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.

The ART of Surveying of Land By the SEA-COMPASS: The DESCRIPTION of the COMPASS, and STAFF, and CHAIN. The Fifth Book. (Book 5)

CHAP. I.

I Have been all this while a shewing the Mari∣ner, How to describe and make his own In∣struments, and the use thereof in Naviga∣tion; I am also willing to shew him the great use there may be made of his Sea-Compass, commonly called the Azimuth, or Amplitude-Compass, which all ingeni∣ous Mariners carry to Sea.

This Compass requires but little descrip∣tion, it being so well known to all Sea-men; for it is the same in a manner as they Steer the Ship by: But it is called by the name of a Meridian Compass. The Chart within the Box is divided as you see in this Figure, each quarter into 90 Degrees, beginning at North and South, numbred East and West∣ward; on the Glass there is a Brass Circle, and Diameter, that goes over the Center of the Compass-Chart, the Brass Circle is about 7 ½ Inches Diameter, and about 6/10 of an inch broad; The outward Circle is divided into 360 Degrees by 90 Degrees in each Quarter, as you see the former was; the Figure makes all plain to the meanest capacity, and numbred as you there see from 15 Degree each way from each opposite Point; The inward Circle is the Hours answering each 15 Degrees and Quarters of the Horizon, and they are numbred as you see in the Figure.

There is a Circle the like divide the high of the Needle and Box-Chart, with lines drawn up the Box at 90 Degrees every way, that the Degrees of the upper Circle, and lower Circle, and Chart, may agree.

In the Diameter FGHK there is a right Line drawn in the midst, as GH, and at each end is two slits of an inch and an half long, each of them, as FG and HK; which are cut right in the middle: by which in taking any Angle, you must be sure to set the North Point right under the slit and line of the one; and the South Point under the slit and Line of the other: and so must you always, when you take the Angle of any

two stations from one place to another, You must be sure to keep the two slits in the Brass Diameter over the North and South Point of the Chart; and turn the Index that is riveted to the Center at C to the Object, and look through the sights that stand upon it; when you find you see it plainly, and have made a good observation of the Angle, look what Degrees the edge of the Index cuts, and upon what Quarter of the Compass: and that number of Degrees is the Angle of the two places from the Meridian.

The sights that stand perpendicular on the Index are 1 inch and ¾ long; the further sight hath a wire that goeth through the midst thereof, by which we cut the Object: that sight next unto you hath only a slit.

Through which you must see the Wire and Object you look at in one and the same Line, when you make any Observation.

Betwixt the two sights is a right line drawn through the midst, and at the further sight is fastened a perpendicular of Brass with a right line through the midst as BD: this perpendicular is fastned with two small Brass screws at M: O to the further sight with a wire; and at D is a hole where is fastned a Silk thred twisted and screwed through a small hole in the Eye-sight at S, and fastned with a small wooden pin.

* 1.1And this is for to take the Sun's Azimuth at any time of the day, by turning the Eye-sight to the Sun; and the slits over the North and South point of the Chart (as before directed) you may set the Index to what Degree you please; and when the shadow made by the Thred DS, comes upon the Line in the midst of the Index on the Line SA, and on the perpendicular Line RD; then on that instant take the Sun's Altitude by a Quadrant or Staff, and note it down: and likewise the Degrees cut by the Index at the perpendicular end, and that is the Sun's Magnetical Azimuth at that time. When you have done,* 1.2 you may unscrew the perpendicular from the sight; and then you have the Compass ready to take an Amplitude of the Sun's Rising or Setting: but more of that in the following Treatise, when we shall touch upon Astronomy

When you make use of the Compass for Surveying of Land, you have a Brass socket screwed fast to the bottom of the inward Box that holds the Chard; In that socket you put the head of your three legged Surveying-Staff with a small screw on the side to fasten it to the head, that it may not stir when the Compass is set North and South as before directed; then you may turn the Index and sights to what object you please, and be sure of your Angle from the Meridian if your Chard be good, and the Needle well touched and placed. Those that make them should have a special care of that; and that the points of the Needle be fastned and cemented together with a little Tin,* 1.3 so that they do not stir abroad, as I have seen many Charts carelesly made, doth; It might be to the shame of them that make them; and likewise the Wires put off one side 5 Degr. more or less, as if in all places there were still ½ a Point-variation, which is a lazy trick as well as faulty in most places. I would advise all Ingenious Mariners to make a constant practice of taking observation of the Sun's Altitude or Azimuth; and Steer a Course, and make allowance accordingly, as hath been shewed elsewhere, with the Wires of the Needle put exactly under the Meridian, as this Compass before-going the Points are; and then in all things this Instrument will come to the Truth, as well as a Needle of greater charge, and Plain Table and their appurtenances of 3 l. price: or the Theodolite, and Circumferenter and Veracter. And yet I cannot but highly commend these In∣struments as very useful for Land-men which have Money enough. Neither dare I re∣ject as useless,* 1.4 either the Topographical Instrument and Cross-Staff of Mr. Diggs, the Familiar Staff of Mr. John Blagrave, the Geodetical Staff, and Topographical Glass of Mr. Arthur Hopton, the Sector Cross-Staff, and the Pandoron of Mr. George At∣wel, or any other witty Invention which hath been devised for the Exact Plotting, and Speedy Measuration of all manner of Superficies, as Land, and the like. But in regard the Authors have in their own Works to their exceeding Commendation described the Making and Use of the said Instruments, I shall say no more.

And for the Mariners Compass in a manner to do the same things for the Surveying of Land, or Plantations, or the like, I hope will be well taken and accepted of all Inge∣nious Mariners, for whose sake I take these pains.

Let the Glass over the Chard be as clear as possibly you can get him.

The Figure of the Staff is plain, it needs no further description: It is to be had at any Instrument-Makers.* 1.5

[illustration] depiction of a three-legged surveying-staff

Of Chains, the several sorts thereof.

Of Chains there are several sorts, as namely Foot-Chains, each Link containing a Foot or 12 Inches; so the whole Pole or Perch will contain 16 ½ Links or Feet according to the Statute Pole.

The Chains now used and in most esteem among Surveyors are Three. The First I will name is Mr. Rathborn's, which had every Perch divided into 100 Links; and that of Mr. Gunter's which had 4 Perches or Poles divided into 100 Links: so that each Link of Mr. Gunter's Chain is as long as Four of Mr. Rath∣born's. And this year Mr. Wing hath de∣scribed a Chain of 20 Links in a Perch for the more ready use thereof in his Art of Surveying; Therefore when we have taken the Angles, and Plotted a piece of Ground, we will shew how to know the contents thereof in Acres, Roods, and Perch by the two last Chains.

SECT. I. Mr. Gunter's Chain.

MAster Gunter's Chain is a Chain most used amongst the Surveyors of this Age, and is always made to contain 4 Poles, and each Pole 25 Links, and each Link 7 Inches 92/100 of an Inch, and each Pole according to the Statute contain 16 ½ Feet, the whole Chain is 100 Links in the Four Pole or 66 Feet. In measuring with this Chain you are to take notice of only Chains and Links; saying, such a line measured by the Chain contains 64 Chains 45 Links, or thus distinguished 64. 45. and this is all you take notice of in Surveying of Land.

Now for the ready counting of the Links; at every Perch let there be two Curtain-Rings fastned, and one Ring at every 5 Links: so you may readily count the Rings at either end. If the Ingenious Mariner wants a Chain; he may mark a six Thred-line or small Belch as before directed with Red Cloth marks and White for distinction, or bitts of Leather as we mark our Dipsey line; and be sure to stretch him well first; or if you can, let it be a Top-gallant Brace half worn; then measure them exactly: and mark him as before directed, and you may measure any place of Land or Plantation, or any distance, as well in dry weather, as with a Chain, without sensible Errour,

SECT. II. Cautions to be used, and to be observed in the use of any Chain.

VVHen you have occasion to measure large distances, or otherwise, you may by chance mistake or miss a Chain or two in keeping your account, which will breed a considerable Errour; and also in measuring of distances, in going along by a Hedge side you can hardly keep your Instrument-Chain & mark in a right line; and there∣fore the distance will be more than in reality it is. For avoiding these mistakes you ought to provide ten small sticks, which let him that leadeth the Chain, carry in his Hand before; and at the end of eve••y one of those Chains, stick one of these Sticks or Arrows into the

Ground, which let him that followeth take up; so going on until the whole number of Sticks be spent, and then you may conclude you have measured Ten Chains without further trouble: and these Ten Chains if the distance be large, you call a Change, and so you may denominate every large distance by Changes, Chains and Links in a piece of Paper you keep the account by. If the distance be far, you must set up a Cloth upon a Stick for a mark betwixt your Instrument and the further mark, and see through your Instrument both the marks in one; then you may be sure to go straight with the Chain.

SECT. III. How to reduce any Number of Chains and Links into Feet and Yards.

IN taking of Heights and Distances hereafter taught, it is necessary in the Practice of my Geometrical Conclusions to give your measure, in such cases, in Feet and Yards by reducing of your Chains and Links thus.

Multiply your Numbers of Chains and Links, as one whole Number by 66, cutting off the Product the two last Figures towards the right Hand; so shall the Figures to the left Hand be Feet, and the Figures cut off shall be 100 parts of a Foot.

5:32	Examples.	8:06
66	66
3192	4836
3192	4836
351,12	531,96

* 1.6

Let it be required to know how many Feet are contained in 5 Chains, 32 Links. Set down the Chains and Links with a Comma (:) thus and these Multiplyed by 66, the sum will be 351 Feet and 12/100 parts of a Foot as thus you see it stand 351:12. This is the Rule by Mr. Gunter's Chain.

If you divide the Feet by 3, the Quotient will be 117 Yards. Now if you have less than 10 Links as 6, you must always remember to put (0) to supply before the 6, and Multiply the number as you see in the last Example.

SECT. IV. How to cast up the Content of any piece of Land in Acres, Roods and Perches by Mr. Gunter's Chain.

BY a Statute made the 33 of EDVVARD the I. an Acre of Ground ought to contain 160 square Perches, and every Rood of Land 40 square Perches, and every Perch contains 16 ½ Foot; and 4 Perches, Poles, or Luggs in breadth, and 40 in length makes an Acre: which multiplyed together is 160, Half an Acre is 80, a Quarter 40 square Perches.

[illustration] geometrical diagram

Suppose the Figure ABCD were a square piece of Ground as the Marsh of Bristol, and were 15 Chain 16 Links every way: Then to find how many Acres, Roods and Perches are in it, do thus. Square the sides, that is, Multiply one in the other, and cut off the 5 last Figures to the right Hand, and that before is Acres: what re∣mains Multiply by 4 (for 4 Roods makes an Acre) and cut off 5 Figures as before, and the comma: is Roods; and that which

remains, multiply by 40 the number of Perch in a Rood, and cut off 5 Figures to the right hand of the Product; and in like manner you have the odd Perches. This Ex∣ample will make all clear and plain.

So you will find 15 Chains, 16 Links Multiplyed together, as before directed, will produce 22, 98256: the 5 last Figures cut off to the left hand, remains before the Comma 22, which is 22 Acres, and the 5 Figures multiplyed by 4, the Product is 393024:

15:16

15:16

90 96

1516

7580

1516

5 Fi∣gures cut off on the left hand, the Comma is 3 Roods, and the 5 last Figures multiply∣ed by 40, cut off 5 Figures, and the rest will be 37 Perch.

Acres 22⌊98256

4

Roods 3⌊93024

40

Perch 37 ⌊20960

By the Line of Numbers.

Extend the Compasses on the line of Numbers on the Scale of Scales from □ which is at 160 unto the side of the Square AB 15 Ch: 16 ••in. which is 60 Perch and above ½, the same distance will reach from the same 60 ½ Perch, to 22 Acres, 3 Roods, and 37 Perch, and the 20960 part of a Perch.

SECT. V. How to Measure a Long Square Piece of Ground by a Chain of 20 Links to a Perch, according to Mr. Wing.

MAster Wing in his Art of Surveying, in the 113 Page hath described a Chain of 20 Links in a Perch, which is somewhat more ready, if you will reckon the Land in Perches for small parcels of Land.

Suppose a piece of Land be in length 36 Perches and 16 Links, and in the breadth 3 Perches 2 Links; By this Chain I desire to know the Contents thereof, having 20 Links in a Perch, I desire to perform the operation in a Decimal way; Count by half the number of Links, and then the Sums will stand thus; and cutting off 2 Figures, and you have for the Contents of the piece of Ground 114 Perches 2/100 parts. But I would advise the Practitioner in greater parcels of Land, to follow Mr. Gunter's Chain, the Surveyors all generally making use of him; therefore, for further Use of Mr. Wing's Chain, I refer you to the Page of his Book of the Art of Surveying.

368

31

368

1104

114:08

SECT. VI. To Measure a Long Square piece of Ground.

LEt the long piece of Ground be ABCD whose length AB is 11 Chains 25 Links, or 45 Perch; and his breadth AC 8 Chains, or 32 Perches.

[illustration] geometrical diagram

Multiply one by the other, as be∣fore in the last Example, directed by Mr. Gunter's Chain; and you will find the Contents of the Ground to be 9 Acres, no Roods; but 0 Perch.

By the Line of Numbers.

* 1.7Extend the Compasses from the □ Center, which is at 160. Perch unto the length AB 45, and the same distance will reach from the bredth AC 32 Perch, to 9 Acres.

SECT. VII. To Measure a Triangular Piece of Ground.

SUppose the Base of a Triangular piece of Ground AB whose mea∣sure is 11 Chains 25 Links, or 45 Perch, and the perpendicular CD 32 Perch, or 8 Chains; Take the half thereof, and Multiply one in the other, will produce the Con∣tents of the whole Triangle to be 4 Acres, 2 Roods, 0 Perch.

[illustration] geometrical diagram

By the Line of Numbers.

* 1.8Extend the Compasses from the ▵ Center, which is at 320 — unto the Base AB — 45, the same extent will reach from the perpendicular CD 32 unto the quantity of Acres, which is 4 A. 5/10 as before.

SECT. VIII. To Measure a piece of Ground of Four unequal sides called a Trapezia.

LEt the Ground given be A, B, C, D; after you have taken the Angles with your Compass, and noted them down in a piece of Paper or Field-Book, (as shall be shewn in the following Discourse) You must Protract or lay down the Figure as I do this, by a Scale of equal parts of 10, or 15, or 20, or 25, or 30 parts divided

[illustration] geometrical diagram

into an Inch; I have laid down all the following by 20 parts or Perch in an Inch: then draw the Diagonal Line AC, and with your Compasses take the distance AC, and ap∣ply it to your Scale of 20 Perch to an Inch; and you will find it 60 Perch, or 15 •…•…hain; and then if you let fall the perpendiculars BF and DE, and measure them in the like manner, you will find by your Scale BF 20 Perch or 5 Chain, and DE 24 Perch, or 6 Chain.* 1.9

In respect the Base is common to both the Triangles: You may therefore add the two perpendiculars together 20, and 24, the sum will be 44, the half thereof is 22 Perch. This Number being multiplyed by the whole length of the Common Base AC, 60 Perch, giveth 1320 Perch, that divided by 160, gives the Contents of the Trape∣zia or piece of Ground to be 8 Acres, 1 Rood, 0 Perch. You might have multiplyed half the Base AC 30 by the sum of the two perpendiculars 44,* 1.10 and it gives you the same as before.

By the Line of Numbers.

Extend the Compasses from the Trine ▵ Center at 320 to half the length of the Diagonal AC— 30

The same will reach from the Sum of the perpendicular 44, to the quantity of Acres, which is 8 25/100 Acres.

After this manner you may measure a piece of Ground of 5-6-7-8, or any number of Sides, by bringing it into Triangles and Trapezias, as shall be shewn.

SECT. IX. To Measure a Piece of Ground which is a perfect Circle.

THe proportion of the Circumference of any Circle, to its Diameter,* 1.11 is as 7 to 22. Example. In this Circle ABCD let the Diameter thereof be 56 Perches, Feet, or Inches, which multiplyed in it self giveth 4136.* 1.12 This Num∣ber multiplyed by 11, gives 45496, which being divided by 14,* 1.13 the Quotient will be 3249 10/14, that is the Area of the Circle.

[illustration] geometrical diagram

How many Poles and Feet, or square Inches, is in any Cir∣cle whatsoever, you may know better by these Rules; First, If you know the Diameter, and would find the Circumference, say, as 7 to 22, so the Diame∣ter 56 to the Circumference 176; Or if you know the Cir∣cumference, and would find the Diameter, say, as 22 to 7, so is the Circumference 176, to the Diameter 56.

The Diameter and Circumference being thus known, the Rule to find the Content is this.

The Diameter being 56 Perch, and the Compass 176, the half of both these multi∣plyed together, and divided by 160, you have the quantity of Acres 15, Roods 1, Perch 24, which is the Contents of that Circle.

By the Line of Numbers.

Extend the Compasses from O Center at (203 7/10 unto the Diameter AC 56, the same distance will reach again from 56 to the quantity of Acres 15 4/10.

I confess though the ordinary proportion of 7 to 22, is somewhat too much; yet it is but about 1 in 3000, which will breed no great difference in these Questions.

SECT. X. To Measure a Ground being a true Oval.

IN the Oval ABCD, let the length be given 40 Perch,* 1.14 or Feet, or Inches; and DB 30 of the same measure: Then to find the Quantity in Perch, Feet or Inches; if you work by the same Denomination of Feet and Inches, as I do of Perches.

[illustration] geometrical diagram

Multiply AC by DC 30, the Product Mul∣tiply by 491, and from that Product cut off 5 Fi∣gures as before directed, and as in the Margin, the Contents will be 5 Acres, 3 Roods, 22 Perch, 72/100 parts of a Perch.

By the Line of Numbers.

Extend the Compasses from the 0 Center in the Line at 203 7/10 to the length of the Oval AC 40, the same distance will reach from the breadth DB 30 unto the Contents in Acres, 5 Acres, 9/19 fere.

SECT. XI. To Measure a piece of Ground lying in form of a Sector of a Circle.

* 1.15LEt the Sector be ABC, whose sides is AB, or AC 48 Perch, and the Arch thereof BC 30 Perch: Then to find the Contents in Acres, Multiply AB 48, by BC 30, the Product divide by 320, the Quotient is 4 Acres, and 160, the Remain divide by 180 the ¼ of 320, and the Quotient is the Roods; if any thing remain, it is Perch; So the Contents of this piece of Ground is 4 Acres, 2 quar. 0 Perch.

[illustration] geometrical diagram

By the Line of Numbers.

Extend the Compasses from the ▵ Center at 320 unto the side, or Semidiameter AB or AC 48, the same distance will reach from BC 30, to the quantity of Acres 4 and 5/10.

SECT. XII. To Measure a piece of Ground that is a Segment, or part of a Circle.

LEt the Segment be ABC; AB 60 Perch, DC 18 Perch:* 1.16 Multiply the Chord of the Segment 60 by the perpendicular Height, and the Product divide by 225 the Gage-Number, and the Quotient will be the Acres, the Remain divide by 1/10 and it is found 4 Acres, 3 Roods, 8 Perch, the quantity of Ground in the Segment,

[illustration] geometrical diagram

By the Line of Numbers.

Extend the Compasses always from 225 unto the Chord of the Segment AB 60: the same distance will reach always from the perpendicular Height, unto the quantity of Acres 4 and 8/10 fere.

SECT. XIII. Having a Plot of Ground with the Content in Acres, To find how many Perch of that Scale was contained in one Inch, whereby it was Plotted.

LEt the long Square piece of Ground, be containing 9 Acres; First, Measure the Plott by a known Scale, which suppose it be of 10 Perch in an Inch; so measuring AB, you find it 22 5/10 Perch; also the breadth 16 Perch.

[illustration] geometrical diagram

By the Line of Numbers.

If you work by the Rule of the last Square Plott, you will find the Contents 2 25/100 Acres. Now on the Line of Numbers, take with your Compasses the distance between 2 25/100; and 9 Acres, the half distance thereof will reach from 10 on the Line of Numbers unto 20: so I con∣clude the Ground was cast up by a Scale of 20 Perch in an Inch.* 1.17

SECT. XIV. A Piece of Ground being measured by the Statute-Perch of 16 ½ Feet, To know how many Acres it is, it being measured by a Perch of 21 Foot, which is the Irish Perch.

* 1.18EXample. The last Piece of Square Ground being found 9 Acres by the Statute-Perch of 16 ½ Foot; and you would know how many it is by the Irish Perch of 21 Foot.

By the Line of Numbers.

Extend the Compasses from the Irish-Perch of 21 Foot, to the English Statute-Perch of 16 ½ Foot, the same distance will reach from 9 Acres turned twice over unto 5 6/10 Acre, fere: Or in the Scale of Reduction extend the Compasses from 16 ½ Foot to 21, the same distance will reach from 9 to 5/10 in the Line of Numbers. And so of any other measure. Now by reducing the 9 Acres into Perches, it makes 1440 Perch; and be∣cause the greater measure is to be reduced into the lesser, Multiply the given Quantity 1440 by 121 the Square of 11, which 11 was found, thus. 16 ½ being a Fraction, it reduced into halfs, makes 33 divided by 3 is 11; So the Irish-Perch 21 Foot in halfs is 42 divided by 3 is 14, those two Numbers squared a 11 is 121, the Square of 14 is 196, the Product of two Numbers 1440 multiplyed by 121, the Product is 174240: that divide by 196, the Square of 14, and the Quotient is 888 192/196 Perch, reduced into Acres, is 5 Acres, 5 Roods, 8 Perch 192/196, almost 9 Perch according to the Irish-mea∣sure.

Suppose you had been to Reduce Irish-measure into Statute-measure; then multiply 1440 by 196, and the Product would have been 282 240: that divided by 121; and the Product had been 2332 ½ Perches fere, which makes Acres 14, Roods 2, Perch 12 ½ fere, Statute-measure.

By the Line of Numbers.

Extend the Compasses in the Scale of Reduction from the Number of Feet in Customary measure, as I do from 21 Foot to the Perch of Irish-measure: the same will reach from 9 Acres Irish in the Line of Numbers to 14 Acres, 2 Quarters, and 12 Perch Statute-measure.

Or if you extend the Compasses from 21 in the Line of Numbers to 16 and ½, the extent turned twice over from 9, will fall upon 14 and ½ Acres, and a little more.

So that if you remember in all sorts of measure to reduce your Fraction into the same Denomination, and seek out the least proportionable terms: by Dividing by 3 if half Foot, and squaring these terms as before directed, you have a Rule that serves for all sorts of Customary or Irish measure whatsoever.

CHAP. II. How to take the Plott of a Field at one Station taken in the middle thereof by the Azimuth-Compass.

BEfore you go into the Field, you must Rule a piece of Paper in 8 Columns as you see the Figure following in this Chapter, makes all plain, without any more Description, which is called a Field-Book. Secondly, when you come into the Field, first place Marks at the several Angles of the Field, as at ABCDEF, in the following Figure; then make choice of some con∣venient place about the middle thereof at 0, to fix your Compass, if you can see all the Marks; and be sure the Brass-Diameter and Slits before descriebd, be set directly over the Meridian or North and South Line of the Chard, and there fixed.

This done, direct your Sights to your first Marks at A, Marking what Degree the Index cutteth, which let be 36 Degr. 45 Min. you may estimate the Minutes; This you must note down in your Field-Book in 1 and 2 Column thereof, as you see in the Book it is plain set down; then measure the distance from 0 the place of the Compass to A your first Mark, which let contain 8 Chains, 10 Links, which must be placed in th 3 and 4 Column of your Field-Book, as you see in the Figure of the Book.

[illustration] geometrical diagram

Then direct your Sights to B the second Mark, and note the Degrees cut by the Inde•…•… which let be South Easterly 80 Degrees 45 Minutes, and the distance 8 Chains 75 Lin. You must put down in the Field-Book, as before; First, the Letter B; Secondly, the Inclination to the Meridian cut by the Index South Easterly 80 Degr. 45 Min. in the third Column; then 8 Chains 75 Links in the fourth, as you may see in the Columns in the Book, all plain; then direct your Sights to C your third Mark, and note the Degrees cut by the Index, which let be S. E. 16 degr. 45 min. and the distance OC 10 Chains 45 Links, put the same down in the Field-Book likewise, as before directed; then direct your Sights to D, and note the Degrees cut by the Index, which let be S. W. 32 degr. 00 min. the distance OD, 8 Chains 53 Links, Note it down in the Book, as before.

Then direct your Sights to E, the Index cutting 72 degr. 45 min. North Westerly; and the distance OE 8 Chains 15 Links: They must be noted in the Book as the rest are.

Lastly, direct your Sights to F your last Mark, the Edge of the Index cutting in the upper Brass Circle N. W. 18 degr. 00 min. the distance OF 9 Chains 55 Links; then will the Observation stand in the Field-Book as in the following Table or Figure; then by a line of Chords, or by the Protractor you may presently Protract the exact Figure of the Field upon Paper thus, By a line of Chords; take 60 degr. and draw the Circle. Secondly, draw the Meridian line of North and South, and parallel-line of East and West. Thirdly, your first Observation and degr. cut by the Index, was 36 degr. 45 min. N. E. Therefore take 36 degr. 45 min. off the line of Chords, and lay from the Meridian line M to N. Fourthly, the distance OA was found 8 Chains 10 Links; take with your Compasses off any Scale of equal parts, 8 Chains and 1/10 that stands for 8 Chains 10 Links; lay this distance from O to A, and draw the prick'd line OA.

Then secondly, take out of the line of Chords the second Angle S. E. 80 degr. 45 min. and lay from the South towards the East on the blind-Arch, and through it draw the line OB; then take off the same Scale of equal parts 8 Chains 75 Links, that is, 8 parts, and 75 parts of 1 divided into 100, and lay it from O to B, and prick the line from O to B, and draw the line AB, which measure with your Compasses, and apply it to the Scale of equal parts as before, and you will find the side AB 8 Chains 75 Lin. The like do by all the other Angles and distances in the same manner as you have been shewed in the two first Angles. The Figure makes it so plain, it need no further precept; and you may put down the Number in the side, as I have done.

Now by the Protractor in the Second Book described.

* 1.19You may lay the Diameter-Edge thereof on the North and South line, and through the Center, put a Pin on the Center of the Plott at O, and note the degr. and distances in the Field-Book, as before: the first was North Easterly 36 deg. 45 min. put the Edge of the Index to 36 degr. 45 min. in the Arch of the Protractor; and by the Edge account in the Scale thereof 8 Chains 10 Links; and by the side thereof draw the line AO, prick'd as before; and so do by the rest of the Angles and sides in like manner, and you may presently draw a Plott of Ground you have measured. This is very plain, and may be understood by the meanest capacity in this Art. The Observations Marked in the Field-Book stand as in the following Table.

The manner how the Field-Book must be Ruled.

Mark.		D. M.	Ch.	Lin.
A	N. E.	36 45	08	10
B	S. E.	80 45	8	75
C	S. E.	16 45	10	45
D	S. W.	32 00	8	53
E	N. W.	72 45	8	15
F	N. W.	18 00	9	55

You are to note, that every Degree in the uppermost Brass-Circle is supposed to be divided into 60 parts, which is called Minutes, which cannot be expressed in regard of the smalness of the Instrument or Circle of Brass on the Glass of the Compass; and therefore the odd minutes must only be estimated: so must the odd Links taken off your Scale of equal parts, and it will breed no sensible Errour.

CHAP. III. How to take the Plott of a Field at one Station taken in any Angle thereof, by the Sea-Compass.

IN the Figure of the Field following, place your Compass at M, set your Brass-Diameter right over the North and South points or Line; then first direct your Sights to A, which let be supposed to be 22 degr. 15 min. N. E. which Note in your Field-Book, as before; then measuring the distance with your Chain MA which let be 8 Chains 46 Links, which place in your Field-Book according to former directions.

Secondly, Direct your Sights to B, the degrees cut off by the Index, suppose 42 degr. 45 min. and suppose the distance measured to be MB 10 Chains 21 Links, and put them down also in the Field-Book.

Thirdly, Direct your Sights to C, the degr. cut is 66 degr. 30 min. and the distance MC 1•• Chains 64 Links, put these in your Field-Book also, as before; and in the same manner you must deal with the other marks DM, and EM, and MF, and MG; and so having them all in the Field-Book, they will stand as followeth.

[illustration] geometrical diagram

The Figure of the Field-Book.

M		Deg. Min.	C. L.	North.	South.	East.	West.
A	N E	22 15	8 46
B	N E	42 45	10 21
C	N E	66 30	11 64
D	N E	86 45	11 23
E	S E	57 30	11 68
F	S E	49 45	10 15
G	S E	18 00	7 72

CHAP. IV. How to Measure any Piece of Ground be it never so Irregular; And how to reduce the Sides into Triangles or Trapezias, and to cast up the Content thereof in Acres and Perches.

SUppose you were to Measure a Piece of Ground, or Wood, or Marsh, or any place whatsoever, by your Compass and a Line marked as the 4 Pole-Chain before described in the first Chapter; and if you cannot see all the Angles by reason of the bigness thereof, then you must measure round about by the sides thereof, as in this Figure following; and the Observations made in the Field are set down in the Field-Book following, so plain, that it need no further precept.

Suppose you made your first Observation at A in the Field in the following Figure, (the Compass being rectifyed as before directed) you direct your Sights along the hedge to the Mark in the corner at B, and the Index cutts 54 degr. from the South Westwards, and the distance is 5 Chain 12 Links, which set down in your Field-Book thus, A B bears S W 54 degr. 00 min. distance 5 Chain 12 Links; Then make your second Station at B, and direct your Sights to C, the Index cuts N W 45 deg. 00 min. distance 2 Chain 89 Links, which note down in your Field-Book, as you did before in the se∣cond place; and so do by all the rest. From C to D N W 76 degr. distance 3 Chains 35 Links, from D to E N E 31 degr. distance 4 Chains 55 Links, from E to F N E 56 degr. distance 2 Chains 57 Links, from F to G NE 21 degr. distance 2 Chains 24 Links, from G to H S E 51 degr. 00 min. 2 Chains 95 Links, from H to K S E 34 degr. 3 Chains 25 Links, from K to A SW 4 degr. 2 Chains 95 Links; Thus you see all the Observations plainly set down in the Field-Book, you may proceed to Protracting your places of Observation and Marks in the Field, and your degrees and length of Lines orderly placed in your Field-Book; We proceed two ways to examine the truth: Thus the Rule is.* 1.20

First,

As the Radius or Sine of 90 degr. is to the length of the side of the Field in Chains and Links, or Perches and 100 parts; so is the Sine of the degree cut by the Index to the length of the Parallel of East and West in Chains and Links, or Perches and 100 parts.

Therefore by your Scale extend the Compasses from the Sine of 90 to the length of the side of the Field in the Line of Numbers, the same distance will reach from the degrees cut by the Index to the length in the Parallel of East or West.

Secondly,

As the Radius or Sine of 90 degrees to the length of the side of the Field in Chains and Links: or Perch and 100 parts; so is the Complement Sine of the degrees cut by the Index to the length of the Meridian of North or South in Chains, or Links, or Perch, or 100 parts.

Wherefore Extend the Compasses from the Sine of 90 degrees to the length of the side of the Field in the line of Numbers; the same distance will reach from the Sine Com∣plement of degrees cut by the Index to the length of North or South in the Meridian.

So that you see the 4 last Columns in the Field-Book are noted North and South, East and West.

Now to know by the Chains and Links, the first Observation from A to B, is S W 54 degr. and the distance A B is 5 Chains 12 Links; therefore by the last Rule extend the Compasses from 90 degr. to 5 Chains 12 Links in the Line of Numbers, that distance

will reach from 54 degr. cut by the Index to 4 Chains 14 Links in the line of Num∣bers, which is the distance in the Parallel of West, and also the same extent will reach from the Complement of 54 degr. which is 36 degr. to 2 chains 97 links in the line of Numbers, which is the distance in the Meridian South, and put it in the South Column of your Field-Book, as you did 4 chains 14 links in the Column of West; and so you may do with the rest of the Observations.

But the most sure way and least Errour, is, to convert your chain and links into Perches and 100 parts of a Perch, and then you can Protract in Perch and 100 parts the better.

Thus if you Multiply the number of chains found in the side by 4, by reason 4 Perches are in every chain; and if there be above 25 links in the place of links, divide by 25, and the Quotient will shew the odd Perch to be added; and what remains is links: that Multiply by 4 likewise, the Product will be 100 parts of a Perch.

As for Example.

The first side AB his distance is 5 chains 12 links, multiplyed by 4, makes 20 Perch,* 1.21 48/100 parts, which put in the next Column to it; Now if you extend the Compasses from 90 degr. to 20 Perch 48/100 parts, the same distance will reach from the Sine of 54 degr. cut by the Index to 16 Perch 56 parts, which is in the West Column, and the same extent will reach from the Complement 54 degr. which is 36 degr. to 11 Perch — 88 parts,* 1.22 which I put in the South Column; and by the same Rule I work in like manner by the rest of the Observations. The second side BC is 2 chains 89 links, reduced as before, makes 11 Perch 56/100 parts; and so work by them, as before directed, you shall have all your Numbers stand as in the following Figure of the Field-Book.

Houses name.		Angle with Merid.	Cha. Lin.	Pol. 100 pts.	North.	South.	East.	West.
	AB	S W 54 00	5 12	20 48	P. pts.	11 88		16 56	1
	BC	N W 45 00	2 89	11 56	8 16			8 16	2
	GD	N W 76 00	3 35	13 40	3 32			13 00	3
	DE	N E 31 00	4 55	18 20	15 72		09 40		4
	EF	N E 56 00	2 67	10 68	6 00		8 88		5
	FG	N E 21 00	2 24	8 96	8 40		3 20		6
	GH	S E 51 00	2 95	11 80		7 32	9 20		7
	HK	S E 34 00	3 25	13 00		10 72	7 28		8
	KA	S W 4 00	2 95	11 80		11 68		0 24	9
				The Sum	41 60	41 60	37 96	37 96

Under the line are the distances in the East Column; and likewise the Figures on the inside the Meridian, are the points of North, as 1, 2, 3, 4, 5, 6 Column; and the Figures on the outside are 7, 8 to A, and are taken out of the South Column, and working as directed in the two first sides, you may find all the rest. The Figure makes all plain to the meanest Capacity; and so you will have the true Plott of your Ground, or Park, or Wood-land, or Plantation, or place whatsoever, drawn on Paper or Parchment. Now if there be any Houses by the hedge-side, made a mark in your Field-Book in that Angle, and how many Chains or Perch from the place you observe, and by it insert it into your Plott.

[illustration] geometrical diagram

As for Example.

* 1.23There is a House in the first side and Angle AB, SW 54 degr. about 2 Chains 42 Links, or 9 Perch 21 parts, and reckon 1 Chain 24 Links, or about 5 Perch; there∣fore put it down in your Book, with the Man's Name that ows the House, as I have done, (John Cooke) or the like; and if any House, Church, or Castle, be in the middle, take the Angle thereof from any Point, and measure the distance, and note it in your Book, and enter it into your Plott, as I have done this House. By these rules you may compleatly take a whole Parish, Plantation, or Island: Now if you draw a Plott by the Protractor described in the Book of Instruments, You must rule your Paper or Parchment with an obscure plummet Merid. Lines, and Parallel Lines about 1 inch and ½ asunder; and put the Pin, the Center and Rivet upon any Point, and turn the side of the Protractor on the Meridians, and look in the Field-Book for the Angle, and put the Edge of the Index to the degrees, and count the Perch on the Index-side, there make a Mark with your Pin for the second place, and draw a Line from that place by the Edge of the Ruler to the Centers for the side of the Hedge or Field.

As for Example.

Suppose you were to draw the side AB in the Plott with your Protractor, lay the Pro∣tractor on the out-side of the Meridian-Line, and the Diameter-Edge thereof to the Meridian-Line; then in the opposite Degree and Quarter as in this Example is NE: I put the Foot of the Index to 54 degrees, and from the Center, the Edge points SW 54 degr. Number the Chains, or Links, or 20 Perch 42 parts, and from that Number to the Center draw a Line by the Edge thereof, and you have the Side AB; by this Rule you may gain all the rest. There is no Man that understands any thing in these Arts, but knows readily how to Plott a Field by the Rule before-going without more Directi∣o••s, for they will be all the same.

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,* 1.24 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.

CHAP. V. How to take the Height of any Island, or Mountain in the Sea by an Example made by the Author of the Height of Tenariff.

MAny Learned Men have writt of the Great Incredible Height of seve∣ral Mountainous Hills and Islands in the World. For taking of the Height of Islands in the Sea, none have greater opportunities than Sea-men. By them may all Men be informed of the truth of such like things; and also of several good Stars that be to the Southward, as the Crofiers and Cannobas in the Stern of the Ship, and any other, did they but observe any such Stars from a known Latitude, and take their Meridian-Altitude and time of Night; or if they cannot, or will not Calculate, and find by it the Stars Altitude, and Longitude, and Declination: yet if they bring it home, and give it to some able Artist, he will do it, and all Men shall have the benefit of it, and by it, it would be a great help to Navigators.

It is reported of Aristotle, Mela, Pliny, and Solinus of the Invincible Height of Athos a Hill in Macedonia, and of Caucasus; and of Cassius in Syria, and many other places: and among the rest one of the most miraculous things which they have observed of the Mountain Athos, is, that it being a Hill and Mountain situated in Ma∣cedonia, it casts a shadow into the Market-place in Myrrhina, a Town in the Island Lemnos, distant from Athos 86 Miles to the Eastward. It is no marvel it cast so large a shadow, seeing by Experience of the shadow of a Mans Body, we find it extraordi∣nary long at Sun-Rising, as well as at Sun-Setting. They report it is Higher than the Region of the Air. Julius Scaliger writes from other Mens Relations, that the

Island Pico of Tenariff riseth in height 15 Leagues, or 60 Miles: Most Writers agree that it is the highest Mountain in the World, not excepting the Mountain Slotus; it self, which I question whether any mortal Man ever see Slotus, besides the Monk of Oxford, who by his skill in Magick conveyed himself into the utmost parts of the World, and took a view of all places about the Pole: yet that this Island cannot be so high, shall appear by the following Demonstration and Observation made by Me; all Sea-men that have used to Sail to the Canaries know, that the Snow is not off it above 2 Months in a Year, that is, June and July.

Patricius not content with the former Measure of 60 Mile high, reaches to 70 Mile high; Now that any Snow is generated 60 or 70 Mile above the plain superficies of the Earth and Water, is more then ever they can perswade any Men that understand these things, seeing that the highest Vapours never arise by Ptolomy 41 Miles, and by Era∣t••sthenes's Measure 48 Miles above the Earth; that is, There is never no Rain, Dew, Hail, Snow, or Wind, but still a clear serenity.

I have been and passed by Tenariff several times my self, in the Year 1652 I was there in the Castle-Frigot of London Cap. John Wall Mr. and Loaded our Ship at Garrachica right under the Pico; and since bound to the West-Indies in the Year 1656, in the Society of Topsam, a Ship I had Command of, was put by Westerly Winds to the Eastward, that we had sight of the Pico of Tenariff, it bore off us South; about Noon I was resolved to make Observations of the height thereof, to try Conclusions with my Quadrant of 20 Inches Semidiameter, described in Chap. 16 of the second Book; and by the Rules of Quadrature I made these Observations following. On the 5th. of May 1656 I observed, and found the Sun's apparent Meridian-Altitude 81 degr. 44 min. his Declination 19 degr. 08 min. the Latitude 27 degr. 20 min. the Latitude of Pico I found formerly to be 28 degr. 20 min. difference of Latitude 60 min. or miles, which in the following Figure I make one half of my Horizontal Base AD; then at the same time observing the Height or Altitude of Pico, I found it 24 degr. 14. min. Therefore according to the Sphericality of this Terrestial Globe consisting of the Earth and Sea, I demonstrated the following Figure. The Section of the Arch A E F S represents the superficies of the Horizon of Tenariff; or a part of an Arch of a great Circle, the Me∣ridian A D, the difference of Latitude 60 mile, D C Pico the perpendicular, E B a se∣cond Observation, N the North part of the Horizon, S the South part,* 1.25 C the Port of Garrachica.

Now to find the perpendicular Height thereof, you have the Rules at large set down in the 16th. Chap. of the Description and Use of the Quadrate and Quadrant; and by the first Rule of the Quadrant I found the perpendicular Height D Pico 27 min. or mile, if the Sea were a flat plain as a Table-board, as the Right-Line A B D S represents.

But having 3 days of Fair Weather, in sight of Pico I made a second Observation, and ran to it with my Ship until I made an Angle with the Pico of 45 degr. 00 min. as Pico E C: or Pico BD; and had the apparent Meridian-Altitude of the Sun 81 degr. 29 min. the Declination 19 degr. 22 min. Latitude the Ship is in 27 degr. 53 min. difference of Latitude 27 min. or miles, being equal to the Height, as B D to the per∣pendicular D C Pico, the Angle of 45 degr. being the most sure as can be made by any Instrument which confirms the first, and the Height of the Pico of Tenariff to be 27 min. or miles High, if the Sea were flat as a Board.

But touching the Hypothesis, that the Earth and Sea makes a Round Body, It is ge∣nerally agreed upon by all the Philosophers, Astronomers, Geographers, and Naviga∣tors Antient and Modern; and therefore the distance of a degree 60 min. reckoned in the Heavens by Observations of the Sun or Stars is more than 60 miles upon the super∣ficies of the Earth and Sea,, as appears by several Experiments made by able Artists: but especially by the Labour and Industry of our own Countrey-Man Mr. Richard Norwood, as you may see in his second Chap. of his Book the Sea-mans Practice, made by him betwixt York and London. He makes it evident that 1 degree of a Great Circle

on the Earth, is near 367200 Feet, which in our Statute-Poles of 16 and ½ Feet to the Pole is 22254 Poles, and about half, and these reduced into Furlongs at 40 Poles to a Furlong, makes 554 Furlongs and 14 Perch; and lastly, these reduced into English-miles of 8 Furlongs to a mile, makes 69 miles and 4 Furlongs 14 Poles, that is 69 and ½ miles and 14 Poles to 1 degree upon the superficies of the Earth and Sea. And see∣ing a Degree is the 360 part of any Circle, equally divided in the Circumference; There∣fore if we can find how many Feet, Perches, Furlongs, or Pieces, are in a Degree of known measure: then can we presently resolve how many of the same known mea∣sure are in the Circumference of any Circle so divided on the Earth and Sea;* 1.26 for if there is 367200 Feet in one degree of a Great Circle upon the superficies of the Earth and Sea, therefore it is evident, that if you multiply 367200 by 360 degr. the Pro∣duct is 132192000 Feet, which reduced into Poles, is 8011636, and these reduced into Furlongs, are 200290 Furlongs, and 36 Poles; And lastly, these reduced into miles, are 25036 English miles, 36 perch for the Circumference of the Earth and Sea.

* 1.27And now if you desire the Diameter and Semidiameter of the Earth, as it is proved by Archimedes, That the proportion of the Circumference of a Circle is to the Diameter thereof almost as 22 to 7; therefore by the Rule of Proportion, Multiply the Circum∣ference of the Earth; namely, 132192000 by 7, and divide the Product 925344000 by 22, the Quotient is 42061091, which is the Diameter of the Earth in Feet: and the half thereof, namely, 21030545 is the Semidiameter of the same, or distance of the superficies of the Earth and Water, to the Center, being 21 millions of feet, and a little more;* 1.28 and these reduced into miles, as we did the Circumference, shews the Dia∣meter of the Earth to be 7966 miles, and somewhat more: and the distance to the Center or Semidiameter 3983 miles; and thus is found the Circumference, Diameter, and Semidiameter of the Earth and Sea, and also the quantity of a degree of the same measure in English measures of Feet, Perch, Roods, and miles. Therefore if you do still retain a degr. in the Heavens to be 60 minutes, you may find how many Feet is in a mile on the Earth and Water, if you divide 367200 feet by 60, the Quotient will be 6120 feet; which doubled, and divided by 33, and half-feet to a perch, the Quo∣tient is 370 perch, and 30 foot remains: divide 370 by 40 perch to a furlong, and the Quotient is 9 Roods or furlongs, and 10 perch or poles remains, divided by 8 Roods to a mile, the Quotient is 1, and 1 remains; so that a minute in the Heavens by this Rule and measure upon the superficies of the Earth and Water, contains 1 mile, 1 rood, 10 perch, and 30 foot; therefore my degr. 60 min. of Latitude at my first Observation, is found by these Rules to be 69 and ½ miles, 14 perch my distance upon the Arch of a Great Circle from the Latitude of Pico: therefore working by the Rules given of Quadrature in the 16th. Chapter of the 2 Book, the true Height of Pico will be found to be 31 29/108 miles,* 1.29 and the distance from the Eye to the Top of the Pico A, P, will be found by the Rules in the 16th. Chap. 76 22/100 miles.

And working the second Observation by the same Rules, your difference of Lati∣tude 27 minutes B D will be found to be 31 miles, 2 furlongs, 14 perch, 18 foot, which is 31 ¼ miles and a little more; which is almost the same Height found by the first Ob∣servation: and the distance from the Eye to the Top of the Pico is 44 24/100 miles.

By these several Rules you may find the Height of any Mountainous Island at Sea, or High-Land on the Main-Land, if you can come bring it North or South of you, and make any Observation of the Sun or Stars; or if you will but trust to a Log-Line marked after the former Experiment, that a mile doth contain 6120 feet, or 1020 fa∣thoms; and so 3 miles or a League contains 18360 feet, or 3060 fathoms: then if you intend to keep a Log by ½ minute-Glass: and because half a minute is 1/120 part of an hour, divide 6120 by 120, the Quotient is 51 feet. Therefore so many 51 feet or knots she runs out in ½ a minute, so many miles she sails an hour. By this Rule you may keep your Reckoning exactly; for I had Experience in sailing North and South by a Log-Line marked after the rate of 6000 in a mile, that is by the same Rule 50 feet or 8 fa∣thoms, and 2 feet to every knot, that I have run or sailed almost 22 Leagues to raise or depress the Pole 1 degr. on a Great Circle; and if any have impartially taken the

same notice and care, (or will) they shall find the like. But many that follow the old Rule 300000 feet to a degree, and 5000 feet to one mile, and 60 mile to a degree, or the 120 part of an hour 41 ⅔ feet, or 7 fathoms to the knots upon the Log: when they Sail North or South, and find the Log to fall too short of their Observation, imputes it to ill Steerage, Sometimes to the Variation of the Compass, or some Errour in their Plotts, or some Current, or other accident, but will not believe the truth a great many without they had Angels should tell them so, a great many have so much Ignorance and Obstinacy. But for confutation of some of the Antient Authors, especially Cleomedes, whom I take to be a Man which did never see, nor observed Tenariff Pico; He af∣firms, that there is no Hill found to be above 15 furlings in Height; and of Mr. Hughes, He saith, that if Mercury himself should affirm a Hill to be above 4 miles in Height, he will not believe him; neither will I believe them that are of that Opinion, be they what they will, without they could prove the foregoing Observation not good, and produce better of their own made by the Pico of Tenariff; and so much for the Alti∣tude of Hills at Sea.

CHAP. VI. How to find the Distance of a Fort, or Walls of a City, or Castle, that you dare not approach for fear of Gun-Shot; Or the Breadth of a River or Water, that you cannot pass, or Measure over it, made by 2 Stations, with the Quan∣tity of the Angle at each Station.

SUppose from some private place as at A, you espy a Castle, Fort, Tree, or place whatsoever, that you dare not approach for fear of Gun-Shot, Marsh-Grounds, or a River betwixt you, or some other Impediments, that you cannot make your second Station in any open place, but are forc'd to make it in some other secure Place at B; therefore plant your Instrument or Compass at A, and direct the Sights to C and B, take the Quantity of the Angle C A B 46 degr. 00 min. and go to B, and take the Quantity of the Angle A B C 79 degr. 0 min. then measure the distance of the 2 Stations A and B 350 fathoms.

Then by a Plain Scale, or by the Line of Sines on the Scale of Scales, you may presently resolve the distance, as I do by the Tables.* 1.30

As the Sine of 55 degr. 00 A C B	991336
to 350 Fathoms, A B	354406
So is the Sine of 79 degr. ABC	999194
to the distance	1353600
AC 419:40/100	362264
As the Sine of 55 degr. 00 A C B	991336
is to A B 350 Fathoms.	354406
So is the Sine of 46 degr. 0 C A B	985693
to BC 307 30/100 Fathoms, the	1340099
distance required.	348763

SECT. I. How to take the Breadth of a River.

SUppose you were to take the Breadth of a River, as I have at Crocken-Pill, which runs betwixt Glocester-shire and Somerset-shire, and found the breadth of the Water upon a Spring-Tide 40 Perch or a Furlong; you must do it thus. Being on the River∣side as in the former Figure at E, there set your Compass; Observe some mark on the other side of the Water, as at D; then set a mark at E, and go square-wise either to the right-hand, or to the left from these 2 marks, so far, until you spie the mark D on the other side the Water doth justly make an Angle of 45 degr. with the mark E; and this will be when you come to F; then measure carefully F E, the distance of the 2 Stations, and that shall be equal to the breadth of the River: so that if FE be 10:20:30:40:50: or 100 Poles, or Yards, or Feet, the breadth is the same. The like may be done by any other Angle, as if you go to G, and make an Angle of 26 degr. 30 min. in D; then is the distance GE twice the breadth; but ever if you can get an Angle of 45 degr. for that is the best and readiest Angle to find out such a distance; therefore if you can, use no other.

And the like way of Working you may do at Sea, if you gain the Sight of any Cape, Head-Land, or Island, set it by your Compass when you see it, without altering your Course, make an Angle of 45 degr. And by your Plain-Scale if you have kept a good account of your Way by the same Rules as before, you shall have the true distance of your Ship from the first Place, or Cape, or Head-Land, or Island whatsoever: Or you may get the Slope-side D F or D G if you measure it with your Compasses, and apply it to the same Scale of equal parts by which you put down the distance E F or E G. Thus you may find the distance from the Ship, to any Cape; These are made so plain by the Rules before-going, that it need no further precept.

SECT. II. Being upon the Top of a Hill, Tower, Steeple, or a Ships Top-Mast-Head, there observing the Angle of distance from you, To find the true distance thereof.

YOu may do this by your Quadrant; thus. Let the height of the Hill, Tower, Steeple, or Ships Top-Mast-Head be 40 yards, or any other measure: and from it you see an House, Tree, or Place whatsoever, and you desire the distance from you. You have been shewed already to find the height of a Tree, Tower, Hill, or Steeple; by this Rule we will shew you how to stand upon them, and take the distance from any thing else, viz.

Let the height of the Tower, or Mast, or Hill be 40 yards, and let the Angle of distance taken with your Quadrant be 80 degrees, being 10 degrees under the Line of Level; this is the Rule for all such Questions.

As the Tangent Compl. 80 degr. which is 10 d.	924631
is to the height 40 Yards.	260206
So is the Radius	10
to the distance from the Top of the Tower or Hill 226 9/10	235575 yards.

SECT. III. By the way of your Ship, and any 2 Angles of Position, to find the Distance of any Island, Cape, or Head-Land from you.

YOu have been shewed how to do it with a right-Angle of 45 degr. already; but with a little more trouble, you shall learn to do it by any 2 Angles what∣soever.

As for Example.

Suppose you were Sailing full South from A towards B, and from A should espy Land at C bearing 2 Points from you to the Westward, as S S W, or S W 22 deg. 30 min. and Sailing still upon your Course until you come to B, you observe the Place bears from you just 4 Points, or S W 45 degr. which is the double of the Angle observed at A. If in this manner you double any Angle; that is, let your first Angle be what it will, you must Sail until you have doubled that Number; then you may assure your self that the distance you have Sailed between A and B, is justly equal to the distance between B and C, B being the second Place where you made your last Observation, and C being the Place observed. So that if A B be 12 miles, B C is likewise 12 miles; and this you may do without further trouble or Calculation, and may lay it down by your Plain-Scale, as I have done this following Figure.

In all such Questions remember that the Angles at the second place of Observation, shall be either just the double, if you go nearer to the Place, or else just the half if you go further off than the Angle at the first place.* 1.31 Therefore the first Angle you may take at Random, no matter what it is, so you be careful to observe when you be just upon the double, or the half; so that by Calculation you may resolve it almost with as little trouble as a Right-Angle, which is made plain thus.* 1.32 In the Triangle ABC the acute Angle being the outward at B, being 45 degr. the obtuse or inward-Angle being the Complement thereof to 180 degr. must be 135 degr. and the Angle at A being 22 degrees 30 min. being added to this, makes 157 degr. 30 min. which Substracted from 180 degr. there must needs rest for the Angle at C 22 degr. 30 min. Now this Angle at C being equal to the Angle at A 22 degr. ½; therefore the side A B opposite to the one Angle, must needs be equal to the side B C opposite to the other Angle, as you see by this Case.* 1.33

As the Sine of the Angle A C B 22 degr. 30 min.	958283
to the distance Sailed 12 mile AB	107918
So is the Sine of the Angle CAB 22 degr. 30 min.	958283
to the distance B C 12 miles.	1066201
To find the distance A C	As the Sine of A C B 22 deg. 30 min.	958283	107918
is to A B 12 miles.	107918
So is the Co-sine of 135 d. which is 45 d.	984948
to the distance from the first Place	1092866
of Observation AC 22 miles. 17/199 parts.	134583

CHAP. VII. How to take the Distance of divers places one from the other, remote from you, according their true Situation in Plano, and to rotract (as it were) a Mapp thereof by the Compass and Pplain-Scale.

THe Problem serveth chiefly to describe upon Paper or Parchment all the most Eminent and Remarkable places in a Country, Town, or City, whereby a Mapp thereof may be exactly made by help of a Table of Observations following, as with a little Practice you may soon per∣ceive.

Upon some high Piece of Ground make choice of 2 Stations as A and P, from whence you may plainly discern all the Principal Places which you intend to describe in your Mapp; then at A Plant or set your Compass fixed, and turn the Index about to P; and let A and P bear one of the other North and South, as you see marked with the Letters N and S: and then direct your Sights to the several Marks from A to B, C D E F G H I K L M observing what degr. the Index cutteth. As suppose your Instrument fixed at A, and the Sights directed to B, the Index cutteth N E 83 degr. 50 min. and like∣wise the Index directed to C, cuts 82 degr. 5 min. and so in like manner take the rest of the Angles, as you see them in the Table following, which were noted down by you in a Paper-Book when they were taken.

The Stationary Distance 730 Perch, or 2 miles 90 Perch.
Places	Angles	deg.	min.
A B	N E	83:	50
A C	S E	82:	05
A D	S E	64:	50
A E	S E	56:	20
A F	S E	45:	26
A G	S E	41:	30
A H	S E	24:	40
A I	S E	09:	00
A K	S W	11:	00
A L	S W	16:	00
A M	S W	23:	00

Next measure the Stationary distance A P, which was found 730 Perch, which you must Note down likewise in your Book; then plant your Compass, and fix him at P, that the Chard may stand North and South on the Stationary-Line P A, then turn the Index to your first Mark K, the Index cuts N W 24 degrees; Likewise turn the sights to L, and mark the Inclination to the Meridian, and put it down N W 17 degr. and so do by all the rest of the former Marks or Points; and Note them down as you see in this Table P K: P L: P M: P I: P D: P B: P C: P E: P G: P F: P H: and where the Lines Intersect each other, drawn from the two Places A and P, there must you de∣scribe the several Places, to which you made Observation, where you may Write the Name of the Places.* 1.34

[illustration] geometrical diagrams

Book V: p.24.25.

Places	Angles	Deg.	Min.
PK	NW	24:	00
PL	NW	17:	00
PM	NW	12:	00
PI	NE	9:	00
PD	NE	21:	00
PB	NE	33:	50
PC	NE	43:	40
PE	NE	54:	10
PG	NE	64:	00
PF	NE	73:	20
PH	NE	87:	15

Lastly, If you would know the Distance of any of the Places thus described,* 1.35 one from another, you have no more to do, but open your Compasses to the two Places on the Paper; and then apply it to the same Scale, by which you laid down the stationary Dist∣ance AP, which in this Figure was laid down by a Scale of 20 Perch to an Inch: the like is to be understood of Fathoms, Yards, or Feet; and so applyed, it will without farther trouble effect your desire.

And you may Protract it by help of your Line of Chords, and Line of equal parts, as this you see is done; or by the help of your Protractor, as before directed: and if there is any other Notable Castle, or Tower, or Place, lying in a right-Line with your Ob∣servation upon any Hill, you must remember always in taking of Inaccessible Heights and Distances; as also in Plotting Unpassable Distances, by reason of Water, that you take these two stationary distances as far asunder as may be. And if at any time you require the Altitude of a Church, Castle, or Tree, standing upon a Hill, you must perform it at two Operations; first by taking the Altitude of the Church, or Castle, or Tree to∣gether as one Altitude; and secondly by taking the Altitude of the Hill alone; then by substracting the height of the Hill from the whole height, the remainder shall be the height of the Castle, or the like.

And here Note also, That in the taking of all manner of Altitudes, whether acces∣sible or inaccessible, you must always add the height of your Instrument from the Ground to the height found, the total is the true height. And thus much briefly touching this Matter.

The ART of Gaging of Vessels. CHAP. VIII. The Ʋse of the Line of Numbers, and the Lines on the Gaging Rod or Staff, and the Rules in Arithmetick in Gaging of all sorts of Vessels, (viz.) to Gage a Cube-Vessel, to Mea∣sure any Square-Vessel, and a Cylinder-Vessel; Also, Bar∣rels, Pipes, or Hogsheads; to Measure a Vessel part out, to Measure a Brewers-Tun, or a Mash-Fat, to Measure a Cone-Vessel, to Measure a Rising or Convex Crown; and also a Convex or Falling Crown in a Brewers-Copper; also a Brewers Oval Tun.

PROBL. I. The true Content of a Solid Measure being known, To find the Gage-Point of the same Measure.

THe Gage-Point of a Solid Measure is the Diameter of a Circle whose superficial Content is equal to the solid Content of the same measure; so the solid Content of a Wine-Gallon according to Win∣chester measure, being found to be 231 Cube-Inches: if you conceive a Circle to contain so many Inches, you shall find the Diameter thereof to be 17:15 by this Rule. Example. A Wine-Vessel at London is said being the 66 Inches in length, and 38 Inches in the Diameter, would contain 324 Gallons. If so, by the Line of Numbers we may divide the space be∣tween 324 and 66 into two equal parts, the middle will fall about 146, and that distance will reach from the Diameter 38 unto 17:15 the Gage-point for a Gallon of Wine or Oyl after London measure: the like reason holdeth for the like measure in all places. Thus likewise you may discover the Gage point for Ale-measure, an Ale-Gallon, as hath been of late discovered containing 282 Cubique-Inches; for as 1 is to 1:273, so is 282 to 356, 3 whose square-root is 18:95 the Gage-point for Ale-measure, because of Wast and Soil exceeding that of Wine above two Inches: or you may find it as before by the Content 256, 3 and the length 66, and the Diameter 38, as before. There are several other Rules to find it, but these may satisfy to save Prolixity, Mr. Phillips, and others, have found and proved by Example. That there is 288 ¾ Cubique Inches in an Ale-Gallon, which I believe is the Truth: But that which is received by Autho∣rity, are these sorts of measures, the Wine-measure is 231 Cubique Inches, and for Ale 282 Cubique-Inches or Beer; and for Drie things, as Corn 272 Inches. These Rules are undeceivable with Authority.

Therefore take notice you must be very careful in all your measures of all sorts of Vessels, their length, breadth, and dephth, as also of the Head and Bong; for all small Errours in them may increase too much in the Content: for the mistake of a quarter of an Inch in a large Vessel, may make you misreckon a Gallon in the Content; therefore how to be careful is best known to the Practicioner more than I can declare by many words.

PROBL. II. The Description of the Gaging-Rod, or Staff.

THe most useful Gaging-Rod is 48 Inches or 50 in length, upon one square there is 2 Lines, a Line of Numbers, and a Line of 48 Inches, every Inch divided into 10 parts for the ready measuring of any Vessels, length, breadth, or depth.

But for the measuring of Great-Vessels, there is two Staffs divided into Inches and 10 parts, made to slide.

On the second side is two Lines, the first to Gage by the Head, and the second by the Bong, which added together multiplyed in the length, will give the Contents; As by Example in the following Problem, and Use of a Table of Wine measure.

And the third square is two Diagonal Lines, for the Gage of Wine the first; and for Ale, the second: which shews the Contents to the 1/10 part of a Gallon according to 282 Cubique-Inches in a Beer or Ale-Gallon, the Use in Probl. 7.

On the fourth side is a Line of Segments, or 63 Gallons divided into 1000 parts, as you may have the Use by the following Table in Probl. 8. The making of this Staff is best known to the Instrument-Maker, by reason it must be exactly done; and you may have them of Mr. Philip Standridge in Bristol, and by Mr. Hays, and John Brown in London, Mathematical Instrument-Makers.

PROBL. III. The Description of Symbols of words for Brevity in Arithmetick.

VVHere these following Characters, are placed, you are to Work by these Rules; and that will resolve your Question.

• + Plus or Addition, which is as much as to say add.
• − Minus or Substraction, then you must substract.
• × In or Multiplication, now you are to multiply.
• /2 To Divide by 2 or any other Number under the line.
• = Equal to the thing desired.
• q Square the Number given.
• 2 − q Twice squared, when 2 stands before the Letters.
• C Cube the Numbers.
• Z Sum and Z q Square of the Sum.
• √ q To Extract the square Root.
• Z The Sums of the Squares.
• X Difference, and X. difference of the squares.
• X q Squares of the difference.
• AE The Rectangular or Plain of them, which is the Product of 2 Numbers multiplyed.

PROBL. IV. How to Measure a Cubical Vessel.

SUppose we have a Cubical Vessel to measure, whose sides let be ABCDEF, which let be every way 24 Inches, and I desire to know how many Gallons of Wine or Ale the same will hold.* 1.36

For Beer or Ale by the Line of Numbers.

Extend the Compasses always from the Gage-Point (which for Ale is 16 8/10) unto the side of the Cube 24 Inches, the same extent will reach from the same 24, turning twice over unto 49 Gallons, and better.

For Wine.

Extend the Compasses always from the Gage-Point, which for Wine is 15 2/10 unto the side of the Cube 24 Inches: the same extent will reach from the same 24, turning twice over unto 59 85/200 Gallons, which is almost 60 Gallons of Wine.

The Arithmetical way.

AB,/282 C = Gall. of Ale 49. AB,/231 C = Gallons of Wine 59 ••5/100.

PROBL. V. How to Measure any Square Vessel.

SUppose we have a Square Vessel to Measure, whose side AB let be 72 Inches, and breadth AC 32,* 1.37 and the depth CD 8 Inches.

By the Line of Numbers for Ale.

You must first find a mean proportion between the length AB 72, and the breadth AC 32, by multiplying it together, and taking the Square Root thereof, or taking the middle way between 72, and 32 on the Line of Numbers, and you will find it 48 for the mean.

Now Extending the Compasses from the Gage-point 16 8/10 to the mean Number 48 Inches, the same extent will reach from the depth CD 8 Inches, turning twice over unto 65 36/200 Gallons.

For Wine.

To find how many Wine-Gallons it is, Work by the Gage-point 15 2/20 as you did in the last Rule, and you will find near 79 8/10 Gallons; or you may find a mean proportion between the breadth AC 32, and the depth CD 8: which will be 16 Inches, and so Work according to the former Rule.

How to Work the same without the Gage-Point.

Example for all. Extend the Compasses from the Ale-Gallon 282 unto the length AB 72: the same distance will reach from the breadth AC 32 unto 8: 17/104 Gallons: for an Inch depth, so for 8 Inches you may presently find it to be 65 36/100 Gallons.

For Wine-Gallons.

Take the Numbers 231 the Gage-point, which by the former work you shall find 9 975/1009 Gallons for 1 Inch depth.

The Mathematical way.

ABX: ACX CD / 282 = Ale-Gallons 8 17/100

ABX AC XCD / 231 = Wine-Gallons 9 975/1000

The Browers Coolers are measured all one as this Vessel is.

PROBL. VI. How to Measure a Cylinder Vessel.

SUppose the Diameter of the Head AB be 24 Inches, and the length thereof AC be 30 Inches, To find the contents in Ale-Gallons.* 1.38 Extend the Compasses always from the Gage-point, which for Ale is 18 95/100 Inches unto the diameter 24 Inches; the same distance will reach from the length 30 Inches turned twice over unto 48 13/190 Gal∣lons.

For Wine.

Extend the Compasses from the Gage-point 17 15/100 unto the diameter 24; the same distance will reach from 30 turned twice to 58 7/10 Gallons.

The Arithmetical way.

For Ale. ABqXAC / 359 = Ale-Gallons (viz.) 48 13/190

For Wine. ABqXAC / 294 = Wine-Gallons, (viz.) 58 75/100

PROBL. VII. How to Measure a Globe-Vessel.

SUppose the diameter or height of the Globe be AB 24 Inches: Then to know the Contents in Ale or Wine, it is thus.* 1.39

For Ale.

Extend the Compasses from the Gage-point, which is 23 21/100 unto the diameter AB 24 Inches; the same distance will reach from the same 24 turned twice over unto 25 2/3 Gallons of Ale.

For Wine.

Extend the Compasses from the Gage-point 21 unto the diameter 24 turned twice over, as before, you shall have 31 ⅓ Gallons.

The Arithmetical way.* 1.40

For Ale AB.C / 540 = Gallons, (viz.) 25 60/100

For Wine. AB.C / 440 = Gallons, (viz.) 31 40/190

PROBL. VIII. How to Measure a Barrel, Pipe, Butt, Punching, Hogshead, or small Cask.

SUppose you have a Cask to measure, whose length is AB 27 Inches, and depth at the Bong CD 23 Inches, and breadth at the Head EF 20 Inches.

You are to find a mean-diameter between the Head and the Bong by these Rules.

Take the difference between 23 and 20, which is 3: which being multiplyed always by 7, the Product here is 21, and divided by 10, the Quotient will be 2 1/10 which added to the lesser diameter 20, you have 22 1/19 for the mean-diameter.

Another way to find the mean diameter is thus. A Vessel having 20 Inches diame∣ter at the Head, 23 Inches 〈◊〉〈◊〉 the Bong, I would know the mean-diameter: 20 and 23 makes 43, the half is 21: 50 the lesser taken out of the greater, the difference is 3, which reduced into 10 is 300; then divide by 45, the Product is 6/10 added to 21 50/100 makes 22 1/10 Inches the mean-diameter required.

Then for Ale.

Extend the Compasses from the Gage-point always 18 95/100 unto the Mean-diameter 22 1/10, the same will reach from the length 27 Inches turned twice over, to 36 7/10 Gallons.

For Wine.

Extend the Compasses always from the Gage-point 15 15/200 unto 22 1/10, the same will reach from 27 to 44 and 8/10 Gallons, as before.

The Arithmetical way.

* 1.41For Ale. CD 2 q +: EFqXAB / 1077 = Gallons (viz.) 36 55/10••.

For Wine. CD 2 q +: EFqXAB / 880 = Gallons 44 78/100.

* 1.42There is another way to Work this Vessel or Question, by the Mean-diameter which was before found to be 22 1/10 Inches; and that is after the Cylinder-Vessel, which may be resolved by the Line of Numbers, as before, and by

Arithmetick thus.

* 1.43For Ale. MDqXAB / 359 = Gallons, (viz) 36 73/100

For Wine. MDqXAB / 294 = Gallons, (viz.) 44 85/100 fere.

By the Diagonal Line on the Rod or Staff.

* 1.44Take the measure with your Rod from the Bong hole at C to the lower part of the Head at F, as the Line FC, which in the Example is near 25 4/10 Inches: so if you would know how much Ale the ••ask will hold, you shall find the Bong Hole to cut in the Diagonal Line 36 7/10 Gall.* 1.45 And for Wine it will cut 44 ¾ Gall, the Contents required.

A Table for the Gaging of Vessels.

	Head.	Bong.		Head.	Bong.
D The Diameter in Inches.	G pts.	G pts.		G pts.	G pts.
01	0,001	0.002	31	1,089	2,178
02	0,004	0.009	32	1,160	2.321
03	0,010	0.020	33	1,234	2.468
04	0,018	0 036	34	1,310	2.620
05	0,028	0.056	35	1,388	2.776
06	0,041	0.081	36	1,469	2.938
07	0,056	0.111	37	1,551	3.102
08	0,072	0.145	38	1,636	3.272
09	0,092	0.183	39	1,724	3.448
10	0,113	0.226	40	1,813	3.625
11	0,137	0.274	41	1,904	3.809
12	0,163	0.326	42	2,000	4.000
13	0,192	0.383	43	2,096	4.191
14	0,222	0.444	44	2,194	4.388
15	0,255	0.510	45	2,296	4.588
16	0,290	0.580	46	2,398	4.796
••7	0,328	0.557	47	2,504	5.007
18	0,367	0.734	48	2,611	5.222
19	0,409	0.818	49	2,721	5.442
20	0,453	0.906	50	2,833	5.665
21	0,500	1.000	51	2,948	5.895
22	0,548	1.097	52	3,065	6.129
23	0,600	1.199	53	3,184	6.367
24	0,653	1.305	54	3,305	6.609
25	0,708	1.416	55	3,428	6.856
26	0,766	1.532	56	3,554	7.108
27	0,826	1.692	57	3,682	7.364
28	0,888	1.777	58	3,813	7.625
29	0,953	1.906	59	3,945	7.890
30	1,020	2.040	60	4,080	8.160

* 1.46

The Use of the two Lines upon the Rod marked Head ••nd Bong; and of this Table for Wine-measure.

The Use of this Table is the Root of the usual Making and Use of the lines on the Rod or Staff only. In the Table you have the perfect Number, but you must number upon the Staff, for 10 account 100, and every small Di∣vision is 10; and you must estimate the parts of these small Divisions: then is the Work all one as with this Table, (viz.)

You must measure the Diameter first at the Head, and find the Num∣ber in the Table, or Staff belonging to it; then measure the Diameter at the Bong, and likewise in the Table, or on the Staff, find the Number belong∣ing to that; then add those two toge∣ther, and multiply the Sum thereof by the Inches of the Vessels length, mea∣sured from Head to Head in the In∣side.

The Table and Staff shews for 20 Inches at the Head.	0,453
For 20 Inches at the Bong.	1,199
These 2 added together, make	1652
	27
Which being Multiplyed by	11564
27, the length,	3304
Makes	44604

According to this Operation, it should be 44 Gallons 604/1000 parts, which difference is of no Moment in these Conclusions.

The Table of Segments.

Gals	Parts.	Gal.	Parts.	Gal.	Parts.
63	10000	42	6288	21	3712
½	9705		6223	½	3647
62	9530	41	6158	20	3582
½	9390		6094	½	3517
61	9280	40	6040	19	3452
½	9170		5976	½	3387
60	9065	39	5913	18	3321
½	8962		5850	½	3255
59	8862	38	5787	17	3189
½	8765		5724	½	3123
58	8661	37	5662	16	3056
½	8580		5600	½	2986
57	8491	36	5535	15	2918
½	8404		5476	½	2847
56	8319	35	5415	14	2775
½	8236		5354	½	2703
55	81••4	34	5294	13	2630
½	8072		5234	½	2556
54	7990	33	5174	12	2481
½	7909		5115	½	2405
53	7829	32	5057	11	2328
½	7758		5000	½	2250
52	7672	31	4943	10	2171
½	7595		4885	½	2091
51	7519	30	4826	9	2010
½	7444		4766	50	1928
50	7370	29	4706	8	1846
½	7297		4646	50	1764
40	7225	28	4585	7	1681
½	7153		4542	50	1509
48	7082	27	4462	6	1420
½	7012		4400	50	1329
47	6944	26	4338	5	1235
½	6877		4276	50	1138
46	6811	25	4213	4	1038
½	6679		4150	50	1935
45	6679	24	4087	3	1035
½	6613		4024	50	830
44	6548	23	3960	2	720
½	6483		3906	50	602
43	6418	22	3842	1	470
½	6353		3777	50	295

PROBL. VIII. By the Line of Segments on the Rod or Staff, and also by a Table, How to find the Quantity of Liquor in a Cask that is part full.

SUppose you would know the Quantity of Liquor in a Cask whose depth at the Bong is 23 Inches, as before, and let the Liquor be in height 16 Inches, and the whole Cask to hold 44 85/190 Gallons.* 1.47

By the Line of Numbers on the Staff, the proportion will be, as the whole depth 23 Inch∣es is to the depth in Liquor 16 Inches, so is 1000 to 692 parts.

Which being sought for in the Segment-line on the Staff, you shall have in the Line by it 46 15/1••0 Gallons.

Now if you extend the Compasses from 63 to 46 75/100 Gallons; the same distance will reach once from 44 85/100, the Contents of the whole Cask to 33 6/10, that is, 33 6/10 Gall. of Wine in the Cask.* 1.48

Then by this Rule always as 63 Gallons is to 46 75/100 Gallons, so is 44 85/100 Gallons to 33 60/100 Gallons of Wine in the Cask.* 1.49

By the same Rule Work for Beer or Ale.

To Work this Arithmetically is somewhat tedious; wherefore I have here Calculated a Table whereby you may perform it very easy by help of the Rule of Three.

Example.* 1.50

In the last Vessel whose depth at the Bong is 23 Inches, and depth in Liquor 16 Inches

The first Rule of Proportion.

As 23 is to 16, so is 10000 to 69 21 parts, which sought for in the nearest Number in the table of Segments you shall have against it 46 75/100 Gallons nearest.

Then again.

As the whole Radius 63 Gallons is to 46 75/100, so is the Gage of your Vessel 44 85/100 Gallons to 33 54/100 Gallons near, as before.* 1.51

After this manner of Working you shall have for 7 Inches depth of Liquor 11 22/120 gallons.

And so by these Rules you may work for any other Cask.

PROBL. IX. How to Measure a Brewers Tun, or a Mash-Fat.

LEt the Tun be ACDE, whose Diameter in the bottom let be ED 98 Inches, and the Diameter at the top AC let be 90 Inches, add both the Diameters toge∣ther, you have 188 Inches; then take the half thereof, and it is 94 Inches, this is the Mean-diameter FG; then get the height of the Tun, which let be AB 40 Inches. Now to know how many Barrels of Ale or Beer it will hold according to 36 Gallons to the Barrel, you shall Work thus.

By the Line of Numbers.

Extend the Compasses always from 113 7/10, which is the Gage-point for a Barrel unto the Mean-diameter 94, the same distance will reach from the height 40 Inches turned twice over unto 27 ½ of a Barrel.

The Arithmetical way by the Mean-diameter.

FGqXAB / 359 = Gallons 984 5/10.

Which being divided by 36, you have 27 Barrels 121 ½ Gallons.

Or thus for Barrels.

FGqXAB / 12924 = Barrels 27 35/••90••, near as before.

This Arithmetical way by the Mean-diameter is not absolute true, yet near enough for Brewers Tuns, by reason there is difference of Diameters between the bottom and the top; yet it is seldom above 7 or 8 Inches: But to have an Exact way which also serveth for Coopers or any, take this way for Working this Tun for an Example.

The truest Arithmetical way.

EDq + AC q ; + EDX. ACZ, XAB / 1077 = 985 Gall. 115/1990

Divide 985 1/10 Gallons by 36 Gallons in a Barrel, and the Quotient 27 Barrels, and 13 Gallons remains: so the one will hold 27 Barrels 13 Gallons 115/1000 parts.

Or thus for Barrels.

EDq + AC q, + EDXAC. ZXAB / 38772 = 27 Barrels 378/1000.

PROBL. X. How to Measure a Cone-Vessel, such as is a Spire of a Steeple, or the like, by having the Height and the Diameter at the Base.

SUppose the Diameter at the Base AB be 98 Inches, and the height DC 490 Inches.

Then by the Line of Numbers for Barrels of Ale or Beer.

Extend the Compasses from the Gage-point 169 9/10 unto the Diameter AB 98, the same will reach from the height of the Cone DC 490,* 1.52 turned twice over unto 121 4/10 Barrels ferè.

This is the best Proportion to Work for great Cones to have it in Barrels, but small Cones have it in Gallons.

Then thus Work.

Extend the Compasses from the Gage-point 32 82/100 unto the Diameter of the Base 98, the same will reach from the height of the Cone 490 twice turned unto 4369 547/1009 Gall.

The Arithmetical way. For Gallons.

ABq × DC / 1077 = 4369 547/1000 Gallons.

Which being divided by 36, you have 121 34/100 Barrels.

Or thus for Barrels.

ABq, XDC / 38772 = 121 347/1000 Barrels.

An Example.

The Brewers Tun before measured may be measured, after this manner by Cones, by this Example in this Figure I have proportioned the same Tun in this Cone, as you may prove thus by, the Rule of Proportion to find the Diameter on the top EF 90, it was before.

Work thus.

As CD 490 is to AB 98, so is CG 450 to EF 90 Inches; and so back again, to find the height of the greater Cone, say, as the difference of the Diameters 8 Inches is to the height of the Tun 40 Inches: so is the Diameter of the bottom AB 98 Inches to the greater height DC 490 Inches, from whence substract 40, there remains the height of the lesser Cone GC 450 Inches.

Now Working as before, for the Contents of each Cone.

The greater Cone will be found to be	4369 Gall.	547 Parts.
And the lesser Cone to contain	3384 Gall.	432 Parts.
Which substracted from the greater Cone, there remains 985 Gallons 115/1000 Parts.	985 Gallons	115/1000

For the Brewers Tun, as before found in the 9 PROBL. which is 27 Barrels 13 Gallons. 1/10

PROBL. XI. How to Measure a Segment or portion of a Globe or Sphere, which serves for a Convex Signet or Rising, or Falling Crown in a Brewers Copper.

ADmit you have the Diameter of the Crown AB 80 Inches, and the height there∣of CD 6 Inches.

A Convex Rising Crown.

* 1.53The Falling Crown is nothing but this Figure, the upper part turned down.

Note that a Crown is seldom less then 2 Inches, nor above 12 Inches; for in Bristol in all their Crowns belonging to the Brewers Coppers, the least that was found, was 1 6/1•• Inch, and the greatest height or depth 11 2/10 Inches.

By the Line of Numbers.

Extend the Compasses from the Gage-point 18 95/100 unto the Diameter AB 80, the same distance will reach from half the height CD 6, which is 3 being turned twice unto 53 Gallons ½ ferè.

The Arithmetical way for Ale or Beer-Gallons.

ABq. X ½ CD / 359 = 53 48/100 Gallons.

PROBL. XII. How to Reduce Ale-measure into Wine; And likewise to Reduce Wine-Gallons into Ale.

For Example.

THere is a Vessel that holds 60 Gallons of Ale; the Question is how many Gallons of Wine it will hold.

The Proportion of the backward Rule of 3.

As 282 Ale is to 231 Wine ∷ so 60 Ale to	73; 19/77 Wine-Gallons.
Or thus. As 94 is to 77 ∷ so is 60 Ale to

The reason is thus, 231 Ale-Gallons is 282 Wine-Gallons, or 77 Ale-Gallons is 94 Wine-Gallons.

Or, as 282 to 231, so is 116. 4 to 95. 30, and as 231:282, so is 95:30 to 116 ••/10, or extend the Compasses from the Ale-gallon 282 to the Wine-gallon 231, the same distance will reach from 60 to 73 2/10 Gallons, or from 77 to 94, or from 94 to 77.

PROBL. XIII. How to Measure a Brewers Oval Tun.

LEt the length in the bottom be AB 120 Inches, and the breadth EF 90; let the length at the top be CD 112 Inches, and the breadth 84; also the depth 40 Inches CA.

* 1.54A Brewers Oval Tun.

Now to Work this, you must find a Mean-proportion between the length in the bot∣tom 120, and the breadth 90 Inches.

The Arithmetical way.

AB × EF ♈ q = 103 − 92. That is, Multiply the two Numbers together, and of the Product thereof extract the Square Root▪ so shall you have the Mean-propor∣tional Number.

[illustration] geometrical diagrams

By this Rule you will find a Mean-proportion between the 120 at the bottom, and the breadth 90, to be 103 and 92.

And likewise for the top between 112 and 84, will be 97; then as before, you shall find the Sum to be 200 − 92; the half thereof is the Mean-diameter 100; ••6/10•• Inches; so shall you Work all one, as you did in the Round Tun.

How to get the Mean-diameter by the Line of Numbers.

Let the Numbers given be 120, and 90. Extend the Compasses from 90 to 120: Divide that in half, the same distance will reach from 90 to 103 92/100 almost 104 the Mean Number required; and so likewise between the Number 112 and 84, you will find it 97; then as before, you shall find the Sum 200:92 and ½ 100 46/100 Inches.

The Arithmetical way, as before, is thus.

M. Diam: XCA / 12924 = 31 3/36 Barrels of Ale or Beer.

And in Gall. M. Diam. XAC = 1119 219/1000 Gallons of Beer or Ale.

By the Line of Numbers for Barrels.

Extend the Compasses always from the Gage-Point 113 7/10 to the Mean-diameter 100 46/100: the same will reach from the height 40 turned twice over, to the Quantity of Barrels of Ale or Beer 31 2/10.

PROBL. XIV. How to Gage a Vessel by Oughtred's Gage-Rule.

THis is an Instrument by taking the length in Inches and 10 parts, and is as Exact as any way Instrumental extant; both the Diameters at the Head and Bong, with a Line called Oughtred's Gage-Line.

The Use is thus.

Take the Diameter at the Bong with those Divisions before said from that end where the Divisions begin to be numbred, and set that down twice: and on the Diameter of the inside the Head in this manner,* 1.55 and then add them together, as here you see the length in Inches. Suppose to be (30. 82) then say, as 1, is to 1:77, so is 30:82 to 54 55/100 of a Gallon, being a little more then ½ a Gallon, or 54 Gallons ½ the Content of a High-Country Hogshead; and so you may do by any other great or small sort of Cask.

The end of the 8 Chapter of Gaging Vessels.

CHAP. IX. Wherein is shewed both Arithmetically and Instrumentally How to Measure exactly all kind of plain Superficies, as Walls, Timber-work, Roofs of Houses, Tyling, Board, Glass, Wainscot, Pavement, and the like; as also Timber and Stone.

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.

PROBL. II. How to Measure Boards, Glass, Pavement, Wainscot, and the like.

IN the last Problem we have shewed that Boards, Glass, Pavement and Wainscot, and the like, they are commonly accounted by the Foot or Yards; Therefore to make this plain, we shall instance only upon Boards which are cut out in long squares commonly.

How to Measure them.

Take the length and breadth in Inches and Parts, Multiply one by the other, the Product will shew the Content in Inches; (that divide by 144 the Numbers of Inches in one Foot, the Quotient will tell you the Number of Feet, and the remainder is Inches.

For Example.

* 1.56Admit I have a Board that is 7 Foot long, and 18 Inches broad; Multiply 84 Inch. which is in 7 Feet by 18 Inches, the Product is 1512; which divide by 144 the Num∣ber of Inches in a Foot of flat-measure, and the Quotient shews 10 feet, and 72 remains, which is ¼ 144; therefore the Board contains 10 foot ½; but many times the Board falls out to be broader at one end, then it is at the other, add together the breadth at each end; then take the ½ for the true breadth.

And Work as before; But commonly Artificers have a Useful Line put upon their Rules for their ready Measuring of Board and Timber-measure; but this is the Exactest way, though that is near; and what have been said of Board-measure, only the same is to be understood is the way of Measuring not only Boards and Glass; but likewise all manner of Wainscot, Pavement, Floors, and such like; they depend upon one and the same Geometrical Ground, though they be reckoned by different measures, as you see by the Perch, Rod, Square, Yard or foot according to the Custom of the Place, there∣fore needs no further Example.

Extend the Compasses always from 12 Inches unto the breadth 18 Inches, the same extent will reach from the length 7 foot, unto the Number of Square foot in the Board, which is 10 5/10 foot.

AB 18 Inch × AD 7 foot/ = 10 4/10 feet.

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.

* 1.57For 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,* 1.58 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/••••.

PROBL. IV. How to find how many Inches in length will make one Foot of Timber, be∣ing alike in the Squares.

SUppose you have a Piece of Timber that is four-square 16 inches every way, and you would know how many inches in length will make one foot of Timber.

By the Line of Numbers.

Extend the Compasses always from 12 inches to the side of the Square, which in this Question is 16 inches, the same turned twice over from 12 inches, will reach to 6 ¾ inch. in length for one foot of Timber.

The Arithmetical way.

1728/AC16q = Cf 6 192/256 or 6 75/100 Inches as before.

Having the side of a Square piece of Timber, at the end and the length in feet, to find how many feet is contained therein.

Admit the side of the Square at the end be AC 16 Inches, and the length thereof 14 foot, Then

By the Line of Numbers.

Extend the Compasses always from 12 Inches unto the side of the Square AC 16 inches; the same distance will reach from the length 14 foot turned twice over unto 24 •• ••/•• feet in the Piece of Timber.

The Arithmetical way.

AC 16 q × BD 14 foot./144 = The Content in Feet 24 12••/1••

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.

PROBL. VI. How to Measure a Pyramedal piece of Timber.

This piece of timber is measured by this Rule,* 1.59 (viz.)

ADmit you have a piece of timber to measure, whose length at the Base is 25 inches AB, and breadth AC 16 inches: and the length of the piece DE 15 foot.

[illustration] geometrical diagram

By the Line of Numbers.

First, by the Line of Numbers find a Mean-proportion between 25 and 16 by di∣viding it into 2 parts, and the middle will fall upon 20 inches, the Mean-proportion required.

Then extend the Compasses always from 20 78/100 unto the Mean-diameter 20 Inch. the same distance will reach from the length 15 foot turned twice over unto 13 88/100 foot of timber.

The Arithmetical way.

AB × AC × DE / 432 = 13 foot 888/1000 parts of timber in the Piece.

AB × ACX ⅓ DE / 144 = 13 foot 888/1000 parts, that is 13 foot and above three quarters.

PROBL. VII. How to Measure a Conical piece of Timber.

ADmit you had a Cone Piece of timber whose Base or Diameter at the End AB is 28 inches, and the length thereof CD 15 foot, it is required to know how many feet of timber is in the Piece.

* 1.60

[illustration] geometrical diagram

Extend the Compasses always from 23 43/100 unto the Diameter AB 28, the same distance will reach from the length 15 foot turned twice over unto 21 4/19.

The Arithmetical way.

ABq × CD / 550 = 21 38/100 foot of timber in the Cone Piece.

And by the former Rule you may Measure any part of a Cone or Pyramide-piece. Admit you were to cut a Piece of 5 foot at the greater End, and you find the Diameter EF 18:95 Inch. First, Mean-diameter 18:95 and 28 Inch. added is 46; 95 the half is 23:48 the Mean: then extend the Compasses from 13 54/100 unto the Mean-dia∣meter 23 48/100; the same distance twice repeated from the length 5 foot, will reach to 15 ••7/10 foot in the ⅓ of the Cone at the great End; And likewise to Measure EFHG the Diameter HG is 9. 45 added to 18 95 EF, the Sum is 28:4.

The ½ is 14; 20 Inches the Mean-proportion the length 5 foot; by the former Rule you will find in that Piece of timber 5 50/100 foot; and to Measure the little Cone GH 9 45/100 inches diameter and 5 foot long; Work as to Measure the whole Cone, and you will find it 81/1••0 parts of a foot.

foot.	parts.
15	07
5	50
0	81
21	38

And so you have truly Measured the Pieces, as you may find by adding them up, and they make 21 foot 38/199 parts, as you found in the whole Cone at first; and so by finding the Area of the Circle and •• part, you may find the Segment of any Cone or Pyramide that is Square in the sides by the Area thereof; by the same Rules you Measure Stone. It is needless to make more Examples in this thing.

CHAP. X. For the Burden of a Ship, or her Tunnage, Take these Rules following.

SECT. I.

SUppose you were to Gage a Ship that the length of her Keel is 45 foot, the breadth of the Beam 17 foot, the depth of her Hould 9 foot always to find the Tunnage.

Multiply the breadth by the length, and with the Product Multiply the depth in Hold, and divide by 100, and the Quotient will shew you the Tun∣nage to be in this Example 68 85/100 tun.

Or extend the Compasses always from 100 to 17 the breadth, the same distance will reach from 45 the length, to 7 65/100.

Then extend the Compasses from 1 unto 7 65/100, and the same distance will reach from the depth in Hold 9 foot to the tunnage 68 85/100 tun of King's tunnage.

But for Merchants Ships who give no allowance for Ordnance, Masts, Sails, Cables, and Anchors, which is all a Burden, and no tunnage

You must siork thus for the tunnage.

SECT. II.

45 × 17 × 9/95 = 72 45/100 Tun Burden.

Or, extend from the Gage-point 95 always to the length of the Keel 45, the same will reach from the breadth 17 of the Beam to a 4 Number, as to 8 1/1••; then extend from 1 to 8 1/10 the same distance will reach from the depth in Hold 9 foot to the Burden 72 45/100 tun.

SECT. III. Having the Proportion of any one Ship in Burden, with the length of her Keel-Timbers; To Build another of any Burden according to that.

PROPORTION.

ADmit I have a Ship of 80 Tun, the length of her Keel is 46 foot. Now I am to Build a Ship whose Keel must be 65 foot; I desire to know how many Tun she must be.

Extend the Compasses from 46 foot unto 65 foot, the same extent will reach from the Burden 80 Tun, being turned 3 times over unto 225 7/19 tuns.

The Arithmetical way.

80 X:65/46 C = 225:71/100 tuns.

SECT. IV.

ADmit you had a Ship of 226 tuns, and the length of her Keel is 65 foot; Now I would Build a Ship of twice the Burden, that is 452 tuns; Now I would desire to know the length of her Keel.

Extend the Compasses from 226 unto 452, the ⅓ of that distance will reach from the length of her Keel 65 foot unto the length of the greater Ship's Keel 81 9/19 foot ferè.

The Arithmetical way.

65. C. × 452/226 = 81 3/1••0 foot ferè.

I could have insisted upon more Examples, but it is to no purpose; by reason the Carpenters have these Rules in Practice most of them; and for Gaging and Measuring Ships, the breadth and sharpness of her bottom is to be considered; and to abate some∣thing of 95 the Divizer, or add something to it according to Judgement and Reason; and so likewise to 100, to find the tunnage.

CHAP. XI. The Application of the Line of Numbers in Common Affairs, as in Reduction of Weight and Measure of Cheese, Butter, and the like.

I Have added this Chapter, not for that I think it absolutely necessary; but only because I would have the absolute applicableness of the Rule to any thing be hinted at, that it may be known; that any thing may be measured by Rule, as well as by Weight, so far as there is Proportion considering that, and any thing else; the Application of which I leave to the Industrious Practitioner, only here I give a hint.

What have been said of other things in Reduction, is general in any other, as from 12 to 10 either Shillings or Inches to tenths, as of a Shilling, or tenths of a Foot, or Pence or Farthings, Ounces or Chauldrons, Hundreds, either weight or tale. The Rule is thus, (viz.) In either one shilling, or foot, hundred, or the like. If 100 is 12 d. what shall 66 be? facit 8 pence or 8 Inches; that is, Extend the Compasses from 100 to 12, the same will reach from 66 to 8; and so of all other.

If 100 be 112 P. what shall 50 be? facit 66 Pound; If 100 be 8 Pints, what shall 25 be? facit 2 Pints; If 100 be 48 farthings, what shall 30 be? facit 14.4, that is 3 d. 2 f. ½ near.

If 100 be 36 bushels, what shall 24 be? facit 8 bushels ½ and better.

If 100 be 60 min. what shall 50 be? facit 30 min. or ½ an hour.

If 100 be 120, what shall 80 be? facit 96. The like is for any Line of Reduction. Now if you would know how many there must be in any greater Number then one; then say, By the Line of Numbers thus: If 48 farthings be one shilling, how many shillings is 144 farthings? facit 3 shillings. For the extent from 48 to 1, will reach from 144 to 3; And again, if a Mark and a half be one Pound, how many Pound is 12 Mark? the extent from 1:50 to 1 shall reach from 12 to 8; which reason must help you to call it 8 Pound. Again, if 3 Nobles be one Pound, what is 312 Nobles? facit 104 l. the extent from 3 N. to 1 P. will reach from 312 to 104: Further, if a Chauldron of Coles cost 36 shill. what shall ½ a Chal. cost.? facit 18. But more to the matter; If 36 bushels cost 30 s. what shall 5 bush. cost? facit 4 s. 2 d. If one week be 7 days, how many days in 39 weeks? as 1 to 7, so 39 to 273 days in 39 weeks; As 8 furlongs make 1 mile, how much is 60 furlongs? facit 7 ½ miles, for the extent from 1 to 8, gives from 60 to 7:50, and the like of all other.

CHAP. XII. The most Excellent Gunners Scale, Which resolves the Chief Principles of the whole Art of Gunnery, in a very brief and Compendious form, never by any set forth in the like nature before; with divers Excellent Conclusions both Arithmetical, and Geometrical, and Instrumental; and by Tables being framed both with, and without the help of Arithmetick. As also divers Artificial Fire-Works, both for Recreation, and for Sea and Land-Service.

SECT. I. The Qualifications every Gunner ought to have, and the Properties, Duty, and Office of a Gunner.

HE ought to have skill in Arithmetick, to work any Conclusion by the single and double Rule of 3, to abstract both the Square and Cube Roots, and to be perfect in the Art of Decimal Arithmetick, and to be skilful in Geometry; to the end he may be able through his knowledge in these Arts, to measure heights, depthts, breadths and lengths; and to draw the Plot of any Piece of Ground, to make Artificial Fire-Works which are used in the time of War: A Gunner that hath a Charge ought to have in readiness all necessary things for his Artillery:

As Wheels, Axle-trees, Ladles, Rammers, Sheep-skins to make Spunges, Gun-powder, Shot, Tampions, Chain-Shot, Cross-bar-shot, Canvas, or Strong Paper to make Car∣tredges, Fire-works, Artificial Torches, Dark Lanthorns; again, to Mount and Dis∣mount Guns, Hand-spikes, Coyns, Budge-Barrels to carry Powder, and Baskets to carry Shot to your Piece. When leisure will permit, he is to choose good Match-cords, to Arm his Linstocks in readiness to light, for to give Fire, and also a pair of Caleper Com∣passes to measure the Diameters of Shot, or the Muzzle, or Base-ring, or the like; and also a small Brass pair of Scales and Weights, a Ruler divided into Inches, and 8 Parts in every Inch, for the ready measuring of Cartredges, how to fill them.

A Gunner should never be without such a Scale as this as I have here described, and to know the Use thereof perfectly; and thereby be ready to give a reasonable answer to any Man of any Question belonging to any sort of Ordnance used in England in a moment, as this Scale will do, as shall be shewn: He should always carry a pair of Compasses with him to measure the Diameter or Bore of any Piece; and also the length of the Cylinder within, the better to fit her with a Shot, and proportion a Charge.

A Gunner ought to know the Names, Length, Weight and Fortification of every Piece about the Chamber (that is as far as the Piece is Laden with Powder;) and be able to tell readily how much Powder is a due Charge for any Piece, what Shot is fit, how many Matrosses must attend the same, how many Horses or Oxen will draw the said Piece, or Men, if occasion be; He must be careful in making Choice of a sober honest Man, for the Yeoman of the Powder; and he must not beat up the Head of his Powder-Barrels with an Iron tool, but with a Wooden Mallet, which can never Fire the same: A Gunner ought to trie his Piece, to know whether it be true bored or not, to proportion his Charge according to the thinnest side of the Metal, and accordingly take his Obser∣vation at the Britch of the Piece, just over, where by his Art he finds the middle of the Bore within the Piece is; by which means a good Shot may be made out of a bad Piece.

Before he makes a Shot, he is to consider, that if the Piece lie point blank, or under Metal, he ought to put in a sufficient Wadd after the Shot, to keep it close to the Powder; for if it should not be close, but some distance between the Powder and Shot, the Piece will break in the vacant place; but in case you mount your Piece, put no Wadd after the Shot.

And one chief thing is to know very well how to Disport his Piece, be it either true bored, or not true bored, which he may try first.

When a fit Man is entertained, the Mr. Gunner (whom he serves,) should bring him to his Pieces, and give him the Denominations of his Piece, and parts thereof; which when he hath learned, which is the base-ring, and trunnion-ring, the mussel-ring, and the like, (you may see their names all plain in the Fig. of the Gun without more words;) and like∣wise the Crows, Handspikes, the Coyn, and the like; and how far in the Bore is called the Chamber of the Piece: These things, with the Gunner's care well understood, he may give them further Directions, (viz.) But it is great pity, that the Gunners at Sea did not exercise the Sea-men in this knowledge, as the Corporal doth in Mustering of them with their Musquets; for want of the like knowledge, the greatest part of common Sea-men, are as dull and ignorant, when they be required to stand by a great Gun in time of Fight; and therefore it would be much for the Credit and Honour of our En∣glish Nation, to train up their Sea-men in this knowledge especially; but it is taken no∣tice of, that if any man have any Art above another, he is afraid to let another see him do any thing, or understand from him such knowledge, for fear he will be in a short time as able as himself; which many do attain unto in a short time to be as able as himself with∣out their help; therefore it is more for their Credit to teach them what they know.

SECT. II. Who were the Inventors of Gun-powder, and some Principles of Philoso∣phy fit to be known.

SOme Italians have writ that Archimides the Philosopher was the first Inventor of Guns and Gun-powder: or whether this be truth or not, Learned Men are of divers minds; Munster, and Gilbert Cognot have written, that Guns were devised first in the year 1370 by a Monk, whom Munster calls Bertholdus; sithen our Country man Dr. Dee in his Mathematical Preface, and Discourse of Menader saith, that an English-man was first Inventor of Gun-powder in another Country, and they first made use of it from him; also our English Chronicles do report, that in the year 1380 a Monk did accidentally let fall a spark of Fire upon Brimstone and Saltpeter beaten to Powder in a Morter cove∣red with a Slat-stone, he seeing this mixture blow off the Stone from the Morter, did thereupon devise a kind of Powder, and taught the Venetians how to use the same in Pipes of Iron against the Ganvates.

Every Simple Body is either Bright and Light, or else Gross and Dark, and Ponde∣rous, and according to the variety and difference, it is always naturally carryed towards some one or other part; the World hath height as upwards, or depth as downwards; and the depth dependeth upon the Influence of the height.

All pure and rare bodies ascend, as the Fire more than the Air; but the thick and gross bodies descend, as the Earth more than the Water.

Nothing worketh naturally, but in that which is contrary to it, and more feeble; the form working, is aided by the Qualities; and the matter suffering, which suf∣fereth by the Quantity.

Nature is extremely curious, as well of her perfection, as her conservation; and then when all things conspire, as well the Action that cometh from the Agent, as the Passion from the Patient, hath proportion.

Accident hath its variety from the Subject, and goeth not from one thing unto ano∣ther.

Every Corporal thing reposeth in its natural place: Motion may be made any where within the Orb of the Moon. Nature admitteth no Empress.

A body rarifying it self, the place thereof increaseth as the body increaseth, the resistance of the moved proportion to the Mover, furthereth the motion; the longer the Chace of a Piece, the louder the Report; also the force of the stroke dependeth on the swiftness of the Course.

SECT. III. The Description and Use of the Gunners Scale, upon which is all sorts of Ordnance, from the Canon, to the Base of their Weight, Lading, Shot, and all other things appertaining to them.

THis Scale is made according to the Diameter of our English Ordnance, but 8 inch. long, the Diameter of a Canon-Royal; and it may be made of Silver, Brass, or Box, or any other f••••e grained Wood, that will not warp. Upon one side I have set the Names of all sorts of Ordnance, and in the Angle of meeting with the Names, is the diameter of the bore; and betwixt that and the next less diameter, is first the com∣mon length of such Pieces; and upon the step of breadth, is how many Paces these Pieces shoot point blank, and right in the Angle of meeting, betwixt the two diame∣ters with the Angle of meeting with the Names, is first the weight of the Gun, the breadth of the Ladle; and thirdly, the length; fourthly, the weight of the Charge in Powder; fifthly, the diameter of the Shot; sixthly, the weight of the Shot; seventhly, a Line of Inches; eighthly, each Inch divided into 10 parts, and likewise into 8 parts, which are parts and half quarters, which the Line of Diameters of the bore comes from. The degrees in the divisions, and on the thickness and length thereof, there is a Line of Numbers, by which you work all the most useful Questions in Gunnery, as you will find in the following page.

The Use of this side is thus.

Suppose you come to a Piece of Ordnance, and it is desired to know what Piece it is; take the Scale, and put it into the bore of the Piece, mark the step of a Diameter that fits it, and the Angle of Diameter goes down into the Line of Inches, and parts, and that diameter goes into the side in the Angle of meeting, and tells you the Name of the Piece: Betwixt the next less Diameter, right under, you have as before, the common weight of the Piece, the breadth and length of the Ladle, weight of Powder, diameter of Shot, and weight.

As for Example.

Admit I came to a Gun, and found by the former directions, that her diameter of the bore is 4 ¼ Inches. And in the Angle of meeting in the side, I find her Name is Demi∣culvering, lower then ordinary; at the end thereof I find 9 or 10 foot the usual length, and betwixt the next less diameter and the step is 174 the paces the Piece carries the Bullet in a level-line, point blank, right against weight in the next less Diameter, which is 4 Inches, is the usual weight 2000 l. breadth of the Ladle 8, and length 12 Inches, the weight of the Powder 6 ¼ or 4 ounces; and next the diameter of the Shot 4 Inches; and next, the weight 9 l. So that you see the next less diameter is the diameter of the Shot, as well as of a less Piece of Ordnance. This I have made plain to the meanest ca∣pacity: Here they are set down in this Table following.

The Explanation of the Scale may serve likewise for the Table; only take notice, that under Inches and Parts, is to be understood the first; to the left hand is Inches, and the other is so, many 8 parts of an Inch.

As for Example.

Admit you enter the Table with a Saker of the lowest sort, the height of the bore is 3 4/8 Inches, 8 foot long, the weight 1400, breadth of the Ladle 6 4/8, length 9 6/8 Inch. weight of the Powder 3 pound 6 ounces, diameter of the Shot 3 2/8, weight of the Shot 4 pound 12 ounces, and the paces the Piece carries, by Alex. Bianco's Tables is 150 of 5 foot to the Piece.

Observe that the Ladle is but 3 diameters of the Shot in length, and 3/5 parts of the Circumference from the Canon, to the whole Culvering, I allow the Charge of Pow∣der to be about two diameters of the Piece: from the Culvering to the Minion; the Charge to fill two diameters and a half; all from the Minion to the Base three dia∣meters of Powder.

The names of the Pieces of Ordnance.	Diameter of the Bore.	Length of the Gun.	Weight of the Gun in pounds.	Breadth of the Ladle.	Length of the Ladle.	Weight of the Powder.	Diameter of the Shot.	The weight of the Shot.	He shoots point blank.
The	Inches. Parts.	Feet. Inches.	Pounds	Inches. Parts.	Inches. Parts.	Pounds. Ounces.	Inches. Parts.	Pounds. Ounces.	Paces.
	⌊8	⌊8		⌊8	⌊8		⌊8
A Base.	1:2	4:6	200	2:0	4:0	0:8	1:1	0:5	60
A Rabanet.	1:4	5:6	300	2:4	4:1	0:12	1:3	0:8	70
Fauconets.	2:2	6:0	400	4:0	7:4	1:4	2:2	1:5	90
Faucons.	2:6	7:0	750	4:4	8:2	2:4	2:5	2:8	130
Ordinary Minion.	3:0	7:0	750/800	5:0	8:4	2:8	2:7	3:4	120
Minion of the largest size.	3:2	8:0	1000	5:0	9:0	3:4	3:0	3:12	125
Saker the lowest sort.	3:4	8:0	1400	6:4	9:6	3:6	3:2	4:12	150
Ordinary Sakers.	3:6	9/9:0	1500	6:6	10:4	4:0	3:4	6:0	160
Sakers of the oldest sort.	4:0	10:0	1800	7:2	11:0	5:0	3:6	7:5	163
Lowest Demiculvering.	4:2	10:0	2000	8:0	12:0	6:4	4:0	9:0	174
Ordinary Demiculvering.	4:4	10/10:0	2700	8:0	12:6	7:4	4:2	10:11	175
Elder sort of Demiculvering.	4:6	12/13:0	3000	8:4	13:4	8:8	4:4	12:11	178
Culverings of the best size.	5:0	12/10:0	4000	9:0	14:2	10:0	4:6	15:0	180
Ordinary Culvering.	5:2	12/13:	4500	9:4	16:0	11:6	5:0	17:5	181
Culvering of the largest size.	5:4	12/10:0	4800	10:0	16:0	11:8	5:2	20:0	183
Lowest Demicanon.	6:2	11:0	5400	11:4	20:0	14:0	6:0	30:0	156
Ordinary Demicanon.	6:4	12:0	5600	12:0	22:0	17:8	6:⅙	32:0	162
Demicanon of great size.	6:6	12:0	6000	12:0	22:6	18:0	6:5	36:0	180
Canon Royal, or of	8:0	12:	8000	14:6	24:0	32:8	7:4	58:0	185

The Description of the other side of my Gunner's Scale.

Upon the other side is a Scale of 8 Inches divided into four quarters, and betwixt each quarter above it is three Columns; the Inches shews the height of all sorts of Iron shots from 2 ounces to 72 pound; and of Lead from 3 ounces to 806 pound ½, and of Stone from 1 ounce to 26 12/16 pounds; each distinguished from other by their names, written in the first Inch, the Table is in the sixth Section, and the weights and measures, accommodated into our English Averdupoiz weight of 16 ounces to the pound, and to our Foot of Assize of 12 Inches to the Foot. The Line of Inches being likewise di∣vided into 10 parts, the whole into 80, may serve for 800; for Protraction as follows: There is also the Gunners Quadrant divided into 90 degr. in the outmost Limb, and in the second Limb within, is divided into the 12 points of the Gunner's Quadrant, and

[illustration] geometrical diagram with representation of a cannon

each point 4 parts; and in the third Limb is a Geometrical division of right and contrary shadows, for the ready taking of heights and distances; but there is also a Geometrical Quadrate, with each side divided into 10 parts, which stands for 100, and each 10 parts divided into 10 more, the Use thereof in taking of heights and distances is in the 16 Chap. of the Second Book of the Description of Instruments: But the Use for to level, or else to mount or Imbase any piece of Ordnance, is in the 34 Sect. of this Book. To the side thereof is fitted a piece of Brass of the same breadth as the Scale in thick∣ness, with two holes within an Inch of each End, and two Screws fitted to serve the four holes, as you may see in the Figure to the side of the Scale, that if you would level or mount any piece of Ordnance, Screw the plate to the end of the side B, with both Screws, and put the plate in the bottom of the metal as far as he will go, and put the tomping in upon him to keep the plate fast, and then level or mount your Piece, as in 33 Section directed.

But if you will Imbase any piece of Ordnance to any place or point assigned, you must screw the plate to the end A, and let the side with the Line of Numbers be next the muzzle, and stop him with the tomping, as before; then Imbase your Piece, or put him under the Line of Level as you will, to what degree you please; and when you have done, screw the plate to the side A B, with a screw at one end, and a screw at the other, (there is also over the weight of the Shot a division of the right Ranges, and likewise a proportion of Randoms of any piece of Ordnance, upon any mounture from degree to degree; and likewise you may put the division of Inches in the 38 Section, for the number of Inches and parts from 5 foot to 14 foot long, requireth to mount her to any degree of mounture with great facility and ease. There is also Triangle-wise a plain Scale, that goes along down by the degrees of diameters, or steps, the Line is a Line of Chords, with the Gnomon-line, and a Line of six hours of the same Radius, and a Line of Rhumbs, with the Line of Sines; and this is for the making any sort of Dial in any Latitude by the following directions, and also for the Plotting any Triangle, or resolving any Question in Navigation, or Astronomy. You must remember, there is a Brass Pin in the Center at C for to hang the Plummet and String, with the Lope upon.

Thus I hope I have fitted all ingenious Gunners with a Scale so useful, that I will leave it to them to give me commendation for my labour and pains. If I might advise Gun∣ners of all sorts, that are able to have one of these Scales of Brass or Wood, to carry a∣bout him, to resolve any Question presently for his own credit, and it is very portable and fit for his Pocket; but it is best to have a case of Leather or Cloth to keep it clean; and you may carry a pair of Compasses with him, and by him you may resolve most of all the Questions in this Noble Art of Gunnery.

On the side of the Quadrant betwixt the Equinoctial, and the Radius, or Suns great∣est Declination is a division to every 10 minutes of the Suns Amplitude Rising and Set∣ting answerable to the Ecliptick Line, and the Declination on the other side the Figure, makes all plain to any Instrument-maker; without further precept.

SECT. IV. The Ʋse of the Line of Numbers on the Scale, for the help of such as cannot Extract the Cube and Square-Root.

How by knowing the weight of one Bullet, to find the weight of another Bullet, the height being given.

A Bullet of Iron of 6 Inches height, weigheth 30 l. what will the like Bullet of 7 Inches in Diameter or height weigh; always take these Rules.

Extend the Compasses from 6 Inches to 7 Inches Diameter, the same distance will reach from 30 l. weight, turned 3 times over unto 47 l. 10 ounces, the weight of a Shot 7 Inch. high.

The Arithmetical way.

C 6 C 7. AE. 30 × 343/216 = 47 l. 10 ounc. ¼

That is Cube 6 makes 216, and Cube 7 makes 343; then by the Rule of Proportion Multiply 343 by 30, the Product is 10240, divide by 216, the Quotient is 47 pound, 138/216 or 63/100, which is 10 ounces ¼ as before; there is something less then 7 Cube Inches in one pound of Iron.

By the Tables of Logarithms.

The Logarithm of 6 is	07781512
The Logarithm of 7 is	08450980
Substract the uppermost Number out of the lower, the diff. increasing.	0669468
	3
The last Number Multiply by 3, and the triple of this difference is	2008404
Added to the Logarithm of 30 l. with no ounces, (which is 3000)	34771212
Gives the Logarithm of the weight 47 64/100	36779616

Now to know how many ounces 64/199 is, work thus by the Rule of Proportion.

If 100 gives 64, what will 16 ounces give? Answer, 10 ounces 24/100; so the Shot of 7 Inches diameter weighs 47 l. 10 ounces 24/100 or 47 64/100 pound, the like way of work is with all such Questions.

SECT. V. Admit the weight of an Iron Bullet being 30 pound, the Diameter was 6 Inches, the weight being 47 64/100 what may the Diameter be?

* 1.61FIrst I will shew you how to turn 10 ounces and 24/100 into 100 parts of a pound; always say, If 16 give 100, what shall 10 give 24/100 (64 as you may see the work in the Mar∣gent, where the weight is known, and the Diameter required.

Always Divide the weight 30 l. and 47 l. 64/100 into 3 equal parts, and that distance will reach from 6 Inches Diameter, to 7 Inches the Diameter required on the Line of Numbers.

By the Tables the Logarithm of 30 is	34771212
The Logarithm of 47 64/100 l. is	36779616
* 1.62Uppermost Substracted from it, leaves the difference increasing,	2008404
The difference divided by 3, or the third part of this difference.	0669468
added to 6 Inch. Diameter, the Logarithm	7781512
Gives the Logarithm of 7. Inch. Diameter required	08450980

This is the most easy, ready, and certain way of Arithmetick; and so work for all such Questions, if three Numbers be given, to find a fourth in a Triplicated Propor∣tion.

SECT. VI. The Geometrical finding the Diameter for the weight of any Shot assigned.

MR. Gunter in his first Book, Section 4, hath shewed the Making of the Line of Solids on his Sector: but this Rule shews the proportion of the Diameters in weight: having a Shot of one pound 2 pounds or 3 pounds weight of the Metal or Stone assigned; if it be of a pound, divide the Diameter into 4 equal parts, and 5 such parts will make a Diam. for a Shot of the said Metal or Stone that shall weigh just two l.

And divide the Diameter of a Shot that weighs just 2 l. into 7 equal parts, and 8 such parts will make a Diam. for a Shot of 3 l. weight; And divide the Liamet. of a Shot of 3 l. weight into 10 equal parts, and 11 such parts will make a Shot for 4 l. weight.

And divide the diam. for a Shot of 4 l. weight into 13 parts, 14 such parts will make a diam. of a Shot for 5 l. weight.

And divide the diam. of a Shot of 5 l. weight into 16 equal parts, 17 such parts will make a diam. for a shot that will weigh 6 l. and so dividing each next diam. into 3 equal parts more then the next lesser was Divided into, and it will with one part added from a diamet. of a shot that will weigh just 1 l. more; and so you may proceed infinitely, in∣creasing or decreasing, by taking one part less, as is appointed to be Divided, for one l. less, and the next into 8 l. less, to abate 1 for the Remainder, infinitely decreasing it.

[illustration] geometrical diagram

A second Geometrical way.

First you must have exactly the diamet. of a shot that weigheth one pound, and then describe a Circle, whose diamet. shall be just equal thereunto; and Divide it into 4 Qua∣drants,

[illustration] geometrical diagram

with 2 diamet. cutting each other in the Centor orthogonally. Then take the Chord of the whole Quadrant 90 degr. BC in your Compasses, and lay it from the Centor of the first Shot one pound D to 2,* 1.63 and so A 2 will be the Diameter of a Shot of 2 pound; Then extend the Compasses from 2 to the Chord C, and lay that distance from D to 3, so will A 3 be the Diameter of a Shot of 3 l. And so likewise extend the Compasses from 3 to C, it will reach from D to 4, and from 4 to C, and it reaches from D to 5, and from 5 to C, lay it still always from D to 6; and so continuing till you have proceeded as far as you will: You shall find that if AB were the Diameter of one pound, A 2 is the Diameter of 2 pound, and A 3 is the Diam. of 3 l. and A 4 the Diam. of 4 l. and A 5 the Diam. of 5 l. A 6 the Diam. of 6 l. and lastly, A 8 is the Diam. of 8 l. and so you may proceed in like manner infinitely.

Likewise having the Diameter of a Shot of any weight, the double of the Diam. is the Diam. of a Shot which weighs 8 times as much. Thus the double of A 1, which is A 8, makes the Diameter of a Shot of 8 pound; and so the double of A 2, which is the Diameter of a Shot of 2 l. makes A 16, the Diameter of a Shot of 16 pounds, that is 8 times 2 pounds; and so the double of A 3 makes the Diameter of a Shot of 24 pounds, and the double of A 4 makes the Diameter of a Shot of 32 pounds, four times 8 being 32; and so you may proceed as you please, and find the bigness of any Shot.

A third way.

This you may do also, having the Diameter of a Shot of one pound, double that diam. it will make a diam. of 8 pound; and treble the diameter of one pound, will make a diameter of a Shot of 27 pound, and quadruple or 4 times the same, will make a diam. of a Shot of 64 pounds, and 5 diameters will make a Ball of 125 l. and 6 diameters of a Shot of one l. will make a diameter of a Shot that will weigh 216 l.

[illustration] geometrical diagram

Now it is convenient to shew how to find the Mean-divisions between these extremes; as for the diameter of a Shot of 2 l. 3 l. 4 l. 5 l. 6 l. 7 l. or what more you will; so as by such progression you may proceed from pound to pound, until you come to the last term of 216 pound; nevertheless the same manner of working will proceed infinitely. Lay the forementioned 6 diameters upon one and the same right Line; you must at the end of them draw another Right-line orthogonally, and set therein the diamet. of 2 such Shot given as at C, and from thence draw another Right-line parallel to the first, as GH, and then draw a Quadrant as A B, and from the Centre G draw right Lines through all the divisions of the diam. marked upon the right Line AF which are all equal, so shall you have 6 divisions to be divided; the first being divided already, and is the diam. of a Shot of 1 l. but the second division is to be in the Circumference or Quadrant divided into 7 parts equally, because it containeth the second diameter unto 8, for adding 1 to 7 it makes 8; the third division is into 19 equal parts, which being added to 8, makes 27; the fourth shall be divided into 37 equal parts; which together with 27, makes 64; the fifth shall be divided into 61 equal parts, which added to 64, makes 125; and lastly, the sixth place must be divided into 91 equal parts, unto which adding 125, you shall make a diameter of a Shot of 216 pound justly.

Now forasmuch as these divisions are difficult to make well, within so small a Qua∣drant: you may therefore describe a greater, as the Quadrant LM, and there the di∣visions are more distinct, and larger than in the lesser they can be; Further, you may note, that Fire-balls, Granadoes, and other Globous Artifices, must have the same pro∣portion to their Grandures from their Ball of one pound, which may be exactly consi∣dered; and so by this Method you may make Balls of Lead, Brass, Stone, and Granadoes, Fire-balls, and all other Spherical Fire-works, of what weight you will, having one of one pound first, to lead you accordingly.

SECT. VII. To find what proportion is between Bullets of Iron, Lead, and Stone, by knowing the weight of one Shot of Iron; to find the weight of any other Shot of Lead, Brass, or Stone of the like Diameter.

THe proportion between Lead and Iron, is as 2 to 3, so that a shot of 2 pound of Iron, is of like diameter or height as 3 l. of Lead.

As for Example.

A shot of 6 Inches diameter weighs 30 pound, to find the weight of a shot of Lead of the same diameter.

By the Rule of Proportion.

First, if 2 gives 30, what will 3 give? multiply and divide, and the Quotient is 45,* 1.64 the weight of a shot of Lead.

By the Tables, the Logarithm of 2 is	03010300
The Logarithm of 30 is	14771212
The Logarithm of 3 is	04771212
Add the 2 lowermost, the sum is	19542424

Substract the upper Num. the Remain is the

Log. of 45 l. the weight of the shot in Lead of the same diam.

16532124

Extend the Compasses from 2 to 30, the same distance shall reach from 3 to 45; (In like manner work by the rest following.* 1.65)

The porportion between Iron and Stone, is as 3 to 8; so that a shot of 30 pound of Stone, is as big as the like shot of 80 l. of Iron; and 11 l. ¼ of Stone, is of the same diameter 6 Inches, as a shot of 30 l. of Iron and 45 l. of Lead; the proportion between Lead and Stone, is as 4 to 1; so that one shot of Lead of 40 l. is of the height as a Stone shot of 10 l.

The proportion between Lead and Brass, is as 24 to 19,

The proportion between Iron and Brass, is as 16 to 18.

By these Rules aforegoing you may Calculate with ease, if Iron shot be wanting, and the other to be had, what height and weight either shot of Lead, Brass, or Stone, ought to be of to fit any Pieces of Ordnance; and by the same Rules here is a Table faithfully Calculated; and doth shew the weight of any shot of Lead, Iron, and Stone, from 2 Inches diam. to 8 Inches, and Quarters of Inches; the proper Stone for this purpose is Marble, Pibble, Blew hand Stone; (there may be a little difference of weight in some sort of Stone: but these do neer agree in weight; you must remember in load∣ing your Piece with a Shot of stone, you must not have so much Powder as you do with Iron-shot, but abate according to proportion, as is between Stone and Iron.

Inches.	Quart.	Iron. Poun. Ounc.	Lead. Poun. Oun.	Stone. Poun. Oun.
2		1 1	1 10 ½	0 7
2	1	1 9	2 6	0 9
2	2	2 2	3 3	0 12
2	3	2 14	4 5	1 1
3		3 12	5 10	1 7
3	1	4 12	7 2	1 13
3	2	6 0	8 15	2 4
3	3	7 5	11 .00	2 12
4		8 15	13 07	3 6
4	1	10 10 ½	16 0	4 0
4	2	12 10½	18 15	4 12
4	3	14 14	22 5	5 9
5		17 05	26 2	6 8
5	1	20 1	30 2	7 8
5	2	23 2	34 11	8 11
5	3	26 6	39 9	9 14
6		30 00	45 00	11 04
6	1	34 00	51 00	12 12
6	2	38 00	57 00	14 04
6	3	42 00	62 00	15 12
7		48 00	72 00	18 00
7	1	53 00	79 08	20 00
7	2	58 00	87 00	22 12
7	3	64 00	96 00	24 00
8		71	106 8	26 10

The use of the Table, to find the weight of any Shot of Iron, Lead, or Stone from 2 to 8 Inches Diameter.

This Table is exactly Calcu∣lated, and the use thereof is very easy; we will make it plain by two Examples; I would know of Shot of 6 Inches, their weight in Iron, Lead, and Stone: the first Column is Inches, the second Quarters of Inch. the third Poun. and Ounc. of Iron, fourth Pounds and Ounces of Lead, fifth Poun. and Ounces of Stone.

Enter the Table with 6 Inches diam. in the first Column, and in that Line you shall have 30 poun. of Iron, 45 pound of Lead, 11 pound 4 ounces of Stone, the weight of 6 Inches diam. And likewise, for 4 Inches ¾ diam. the weight of an Iron Shot is 14 pound, 14 ounc. of Lead 22 pound 5 ounces, of Stone 5 pound 9 ounces; and so of the rest.

SECT. VIII. How by knowing the weight of one Piece of Ordnance, to find the weight of another Piece being of that very shape of the same Metal, or any other Metal.

FIrst, with a pair of Crallapers take the greatest thickness of your Piece, as at the Base-Ring; and also the Piece, whose weight you know not.

Example.

Admit a Brass Saker of 1900 weight, hath his greatest thickness 11 ½ Inches; Now I find the diam. of the other Brass Piece, whose weight I know not, to be 8 ¾: then always by these Rules:

If the greatest diam. and weight is given, to find less weight, or else the contrary.

As the Logarithm greatest diameter, 11 50/100	306069
The Logarithm of the least, 8 75/100	294200
The Difference increasing.	11869
	3
× 3 or the Triple of this Difference Substract	35607
From the Logarithm of the weight given 1900	327835
Rest the Logarithm of 837, the weight required,	292228

Or extend the Compasses from 11 ½ to 8 75/100 Inches diam. the same distance will reach from the weight given 1900 pound turned 3 times over to 837 pound.

The Arithmetical way.

C 8 ¾ × 1900/C 11 ½ = 837 l. weight almost in Brass.

But if the Piece had been Iron whose weight you sought, you must always do as before with the Brass, and find the difference of their Metals by the last Problem, which is 16 to 18, then say by the Tables,

As the Logarithm of Brass, 18,	125527
is to the Logarithm of weight in Brass 835	292272
So is the Logarithm of proportion of Iron 16	120412
The Sum	412684
to the Logarithm of the weight in Iron 744	287157

Or extend the Compasses from 18 to 837, the same distance will reach from 16 to 744 l. weight in Iron.

Arithmetical way.

X 837 by 16/18 = 744 l. of Iron almost.

SECT. IX. How to make a Shot of Lead and Stone, the Stone being put in the Mould in which the Leaden Shot should afterwards be cast, to be of the like Dia∣meter and Weight as an Iron Shot is of.

Inches.	Quart.	Lead. Poun. Ou.	Stone. Poun. Oun.	Both together. Poun. Oun.
1		0 1 ⅔	0 0 ⅓	0 2
1	2	0 6¼	0 1 ¾	0 8
2		0 14	0 4	1 2
2	2	0 12	0 8	2 4
3		3 2	0 10	3 12
3	2	5 0	1 0	5 0
4		7 7	1 8	8 15
4	2	10 8	2 2	12 10
5		14 7	2 14	17 5
5	2	19 4	3 12	23 0
6		25 0	5 0	30 0
6	2	32 0	6 0	38 0
7		40 0	8 0	48 0
7	2	48 0	10 0	58 0
8		59 0	12 0	71 0

It is found by experience, that if you take 5 parts Lead, and one part Stone, it will come very near the mat∣ter, wanting not above 3 Ounces, which is nothing, respecting the diffe∣rence you shall find in Pibble Stones. Here you have a Table how much Lead, and how much Stone must be together, to make the equal of Iron Shot, from 1 Inch, and to every half in the first and second Column to 8 Inch. Diameter; the third Column is how much Lead, the fourth how much Stone, the fifth how much weight both together.

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

* 1.66So 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,* 1.67 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.

SECT. XI. How to know whether your Piece be Chamber-bored.

FIrst you may Dispert your Piece the three first ways, and when they agree in one, take that for the true Dispert; then with your Priming Iron take the Dispert this last way; which done, compare it with the other Dispert first found, and what it wants, is the just difference of the Chamber from the Bore of the Piece.

Admit the Dispert truly found by the two first ways be three Inches, as by this last way is but two Inches, it shews that the Chamber differs from the true Bore on each side one Inch; so that if the Bore of the Piece be five Inches high, the Chamber be∣ing one Inch on each side lower, is, but three Inches high: the like Observation we would always have you to make, that you may not afterwards be deceived in making Cartredges of Canvas or Paper to load the same.

SECT. XII. How to know what Diameter every Shot must be of to fit any Piece of Ord∣nance, or to choose Shot for Ordnance.

TAke the Diameter of the Bore of the Piece, and Divide into 20 equal parts, and one of those parts is sufficient vent for any Piece, the rest of the 19 parts must be the height of the Shot; but now adays most Gunners allow the Shot to be just one quarter of an Inch lower than the Bore; which Rule makes the Shot too big for a Cano••, and too little for a Faulcon; but if the mouth of the Piece be grown wider, then the rest of the Cylinder within by often shooting; to fit Shot to such a Piece, you must trie with several Rammers-heads, until you find the Diameter of the Bore in that place where the Shot useth to lie in the Piece; and a Shot of one twentieth part lower than that Piece is sufficient; therefore let Gunners remember to trie the Piece, as di∣rected.

SECT. XIII. How to find what Flaws, Cracks, and Honey-combs are in Pieces of Ordnance.

THere is one good way, as soon as you have discharged a Piece of Ordnance, cover the mouth of the Piece close, and stop the Touch-hole at the instant time; if there be any unknown Cracks or Flaws which go through the Metal, a visible Smoak will come through those Cracks and Flaws; if not, the Gun is not cracked.

There is a way to reflect the Sun-beams when he shineth, with a Looking-glass or Steel in at the hallow Cylinder of the Piece; for by this means a bright and clear light will be within, and by that light you will see every Flaw, Crack, or Honey-comb.

But this way you may see at any time; take a Stick something longer than the Piece, cleave the end of the said Stick, for to hold an end of a Candle, light the Candle, and put it into the cleft end of the Stick, and put it into the Piece; by this light observe by degrees whether from the one end to the other there be any of the foresaid Flaws, Cracks or Honey-combs in the Piece.

This is a usual way likewise, if in striking a Piece upon several places of the Metal with a Hammer of Iron, you shall at any stroak hear a hoarse sound; then without doubt there is Honey-combs: but if in so striking the Piece, you shall at every stroak hear a clear sound, then may you be sure your Piece is clear of any Honey-combs, Cracks, or Flaws.

SECT. XIV. How to find whether a Piece of Ordnance be true bored, or not.

FIrst, there must be provided a Staff, and two Rammer heads upon the Staff, and on the Rammers heads there must be two right Lines drawn upon them; that is, Divide the two Rammer heads that are the just height, and fit the bore into two equal parts opposite to each other, and draw Lines thereon; the like do by the Staff, that the Lines on the Rammer heads may stand alike, one at one end, and at the other end, as you see in the general Figure LM.

And let the Staff come through one of the Rammer heads about 9 Inches longer than the Cylinder of the Gun; then lay a flat Stick on the Muzzle-Ring, and hold the side of the Quadrant on the Scale to the Stick, and it will by the String and Plummet find the middle, or upper and lower place of the Metal; or by hanging a Plumb-Line and Quadrant before the concave, and the Stick on the top; then after you have found the Point, and upper and lower place of the Metal, put the Rammer head L into the Gun, and let one hold him hard, and right with the Line or Mark on the upper part of the Gun, and lower part with the Line on the Rammer head on the Staff above and below, whilst you put in a Priming Iron in at the Touch-hole, and strike hard the Rammer head, make a Mark; then pull him out, and apply the Line on the Ram∣mer head to the Mark on the upper and lower edge of the Muzzle of the Gun, and you may presently see how much the Mark is from the right Line of the Ram∣mer head, to the right hand, or to the left; that is, if the Mark is just on the right Line, the bore is in the midst: but if you find it a quarter of an Inch on the right or left hand, so much lyeth the bore either to the right or left; and in Shooting, the Piece must be ordred accordingly.

But now to know whether it is thicker upwards or downwards, or how the bore is; the way to know this, find the Diameter of the Piece the Touch-hole, as is already taught in 10 Chap. bend a Wire a little at the very end, that it may catch at the Metal when it is drawn out; after the Wire is fitted thus, first put it into the Touch-hole till it touch the bottom of the Metal in the Chamber; then holding it in that place, make a mark upon the Wire, just even with the said Touch-hole; afterwards draw up the same Wire, untill it catch at the Metal at the top of the Chamber; at that instant make a mark upon the Wire just even with the Touch-hole: the difference betwixt the two marks, is the just wideness of the Chamber, and the distance between the first mark, and the end of the Wire, having half the Diameter of the Chamber of the Piece Sub∣stracted from it, will leave the half of the Diameter of the Piece, if the Piece be true bored; but if this number be more then half the Diameter, then the bore lyeth too far from the Touch-hole, and the upper part of the Metal is thickest; but if less, the under part hath most Metal.

One Example will make it very plain.

Suppose that the Metal at the Britch be represented by ABCD, and the Metal at the Muzzle by efgh, and the bore of the Piece I, whose Centre is l, or the bore K, whose Centre is m: (and I find the Diam. of the Piece to be 21 Inc. at the Touch-hole, the half thereof is 10 ½ inch. Then I find by a Wire the Diam. of the bore to be 5 Inch. but the bottom of the Metal is 8 ½ Inch. half the Diam. of the bore being 2 ½ Inches to a 10 ½ makes 13 to the bottom of the Metal; but if you add to 8½ half the diam. of the bore 2 ½ it is 11, which is half an Inch more than 10½, that shews the Centre of the bore to be at R, and the thinnest of the Metal is undermost, and there he is like to break first; besides, it shews that you must add half an Inch to your Dispert of a true bored Piece, to make a Dispert for the Piece to shoot well: but if you had found by the direction before given, that the ½ an Inch had been less, as 10 only, and the greatest part of the Metal had been under; and therefore you must cut the Dispert ½ an Inch shorter then a Dispert made for such a true bored Piece; and likewise if you find by the Rammer head, and prick with a Wire at the Touch-hole ½ an Inch difference to the right or left hand, as l or m, that side which is the thinnest, you must put the Dispert cut ½ an Inch shorter, the three Figures makes all plain as it is written, as you may see by the direction of inches.

[illustration] geometrical diagram

SECT. XV. Of Iron Ordnance what quantity of Powder to allow for their Loading.

YOu must first Calculate a Charge of Powder for the said Iron Piece, as if it had been a Brass Piece, and in case you want the weight of the said Iron Piece, you must find it as you were taught in Chap. 7; and when you have found it as is taught in Chap. 9, how much Powder will Load the same if it were of Brass, then just 3 quarters so much is sufficient to Load an Iron Piece.

As for Example.

A Brass Saker of 1500 weight requires 4 l. what will an Iron Demi-Culvering of 2800 weight require? Work as in the 9 Chap. and you shall find 6 l. 6/10 or 6 l. 14 1/2 ounces, so well fortified as the Saker, will serve a Brass Demi-Culvering for a Charge.

The which we will likewise examine by the Rule in the 7 Chapter.

The Brass Saker's diam. is 3 35/100 inch. Logarithm	257403
The diam. of the Demi-Culvering Brass 4 50/100 inches	265321
The difference increasing.	7918 (3
The triple of the difference.	23754
The weight of the Saker added to it 1500	317609
gives the Logar. of the weight of of the Demi-C. Brass 2592 l.	341363

Or by the Scale, extend the Compasses from 3 75/100 to 4 50/109 the same distance turned 3 times from 1500, will reach 2592 l. as before.

The Arithmetical way.

4 50/100 C × 1500/3 ¾ C = is equal to the weight 2592 pound, which is the weight such a Demi-Culvering should be of that burneth 6 l. 14 ½ ounces of Powder.

To find what a Demiculvering of Brass of 28 hundred will require, Work thus.

The Logarithm of 2592	341363
The Logarithm of 2800	344715
The difference increasing.	3352
The one third of the difference,	1117
The weight in Powder 6 90/100 l. added	283884
gives the weight 7 l. 8 ounces	285001

Or extend the Compasses from 2592 to 2800, the same distance will reach from 6 9/10 to 7 ½ l. as before.

The Arithmetical way.

2800 × 6 9/10/2592 = 7 pound 8 ounces, as before.

Of which number you must take 3 Quarters for a Charge for the said Demi-Cul∣vering, ¾ thereof, being 5 pound 10 ounces, will be a sufficient Charge for such a Piece; and also whatsoever you find on the Scale, and in the Table in the third Chapter for Brass Pieces, take three quarters thereof for the Charge of your Iron Piece, if they be near that weight.

SECT. XVI. To know what quantity of Powder should be allowed to a Piece of Ordnance not truly bored.

ADmit the diameter of the Metal of the Piece at the Touch-hole be 16 inches, and the diameter at the bore is 5 ¼ inches, the weight of the Piece 4850, as you may see by Chap. 7, such a Piece you may find in the ninth Chap. requires 11 l. for her due Charge, being near two Diameters of her bore in Powder; But by my Instru∣ment in the general Figure, with the two Rammers heads at the two ends LM (at the Rammer end L that was in the Gun at the Touch-hole, I find by the prick at S on the Rammer, the soule or bore to be 1 inch out of his place, or 1 inch from the middle of the Metal; then I conclude, that the thinnest part of the Metal is 4 inches 3/2 parts, and the thickest side 6 and ⅜ parts; by which it appears, that one side is just 2 inches thicker than the other side, as you may see plainly by this Figure; the Line AB divided is the diameter or greatest thickness at the Touch-hole, every Division signifies an inch from the inward Circle to the outward Circle, is the thickness of the Metal; the inward Circle signifies the bore of the Piece, which you may see is just an inch from the true bore or Centre of the outmost Circle; therefore you must work as if the Piece were fortified no more than only so much as the thinnest part of the Metal is, which here doth appear to be 4 inches ¾ parts, the ½ of the diameter of the bore is 2 ⅝ inches added, makes 7 from A to D, the Centre of the bore being the thinnest part of the Metal, the whole diameter being 14, which is the true diameter, by reason the thinnest side of the Metal is but 4 ⅜ inches thick.

[illustration] geometrical diagram

* 1.68

And by this you must proportion your Charge by the former being 16 inches, if the bore had been placed at C in the true Centre, then evermore by these Rules.

* 1.69

The Logarithm of greatest diameter 16 is	220412
The Logarithm of the less diameter 14: 0 l.	214612
The difference decreasing,	5800
	3
The triple of the difference Substracted	17400,
from the Logarithm of 11 l. Powder 0 ounces,	204139
Leaves the Logarithm of the Powder 7 4/1•• pound	186739

So that 7 pound 4/19 or 6 ounces, is a sufficient Charge for such a false bored Piece; or extend the Compasses from 16 to 14, the same distance 3 times repeated from 11, will reach 7 4/19 pound, as before.

The Arithmetical way.

C 14 is •• 2744 × 11/C 16 is / 4096 = 7 pound 6 ounces, as before.

SECT. XVII. How Moulds, Forms, and Cartredges, are to be made for any sort of Ordnance.

CArtredges are usually made of Canvas and Paper-Royal; first take the height of the bore of the Piece of your Scale a little less 1/20 part of an inch of the diameter for the Vent, and three diam. of the Chamber of the Piece in breadth, cut the Paper and the Canvas, and for the Canon in height to the whole Culvering, is allowed about 2 diam. of the Piece, from the Culvering to the Minicn, the Charge the length of two diamet. and ½ all from the Minion to the Base 3 diameters of Powder, and make them at first about 4 diameters long, and according to the directions here given, mark them, or put a pound of Powder into each Cartredge, and measure how full it fils by your Scale for each Gun in your Ship, or Army; and by that Rule you may know how to make a Table, to make a Scale, to mark the Cartredge for the full loading, or diminish∣ing of your Powder, according to the goodness or badness of the Powder; and to the exraordinary over-heating of the Piece, having resolved for what sort of Ordnance are to serve you, and accordingly to have a form of Wood turned to the height of the Cartredge, which is the 21 part of 22, the diameter of the bore, and ½ an inch longer than the Cartredge is to be, before you paste your Paper on the form, first Tallow him, so will the Canvas and Paper slip off without starting or tearing; if you will make for tapered bore Guns, your Forms must be accordingly tapered, if you make Cartredges of Canvas, allow one inch for the Seams; but of Paper ¾ of an inch more than 3 diameters for the pasting. If once about the former, having a bottom fitted upon the end of the former, and Cartredge; you must paste the bottom close, and hard round about, then let them be well dryed; and then mark every one with Black or Red Lead, or Ink, how high they ought to be filled; which if you have no Ladles, Scales, nor Weights, these diameters of the Bullets make a reasonable Charge for the Canon 2 ¼ for a Culvering 3, and for the Saker 3 ½ for the lesser Pieces 3 ¾ of the diameter of the Bullet, and let some want of their weight against time they are over hot, or else you may endanger your self, and others.

SECT. XVIII. How to make Ladles, Rammers; or Spunges for all sorts of Ordnance.

EVery Mr. Gunner doth, or should know how to Trace, Cut out, and also make up and finish all Ladles, Spunges, and Rammers, and direct others how to make, and finish the same ready for use.

You have in the Table in the third Chapter the length and breadth of the Ladle, answerable to each Gun in inches and parts, and you must allow ½ a diameter more to inclose the head of the Staff within the Plate; the Button, or head of the Ladle-staff must be the height of the Shot almost; for Spunges, their bottoms and heads are to be made of soft Wood, as Asp, Birch, Willow, to be one diameter ¾ in length, and ¾, or a very little less of the height of the Shot, and covered with Sheep-skins, Wool, and nailed with Cooper's Nails, that together they may fill the concave of the Piece.

Let the Bottom or Head of the Rammers be of good hard Wood, and the height, as before one, and the length ⅓ of the diameter of the Shot at one end next the Staff, it must be so turned, that a Ferril of Brass may be put thereon, to save the Head from cleaving, when you Ramme home the Shot, the Buttons must be bored ⅔ for the Staff to be put in and fastned with a Pin through, and his length a Foot more than the concave of the Gun.

To make a Ladle for a Chamber-bored Piece, your Compasses opened to just the diam. of your Chamber within ⅛ part of an inch, Divide the measure into two equal parts, then set your Compasses to one of them, and by that distance draw a Circle on a Slat or Paper, the diam. of that Circle is ¼ shorter than the diam. of the Chamber, and take ⅗ parts of the Circle for the breadth of the Plate of the Ladle; and for Cannons, the length ought to be twice and ⅔ parts to hold at two times, the just quantity of Powder.

SECT. XIX. How the Carriage of a Piece should be made.

MEasure the length of the Cylinder of the bore, and once, and half that length should be the length of the Carriage, and in depth 4 diameters of the bore of the Piece at the fore-end, in the middle 3 and ½, and at the end next the ground 2 and ½, the thickness the diameter of the Shot; the Wheels should be one half the length of the Piece in height; the Saker and Minion must exceed the former by 1/12 part, the Faul∣con and Faulconet by one sixth part. Sea-Carriages are made less, as the Block-maker that makes them hath Rules for.

SECT. XX. To know whether the Trunnions of any Piece of Ordnance are placed right.

MEasure the length of the Cylinder of the bore from the Muzzle to the Britch, Divide the length by 7, and Multiply the Quotient by 3, and the Product will shew you how many Inches the Trunnions must stand from the lowest part of the con∣cavity of the Piece, and you must know that the Trunnions ought to be placed, so that ⅔ of the Piece may be seen above, or in that place where the Trunnions are set.

SECT. XXI. How much Rope will make Britchings and Tackles for any Piece.

IN Ships that carry Guns, the most experienced Gunners take this Rule. Look how many foot your Piece is in length, four times so much is the length of the Tackle, and their Britchings twice the length; and if the Ropes be suspected not to be good, they nail down Quoyners to the Fore-Trucks of heavy Guns, that he may not have any play; and if Britchings, and Tackles, and Quoyners should give way in foul weather, presently dismount her, that is the surest way. The Rammers and Spunges are made of four Strand-Ropes best, and served close, and sewed with Yarn, that they may be stiff to Ramme home the Shot and Wadd.

SECT. XXII. What Powder is allowed for Proof, and what for Action of each Piece.

FOr the biggest sort of Pieces and Canons; for Proof ⅘, and for Service ½ her weight of her Iron Shot, for the Culvering the weight of the Shot almost for Proof, and for Action ⅔, for the Saker and Fauloon ⅘, and for lesser Pieces the whole weight of the Shot, until they grow hot; and for Proof, the lesser Pieces give them 1 and ⅓ of the weight of the Bullet in Powder.

SECT. XXIII. The difference between the Common Legitimate Pieces, and the Bastard Pieces, and Extraordinary Pieces.

GƲnners call them Legitimate Pieces, as have due length of their Chase, accord∣ing to the height of their bores; Bastard Pieces are such as have shorter Chases, than the Proportion of their bore doth require; and Extraordinary, are such Pieces as have longer Chases, than the proportion of their bore alloweth; and these are called Bastard Canons, Culverings; and so likewise of Saker and Faulcon, which by your Scale, and the Rule thereon, you may presently find them.

SECT. XXIV. How Powder is made, and several ways to know whether Powder be de∣cayed or no, by moisture or Age, in part, or in whole.

POwder was always made of Salt-peter, Brimstone, and Char-cole; but in these latter times experience hath still mended the goodness or strength of it more, than it was in former times by much: but briefly thus; the best sort that is made at this pre∣sent time is made of six parts Salt-peter, Brimstone, Char-cole, one part.

the Musquet or Pistol Powder is now commonly made of Salt-peter five parts, one part of Brimstone, and one of Cole; Canon-Powder of Salt-peter four times as much as of Brimstone, and as of Cole. The reason why Pistol-Powder being the strongest of 6 - 1 - 1 is not so good for the Canon as 4 - 1 - 1 the weakest, although you take but so much of the Pistol Powder as you find by an Engine to be of like strength with another quantity of Canon-Powder.

The reason why Canon-Powder is best for Ordnance, is, because it taketh up a grea∣rer room in the Cylinder of the Piece, than Pistol-Powder; for in taking up much room it hath the greater length or fortification of Metal about it in the Piece.

Suppose a Saker require four l. of great Powder for her loading, and I would know how much Pistol Powder is equal in strength to four l. of Canon-Powder, trying by an Engine made on purpose to try Powder, I find 3 l. of Pistol-Powder; therefore you easily concieve, that 3 pounds have but 3 quarters of the Metal of the Piece to keep it from breaking, when 4 pound had a quarter more Metal, than the other had.

Nath. Nye Mr. Gunner found by an experiment made by him at Deriton the 17 of March Anno 1644, he loading a Saker-bore Piece of Iron,* 1.70 and the thickness of the Metal about the Chamber was 2 inch. and load her with 4 pound of weak Canon-Powder, which filled the Cylinder of the bore 9 inch. just, which 9 inch. in length, and two inch. in thickness is 225 inches of Metal about the Powder, which was 6 ounces more than the Piece should have had in proportion to Pistol-Powder: He fired, and the Piece went off safe; and he saith, he loaded her again with one pound and ¼ of fine Powder almost, which filled the bore but 2 inches and ¾, and had to its Fortification but 6, 8 ¾ inches, which in weight is 15 l. and when the Gun was discharged, it broke into divers pieces, as there is witness enough in that Town.

The harder the Corns of Powder are in feeling, by so much the better it is. Secondly,* 1.71 Gun-powder of a fair Azure or French Russet colour is very good, and it may be judged to have all its Receipts well wrought, and the proportion of Peter well refined. Thirdly, Lay 3 or 4 Corns of Gun-powder upon a white piece of Paper, the one three fingers distant from the other, and fire one, if the Powder is good, they will all fire at once, and leave nothing but a white chalky colour in the place where they were burned, neither will the Paper be touched; but if there remains a grosness of Brimstone and Salt-peter, it is not good. Fourthly, If you lay good Powder on the palm of your Hand, and set it on Fire, it will not burn you. Fifthly, To know the best amongst many sorts of Pow∣der, make a little heap of every sort, and then setting those heaps one from the other, mark well when you put Fire into them, which of the heaps did take Fire the soonest; for that Powder that will soonest be on Fire, smoak least, leave least sign behind it, is the best sort of Gun-powder.

SECT. XXV. How to make an excellent good Match to give Fire to any Ordnance.

TAke Cords made of Hemp that is not very fine, or of Tow which is better, (al∣though it will consume sooner,) and twist it until you have made the Srands as big as a mans little Finger; this done, boyl the said Cords in strong Lye ashes, and a little Salt-peter, until all the Lye be wasted, and then make it up, and take the feces or re∣mainer into your hand, and with the other draw the Match through twice or thrice, then drie it, and keep it for special uses, for Vaults, Mines, and moist weather, and it is very fit for your use any where.

SECT. XXVI. How to make Powder it shall not wast with time, and preserve that as is good to keep it from decaying.

THat time shall not wast it, take what quantity of Powder you will, and mix it with Brandy, and make it up in Balls, and drie them well in the Sun, or in a warm place, and keep them in Earthen Pots well glazed until you have cause to use them; this Pow∣der will not wast with age, nor decay.

To preserve Powder that is good, all Gunners have, or should have that reason to keep their Powder and Store in as good a drie place as is to be had in Fort or Ship con∣venient, and every Fortnight or at most three weeks turn all the Barrels, and Cartredges Barrelled up for readiness, turn them upside down, so will the Peter be Dispert into every place and part alike; for if it should stand long, the Peter will descend down∣wards always as it lies, and if it is not well shaked and moved, it will want of its strength at top very much, and one Pound at bottom with long standing, will be stronger than three at the top; keep all Cartredges which are filled for the Piece against he is hot in Barrels by themselves, that you may know them by a mark when need requires.

SECT. XXVII. To renew and make good again any sort of Gun-powder that hath lost its strength by long lying, or moisture, or any other means.

FIrst moisten the said Gun-powder with Vinegar or fair water, beat it well in a Mor∣tar, and then sift it through a fine Sieve, or a Search; with every pound of Gun-powder mingle one ounce of Salt-peter that hath been mealed; and when you have so done, beat and moisten this mixture again, until you see by breaking, or cutting with a Knife that there is no sign of Salt-peter or Brimstone in it; moreover, corn this Powder when it is incorporated with the Peter as it ought to be; then prepare a Sieve with a bottom of thick Parchment made full of round holes; then moisten the Powder which shall be corned with Water, put the same, and also a little Boul into the Sieve; and when you have so done, sift the Powder so as the Boul rolling up and down in the Sieve may break the clods of Powder, and make it by running through the holes to corn; and if it will not go through, you must beat it again until it will.

SECT. XXVIII. To make Powder of divers Colours, and first to make White Powder.

TAke of Salt-peter 12 parts, of Brimstone two parts, and of Camphir one part, beat, and sift, and incorporate all these things together; and after you have so done, beat them again, and so oft until you are sure they are well incorporated, then moisten it with Aqua Vitae; and when you have thus done, corn the Powder, as you are taught before.

To make Red Powder.

Take the same things, and work them as before directed for White Powder, and as that was moistned with Aqua Vitae, now you must moisten this with Vineagar, being Red as Blood, which will make the Powder likewise so in moistening of it, and then corn it, as is before taught.

To make any Coloured Powder.

Boil the Vineagar in such transparent Colours as you would have the Powder to be of, as if Blew with Blew Bice, of Green with a little Verdigreace, and the like: always take care that the Colour be not too thick, but very thin, or else it will weaken the Powder that you do make.

SECT. XXIX. Of several sorts of Salt-peter, and a way how to make a sort of Salt-peter very excellent, with ease, and less cost than any way.

ARtificial Salt-peter is a mixture of many substances gotten with Fire and Water out of drie Dirt and Earth, as out of Vaults and Tombs, and also Charnel-Houses; the best of all is of Beast-dung converted into Earth, in Stables, or Dunghills of a long time not used; and when it is to be made, it is made with a great deal of Charge. Another excellent sort of Salt peter is made on Flower that is called Plaster that groweth on Walls four parts, of Unslak'd Lime one part, and so boiled over the Fire with Water, which is to no purpose to make relation how for to make full direction will fill my live-sed sheets too fast; but this one way, which is the most easie and least cost, I will write the Receipt thereof, which is this.

Take quick Lime, and pour warm Water upon it, and let it stand six days, stirring it twice or thrice a day; and take the clear of this Water, set it in the Sun until it be wasted, and the Salt-peter will remain in the bottom. To refine Salt-peter, and make it fit for use, there is several ways, but this by Fire I shall only write thereof. Do thus: take an Iron Pot or Skellet, and fill it with Peter, set it on the Fire, and cover it close with an Iron Cover on the top, or with a Stone; when the Salt-peter is melted, take Brimstone most finely beaten, and cast some thereon; kindle it, and let it burn until all the upper part be burned, which when effected, will leave the Salt-peter close like to a piece of Marble, for the Brimstone will burn up the gross victiousness of the Salt-peter; It is to no purpose to give a further relation of this, by reason every Gunner may have his Peter ready made refined and in Meal at the Powder-mens, or Chandlers; or if he is constrained to make Peter or Powder, he may have several Books which give a full and large description of the making thereof, as Nath. Nye Tarta glia, or Norton's; but for what is useful for a Gunner in particular, is sufficiently spoken already; therefore let it suffice now, having shewed sufficiently how to make Powder, and trie the strength of Powder; to know what Shot and Powder is meet for every Piece, to find whether the Pieee be true bored or not, to load a Piece with discretion, if not true bored to make the Dispert; and also to know the difference betwixt Iron and Brass Pieces. I shall come to touch how to make a good Shot either of Point-blank, or at Random, with as much ease and plainness as ever was taught by any before.

SECT. XXX. How to Load and Fire a Piece of Ordnance like an Artist.

BEfore we shoot at a Mark, it is best to Load our Piece, in which, first observe the Wind, and be sure to lay your Budge-Barrel, or Cartredge of Powder to Wind-ward of your Piece, and place your Linstock to Lee-ward, clear the Touch-hole, and Spunge her well, and strike the Spunge on the Muzzle to shake off the foulness two or three blows.

Then let him stand on the right side of the Gun, and hold the Barrel, so that his assistant may thrust in the Ladle; being full, give it a shog, then strike off the heaped Powder, he being on the right side likewise, with his Body clear of the Muzzle, put the Ladle home to the Chamber stedily holding your Thumb upon the upper part of the Ladle-staff, then turn the Staff until your Thumb be quite under it, and give a shake or two to clear the Powder out of the Ladle; as you hale him out, keep him up that you may bring no Powder out with the Ladle; then with the Rammer put the Powder home gently, and after put in a good Wad, and thrust it home to the Powder, and give it two or three stroaks, to gather the loose Powder together, and it will fire the better; be sure your assistant have his Thumb on the Touch-hole all this while; then put in the Shot with the Rammer home, and after him another Wad, and then with the Rammer give two or three strokes more to settle it home, that there may be no vacuity between the first Wad Bullet, and last Wadde; your Budge-Barrel and your self standing to Wind-ward always, and your Piece by the Dispert directed to the Mark, Prime her, and let the Powder come from the Touch-hole to th•• Base-ring, your Leg standing for∣ward, and fire the Powder on the Base-ring, and draw back your Hand, and you have fired like the best of Gunners; but if you had given fire upon the Touch-hole, the Powder there would have endangered to have blowed the Cole and Linstock and allon of your hand; therefore you must have a care of a great Touch-hole.

SECT. XXXI. The difference of Shooting by the Metal, and by a Dispert by a Right Range, and at Random, by the Figures following.

SHooting by the Metal* 1.72 is the Figure AB, that is, admit you raised the Muzzle-ring, and the Base-ring, and the Mark, and your Eye in a Right-line, if you put the Scale into the Muzzle with the Plummet hanging to it, you shall find it differ 4 or 5 or 6 degr. according to the length or Mark of the Piece, and in regard of the several diffe∣rences of the length and marks, or Diameter of her Base and Muzzle-ring, no certain proportion can be generally assigned; yet for most Pieces it hath been well observed, that the Piece directed by her Metal, will shoot about twice as far as when the Mark is level and set by a Dispert & Quadrant and the Sight-line parallel to the Horizon; so that admit a Piece were laid by the Metal of Base and Muzzle-ring, and that it differed from a right Level 6 degr. as you found by your Quadrant in the Scale, you fired at the Mark, the Gun so layed, and measuring the distance you find it 412 Paces, which is as much beyond the Mark, as it is to it, which is the difference of Shooting by the Dispert* 1.73 or Axis of the bore in right bored Pieces following, this is chlled Point-blank; for if you acknow∣ledge the higher the Muzzle of a Piece is elevated, the farther the Shot is carryed in a Right-line. There can be no Point-blank directly known, nor Rules to know them, without you take a Piece and make 11 Shots out of her, and so by it proportion a Table, as here is one following. You must have leave, if possible, to Shoot so many Shots in a Piece at such elevations with the like goodness and quantity of Powder, as will make you such a Table of the Proportions of Right Ranges, called Point-blanks, before you can have any guess certainly of Proportion for other Guns; but to make a good Shot at a Mark, first be sure your Guns Trunnions be placed right, the Carriage well made, the

Platform clean swept, and that the ground be Level, and that the Carriage-Wheels be one as high as the other, and whether the Axle-tree be placed just across the Carriage, or not; or whether the Piece be true bored or not, if it be a true bored Piece, set your Dispert on the Muzzle-ring, just over then Centre of the Muzzle of the Piece, which may be done by holding a Line right before the Muzzle, and two Sticks or Notches made in Sticks put on the Muzzle-ring, and by the Line you may easily find the middle where to put the Dispert; and likewise if the Line touch the upper side & lower side of the Metal alike, you may be sure the Gun lies Level, or by the Scale and Quadrant on it and Plumb-line, if it hang in the Mouth of the piece, and no degrees of Altitude, but by the Long Side-line thereof, be sure the Piece is Level, and will carry the Bullet Horizontally in his violent Course; therefore by your Crows and Standers by, or Matrosses set about the Piece to the Mark, as at D, that with your Eye two foot from the Base-ring you may see the Mark on the upper part of the Base-ring, the top of the Dispert, and the Mark or Turret you Shoot at in a Right-line, as CD, and this you may call Point-blank, and all Shooting in this Form, and no other.

A Table of Point-blanks.

d••g.	randoms
0	192
1	209
2	227
3	244
4	261
5	278
6	285
7	302
8	320
9	337
10	354
20	454
30	693
40	855
50	1000

On the upper part of the Base-Ring, the top of the Dispert, and the Mark or Turret you Shoot at in a Right-line, as CD; and this you may call Point-blank, and all Shooting in this form, and no other.* 1.74

But for Shooting in a Right-line called the Right Range of a Bullet out of any Piece for making of Batteries, or Shooting at Random at any advantage, you may make use of this Table, until by your own experience, you have made out of a Gun by Shooting first Level, and afterward from degree to degree to 10 degrees mounture, or more in a Right-line.

The use of the Table of Right-Ranges, or Point-blanks before-going, it is found by experience, that the Piece assigned at six degrees of mounture Shoot 200 Paces in a right or insensible crooked Line; I desire to know how far the same Piece will Shoot in a straight Line, being mounted to 10 degrees? say by the Table if 285 the Number against 6 degrees giveth 200 paces, what will 354 the Number against 10 degrees give? I answer, 248 4/10 paces.

The Logarithm of 6 degr. is 285.	245484* 1.75
The Logarithm of the Paces known 200	230103
The Paces against 10 degr. is 354 is	254900
The Sum	485030
give the Logarithm of 248 4/10 Paces	239519

Or extend the Compasses from 285 to 200, the same distance will reach from 354 to 248 4/10 Paces as before 200 × 354/285 = 248 4/10 Paces, as before.

And the Figure is from E the top of the Castle to F the side of the Tower at 10 degr. mounture, carries the Bullet violently 248 Paces.

SECT. XXXII. How to Order and Direct a Piece, and amend an ill Shot that was made, either by the Metal, Level, Right-line, or Advantage, or Mount.

AFter you have made one Shot, and find the Piece carry just over the Mark, then do all as hath been before taught again; and when your Piece lies directly against the Mark, observe how much the last stroke of the Shot is above the Mark, so much longer make your Dispert, that the top of it may be just seen from the Britch of the Piece in a direct Line with the stroke of the Shot; and being so fitted, Level your Piece with this new Dispert to the assigned Mark, give Fire, and without doubt it will strike the same; if the first Shot had struck under the Mark, then bring the Piece in all points, as before; mark how much of the Dispert is over the Shot, and cut it just so short, as being at the Britch, you may discern the top of it, the Mark of the Base-Ring, and the stroke of the Shot in a Right-line, when you percieve it is of such a length, Level the Piece to the intended Mark as at the first, Prime, and give Fire.

If the first Shot had struck on the right Hand of the Mark, to mend it, you must Level the Piece as formerly, you standing behind the Britch of the Piece, observe the stroke of the Shot over the Dispert, that part of the Base-ring which you at that instant looked over in a Right-line towards the Dispert, and the stroke of the Shot, set up a Pin with a little soft Wax on the Base-ring, so this Pin will be in a Right-line with the Dis∣pert and stroke, then Level your Piece to the Mark intended by this Pin, and the first Dispert, and without question you will make a fair Shot; for when you Level by the Metal of the Base-ring where the Pin is placed and the Mark; the Piece standing at that direction, look over the top of the Dispert from the Mark in the Base-ring, and you shall find the Piece to lie just so much to the left, as the former Shot struck to the right, from the intended Mark, which should in all likelihood now strike the Mark.

But if the Shot be both wide and too low, then you must use both directions, as before taught to make the next Shot; first regulate the Dispert by cutting it shorter, according as the Mark of the Shot is lower than the intended Mark, then by the last Rule mend the Shooting wide; these things done with care and diligence, you may be sure will mend a bad Shot.

SECT. XXXIII. Of Shooting upon the Advantage or Random, at a Mark, beyond the Right-line of the Pieces reach, or Right-range of the Shot, and of the Dead-range for every Degree.

IN the two last Sections we have shewed for the Right-range; now we come to shew for the Dead-range, which consisteth of the right and crooked Range together in one, and then called the Dead-range, which is the whole distance from the Platform upon which the Piece intended or assigned is discharged unto the first fall or graze of the Bullet on the Level-Line, or on the ground called the Horizontal Plain, (by reason the different length of the Piece, and strength of the Pow∣der increaseth or diminisheth the course or fury of the Shot, and therefore more difficult to be found out, but only by Experience, or Diagrams, Tables, or Scales made by Experiment; now it vis ery diffiault, and a thing uncertain also to arrive here∣in unto exactness, without some Experience of the Piece; and therefere every one that will learn to Shoot at Random, must draw his Piece in a Level Ground, where first Shooting Level, he must observe that distance in Feet and Paces; then Mount his Piece to one degree, and mark where that shall Graze, and thus find the distance of every degree from the Level to the 10 degree, and by these distances make a Table, to which

annex the degrees against the distances, by which Table, and the Rule of Proportion, or Logarithms, or Line of Numbers, find how far another Piece will convey her Shot from degree to degree; but in case you cannot have the Liberty, nor Powder to do the aforesaid, you shall have a Table here that was made out of a Saker eight Foot long (by Nath. Nye, as in the 40th. Chap. of his Book,) where he saith, he Loaded her with three Pound of Powder, the Shot at one degree of mounture was carryed 375 Yards, or 225 Paces; the next Shot was at five degrees Random, and at that mounture the Shot was conveyed 416 Paces; and the next tryal was at seven degrees mounture, and the Random produced 505 Paces; the last tryal was at 10 degr. mounture, which sent the Shot 630 Paces of five Fort to a Pace.

Whilst he made these Shots, he loaded the Piece himself with loose Powder, exactly weighed, and weighed the Wad also, and beat down the said Wad with four strokes so near as he could by the same strength, as he did the time before; also he let the Piece cool betwixt each Shot of it self, staying above half an hour betwixt each Shot, he put no Wad after the Bullet, because the Piece was mounted, he tryed the strength of his Powder, and noted it down, to compare with other Powder, to know its strength by; and that is the way all Gunners must take, that intend to make good Shots at Random. All Mr Gunners should be able to draw an exact Description of the said Garrison, and every object as lyeth near his Works by the Rules of the 7th. Chap. of the Art of Surveying by the Sea-Compass in this 5th Book; so that he may know what is within reach of his Guns, by which means he shall not be troubled to take Distances, but be ready at all times to know his Distances by his Maps: then after he hath made one Shot, he may make another Shot to any Distance he pleaseth.

Example.

Suppose I know the Distance by my Map where the first Shot grazed to be 704 Paces, as you may see by the Figure out of the lowermost Gun of the Castle from S to the graze at A, the mounture of the Piece being 4 degr. how much must I mount the Piece to convey her Shot 900 Paces, as you may see by the Figure B the Gun, to C the Shots graze, or place required.

You must proportion these Distances of Random, to those in the Table following; saying, if 704 Paces require 370 Paces, as is in the Table at 4 degrees of Random, what number will be found against the degree in the Table; I must Mount the Piece unto 900, and work by these Rules.* 1.76

370 × 900/704 = 473

The Logarithm of the Shot made 704 is	284757
The Logarithm in the Table against 4 degr. is 370)	256820
The Logarithm of 900 Paces Random is	295424
The Sum is	552244

gives the Logar. of 473 Paces,* 1.77 which I look for in − 267487 the Table of Randoms, but find no such number there, but the next less is 461, and the next greatest is 550 against 7 degrees, the difference between these two Numbers, is 44 and 461 is 12 less than 473, and 12 is almost the one fourth part of 44,* 1.78 and therefore it shews that the Piece must be mounted at 6 degr. 15 min. or one Quarter to reach the Distance of 900 Paces as from B or b to C.

A Table of the proportion of dead Ran∣ges.

Deg.	Randoms.
0	206
1	225
2	274
3	323
4	370
5	416
6	461
7	505
8	548
9	589
10	630

Here is a Table of Randoms that was made out of the fore-named Saker of 8 Foot long, and loaded with 3 Pound of Powder, and every Gunner is advised, if possible, to get Powder, to make one by his own experience, and always to keep some of the same Powder to try his Proportions by; the Rule in the 24 Section by any other Powder he shall have occasion to use, for this is 1 of the material things belonging to a Gunner, without which knowledg hee an never make a good Shot; for at the time of a Leagure he must expect often to change his Pow∣der, as sometimes you shall have 9 Pound of one sort as good as 15 of another sort, as by Instrument and Shooting you may have expe∣rience.

SECT. XXXIV. How to make an effectual Shot out of a Piece of Ordnance at Random.

EVery one that hath Charge of a Gun, must at one time or other get leave of his Commanders to make two or three Shots at least out of the same Piece, and mea∣sure the Distance from the Platform to the first graze of the Shot, you must apply it to this Table by the last Rules of Proportion in the last Section, and find what deg. you shall need Mount the Gun to for any other Shot at any other time, when you shall have oc∣casion; when you have Loaden your Piece, as you are directed in Sect. 32, take the Distance to the Mark in the XVI Chap. of the second Book of the Description and Use of the Quadrant I have shewn you; and also observe how many degrees the Platform is higher or lower than your Mark by your Quadrant on the back-side of your Scale; after you have done that, then Calculate by the last Rules what degree the Gun must be Mounted to, to reach the Mark, if the said Work be under the Platform, Substract the Difference found by your Quadrant, out of the degree of the Random; but if the said Mark be higher than the Platform, Add the degr. of that Altitude to the degree of the Random, and at these corrected degrees Mount your Piece.

How to Mount your Piece by your Scalc and Quadrant thereon.

* 1.79To the side of the Scale or Quadrant is a piece of Brass fitted of the same breadth, with two Screws, and holes fitted to screw the Brass Plate two Inches of the former length, without the Edge or Side of the Line of Numbers, for to take any Angle that is under the Line of Level; for if you put the Brass into the Mouth of the Piece, the Line of Numbers being next unto it, and put in the Tompkin into the Mouth likewise to stop it fast in the middle of the Metal at the bottom, and then the standers by raise the Britch with Crows to what degree you please; and so likewise if the Mark or degr. assigned be above the Line of Level, if the Scale will not stand fast by the degree of the Diameter that fits the Bore, putting of it just into the Mouth of the Piece, then screw the Brass Plate to a hole made on purpose for the other side, and turn the degrees of the Diameter to the Bore, and fasten it with the Tompkin in the middle of the Mouth, as before; and so this Instrument will be most useful for all things as belong to a Gunner, with less trouble and Charge, than any other that ever was made by any other Men, and far more useful.

Then the Instrument being in the Mouth of the Piece, as before directed, mark di∣ligently until the Plumb-Line, which proceeds from the Centre of the Quadrant, cut these assigned degrees and Parts of degrees that you are to Mount the Gun by, in the Arch which is Divided into 90 degrees in the outward Circle thereof; your Gun so Loaded and fitted, as beforesaid, make your Shot, for without question, you will make a good Shot, and strike or came near the Mark.

As for Example.

Suppose you make tryal of your Gun as is spoken of in the last Section 32, you find that at 4 degrees of Random upon a Level-Ground the Shot is conveyed 704 Paces, if you be called out in hast upon Service against a City, or other Fort, and being ap∣pointed to play your Gun towards it, you also find it to be beyond the reach of the Right-range of your Shot, and the Distance being 560 Paces; and also that the place is lower than where you can Plant your Gun by one degree and ⅙ or 10 min. then to know the degree of Mounture, you may work as by the last Rule, if 704 gives 370 against four degrees, what will 560 give? the Distance to the Mark, it will give you the Number 295; look for this Number in the last Table 295, or the nearest Number to it, and against that degree and Part of a degree, which must also be found by Sub∣stracting the nearest less Number out of the nearest great Number, the greatest Num∣ber in the Table is 323, the nearest least is 274, the Difference is 49, the difference betwixt 323, and 395, is 28, the half of 49 is 24 ½, which shews that degree is 2 and a little above ½ of Random; but because the Mark is lower than the Platform, Sub∣stract one degree ⅙ or 10 min. out of 2 degr. 32 min. and the Remain is 1 degr. 22 min. the true height the Piece must be elevated, to reach the Mark; but if the Shot graze to the right or left, you are to mend it by direction in Sect. 31, but ever by the Example or Direction there.

Suppose the Shot graze over the Mark 20 Paces, Substract this 20 out of 560 the Distance, and Mount the next Shot according as if the Mark were but 540 Paces distant, if 20 Paces too short, make the next Shot as 580 Paces, that is the degree that is found by that Proportion to reach so far.

SECT. XXXV. How to find the Right-Line, or Right-Range of any Shot discharged out of any Piece, for every elevation by one Right or Dead-Range given for the Piece assigned.

FIrst, you must have the help of this Table of Dead-Ranges,* 1.80 which was made by Experience of Mr. Norton, and the Table of Point-blanks, or Right-Ranges, was the same Shots in a Right-line at every degree of Mounture, as this Table is the Dead-graze of the Bullet at the same Shot with the same Gun, for he made 200 Shots for tryal.

Now although it be a thing very difficult, and likewise uncertain to arrive herein to exactness, without some Experiments made with the assigned Piece and Powder; yet to come to a necessary nearness at first, far surer than by uncertain guessing by this Table, or by my Scale, and the Rules therein directed.

As for Example.

Admit you were to seek the Right-Range of a Bullet, that the Piece was fired at 30 degrees Mounture, and the Dead-Range of the Bullet was known to be 2200 Paces.

2200 × 693/2150 = 710 Paces.

A Table of Pro∣portion of Dead-Ranges.

Degr.	Paces.
0	192
1	298
2	404
3	510
4	610
5	722
6	828
7	934
8	1044
9	1129
10	1214
11	1296
12	1394
13	1469
14	1544
15	1622
16	1686
17	1744
18	1792
19	1849
20	1917
25	2013
30	2150
35	2249
40	2289
42 ½	2296
45	2289
52 ½	2283
60	1792

Or look in this Table of Dead-Ranges against 30 degrees is 2150)	333243
And the Dead-Range given or known for 30 degrees to be 2800 Paces.	334242
The Number against 30 degrees in the first Table of Point-blanks 693	284073
The Sum	618315
Gives the Logarithm of 710 Paces for the Right-Range of	285072

The Bullet carryed violently in a Right-Line at 30 degr. Moun∣ture.

But admit the Level Right-Range is given, and the Right-Range of 30 degrees Mounture be sought.

Work by these Rules.

The Logarithm of Point-blank 0 degr. is 192	228330
The Num. against 30 d. is 693 in the Table Point-blank	284073
The Level Right-Range of this Piece is 197 Paces	229446
The Sum	513519

Gives the Log. of 711 Paces for the Right-ranges required 285189

And as the Numbers are in the Logarithm, so you may do by the Line of Numbers.

693 × 197/192 = 711 Paces the Range in a Right-Line.

SECT. XXXVI. To know how much of the Horizontal-Line is contained directly under the Right-Line of any Shot called the Right-Range made out of any Piece at any Elevation assigned.

BE it propounded to find what part of the Horizontal-Line lyeth directly under the Right-Range of the Piece assigned at 30 degr. Elevation, the Right-Range for 30 deg. Mounture, by the last Rule is found to be 711 Paces, Work with the Complement of the Pieces Mounture 60 degr. thus always.

As the Radius 90 degr.	1000000
is to the number of Paces in the Right-Range 711 Paces	285186
So is the Compl. Sign of 30 degr. Mounture, which is 60 degr.	993969
to the Logarithm of the Horizontal-Base 619 Paces	279155

Now you find that 619 Paces lies under the Right-Range of the Shot, you may pre∣sently find how much of the Horizon is contained under the Crooked-Range of the Shot, if you Substract 619 the Horizontal Distance out of 2200, the Randoms at the first graze of the Bullet from the Piece, the Remainer is the Horizontal Distance 1581 Paces, which lies under the way of the Shot, as it goeth helically between the Right-Range, and the natural or perpendicular motion, or before it make the first graze; the like in all other questions.

SECT. XXXVII. Of the violent, crooked, and natural Motion or Course of a Shot discharged out of any Piece of Ordnance assigned.

BY the third and fourth Proposition of the second Book of Tartaglia, his Nova Scientia▪ shews that every body equally heavy, as a Shot in the end of the violent motion thereof, being Discharged out of a Piece of Ordnance, so it be not right up, or right down, the Crooked-Range, shall join with the Right-Range, and to the natural Course and Motion betwixt them both.

[illustration] geometrical diagram

As for Example.

The Right-Range being all the Right-Line AB which is properly called his Violent Motion, and BC will be the mixt or Crooked-Range, and CD the Natural Motion, wherein from A to B is the furthest part of the Violent Motion, and from C to d the end of the Natural Motion.

And in the seventh Proposition of the same Book, he proveth that every Shot equal∣ly heavy, great or little, equally elevated above the Horizon, or equally Oblique or Levelly directed, are among themselves like and proportional in their Distances, as the Figure following sheweth, as A:E:F is like and proportional in the Right and Crooked-Ranges unto H:I, and in their Distance or Dead-Ranges AF unto A:I.

And in his fourth and sixth Propositions of the same Book, he proveth that every Shot made upon the Level hath the mixt or Crooked-Range thereof, equal to the Arch of a Quadrant 90 degr. and if it be made upon any Elevation above the Level, that then it will make the Crooked-Range, to be more than the Quadrant.

And if that be made Imbased under the Level, that then the Crooked-Range thereof will be an Arch less than a Quadrant.

And lastly, in his ninth Proposition of the same Book, he undertakes to prove if one Piece be Shot off twice, the one Level, and the other at the best of the Random at 42½ degr. Mounture, that the Right-Range of the length is but ¼ of the Right-Range of the best of the Randoms, and that the Dead-Range of the Level is but 1/20 of the Dead-Range of the best Random, whereto he that desires a further Demonstration of these Propositions in his said second Book of Nova Scientia.

[illustration] geometrical diagram

SECT. XXXVIII. How to make a Gunner's Rule, being an Instrument which will serve to ele∣vate a Piece of Ordnance with more facility than the Gunner's Qua∣drant.

[illustration] geometrical diagram

BEcause the Quadrant on the back-side of the Scale cannot be conveniently used at all times, especially when the Wind blows hard, and being near the Enemies Guns, the Plumb-Line is so long, or too long before he stands still; to remedy this, the Gunner's Rule was invented; the Figure thereof you may here see; this Ruler must be 10, or 12, or 14 Inch. long according as the Gun will require, it must have a long slit down the middle thereof like an Eye-vane of a Quadrant or Back-staff, the Head thereof make Circular according to your Gun, as you see in the Figure; the Instrument is described standing upon his Britch of a Piece of Ordnance; in the middle of the small narrow slit you must place a Lute-string, a well twisted Thrid, or Silk-string may serve; this Bead must be set to such an Inch and Parts, as you find is agreeable to such a degr. as you must Mount your Gun unto, and on one side the slit you must place a Division of Inches, and every Inch into 10 Parts Divided, and thus it will serve for all sorts of Guns; but if it be for a particular Gun, then on the other side you may place the degr. and min. when you shall find by the length of your Gun, how many Inch. and Parts goes to make one degree; but to use it with all sorts of Ordnance, let it only be Divided into Inches and Parts, the Bead stands at Inch. four in the Rule.

SECT. XXXIX. How to Divide the Gunner's Rule into degr. by help of a Table, sitting it for any Piece from 5 foot long to 14 soot long; and by the help of this Table, any Piece may be Elevated to any degr. without the help of a Quadrant, Ruler, or any other Geometrical Instrument whatsoever.

TO fit the Ruler for one Gun only, here is the Rule for the Deviation of the degr. Note, this Table hath 11 Columns, the first shews the length of the Piece in Feet and half Feet, the other 10 in the Head is 10 degr. and under is Inches and the 100 part of an Inch, from 1 degr. to 10 degr. and so you may take them out of the Table, and set them on the Rulers opposite side.

The use of the Table

If your Gun be 8 Foot long one Inch 68/109 makes one degree; your Gun 12 Foot long 5 Inches 9/100 makes 2 degrees.

Or you may set your Bead to 5 6/100 Inch, to Mount him 2 degrees.

The len. of the Piece	1 Degree.	2 Degrees	3 Degrees	4 Degrees	5 Degrees	6 Degrees	7 Degrees	8 Degrees	9 Degrees	10 Degr.
Feet and ½ Feet.	Inch. 100	Inch. 100	Inch. 100	Inch. 100	Inch. 100	Inch. 100	Inch. 100	Inch. 100	Inch. 100	Inch. 100
5 Foot long.	1 3	2 6	3 8	4 11	5 14	6 16	7 19	8 82	9 25	10 28
5 Foot and half.	1 14	2 28	3 42	4 56	5 70	6 84	7 98	9 12	10 26	11 40
6 Foot long.	1 22	2 44	3 66	4 88	6 10	7 38	8 58	9 78	11 8	12 29
6 Foot and half.	1 36	2 72	4 8	5 44	6 80	S 17	9 53	10 89	12 25	13 68
7 Foot long.	1 47	2 94	4 41	5 88	7 35	8 82	10 30	11 77	13 24	14 78
7 Foot and half.	1 58	3 14	4 71	6 28	7 85	9 42	10 99	12 55	14 14	15 71
8 Foot long.	1 68	3 36	5 4	6 72	8 40	10 8	11 76	13 44	15 12	16 82
8 Foot and half.	1 79	3 58	5 37	7 16	8 95	10 74	12 53	14 32	16 12	17 92
9 Foot long.	1 89	3 79	5 68	7 58	9 47	11 37	13 27	15 18	17 8	18 98
9 Foot and half.	2 00	4 0	6 0	8 0	10 0	12 10	14 2	16 3	18 4	20 4
10 Foot long.	2 10	4 20	6 30	8 40	10 30	12 61	14 73	16 84	18 56	21 8
10 Foot & half.	2 21	4 41	6 69	8 88	11 81	13 28	15 48	17 68	19 89	22 10
11 Foot long.	2 31	4 62	6 93	9 24	11 56	13 88	16 22	18 51	20 82	23 14
11 Foot & half.	2 42	4 48	7 26	9 68	12 10	14 53	16 95	19 37	21 80	24 21
12 Foot long.	2 53	5 6	7 59	10 12	12 65	15 18	17 71	20 25	22 78	25 33
12 Foot & half.	2 63	5 20	7 89	10 52	13 15	15 78	18 41	21 4	23 67	26 33
13 Foot long.	2 74	5 48	8 82	10 96	13 70	16 44	19 48	21 92	24 68	27 40
13 Foot & half.	2 84	5 68	8 52	11 36	14 20	27 4	19 88	22 72	25 56	28 42
14 Foot long.	2 95	5 90	8 85	11 80	14 75	17 70	20 65	23 60	26 56	29 53

SECT. XL. How to give Level to a Piece of Ordnance, with the Gunner's Rule at any Degree of Random.

YOur Piece being Loaded in all points, as is before taught, and you have brought the Piece in a Right-line with the Mark, the Dispert being placed upon the Muzzle-Ring; in like manner place your Ruler upon the Base-ring, and let one standing by hold it, for the Foot of it fitted round to the Gun, you may be sure to put it right, and you may estimate on its perpendicular near enough; now having before the Distance to the Mark you intend to Shoot at; and admit you have found it to be 461 Paces, and the first Shot you made for Practice out of that Gun, conveyed her Shot at two degrees of Mounture 274 Paces, then according to the Rules in the 32 Section, and the Tables of Random, there I find 461 against 6 degr. which I must Mount the Gun to reach 461 Paces.

Then to find by this Table how many Inches, and hundred parts of one Inch 6 degr. will require; look in the Table above, and find on the left Hand in the first Column the length of the Piece 13 Foot just, under 6 degr. in the Common-Angle, you shall find 16 44/100 Inches, and to that height I set the Bead on the Lute-string, to 16 44/100 Inch, or 16 4/10; for every Inch is Divided into 10 Parts, and every Part is supposed to be Di∣vided into 10 more; then cause the Piece to be Mounted higher or lower, until you bring the Bead, the top of the Dispert, and the Mark all in one Line, stop the Piece in that position with a Coyn, Prime, and give Fire.

If you will Shoot by the Metal of the Piece, Substract the height of the Dispert out of the Inches found by the Table, and the Remainer, Mount your Piece unto; if the Dispert be 3 Inches ¼ long, Substracted from 16:44 found in the Table, leaves 12 19/100, or 122/50 of an Inch, you must set the height of the Bead to Shoot the same Di∣stance, by the Muzzle-Ring without the Dispert.

SECT. XLI. How by the Table to give Level to a Piece of Ordnance, without the Gunner's Rule.

IF you have not a Quadrant, nor a Ruler, and would make a Shot at 4 degrees of Elevation, look in the Table, and find the length of the Piece, which suppose to be 9 Foot and half, right againg 9 ½ in the Angle under 4 degr. you shall have 7 Inches to be the length of any Stick, cut, and set it upon the Base-Ring, and bring the top of the said Stick, the top of the Dispert, and the Mark in a Right-line with your Eye, and Prime, and give Fire, and you will make as good a Shot, as if you had the Ruler, and Bead, or Quadrant; if you will have no Dispert, take the Dispert, and Measure it upon the foresaid Stick at the Base-Ring, and from it cut off its lenghth just, and the Remainer you may use upon the Base-Ring, and it shall mount the Gun to 4 degrees, as before; and bring the top of the Stick, the Muzzle-Ring, and the Mark in a Right-line, and you may be sure to make a good Shot; if the Dispert were 3 Inches, that cut from 7 Inches, the Remain is 4 Inches, for the length of the Stick to be set on the Base-Ring, for to Level the Piece without a Dispert.

SECT. XLII. How to make a Shot at the Enemies Lights in a dark Night.

UPon such occasion, to Shoot at a Light seen in the Night, Dispert your Piece with a lighted and flaming Wax-Candle, or with a lighted piece of Match, that with your Eye you may bring the Base-ring, the fired Match on the Muzzle-Ring, and the Enemies Light in a Right-line, (or mark) then give Fire, and you will make a good Shot.

SECT. XLIII. How to make a perfect Shot at a company of Horse-men, or Foot-men passing by the place where Ordnance doth lie upon a Level-Ground; and also to make a good Shot at a Ship Sailing upon a River.

TAke a Piece that will reach the way or Mark in a Right-Line that the Horse or Foot are to pass by, then your Gun Loaded so with Powder as it may presently take Fire, and Shot fit for that use; and seeing a Tree, Bush, or Hillock, or some turn∣ing cross way for his Mark, and when the Enemies come near to that way in a Right-Line with his Gun, give Fire: and at Shooting at a Ship in a River, he must put his Piece to some evident Mark on the other side the River, and when the Head of the Ship shall begin to be betwix the Piece and the Mark, and then give Fire.

SECT. XLIV. How to cause the same quantity bosh of Powder and Shot, discharged out of the same Piece, to carry close, or more scattering.

IN the Book of Mr. John Bate of Extravagants, he saith, take the quantity of a Pease of Opium, and charge it among the Case-Shot, and it will make the said Shot flie closer together, than otherwise it would; for Opium is of congealing and fixa∣tive nature; this a Sea-man found by experience.

SECT. XLV. How a Shot which sticketh fast within the Concavity of a Piece, that it can∣not be driven home unto the Powder, may be Shot out, without hurt to the Gunner, or hurt to the Piece.

VVHen any Piece of Ordnance is Charged with such a Shot as will not be driven home unto the Powder, then the Gunner to save his Piece from breaking, must so Imbase the Mouth thereof, or put him under the Line of Level, that fair Water for two or three days being put into the Touch-hole at several times, may run into a Vessel set under the Mouth of the Gun, to save all the Salt-Peter that was in the Powder: and then let the Gunner clear the Touch-hole, and put in as much Powder as possible he can, and Prime, and give Pire, and it will serve to drive out the Shot.

But when a Shot hath lain long in a Piece, until he is grown rusty, and so stick fast; put strong Vinegar in the Mouth of the Piece, and with the Rammer strike the Shot until it doth move, then put in Vinegar until it run clear through the Powder and Shot, Prime, as before, and give Fire with good Powder; and if it do not run through after it hath stood 3 days, clear the Touch-hole, Prime, and give Fire.

SECT. XLVI. A Piece of Ordnance at the same Elevation, and towards the self-same place, with the like quantity of Powder and Shot, discharged several times, what difference there is in their Ranges.

THere hath been a Piece discharged in the space of an Hour seaven times, with the like quantity of Powder, Shot, and Mounture, and their Ranges have been fonud as followeth; the first Shot was conveyed 418 Paces, the second 438, the third 442, the fourth 434, the fifth 427, the sixth 412, the seaventh 395; so that the greatest difference from the first Shot was 24 Paces; this every Gunner must take notice of, if he intends to Shoot well at Random; the reason of these things is this, the first Shot of Powder found, the Chamber of the Gun moist, and the Air quiet, the second Shot, the Chamber was dryed, and the Gun in a good temper, and the Air moved towards the Mark with the first Bullet, and having less assistance than the first, went beyond, and made the best Shot; and every Shot after, will come shorter and shorter, as the Gun grows hotter and hotter; the reason is, by how much hotter the Piece is, by so much the more attractive is the concavity of the Piece made; and because the Shot is driven forth or expelled with no other thing, than by the Air's exaltation, or Wind, caused through the Salt-Peter; and therefore the oftner the Piece is Fired, and the more heat, the more attractive, which suppleth and retaineth continually more of that Wind, which should serve to expel the Bullet; and therefore the virtue expulsive in that Piece, doth more and more decrease, and the Shot flyeth not with that swiftness, as it did before in the 2 first Shots, which dryed and brought the Gun into his best temper; but the third and fourth Shot is but little difference from the first, but the rest will differ every Shot.

Nicholas Tartaglia doth report, that many Shots being made at a Battery by a Piece, it chanced by some occasion, the Piece rose up in such sort that the Piece touched the ground with its Mouth; a little Dog running by, did smell into the Mouth of the Piece, and after a little time, was drawn almost to the further end of the conca∣vity: they pulled him out almost dead; this was done by the virtue Attractive.

SECT. XLVII. How to Weigh Ships sunk, or Ordnance under Water: or to know what empty Cask will carry any sort of Ordnance over a River.

NIcholas Tartaglia hath well collected from the Learned Archimedes, and hath calculated the Proportion of Stone, and other Mettals, what they will weigh in the Water, and in the Air.

All Men know by reason, that whatsoever is heavyer than so much Water, as the body of the Metal thrusteth out of the place, or Vessel, will sink; and being lighter than so much Water, will swim.

Tartaglia saith, that ordinary Free stone weighing 93 l. in the Air, will weigh but in the Water, which is near as 2 is to 1, between the Free-stone, and the Water. And that Marble-stone that weigheth 7 l. in the Air, will weigh but 5 l. in the Water, which is near as 7 to 2, between the Marble and the Water.

And Iron and Tin, that in the Air weigheth 19 l. will weigh 16 l. in the Water; so it is as 19 to 3.

Brass weighing in the Air 65 l. will in the Water weigh 55 l. and so Brass is to Water, as 65 to 10.

And Lead weighing in the Air 30 l. will weigh in the Water but 27 l. so Lead is to Water, as 30 to 3.

And lastly, Gold in the Air being 17 l. in the Water,* 1.81 it will weigh but 16 l. so Gold is to Water, as 17 to 1. He also layeth down Rules to weigh Ships, or Guns, or any thing else in the Water, that hath not lain too long, and docked it self in Oaze: for if the thing sunk be upon Sands or Rocks, it will weigh the better. He describes Vessels Loadeu to be brought to the place where the thing is sunk, and a Globe of Glass put in a Frame of Wood, and a place in the bottom of the Glass to put his Head into the concave, he may both see and breath, and by a Windless Rope, and weight to sink it, he may first let down the weight, and after have himself down in that Frame, that is in a form of an Hour-Glass, to the bottom of the Sea, and do the work, and sling the ••hip, and Guns, and when he will come up to the top again, to un-wind the Rope, and the Frame will be guided upright, and he and it will come to the top of the water very safe, and fasten this Rope brought from the Ships, and un-lead the Vessels, then will they Buoy up the Ship sunk, or any thing from the ground.

Or by a Float-Stage & Windless, Capston, and Trunk of Leather made so thick, that no Water can come in, and with a pair of Glass Eyes fastned, that no Water can go through, fitted to the Case of Leather within, and two Bladders blown at the brim or too of the Water, made fast to the Case of Leather to swim, the Mouth of the Case,* 1.82 while the Man goes down with Ropes fit to sling it, and makes them fast at liberty; then hale him up after a time fit, and by your Vessels, as before, and Float-Stage, Heave and Buoy up the thing sunk.

Know this, that 5 Tun of Cask will swim a Canon of 8 or 9000 weight, 4 Tun a Demi-Canon, 3 Tun a Culvering, and 2 Tun a Saker, with all things belonging there∣unto, as Planks and Ropes.

SECT. XLVIII. How many Horses, Oxen, or Men will serve to draw a Piece of Ordnance.

FOr every hundred weight of Metal, one Man; so a Piece of 8000 Pound weight requires 80 Men, and as many more Men as the Carriage may be in hand weights; for every 00 weight of Metal, one Horse, then 16 Horses will draw a Cun of 8000 weight; but in the Winter 24; also 17 Yoke of Oxen is thought sufficient to draw a Piece of 8000 weight, but in the Winter, they had need be one third part more.

SECT. XLIX. How Gunners may take a Plott of their Garrison, and every object near it.

HE may by the Compass and Ruler directed in the seventh Chapter of Surveying of Land, take the Plott of his Garrison, and every noted place or way within Gun-shot, and draw it into a Map, and have it in a readiness, and need not be troubled to make Distances every time he hath an occasion to make a Shot; but by his Scale and Map, may know if his Gun will reach any place thereabouts; and by the fourth Chap. of the General use of the Canon of Logarithms in Mr. Gunter's Works, learn the Pra∣ctice of Fortifications, there it is put down for him at large.

OF ARTIFICIAL FIRE-WORKS, FOR Recreation, AND SEA and LAND-SERVICE. CHAP. XIII.

SECT. I. A Description of the Mortar-Piece, and how to make one of Wood, and Past-Board (for a need,) Brass and Iron ones being wanting.

THe same Metal that makes the best sort of Brass-Ordnance, they make Mortar-Pieces with, and by these Measures; if the Diam. or Bore be 9 Inches, let the Mortar be one Foot and half in length, and let the Chamber in which you Load your Piece with Powder be 3 Inches Diam. and 4 and a half deep; the thickest of the Metal above the Touch-hole 3 Inches, and the upper part thereof 1 Inch ½.

To make the Mortar-Piece of Wood and Past-Board.

Provide a Wooden-Ruler of such bigness as you desire to make the Diameter of the Morter, then grease your Ruler well, that the stuff may slip off that is put about him, which is Past-Boards and Canvas, and very well plyed with hot Glue; and after let it dry a little while on the Rowler, and another while off from the Rowler; and when this kind of Trunk is very dry, put it on the Ruler, and set it in a Lathe, and cut off both ends of the Trunk with a Chizel very even, then turn a Foot thereto with a shoulder to put the Trunk upon, and in the middle thereof make the Chamber for your Powder; if the Piece be 8 Inches in the Mouth, let the thickness of the Past-Board-Trunk be two Inches thick, and 18 Inches long, the Britch or Foot 10, the Shoulder 2 Inches long, and 2 high, that when the Trunk is put on this Shoulder, and joyned with the

Wood, it may be just even with the same; the Bore into which you put your Powder must be two Inches high, and three deep, Plated with Copper, Lattin, (if it be possible) as also all the rest of the Wood that goeth into the Trunk; when you have put the Trunk into the Britch of Wood, nail it round about the Shoulder, by making holes for the Nails, and then driving in the Nails upon that Wood, that you made to receive the Past-boards or Trunk; then cover both Wood and Trunk with good Belch-Cord and Glue again, and let it be well dryed, it will last a long time; and with such you may Shoot Ballouns into the Air for Recreation.

SECT. II. How to fit and prepare Granadoes for the Mortar-Piece.

THe Shot of great Mortar-Pieces are most commonly one tenth part lower than the Bore, because of Cording them, to sling into the Mouth of the Piece; and for fear of secret Cracks, which cannot be easily espyed, they are coated with Pitch, so that being fitted and prepared, they do but just fit the Bore.

How to make Fuses.

Every Ball hath an hole left to put in a Fuse, or piece of Wood, just like a Faucet for a Spiggot; this hole must be just one quarter of the Diameter of the wooden Fuse, which Fuse must be in length three quarters of the height of the Granadoe; make it taper, and then filled with composition, and driven gently into the Powder that is in the Ball, leaving a little of it without: the Composition of this Fuse is made thus; take one Pound of Powder, four Ounces of Salt-Peter, and one of Brimstone, first beaten to Powder, and sifted in a Sieve severally, these Ingredients being mixt together, your Composition is fit for use.

SECT. III. How to make Granadoes of Canvas for the Mortar.

THe operation of these Granadoes made of Canvas is quite contrary to these already set down: these are only Fit to Fire a Town, they are not of so violent execu∣tion, as the precedent, yet altogether as costly in the making; for the making of them, fit a piece of Canvas upon a round Ball of Wood or Form, so big as you would have your Granadoe, then take this Composition following; four Pound of Salt-peter, two Pound of Gun powder dust, and two Pound of Brimstone; all these incorporated, and moistned with Oyl of Salt-peter; fill your Case with this Compound, and cover it with Cords, and pierce the Sack full of holes, and in every hole put an Iron Barrel, Charged like a Pistol; these must be driven into the Sack unto the head, then let there be an hole about an Inch deep, which shall serve to Prime it with Powder-dust, moisten it with Oyl of Petrol; be sure your Barrels have great Touch-holes, that the rust through time may not choak them, and they will be ready for service many years.

SECT. IV. How Granadoes are to be Charged in a Mortar, and Fired.

YOu must take great care in the Loading or Charging the Mortar, thus; first, weigh the Powder to a Drachm that you put into the Chamber, and after it put a good close Wadd of Hay, or a Tampion of Wood, then cut a Turf off the Ground that may just fill the bottom of the hole or bore of the Mortar next the Wadd; your Gra∣nadoe being prepared, with a coat of Pitch and Cord, as before taught, sling it into the Mouth of the Mortar; observe to have the Fuse of the Granadoe in the middle of the Bore, then go to the Britch, thrust up a Wire in the Touch-hole to make sure, then

Prime with the best drie Powder you have; for (believe me) this is a ticklish sort of Shooting; without care, your Life, and Mortar-Piece is now at stake; but we will give you very sure directions how to give Fire.

Provide small Fuses, such as we taught you to make before for the Shells, but less, about a quarter of an Inch bore, three quarters of an Inch thickness, and eight Inches long, fill these with good Powder-dust, moisten it with Oyl of Salt-Peter but a little, and put it in with an Iron Rammer, try whether you like the time, they continue burn∣ing; if too slow, abate Oyl of Peter; if too fast, add more to it.

Thus being prepared, the use is, (viz.) thrust the Pick of your Linstock in at one end of the Fuse you mean to give Fire withal, bid one of your assistants come to one side of the Mouth of the Piece, and give Fire to your Fuse, wherewith Fire the Fuse in the Mortar, and then with great speed give Fire to the Touch-hole; these Fuses are very certain to give Fire, but Match doth ofttimes fail.

SECT. V. How to make Hand-Granadoes to be hove by Hand.

THere is good use made of Hand-Granadoes in assaults, and Boarding of Ships, and there be two sorts of them made; the first is shewed already,* 1.83 the second is made by Sea-Gunners upon a Mould made with Twine, and covered over with Car∣tredge-Paper, and Musquet-Bullets cut in two, put with Past and bits of Paper thick on the out-side; after you have doubled the Shells, Paste on some at a time, and let it drie, and then some more, until he is quite full; then dip him in scalding Rozin, or Pitch, and hang him up, and he is for your use; but you must have the innermost end of the Twine. which must be left out at the small hole for the Fuse; and before you Pitch it, you are to wind it out, and stop the hole, and then Pitch it.

To Load them, fill these small Shells with Gun-Powder, then make a Fuse of one Pound of Gun. Powder, six Ounces of Salt-Peter, and one of Char-cole; or if you will have them of less durance, you may take the Composition made for the Fuses be∣fore spoken of for great Granadoes, knock the Fuse up to the head within one quarter of an Inch, which is only to find it by in the night; stop well the rest of the holes if any Chinks are open, with soft Wax; then your first Shells must be coated with Pitch and Hurds, lest it should break with the fall; and be sure when you have Fired the Fuse, suddenly to cast it out of your hand, and it will do good execution.

SECT. VI. How to make Fiery-Arrows or Darts like Death Arrow-Heads.

MAke your Head of Iron, sharp and bearded, to stick fast; and to it have an Ar∣row or long shaft of Wood, and about the middle of that Head make fast a Lin∣nen Bag in form of an Egg, leaving open at the end a hole, that it may be filled with the Composition following; take one Pound of Peter, half a Pound of Gun-powder, and as much Brimstone in Powder; all these Ingredients being mixt well, and mingled with Oyl of Petriol; with this fill the Bag round about the Arrow-head, then let all be bound about with Wire; and for Priming of these, dip Cotton-week into Gun-Powder wet with Water; and well dryed again before it is used, and let the Arrows or Shafts be so put into the Head, that when they be stuck in a House or Ship-side, or any where else, the Man which endeavours to pull them out, may be deceived, and pull only the Shaft, and leave the Head to burn the House, or Ship, or Mens Cloaths, or any thing else; if you throw or shoot it well, it will Fire whatsoever combustible stuff or matter shall be near it, as Sails, Timber, Pitch, Tarred places; and this will much as∣sault Enemies in storming a Work, or Boarding a Ship.

SECT. VII. How to make Fire-pots of Clay.

FIre-Pots, and Balls to throw out of Mens Hands, or with a Bascula, may be made of Potters-Clay, with Ears baked, and to it hang lighted Matches, and throwing them, if it lighteth on a hard thing, it breaks, and the Matches Fire the Powder, and the half Bullets of Musquets contrived upon them, as before, disperses, and doth much mischief; their mixture is of Powder, Peter, Sulphur, and Sal-armoniack of each one Pound, and 4 Ounces of Camphire pounded, and Searced, and mixed well together with hot Pitch, Linseed-Oyl, or Oyl of Peter; prove it first by burning it, if it be too slow, add more Powder, and if it be too quick, more Oyl, or Rozin, and then it is for your use.

SECT. VIII. How to make Powder-Chests.

YOu must make them with 2 Boards to be nailed together, like the ridge of a House, and one longer and broader to the bottom thereof; between the three Boards put a Cartredge, then make it up like a Sea-Chest, and fill it with Pibble-stones, Nails, Stubs of old Iron; then nail the Cover on, and the end to the Decks, in such a place as you may Fire the Powder underneath through a hole made to put a Pistol in.

SECT. IX. How to make Artificial Fire-Works for Recreation and Delight.

VVE shall not describe the Moulds in particular, being needless; for such Men as are inquisitive into these things, let them buy Mr. Babrington, or Bate, or Malthus, or Norton's Fire-Works; here we will lay down such Rules, as shall be as soon conceived without Figures, only a Rowler or Mould for to make the Paper upon; and that may serve for all the rest, they being made in the same manner.

To mak good experienced Rockets our way, do thus; get a Form or Rowler to be turned in a Lathe, what thickness you please, and intend to make your Rockets, and let his length be 8 times the Diameter; if it be ¾ of an Inch in thickness, the length will be 6 Inches, put so many Rowls of Paper on this Form, until it is ½ an Inch thick, or make it ¼ Inch the whole then Paste the upper side to the rest; then you must contract the Paper together an Inch from the Mouth, thus: dip an Inch of the Case in Water, the Formor in him, and with Twine, about ¾ of an Inch from the end gather it in; but let a Formor, or a thing near the bigness be put into his Mouth, while you draw it in with the Twine and choak it; you must remember to leave a small hole to put in a Wire through the Composition half way the Rocket, as big as a Bod∣kin; then take out the Formor, and dry them, and they are for use at any time; the Figure following makes all plain; A is the Mouth of the Rocket, B so far the Bodkin must be thrust up the middle; you must be provided with a smaller Bodkin, which when your Rocket is filled with the Composition, and tyed to the Rod, you must thrust this Wire Bodkin in at the Mouth, straight up to the midst of the Rocket, having a care not to thrust it more upon one side than the other.

SECT. X. To make the Composition for Rockets of any size.

[illustration] diagram

THe Reader may make use of these Rules, not upon trust out of Authors, but found by Practice and Experience; and first for Rockets of 1 Ounce; you must use only Canon-Powder-dust, being beaten in a Mortar, and finely Searsed; this makes him rise very swift, making a great noise, but car∣ries no Tail. These of more Operations are made by putting one Ounce of Char-cole-dust to 8 Ounces of Powder; this Composition will hold for Rockets of one, two, and three Ounces; but for these of four, take three Ounces of Char∣cole-dust, to one Pound of Canon-Powder-dust, continuing that Rule, until you come to Rockets of 10 Ounces; and also for Rockets of a Pound, take one Pound of Powder-dust, and four Ounces of Char-cole-dust, and these are big enough for any Recreation or Delight.

To fill the Rockets with this Composition.

Hold the Mouth downwards where it was Choaked, and with a knife put in so much as you can of the Receipt provided for that size at one time, then with a Rammer fitted to the Case, and with a Mallet give three or four indifferent knocks, then put in more Composition until it be full, every time knocking the Rammer, as before, until the Composition come within one Diameter of the bore of the top; then put down a piece of Paste-board, and knock it in hard, prick three or four little holes therein; then put fine Pistol-Powder in almost to the top, and upon that another cap of Paper, upon which put a Piece of Leather, that it may be tyed on the top of the Rocket, and fast Glued on; then get a straight Twigg, and bind it upon the Rocket with good Twine; it must be no heavier, than being put upon your Finger an Inch and a half from the Mouth of the same, that it may just ballance the Rocket, then it is prepared for use.

To give Fire to one or two Rockets.

Set your Rockets Mouth upon the Edge of any piece of Timber, that stands so high from the ground, that the stick may stand perpendicular from it downwards or upon a side of a Wale or Carriage-wheel, or any dry place whatsoever; then lay a train of Powder that may come under the Mouth thereof; give Fire thereto, and you have done; but to Fire more Rockets than one, that as one descendeth, the other may ascend by degrees: make this Composition following; of Roch-Peter eight Ounces, Quick-Brimstone four Ounces, and fine Powder-dust two Ounces, which lay in a Line, from one Rocket to another, they being placed ten Inches, or a Foot one from another; give Fire to this Composition, and you have your desire, if you did prick the Rocket with the Wire, as directed; you shall see how gallant one will mount the Air, when the other is spent.

SECT. XI. How to make flying Serpents and Rockets that will run upon a Line, and return again.

FOr this you must provide a small Rowling-Pin about one quarter of an Inch in thickness; upon which Roul seaven or eight thickness of Paper; fill them four Inches with Powder-dust, sometimes putting between the filling a little of the Compo∣sition for Rockets of ten Ounces, and at the end of four Inches choak him; fill two Inches more with Pistol-Powder, then choak the end up, and at the other end put in a little of the mixture for Stars, which follows, and choak between them and the Com∣position, and it is fit for use; but divers of those with the Starry end downwards upon the head of a Rocket and Powder-train to blow them out, when the Rocket is spent, they will first appear like so many Stars; when the Stars are spent, taking hold of the Powder-dust, they will run riggling to and fro like Serpents; and when that Composi∣tion is spent, they will end with every one a Report, which will give great content to the beholder.

I did omit to speak of Runners in its proper place in the last Section, for that is the Composition, which you must make them of, very carefully whether they be, double or single, or those that carry Dragons, Men, or Ships, or other Shapes in motion, least they shame their Master; the Line must therefore be fine, even, and strong, and being rubbed over with soft Sope to make it slippery, and not easily to take Fire; Those that turn Wheels, may have a further addition of Roch-Peter in their Receipts to add plea∣sure and life to the beholders; You must have a piece of Cane as long as the Rocket, and bind to the Rockets, and so that ones Head may be to the others Vent, that when one hath carryed the Cane on the Line to the end thereof, the other may Fire, and bring him back again to the Tower or place where it was fired; these Figures are made with strong Paper or Parchment, and with Lattin, and Wire, and Twine, until they be brought into these Shapes, and then painted like Ships, or Dragons, or like the thing it carries with it.

SECT. XII. How to make Fire-Wheels, or as some call them Girondles.

FIrst be provided with Spinning-Wheels or the like, made easy to run round upon its Axis, Horizontal, or Vertically; and put Flags on the top of the middle, to set out the Wheel; bind Rockets to the Wheel, and Crackers betwixt each Rocket, with the Mouth of one towards the Tail of the other; thus continued, until you have fitted the Wheel quite round; which done, cover them with Paper pasted over, and coloured handsomly to set it out, that one taking Fire, they may not Fire all, and daub Soap upon them quite round, leaving the Mouth of one of them open, to give Fire thereto; the first Rocket being burned, will set Fire to the rest one after another, keep∣ing the Wheel in a contional motion, until they be all spent; you may bind Fire-Lances to these Wheels, either upright, or near over athwart, which will make to appear diversity of Fire-Circles; you must take care to place your Wheels called Gi∣rondles at convenient distance from other Fire-Works, least they should make a confu∣sion, and spoil all the Work.

SECT. XIII. How to make divers Compositions for Starrs.

FOr Starrs of a Blew colour mixed with Red, the Composition is of Powder-mealed eight Ounces, Salt-Peter four, Quick Brimstone twelve Ounces, Meal all these very fine, and mix them together with two Ounces of Aqua Vitae, and half an Ounce of Oyl of Spike; which let it be very dry before you use it.

Another Composition which will make White and beautiful Fire; take Powder eight, Salt-Peter 24, quick Brimstone two, Camphire one Ounce, Meal these Ingre∣dients, and Incorporate them; make the Camphire with dipping your Pestil into a little Oyl of Almonds, and it will Meal presently, and keep it close from the Air, or else it will become of no use.

Another White-Fire which lasteth long, take Powder four, Salt-Peter 16, Brim∣stone eight, Camyhire one, Oyl of Peter two Ounces, Meal these that are to be Mealed, and mix them according to the former directions.

SECT. XIV. How to make and use the Starrs.

TAke little square pieces of Brown Paper, which fill with either of the foresaid Compositions which you like best, fold it down, rowling it til you make it round, about the bigness of a Nut or bigger, according to the size of your Rocket that you intend them for, Prime them with drawing through them Cotton-Week, and they are prepared to make fast to the Wheels: you may also make them thus; you must have a Rowler which must be as big as an ordinary Arrow, which shall be to Rowl a length of Paper about, and Paste it round, and dry it well, fill it with a Thimble, and thrust it down with a Rowler, and then cut it in short Pieces about half an Inch long; then you must have in readiness either hot Glue, or Size mingled with red Lead, dip therein one end of your short Pieces, least they take Fire at both ends together; besides, it will not so easily blow out; these being thus done, set them to dry until you use them, and in the top of the Rocket, whereas in the 10 Section you were to fill it with Pistol-Powder, now you must put none, but a very little, and that is to blow one of the bits of Starrs out, which must stand in the room of the Powder, and on the top of that another Tire, with strewing a little Powder and dust; and in like manner another, to a third or fourth, putting a little small corned Powder between them, until you come unto the top of the Rocket-case, there put a Paper over the Head of it, and tie it close about the top, that none of the Powder come from between the Stars; the Cotton-Week is such as the Chaundlers use doubled 6 or 7 times, dipped in Salt-Peter Water, or Aqua Vita, wherein some Camphire hath been dissolved; or for want of either, in fair Water, cut it in divers pieces, Rowled in Mealed Powder dryed in the Sun, and it is done.

SECT. XV. How to represent divers sorts of Figures in the Air with Rockets.

VVHen you have divers Rockets to make for a great Fire-Work, let one be with a Report, another with Starrs, another with Golden Hair or Rain, one with Silver Hair or Rain, which it seems to be when you are right under; and upon the Head of another Rocket place the Serpents, and they will make most delight∣ful sport.

SECT. XVI. How to make Silver and Golden Rain, and how to use them.

YOu must provide store of Goose-Quills, which being provided, you must cut them off so far as they are hollow; the Composition to fill them is, two Ounces of Cole-dust, and one Pound of Powder well mixed; having filled many of these Quills, you shall place them in the same place as I told you to put the Powder and Stars, put∣ting a little Pistol-Powder to blow them out, as you did the Stars, and fill the top of the Case as full of them as you can, with the open end downwards; so soon as the Rocket is spent, there will appear a Golden Shower, or Rain; or with the Compo∣sition for White-Stars filled in the Quills, will make a Shower of Silver Rain.

SECT. XVII. How to make Fire-Lances.

MAke them thus; first, you must make Cartredges, or Cases just like the Cases for Rockets, only those for a need may be made with Past-Board, and Glued, as they are formed round, but the former is better; let them be filled with the drie Com∣position for Stars in the 13th Section; Prime them with wet Gun-Powder, the lower end of the Case is stopped with a piece of Wood, to the end they may be nailed and stirred when and where they shall be used, the Wood being about three Fingers breadth long out of the Case or Cartredge, or as long as you will.

SECT. XVIII. The manner how to make Balloons for the Mortar-Piece.

YOu must have a Formor or Ruler twice the length of the Diameter and of the bigness, as you will have the inside of your Balloon, and upon that Formor put so many Past-Boards, as you shall think sufficient for strength, then Paste or Glue them well together, and choak him at the end with a String, leaving a small hole for a Port-Fire, which must be made just like a Rocket but no holes in it as the Rocket hath, and of such length as is fit: now to fill the Balloons, place all your Serpents within it together, with Stars, Rockets, and Crackers, leave very little room within the Case, or Cartredge; and being filled, put in as much Powder-dust as you can, that it may run every where through the Chinks between the Serpents, Rockets, and Stars, that they may all Fire, and that the said Powder-dust may break the Balloon; these things thus done, choak up the other end close, and Charge it in the Mortar, as we have taught you to do the Canvas Granadoe in the fourth Section, and you may shoot it when you please, and you will make most excellent delight to the Spectators, and credit to your self; for this is part of the way of Mr. Malthus's Fire-Works, which were the best that ever I practised.

[illustration] depiction of various fireworks

Rockets single or doble made to run vpon a line from tower to tower is in 12 sectio.

The Ball A is a Granado, coated armed and lopdeg sect: 4▪

Fire Potts of Glay w^th: eares and markes is B section. 7.

Balls to fire and stick is D made of y^e same stuffe a•…•… 7 section

Fire Arrowes or darts sec•…•… y^e 6 is E

FG is a sillinder Granad•…•… of turned timber to shoote fliers section the 10.

Vertuall wheele is H se•…•… 12 by w^ch: you may vnd•…•…¦stand y^e form of horizo•…•…¦tall wheeles or any oth•…•… sort:

ABCD are the mo•…•…

Peice mould and Ball•…•… section 18.

And M N is 5 woode•…•…

Morters or Chambers a•…•… in section 18

SECT. XIX. A most precious Unguent for any Burning.

DIvers Men in the Practice of Fire-Works one time or other chance to be burned, or blown in the Face by Powder; here you have Mr. Malthus's Salves, which is known by often Experience to be very good, and will fully cure you.

The SALVES.

Take fresh Hogs-Grease, or Lard, as much as you please, and boyl, and take off the Scum, until there arise no more Scum; then set the Lard three or four nights abroad, after which it must be washed in running Water to take away the Saltish nature, and to make it White; then melt it, and keep it for your use.

Otherwise,

The White of an Egg, and fresh Butter being mingled together, and well beaten into an Oyntment, is excellent good.

SECT. XX. Another Salve most Excellent.

TAke a Stone of Quick Lime, and let it be dissolved in clear Water, and when the water is settled, pour it out gently from the Lime through a Linnen cloath, then put as much Sallet Oyl, as you have Water together, and beat it all to an Oyl; you may keep it for such uses, and you have a most Sovereign Cure for all manner of Burning whatsoever.

The End of the Fifth Book.

Notes

• * 1.1

  The Use of the Azimuth-Com∣pass.
• * 1.2

  The Amplitude Compass.
• * 1.3

  How the Nee∣d••s of the Compass must be set.
• * 1.4

  Of the Devices of Instruments.
• * 1.5

  The Staff.
• * 1.6

  〈 math 〉〈 math 〉
• * 1.7

  〈 math 〉〈 math 〉
• * 1.8

  〈 math 〉〈 math 〉
• * 1.9

  〈 math 〉〈 math 〉
• * 1.10

  〈 math 〉〈 math 〉
• * 1.11

  〈 math 〉〈 math 〉
• * 1.12

  Acres as 5:1:24 Per.
• * 1.13

  〈 math 〉〈 math 〉
• * 1.14

  〈 math 〉〈 math 〉
• * 1.15

  〈 math 〉〈 math 〉
• * 1.16

  〈 math 〉〈 math 〉
• * 1.17

  〈 math 〉〈 math 〉
• * 1.18

  〈 math 〉〈 math 〉 The Square of a 11 is 121. and of 14:196 196:121:1440 〈 math 〉〈 math 〉
• * 1.19

  Turn the Pro∣tractor after you have laid down all the Angles in the NE. and S. E. quarterly, and lay the Center-Pin of the Pro∣tractor on the Point O, as be∣fore; and the Diameter on the Meridian-line••
• * 1.20

  How to know if the Sides be rightly measu∣red before you go out of the Field, and Pro∣tract the Plat∣form thereof.
• * 1.21

  〈 math 〉〈 math 〉
• * 1.22

  〈 math 〉〈 math 〉
• * 1.23

  How to draw the Plott by the Protractor.
• * 1.24

  Reduce Perches into Acres, Roods, and Perches.
• * 1.25

  See Fig. 98 in the following Schemes. ☜
• * 1.26

  How to know the Circumfe∣rence of the Earth.
• * 1.27

  How to find the Diameter & distance to the Center of the Earth and Sea.
• * 1.28

  〈 math 〉〈 math 〉
• * 1.29

  The true height and distance from the Eye.
• * 1.30

  See Figure 99 in the follow∣ing Schemes. ☜

  46 d.	00 m.
  79	00
  125	00
  180	0
  125	0
  55	0
• * 1.31

  See Figure 100 in the follow∣ing Schemes. ☜
• * 1.32

  180	0
  45	0
  135	0
  22	30
  157	30
  180	00
  d. 22	30
• * 1.33

  And by these Rules you may find all the op∣posite sides.
• * 1.34

  See Figure 110 ☞
• * 1.35

  See Figure 101 ☜
• * 1.36

  See Figure 102 in the follow∣ing Scheme. ☞
• * 1.37

  See Figure 103 ☞
• * 1.38

  See Figure 104 ☜
• * 1.39

  See Figure 105 ☜
• * 1.40

  〈 math 〉〈 math 〉
• * 1.41

  M stands for Mean, D. for Diameter, MD for mean-Diameter.
• * 1.42

  See Figure 106 ☞
• * 1.43

  These sort of Cask Gaged 5 several ways.
• * 1.44

  To know what it shall hold in all.
• * 1.45

  Extend the Compasses from 231 to 282, the same ex∣tent will reach from the Con∣tent in Wine-Gallons 44 8/10 to 36 7/10 the Contents in all Gallons.
• * 1.46

  By the same Rule you may know what an Ale-Cask will hold in VVine.
• * 1.47

  See Figure 107 ☜
• * 1.48

  33 − 6/10
• * 1.49

  This table is made to ½ or 50/100 parts of a Gallon: by same Rules you may make him Quarts or Pints.
• * 1.50

  The top or Bong is up∣permost in the Column to the left hand 63 Gal. the bottom is ½ to the right hand Colum.
• * 1.51

  23 − 7:10000 to 3049

  3043 answers 15:76/100

  63; 15.76 so 44 85/290 = 11 22/100 Gall.
• * 1.52

  See Figure 109 ☜
• * 1.53

  See Figure 110 ☞
• * 1.54

  See Figure 111 ☞
• * 1.55

  0	63
  0	63
  0	51
  1	77
• * 1.56

  Su••h Rules are made by Walter Hays in More-Fields, and in Brictly by P. Staynard.
• * 1.57

  To find the Square-Root by the Tables.
• * 1.58

  A common Er∣ro•• amongst most Carpen∣ters.
• * 1.59

  A right Lined sharp Piece of Timber is cal∣led a Pyramide
• * 1.60

  But the Base thereof Round it is a Cone.
• * 1.61

  16:100 10 24/100

  10

  000

  100

  1000

  24

  1024
• * 1.62

  〈 math 〉〈 math 〉
• * 1.63

  The Diameter of a Shot of 1 pound is 1 Inch 94/100 parts.
• * 1.64

  〈 math 〉〈 math 〉
• * 1.65

  〈 math 〉〈 math 〉
• * 1.66

  〈 math 〉〈 math 〉
• * 1.67

  By the same Rules you may find the Dia∣meter of a Shot with a String.
• * 1.68

  thinnest	4:3
  ½ Diam.	2:5
  Centre	6:8
  thinnest	4:3
  of Met.	4:3
  	5:2
  Dem.	14:0
• * 1.69

  〈 math 〉〈 math 〉
• * 1.70

  47 Pound of Metal.
• * 1.71

  How to know good Powder.
• * 1.72

  Shooting by the Metal.
• * 1.73

  of Shooting by a Dispert.
• * 1.74

  To Shoot in a Right-Range, that is, as far as the Bullet doth go in a Right-line at any Degree of Elevation.

  By the Rule of Proportion.

  Paces.

  248	239519
  d.
  10:354	254900
  200	230703
  Sum	485003
  285	245484
• * 1.75

  Which done backwards, is 6 degr. against 285 in the last Table.
• * 1.76

  Extend the Compasses from 704 to 370, the same will reach from 900 to 473.
• * 1.77

  505

  461

  44
• * 1.78

  505

  473

  32
• * 1.79

  The use of the Quadrant on back-side of the Scale in the third Chap. for the Mounting of the Piece.
• * 1.80

  You may make use of this Ta∣ble by the same Rules in the 32 Sect. and Table of dead-ranges,
• * 1.81

  Bristol, Septem. 12. 1667 by experience of a Spanish Ship called the Victory of Majork, sunk in Hung∣rode at the Pill; her Bur∣then about 300 Tuns; we weighed her with 4 empty Lighters of 30 Tuns a piece, by lashing the Ligh∣ters at Low-water, Head and Stern; and at High-water the Ship we heav'd A shore by a Grabble, and did rise as the Water did flow; and the Low-wa∣ter or two afterward, the Ship was free, and swim∣med; the Ship and Water was Estimated to weigh 1000 Tuns, that the four Lighers weighed; she had no Goods in, but turned over as she was, having done to Carein.
• * 1.82

  The best weigh¦ing of Ships, is where the water ebbs and flows much.
• * 1.83

  The Sdells are made of Glass, or nelld Clay, or Paper.