ounces of Powder for to load a Demi-Canon.

You are likewise to understand that the Demi-Canon should be fortified so well as the Saker by this Rule.

The diameter of the Saker is 3 75/100 Inches	257403
The Demi-Canon diam. is 6 50/100 Inches	281291
the difference increasing,	23888
	(3
The triple of the difference by (3)	71664
added to the Logar. of 1600 weight of Saker	320412
gives the Logar. of 8332 the demi-Canon,	392076

Also by the Scale, and Arithmetick Rules, as in the foregoing Rules you will find the weight of the Demi-Canon 8332 pound, proportionable according to the Saker; but suppose the Demi-Canon to be no more than 6000 weight, then you must use these Rules.

The supposed weight of the Demi-canon 6000	377815
add the weight of the Powder well fortified, is 20 84/100	331889
The sum is	709704
Substract the weight of the Gun well fortified 8332	392074
leaves the weight of the Powder 15 pound,	317630

Fifteen pound being a sufficient Charge for that Piece: or extend the Compasses from 6000 to 8332, the same distance will reach from 20 84/100 to 15 l. of Powder, as before.

The Arithmetical way.

6000 × 20 pound 13 ounces./8332 = 15 pound almost, as before.

Thus you are always to take care of over-loading your Piece, which error many run into, when they call a Piece a Demi-canon, they presently load her with so much as is allowed for such a Piece so named, seldom examining whether the Piece have Metal enough for such a Charge; by which mistake they endanger their own lives, and others which stand near. Now, for easy plain Rules, I say you never had before laid down in this manner, to resolve these things; for if you compare these Rules with Nath. Nye, Master Gunner of the City of Worcester, or any other Art of Gunnery, you will find a great deal of difficulty in Cubing and Extracting the Cube Root, and with re∣ducing and Fractions (which here you may do five Questions, for one that way, and more true and near, therefore I compare them to his Rules.

How to make the true dispert of any true bored Piece of Ordnance.

Now we have found how to proportion Shot and Powder to any Piece of Ordnance true bored; before we Load and Fire,* 1.2 let us find the true Dispert to direct the Shot to the assigned mark.

Girt the Piece about the Base Ring round at the Britch with a Thred, and also the Muzzle Ring at the Mouth, and divide them two measures into 22 equal parts, which you may presently do, by applying it to a Scale, that hath an inch divided into 10 parts, and Divide the parts by 7, and Substract the greater out of the lesser, and take half the difference, is the true Dispert.

As for Example.

Suppose when I have measured the length of each String, and Divided, it into 22 equal parts, I find that 7 parts of the longer String is 11 inches, and 7 parts of the shorter is 9 inches; I Substract 9 out of 11, and the remain is 2, the half is 1, which is the true Dispert.

Another way to Dispert any Piece.

If you have a pair of Callipers, as in the general Figure ACB, as you take the diameter of a Shot, and apply it to a Scale Divided into 8 or 10 parts, to know the Contents thereof; so with the Callipers take the greatest thickness or diam. of the Base Ring, and by your Scale see how much that is; as admit that the length of the Line a:b:c:d, where the diam. of the Base Ring, then take the diam. of the Muzzle Ring; as admit it be a, b, as you may try by the Figure of the Gun in the general Figure; then Divide the difference b d into 2 equal parts, and one of them is the Dispert, put it upon the Muzzle of the Gun as CB, and stick it fast on the top of the Muzzle Ring with a little Pitch or Wax, and from the Base Ring at A in the Fi∣gure to the top of the Dispert at B, take aim to the Mark you would shoot to, and that is the way to hit; but it Callipers be wanting, take a Stick that is straight and flat, and 2 Strings with two Musket Bullets at the end, and two Loops made at the other end, the Stick being something more than the diam. at the Base Ring, and put the Stick upon the top of the Ring at the Muzzle, as you see the Fig. HK on the Gun, and put the Strings so nearer and farther, until they only touch the side of the matter of the Muzzle Ring, and mark the Loops on the Stick, and put the Stick on the Base Ring, and do in like manner, and mark the Sticks; and the Work will be the same, as it were taken by the Callipers; and the difference of the two Notches on the Stick will be ab the Base Ring, and ab the Notches of the diam. of the Muzzle Ring, and half the dif∣ference bc or cd is the Dispert, as before, if the Piece be true bored.

A fourth way to Dispert a Piece of Ordnance.

If the Piece be not Chamber-bored, take the Priming Iron, and put it down in the Touch-hole, until it rest upon the Metal in the bottom of the bore, there make a mark with the Base Ring; likewise apply the Priming Iron to the bottom of the Metal at the mouth, and so much higher as the mark is which you made at the Base Ring, than the Muzzle Ring, the difference is the true Dispert.

Notes

• * 1.1

  〈 math 〉〈 math 〉
• * 1.2

  By the same Rules you may find the Dia∣meter of a Shot with a String.