THE GUNNER SHOWING THE WHOLE PRACTICE OF ARTILLERY: With all the Appurtenances thereunto belonging.  
Together with the making of Extraordinary Artificial Fireworks, as well for Pleasure and Triumphs, as for War and Service.  
Written by ROBERT NORTON, one of his Majesty's Gunners and Enginiers.  
LONDON, Printed by A. M. for HUMPHREY ROBINSON, and are to be sold at the three Pigeons in Paules-Churchyard, 1628.   

TO THE IMPERIAL MAJESTY OF GREAT BRITAIN, FRANCE, AND IRELAND, KING CHARLES.  
ALmighty GOD having made your Majesty Sovereign over many strong Nations, naturally Martial, and Artificially exercised in Arms: Yet if they want Discipline (though many) they are but few; and though else strong, yet therefore weak. Your mighty Kingdoms also being strongly situated by Nature, Entrenched about with a broad Dike the Seas, Pallisadoed with Rocks and Sands, Sentinelled with strange setting Tides of Ebbs and Floods, Defended by frequent Storms and Tempests, highly Inritched with fertility of Nature, Furnished plenteously with all manner of materials fitting the felicity of Man's life upon Earth, both for time of Peace and War; So that nothing can seem to be more wished for, if Industry be used; but especially, if Correspondency be found in a good and due temper between the Head and the Members, as perfect Obedience and Service from the Members to the Head, and entire love and care from the Head to the Members, for their good and safety. Guns your Majesty hath, but want Gunners, because they want Respect and Encouragement: let Occasions be ruled with Reason, Wars managed with Discipline, judgement, and Policy: Let stubborn Offenders be punished, Deserving Men preferred, Eminent Places not granted for Favour to insufficient Men or Strangers, having honest Subjects fare more able to perform the Service: So we shall all make Holiday to serve our God, obey our King, and enjoy God's blessings bestowed upon us, every Man Eating his Grapes under his own Vine, without fear of foreign Enemies: To conclude then, nothing can be wanting, Men, Money, Means nor Prosperity; when the God of Order hath settled such a congruity. Now that your Majesty may the better be provided hereafter of understanding Gunners to manage your Artillery, the powerful Regent of modern War: I have endeavoured in this Practice of Artillery, to supply their wants the best I can, not doubting but in short time it may work good effect therein: If your Majesty will be graciously pleased to countenance these few Lines under your Royal Patronage. My wrongs and discouragements hath hitherto hindered the publication hereof: Which, if your Majesty would be pleased to refer to be examined and relieved accordingly; It will then appear I had cause to speak; And I should be again encouraged for greater and further Services hereafter: So most humbly craving pardon for my boldness, prostrating myself at your Sacred Feet, as by Oath and Duty bound, will ever remain,  
Your most Faithful and Loyal Subject and Servant, ROBERT NORTON.   

To Mr. Robert Norton, and his Practice of Artillery.  
When first I knew the difference of Time, and several Climates of the World's round Globe,  
I then thought Artists fittest Men to climb to Honour, and to wear the Golden Robe;  
But now these Times do differ from that Time,  
Strangers respected are By Courtier's crime.  
Then when I knew the Seas, my whole delight was how to trim a Ship prepared for War;  
But all was vain, till Gunner's Skill and Might, with practised Forces all excels so fare;  
Let Seamen, Land-men, all Men truly know  
That Gunners Art's of Substance, not of Show.  
The Land-man, he most boldly makes Approach with Horse and Foot, with Sword, and Shield, and Spear,  
But all were vain, he never could encroach, if Guns and Gunners should be wanting there;  
Therefore such Artists sure 'twere best to cherish,  
And expert Gunnered Engeneers to nourish.  
For proof whereof, let every Artist view, why such Men should not to preferment mount,  
Peruse this Book, its Lynes, and Fgures true, so may he find the difference of Account  
Twixt th' English, and the Dutch, Norton, and Born,  
Then give our own their due without demor. 
Moratur in lege.   
But Norton, I have been something to bold to Paraphrase upon thy Worth and Quality,  
Because I want sufficient, to unfold them, and th'Ingenious Works reality;  
Let this suffice, thy praise will show itself,  
It's worth the Golden-Fleece, the Indian Pelf.  
Captain john Butler.   

A Due to the Author, his Work and Worth.  
SInce mongst all Nation's War itself doth show,  
It behoves Man War's Weapons for to know,  
Who here may learn the Gunners aiming Arts,  
Which thy free industry to all imparts;  
The fittest subject now it is by fare,  
At these times, when such Rumours are of War,  
And fills the Ears, and Courages awake,  
Go on then, and to Thee this glory take,  
That he that reads these things which thou dost write,  
May know a Gunners part, though he ne'er fight,  
And know Wars chiefest Engines use and strength,  
In Boar, Cilinder, Axis, and in Length,  
In Touchhole, Carriage, Wadd, in Shot and Charge,  
Of Fireworks in brief thou speak'st at large;  
French, Spanish, Dutch, Italian, veil your Caps  
To Nortons' skill, in Mars his Thunderclaps.  
john Rudstone a Lover of the Arts Mathematical, Theoric and Practic.   

To his good Friend Master Robert Norton, on his Practice of Artillery.  
I Told you Friend, before your Book I'd write,  
But not Idolatrize with Poetic spirit,  
Doing our loves much wrong, in little right.  
The Time's necessity, and each Studious mind  
Will make it praise itself, which you shall find  
By'ts oft impression, thou'rt being here refined.  
Yet (justly I confess) I have been shown  
Books that sell well, yet not for what's their own,  
But for Commendators before them known.  
And this integrity Commands me say,  
That to the Truth thou showst the rightest way,  
For Young Artists, and here the Old may stay.  
For here theyare satisfied with small dispense  
Of Purse, or Brains, of Skill the quintessence,  
Drawn from the Antic Artists excellence.  
I know rich jewels may themselves commend,  
Which be such Books (that for the public end)  
With judgement written are, So thine good Friend.  
Richard Robinson.   

In the due Honour of the Author Master Robert Norton, and his Worke.  
PErfection, if't hath ever been attained,  
In Gunner's Art, this Author hath it gained,  
By Study and Experiences, and he  
The Fruit of all his Pains hath offered Thee,  
A Present well befitting this our Age,  
When all the World is but a Martial Stage:  
Let sweeter Studies lull a sleep and please  
Men, who presume security, but these  
Thy Labours practised, shall more safely guard  
Those that foresee the Danger, th'other barred  
This benefit: We Soldiers do embrace  
This Rare and useful Work, and o'er the face  
Of all the World, let thy Fame's Echo sound,  
More than that roaring Engine, and redound  
To th'honour of our Nation, that thy Pains  
Transcends all former, and their glory stains.  
Captain John Smith, HUNGARIENSIS.   

A Table of the Contents.  

DEfinitions Page 1  
Demands Page 2  
Maxims Page 3  
Theorems Page 5  
Arithmetic Page 17  
Geometry Page 23  
Perspective for Heights, Breadths, Distance, and description by Plat. Page 30  
Chap. 1. Of the general definition of Artillery. Page 35  
Chap. 2. Of the first invention of Guns and Gunpowder. Page 37  
Chap. 3. Where Ordnance were first used in these parts. Page 40  
Chap. 4 Of what forms and fashions Ordnance were first made. Page 41  
Chap. 5. Of former foreign foundings of Ordnance, and of French Ordnance. Page 42  
Cham 6 Of founding legitimate Ordnance, with a Table, and Venetian Ordnances Page 44  
Chap. 8. Of Bastard Pieces with their Table of Names, Weights, and Measures. Page 44  
Chap 9 Of extraordinary Pieces and a Table of their Names, Waight, and Measures, and of the Drakes, and their Inventor. Page 46  
Chap. 10 Of English Ordnance distinguishing into 4 kinds, and those into sorts, beginning with the Cannon. Page 51  
Chap. 11. Of the Cannons of Battery in particular, or of the first kind, and the sorts thereof. Page 54  
Chap 12. Of Culvering the second kind, and the sorts thereof, Page 55  
Chap 13 Of Canon Periors the third kind and their sorts. Page 57  
Chap. 14. Of Mortars the fourth, and the square Murderer Pettar, etc. Page 59  
Chap. 15. Of several ways to prevent a Pettard. Page 64  
Chap. 16. With what Instruments to break palisadoes, Grates, Percullisses, etc. Page 65  
Chap. 17 To dispart a Piece true bored. Page 66  
Chap. 18. Of certain faults in foreign foundings of Ordnance. Page 67  
Chap 19 Of the Ligue or Aligation of Metals for brass Ordnance. Page 69  
Chap 20. Of Earth's or Powders for Moulds to cast them. Page 70  
Chap. 21. Of making Moulds for the founding of Ordnance. Page 71  
Chap 22. Of the Place, Measure, and use of the Trunnions. Page 72  
Chap. 23. Of Examining if a Piece of Ordnance be well made, and of what kind and sort it is. Page 74  
Chap. 24. To tertiate Ordnance, and find what Powder they can bear. Page 77  
Chap 25. To find if her Soul lie in the middle of her Body. Page 88  
Chap. 26. To disport a Piece, whose Soul lieth Horizontally and paralelly awry in her Body. Page 81  
Chap. 27. To dispart a Piece whose Soul lieth vertically and paralelly awry in her Body. Page 82  
Chap. 28. To dispart a Piece, whose Soul lieth awry Traversly and not paralelly in her Body. Page 83  
Chap. 29. Of the Large and Large Line in wry bored Pieces. Page 86  
Chap 30. To find the Weight of any Shot by the Diametre Arithmetically. Page 87  
A Table of the Weightes and Measures of all Metals and Stones named. Page 90  
Chap. 31. To find the same Geometricaly and Instrumentally. Page 91  
A Table to mount any Piece by the Jnch Rule as well as by the Quadrant, to any Degree assigned. Page 93  
A Table for every quarter of an Inch height, for Weight of Jron, Lead, and Stone Shot. Page 94  
The Description and use of my Gunner's Scale. Page 94  
Chap. 32. Of the Rule of Calibres, or due vent for each Shot. Page 95  
Chap 33. Of the Gunner's Quadrant. Page 95  
Chap. 34. A new Devise of the Authors, to Level, Mount, or Embase a Piece of Ordnance by a Staff or Halberd. Page 96  
Chap. 35. To find the right Range of a Piece for every Mounture. Page 97  
Chap. 36. To find the Level under the right Range. Page 98  
Chap. 37 To find the Level under the Crooked Range. Page 99  
Chap. 38. Of the violent Crooked and Natural Course of a Shot. Page 99  
An excellent Dyagram of Randons'. Page 99  
A Table of Randons', and a Table of secant Ranges and their uses. Page 100  
Chap. 38. To load a Piece Gunner-like. Page 101  
Chap 39 Whether the longer Piece will out shoot the shorter of equal height. Page 102  
Chap. 40 Of shooting Myra Commune or by the Mettle. Page 103  
Chap 41. Of shooting by the Axis or desperate. Page 104  
A Table of right Ranges. Page 105  
Chap. 42. Of shooting upon the advantage. Page 105  
A Table of dead Ranges. Page 106  
Chap. 43. To amend a fault at the second shot. Page 107  
Chap 44. To make an assured good shot. Page 109  
Chap. 45. To make Ladles and Sponges for each Piece. Page 110  
Chap 46. To make Bridges over Rivers for the Army and Ordnance. Page 112  
Chap. 47. How to defend a Fortress besieged. Page 113  
Chap. 48. To make an extraordinary safe Counterbattery. Page 114  
Chap. 49. Reasons of failing of a shot. Page 115  
Chap. 50. To conduct a Mine to blow up a Place, and of Galleryes Page 116  
Chap 51. Of the Windles, Martinet, and Archimedes endless Screw. Page 118  
Chap. 52. To draw Ordnance to the top of steep and rough Mountains. Page 120  
Chap. 53. How the Train of Art should be ordered in a March. Page 121  
Chap. 54. To draw Ordnance by labour and Pioneers if Cattles want. Page 122  
Chap. 55. Extraordinary privileges of the Train in Marching and lodging. Page 124  
Chap 56. To weigh a sunk ship and Ordnance surrounded. Page 125  
Chap. 57 To make Cartredges to load Ordnance without Ladle. Page 127  
Cham 58. The names of the parts of a Piece. Page 123  
Chap. 59 The making of a Field Carriage in proportion. Page 129  
Chap. 60. To make Wheels and Axtrees for Carriages for Ordnance. Page 130  
Chap: 61. To make Candlesticks, Blinds, Saussedges, and Saussons to hide. Page 132  
Chap. 62. To plant Ordnance in secret and double Battery. Page 133  
Chap. 63. To plant Ordnance where the Rampart is to narrow, and earth wanting. Page 134  
Chap. 64. To make a Battery with Pieces interred. Page 135  
Chap. 68 How the Ordnance are to be placed at the time of joining of 2 Armies in Battalia. Page 138  
Chap. 69. How to fill up a wet Dyke, to approach a Breach made. Page 139  
Chap. 70. Of the Gunner's service in general. Page 140  
Chap. 71. Of the difference of our English measures and weights, from forraigue Nations of Feet and Pounds. Page 141  
Chap 72. Of making of Salpetre, whether Natural or Artificial. Page 142  
Chap. 73. Of Gunpowder, and the making of the usual sorts thereof. Page 144  
Chap. 74. Of the making Matches to fire Ordnances, Trains, Artificial Fireworks etc. Page 147  
Of Fireworks for Triumph. Page 149  
Of the Rocket and Structures, etc. Page 150, 151, 152  
The description of certain Wheels of Artificial Fireworks, etc. Page 153  
How to make a Rice, and a Castle, and a Trunk of Artificial Fireworks. Page 154  
How to make flying Dragons and Rockets that will run upon a Line and return again, etc. Page 155  
How Artificial Fireballs and Granades are to be form & loaded with their mixtures. Page 156  
How to convoy or direct Fire into a place assigned, or upon the Enemy in an Assault. Page 157  
Of the Piked Trunk Gun, and quadruple Barrell-Peeces. Page 157    

I hope with Scapes that altar not the sense,  
The friendly Readers will for Love dispense:  
And those that are in th'Errata here expressed,  
His loving Pen will mend, and thus digest.  
Page Line  4 8 For bodies more, r. bodies move. 18 13 in the total for 2536, r. 2356 Ib. 40 for 31701, r. 31941, & Jb. 43 for 49861, r. 1492101 19 vlt. for the 2 and carry, etc. r. the 2 and 2 times 6 make 12, set down the 2 and carry 1, etc. Ib. 10 for 149861. r. 149210 20 vlt. for files and flank, r. Front 21 1 for Front multiply, r. Flank divide. Ib. 3 for Front, r. Flank 22 10 for double, r. double 3 and have 6 Ib. 22 for 22/300, r. 233/300. Ib. 23 for thirty, r. three hundred. 23 7 for ●/61, r. 8/12 27 22 for subscribed, r. circumscribed 29 36 for B to D r. B to C. 30 41 for parts the, r. parts give the. 31 1 for 8000, r. 24000. Ib. 2 for 66 r. 200. 32 1 for 20, r 29. 35 16 for near joined, r. near or joined. Ib. 26 for and both the ancient, r. and the ancient. 39 19 for, For that now, r. That now. 39 27 for Aiming, r. Aim at. 42 24 for, For I say, r. I say. 44 3 for ½, r 1/20 and in the Table under for deg. r. heights, and for de, r. lengthes. 45 30 and 31, for leveleth, r. level. 53 13 for 1 ½, r. 17 ½. 54 42 for 143, r. 250. 67 43 for afterwards, r. forwards. 69 24 for 16, r. 100 78 22 and 23, for ordinary Culvering, r. lessened Culvering. 94 vlt. for Table following, r. former Table. 97 39 for right range, r. dead range. 105 17 in the Table for 424, r. 524. 106 35 for 2000, r. 1000 142 33 for to dissolve, r. to vapour. 144 Between lines 5 and 6, r. The 73 Chapter. 146 6 for asle, r. add. Ib. 27 for topped, r. Tapped. Ib. 31 for top, r. tap.   

THE PREFACE TO THE courteous Readers.  
THe Art and Practice of Artillery (the subject of this present Treatise) being as Bianco saith, the Crown and Palm of the Wars and Military discipline, teaching how to overthrew & demolish Cities, Towns and Castles, to sink Ships, and inhumanely even to tear the life and souls from the bodies of innocent men, women, and children, viet armis, to get the possession of the Goods and Lands that rightly belong to others for ourselves: it may therefore at the first blush seem to be absolutely contrary to all Christian charity. But when on the contrary we come to find, that War is even the Mother and Nurse of Peace, the Rampart of justice, and the Law of the World; yea, the Scriptures affirm that War was a thing authorized by God himself, who commanded Saul thereby to destroy the Amalekites, and not to spare either Man or Beasts, etc. As also that War was exercised in Heaven by the good Angels against the bad: So likewise hath Nature armed the Beasts of the Field, the Fowls of the Air, and the Fishes of the Sea, and as it were by instinct, taught them with their Horns, Talents, Teeth, and Fins, to fight one with another, to defend themselves, and offend others. But more especially, when we truly consider, how that without War and Warlike Amonition, and Discipline, no Kingdom or Commonweal can long subsist in Peace, or be able to defend itself, nor offend their Enemies: the case will then seem to be much altered. These then, and the great preparations, the Martial policies, cruel stratagems, and devilish inventions of the common Enemies of our King and Country (whereby they intent, and with malicious greediness daily endeavour to destroy us all with our Wives, Children, and Families, to the end to possess our goods and lands.) These I say may more than incite us now (though late) to learn, know, and use to practise this principal and potent part of War, so that thereby with God's assistance (always making him on our side) we may become able and prosperous in resisting those their intended mischiefs, and break the necks of their cursed designs, and so consequently escape those eminent and threatened dangers.  
Now for as much as the most presperous effects have usually succeeded and most vigorously prevailed, when ingenious inventions and religious politic diligences hath been joined with Arms (good Policy fare exceeding Force.) Therefore for the better understanding of the sequent discourses, we shall do well first to conceive that every material thing is either to be lineally described, or else intellectually understood by some proper Figure, or apt word, name, or definition, which properly belongeth thereunto: For as every Art hath certain Rules and Principles (to preceade) without the knowledge of which no man can attain unto a necessary perfection for practise thereof, unless he first endeavour to learn (rather by Reason then by Rote) what each part thereof is, with the Name and Nature of each Member and part of it (without which first obtained) And I say, let a man take never so much pains and study therein, he shall but in vain puzzle his brains and not benefitting himself. The neglect of which is the cause why many (otherwise well affected to Art) do so fruitlessly bestow both their Time, Labour, and cost, to no purpose, often condemning the Art as too hard for them, when (God knows) the only cause is their disorderly progress in the study and practise thereof: And I dare say for the Gunner's Art, although it be deep (even able to suppose the known parts of Natural Philosophy, Arithmetic, Geometry, and Perspective, each of which her handmaid is) yet by the Definitions, Theorems, and Questions contained in my former Book extant, Of the Art of great Artillery, and in this of the Practice of Artillery, I hope the willing may (with small pains joined with orderly and diligent practice) wade over this Ocean safely satisfied; nevertheless that if Archimedes' (were he now living) without experience and long practise therein) with sundry trials he could not possibly demonstrate the manifold varieties of that Mixthelicall arch or circuit of the Bullets courses, compounded of violent and natural motions, and receiving infinite diversities, according to the several proportions and temperatures of the Powder, length of the Piece, matter of the Shot, Mounture, and Mettle, lead on by Experience the Mistress of all Arts, Action being the best Tutor: Much less I (the most unable of many) who have endeavoured herein more to respect a few experimented truths, than many Rhethoricall embellishments of words. Therefore neither can, or will, I presume to assume so exact perfection to be herein: although I have endeavoured to avoid the apparent errors of Santbech, the erroneous principles of Tartaglia the false rules of Rosselli, the time-overwerne directions of Cataneo, the gross allowances of Collado for Mountures & Imbasings, but especially the arch false proportionality taught in Mr. Smith's Art of Gunnery, now entitled the Complete Soldier (many of which are by Mr. Diggs and myself noted, at the end of my said Book of the Art of great Artillery, and a number more there are most intolerable false, For the positions which he there incerteth, are fit only to lead young Gunners out of the right path and way they should walk in, with a seeming easiness by tying (as he would) such things to Arithmetical works and proportions, as are directly contrary, and of another nature, as a small trial will manifest, which in crutesie, I thought fit to advertise the Reader of: But as Palingenius saith, 
Frivola si fuerint fundamina tempore paruo  
Deficiet, quiquid super his fabricare volimus.   
Some men also may imagine because the figures herein are many of them, the same that were cut for Captain Vffanoes' Book of Artillery, Printed at Frankford, that therefore I have only translated the same. I confess the figures most of them being good, and he for this and the most part he hath written of this practice, being the best of any the Authors that I ever read: yet had I only translated him, I should but little have helped English Gunners their Measures, Weights, Ordnance, and Powder so much differing from our English, as in their places I have showed, it would not have been operae pretium so to have done: But that I have from him and other Authors made choice of some things, and refined & applied others for our benefits, I am not to deny; nor that the Figures are many of them his that I have herein written upon, which was by reason of their goodness, faireness, and cheapness; for the Figures, had they been cut of purpose in England, would have made these Books too dear for Gunners, for whose good they were originally destined, wherein I have roughly endeavoured in well meaning, which if it be well taken, I shall be therewith well satisfied, and restreadie to explain whatsoever shall herein seem difficile.  
Now that this my Treatise for the practice of Artillery, may the more currently proceed, & be the plainer to the understanding and satisfaction of the Reader, I held it necessary first to show by certain Definitions, Demands, Axioms, & Theorems (besides those in my former Book) called the Art of great Artillery (which I wish every young Gunner to peruse also with diligence) the names, natures, and operations of such things as are necessary to be known, used, and done in the Practic part thereof, without which it were impossible to conclude any thing well, and as it ought to be. Therefore as in the Wars of our age, there is no earthly force that can more command the Fortified, or resist the assaulting Enemy then great Ordnance duly used. So the Gunners therefore ought to endeavour to understand these so well, that they discharge them not in vain. First, in regard of the great expenses of Ammunition thereby cast away: Secondly, lest thereby they frustrate the wished service. Thirdly, in laying themselves and their Companies open and undefenced to the Enemy's Forces, which will (in them) increase valour, and in yourselves terror, thereby also deserving to purchase great blame and dishonour from the hands of their Commanders, with the loss of the Prince's favour, and utter overthrow of their own preferment ever after. Wherefore seeing that such fruitless discharging of Ordnance in the time of service, is so great an inconvenience, and happeneth most commonly for want of knowledge, or ready means to direct the Pieces precisely to the mark; I have thought it worthy my labour therein to show Artificial means (to such as are desirous to learn) how to know, direct, and prepare the Pieces committed to their charge; so, that in time of need they may be assured to make their Shotts take good effect, only by applying themselves to understand and practise these few things following.   

THE PRACTICE OF ARTILLERY.  


The first Definition.  
PLACE is the space environed with the interior superficies which containeth and enuellopeth each thing, 
Euclid. def. 5. lib. 1.  limited in every sense with the proper dimensions of the thing contained.  
As the Place of my Body hath the same dimensions that my Body hath.   

Definition 2.  
Empty, is the Place in which no corporal thing is contained.  
But nature abhorring Emptiness hath left no place for it in this sublinar world. 
Arist. lib. 4. tex. 57    

Definition 3.  
Rare, Is that which under large dimensions hath but little matter.  
Contrariwise Thick or Grose hath under little measure much matter for Thickness and Thinness are such bodies consequent qualities, 
D. Tho. 3. pant. qua. 77.  as have much or little matter under their dimensions.   

Definition 4.  
To Increase, is to enlarge the former dimensions.  
Increasing cometh of changing of quantity from little to more which may be without changing the figure, As the Gnomon added to the Square increaseth it, yet the figure remaineth square still.   

Definition 5.  
To touch, is to have their extremes together.  
As touching is proper only to a Body, so is it also proper unto all Bodies, 
Arist. si. 4. Phis. tent. 13.  for it is reciprocal with the quantity of a Body.   

Definition 6.  
To Moon, is to transport from one place to another, or to turn into the same, or change the quality.  
Because that which we entreat of is Material, and depends upon an Action of Nature, 
Cap. 7. lib. 8. Phis.  we will define changing of Place to be made by mutation from the Place, or from the Grandeur: as that which rarifieth, extendeth, and changeth place by increasing more, and one thing may move another by removing it, or by drining it away.   

Definition 7.  
To remove, is to thrust out of the Place without expulsion or driving it away.  
So to carry, 
Arist. lib. 7. Boys. ber. 10.  to lead, to put from, to press down, to draw, and such like moving rare-things in that manner said to be removed without being driven, cast, or shot away.   

Definition 8.  
To Expel is to Remove by driving out, darting, or shooting away, which is either slowly and easily, or swiftly and rudely.  
Either as the Ram Engine doth slowly, 
Eodem.  or as the Cannon doth swiftly drive away.   

Definition 9  
swiftness, is a force that doth much in a little time.  
As any thing that is transported a long distance in a little space of time, 
In Lache.  is said to be swift.   

Definition 10.  
To Mount, is to raise or elevate upwards towards the Sky above the Horizon: To Embase is to descend, or depress under the same, downwards, from the Heaven's ward.  
Those are terms depending upon the disposition of Men.   

Definition 11.  
Under the name of Artillery we compehend all Arms of Fire.  
As Gunns and Fireworks, etc. for Warlike services.    


Demand 1.  
THat the Superficies of the Column of the Piece be perfectly round, or else regularly squared, especially at the thickest of the Mettle at the Mouth and Breech.   

Demand 2.  
That the Axis of the Boar or Cavity (of the Piece given) be strait from the one to the other end of the Column, and equidistant and parallel from the concave Circumference thereof, at all places so fare as the Shot descendeth into the same, being of equal wideness.   

Demand 3.  
That the Piece given to be prepared have her ordinary Carriage and Platform given, so right and duly fitted, as will neither cause nor suffer the Piece delivering and reversing to start from the level or direction given.   

Demand 4.  
That the Shot keep his course so from his due resting place in the cavity of the Piece unto the Point Blank, or end of the right range thereof, so as that the centre of it be always in the Axis of the Boar (supposed infinitely to proceed) without any sensible declination from the same. The said Bore being part of the way of the said shot, and the director of theresidue of the course of the same.   

Demand 5.  
That the Point Blank, or right line or Range be that point in the Axis of the Boar imagined to proceed and be infinitely continued unto that place where the Centre of the Shot shall in his course sensibly begin to decline from the said continued imagined Axis downwards.   

Demand 6.  
That the visible right line made or imagined to pass from the Breech of the Piece to the Mouth of the same upon the highest ring or supersicies of the Mettle (she lying on her Catiage and Platform) be called the Middle line of the Piece.   

Demand 7.  
That the visible right line made or imagined to pass from the Breech to the Mouth upon the surface of the Mettle vertically over the Axis of the Boar of the same Piece (she lying upon her Carriage and Platform given) be called the Large line of that Piece.   

Demand 8.  
That the shortest distance between the vertical plane of the Axis of the Body of the Piece, and the vertical plane of the Axis of the Soul or Boar of the same Piece, taken upon the Baseringe at the Breech thereof (for the carriage Piece and Platform given) be called the Large of that Piece.    

Maxims of Natural Philosophy necessary to be first known.  

1 EVery motion in the world endeth in repose.  
2 All motions are made upon some quantity.  
3. Every simple Body is either Rare and Light, or else Thick and Heavy, and according to these differences it is Naturally carried towards some part.  
4 The world hath high or upwards, and low or downwards, and the Low dependeth upon the influence of the high.  
5 The rare bodies mount, the fire, more than the Air. The thick and gross bodies descend, the Earth more than the Water.  
6 The lighter are more movable than the heavier.  
7 Nothing worketh Naturally in that which is wholly like or wholly dislike, but in that which is contrary to it, and more feeble.  
8 The Form working, is aided by the Qualities, as the matter suffering, which suffereth by the quantity.  
9 Nature is extremely curious, as well of her perfection, as of her conservation; and then when all things conspire.  
10 Aswell the Action that cometh from the Agent, as the Passion from the Patienthath proportion.  
11 Accident taketh his unity from the Subject, and goeth not from one thing to another.    


THEOREM. 1. Every Corporal thing reposeth in its natural place.  
LIght body's 〈◊〉 towards the heavens upward, and heavy bodies towards the Earth's centre downwards, each Body is light or heavy; if it be heavy, it will then move downwards; if light upwards Now the circular motion is neither upwards or downwards, therefore no Motion can be circular but by violence.   

THEOR. 2. Motion may be made in any place within the Moon's Orb.  
Every thing that is within the Lunar Orb may make motion or change,   

THEOR. 3. Before any thing moveth towards its Natural place, from its first being, it goeth stretching unto the natural measure.  
Neither augmentation nor diminution is made but only by changing of the qualities or forms, for the qualities alone (incontinently following new generation) do cause either stretching or shrinking. And true it is, that in such Mooving as tend unto the entire ruin of the forms, the just dimensions are not found to be but either greater or lesser according to the quantity agitating most forceably therein, and so it moveth most violent and longest.   

THEOR. 4. Nature admitteth no emptiness.  
Nature pursueth and entertaineth perfection as much as is possible. Now the perfection of Motion is the end thereof; namely the repose, that the simple Body would find either upwards or downwards in all places: therefore in the Elementary universe, they affect their repose either upwards or downwards. So there is not by Nature any such thing as vacuity, for the avoiding of which, nature maketh heavy things mount, and light things descend, whereby marvelous things are performed. As we may see by our Pumps, which make water ascend as high as the clouds, and by the spirituals the air is retained beneath. And diverse other effects seeming so miraculous to such as see them as they cause them to wonder thereat. For whence cometh it that a vessel of Marble filled with water, when the water cometh to be frozen into ye, that it break the same though a foot thick? but that the water thickneth thereby, and so breaketh the volume of the ordinary quantity thereof, the cause preceding, the effect followeth. So also a narrow necked bottle filled with liquor, and turned the bottom upwards, yet retain the liquor from running out: because Air cannot enter therein, to fill the place, whereupon we may judge that the Law of fullness is more general, and precedeth that of the Moving of simple Bodies.   

THEOR. 5. Every Body hath a place.  
A point which cannot be marked in essence, not having any parts, is no Body, and therefore is contrary to the Hypotheses. But a Body hath place of dimensions, so if the surface of the body which approacheth on all sides, and toucheth every where, tying the superficies to close the body, it is then in such a place as hath the very same dimensions within, that the body hath without, or else there must be emptiness, which by the precedent were absurd.   

THEOR. 6. A Body rarifying its self, the place thereof increaseth as the Body increaseth.  
As a Body of Earth that then contained one  foot in measure be made water, which adding thereto, one other solid foot, the place also must increase, from one to two solid feet, or else it hath not the same just dimensions within, that the body hath without, and so it is not the place of that body of water; so if the place also were greater than the body filled, there must in that place be emptiness between it and the body, which were absurd: therefore the place increaseth as the Body ratifying doth.   

THEOR. 7. Two Bodies cannot be together in one and the same place.  
If several Bodies could be together, all the members of one same Body might also have one and the same place, and each part might one fall into the range of the other, which were to take away from the quantity, the true Nature thereof, and which by its essential property setteth out the parts severally one from another: Nevertheless that some sleight appearances have seemed to yield a suspicion that it might be so: As take a vessel full of ashes finely sifted, and you may put into the same as much water also as would without the ashes have filled the vessel. So by the vessel full of ashes, and the same vessel full of water, two Bodies seem to be in one place: So into a glass full of water you may put in many pieces of money before it run over. And likewise an iron heated red hot, is it not fire and iron together, and so two bodies in one place?  
No, for these are but illusions: for the first vessel filled with ashes (that are very volaryle) part flieth, and the rest hath place doubtless, but the water swelleth by means of its unctuousnes received, unto a roundness above the brims of the vessel as much as the true body of the ashes is over, and yet spilleth not. And so in the glass likewise the supreme surface of the water swelleth as much above the brims of the glass as the Body of the piece of money hath received place. And lastly, seeing it is but the form of fire or quality of heat lively lent unto the iron, it can not be truly said, that therefore two bodies are together therein, for there is but one matter under those two forms having but one quantity, so neither are two bodies mingled in one Place, nor penetration of dimensions, which is impossible: from whence the ingenious practizer may extract admirable effects.   

THEOR. 8. A place filled cannot receive another Body in without expelling the former one.  
Amongst Bodies, some are hard and robust, and some are soft and tender, so that if unto a soft body in a Place, a hard body should enter, it would violate the dimensions of the soft body. And seeing Plato himself said there was no solid things, but terrestrial, this difficulty were fit to be resolved. Plato then spoke not of Mathematical solidity, or of shorter or longer dimensions, but of that rather which is called firmness or hardness: as we usually say stone to be more solid than wood, and iron to be more solid than stone: also if we have only respect to the demonstration, than there is as much solidity in a Cubick foot of Butter, as in a Cubick foot of Marble stone: And so if the Air or Water do give way to Bodies that are more firm or heavy, it is not because they are less solid, but that they are more movable and lighter. Therefore if a vessel full of Air or Water had an other hard or heavy Body put thereinto without expulsing of the Air or Water proportionally. Then two Bodies would be in one place, which is a thing by the former impossible.   

THEOR. 9 The Resistance of the Moved proportioned to the Mover, furthereth the Motion.  
The Action and ●assion must be proportionals amongst themselves: It were but vain for the Agent to give a strong stroke, if the thing that is to be moved receive it not: And it cannot receive it well, if there be not contrariety, (which resteth in the Resistance) for so in the object that should obey entirely, 
Ma●●●. El. Artil.  there would be no Action at all: For nothing worketh that is wholly unlike. Contrariwise, also if the Resistance were wholly like, or equal to the force of the stroke, there would be no Motion: For nothing worketh in that which is wholly like, wherefore there must be a proportion exercised between the Mover and the Resistance, 
By the same,  to attend the entire impression of the stroke: for if the Resistance be greater than the force of the stroke, the Chaser shall be chased: for of two Adversaries, the most violent is the Master. Besides, the more an Action is continued, the greater it is. Therefore the longer time the Moner toucheth the Moved in expulsion, the more the force of the Moving impressed, is entertained, and longer doth it endure. And this is the reason why the Powder, Wadd, and Shot, are driven into a Piece, but with mean force: For if the Shott be too lose put in, it would not well receive the fury of the Powder inflamed, and the force of the blow will be but weak. And when the Shot goeth in too stiff, or is forced in too hard, or the Powder over-rammed, than the Powders Come, being thereby broken, will be cloyed so close, that it will blow much of the force thereof out of the Touchhole, before the Shott be discharged: But if the Shot were oval or too high, and being forced in, doth stick by the way; it breaketh the Piece, and causeth often lamentable and dangerous effects, without performing the expected service.   

THEOR. 10. Fire taking the Powder, of necessity the Shot must be driven forth, and the Piece discharged.  
At the moment of the inflammation of the Powder, the Piece must necessarily shoot off, and discharge the Shot, for the Powder is then in his last power to be inflamed, and the Fire taketh in an instant. Now that which is burned is rarified, and so extends itself (Fire being the rarest of the Elements) but being so blocked up within the concave ciillnder of the chamber, that it is impossible to extend itself, unless it remove the shot which occupyeth the place it must extend into (for penetrate the Mettle at the Breech and sides it cannot) Nature than otherwise absolutely commands this extension by the perduction of this new form of fire. Wherefore from a Natural violence, and from a force unto which all things conspire, and nothing can resist, the shot is chased, and the piece discharged: whereby we may see how Philosophy and the knowledge of Nature's works, may guide us to admirable inventions, The impossibility of the penetration of dimensions and the necessity of this sierie generation, when the Active forces are united to the passive, this hath lead our predecessors by the hands to the fabric of the fearful Machyve the Gun beyond all that ever the Art of Man could think upon.   

THEOR. 11. The Ballet gins to fly before the perfect firing of the Powder.  
The Powder is not perfectly fired, unless it be all on fire; now before the form taketh into the matter (to give it that being) and to change the nature thereof. Namely, from the first rudiments of being, the Matter rarifieth, for the qualities of the Agent preceadeth. Therefore the Place augmenteth, which cannot be unless the shot quit the place: wherefore it beginneth to suffer before the instant of perfect firing of the powder; for that depart is so sudden, that sometimes a great part of the powder goeth out whole and unfired, which could not be if it were perfectly inflamed, and therefore the greatest inflammation maketh the greatest force.   

THEOR. 12. The force of the stroke dependeth on the swiftness of the Course.  
To Strike is a matter of Moving, as is the Time & the Quantity or the distance upon which it is made, which if the time be short wherein it is carried home afar distance, than it is called Swift: Therefore the shorter the Time is, the swister and stronger is the stroke; Now to Move more is to act more in corporal things, and the more quick the Action is, so much the stronger. Wherefore according to the measure of the Agents motion, the swiftness of the course, the stroke is reckoned strong. This is the Enginieres Helicon from whence the most of their strong Engines are drawn, the greatness of the distance is nothing if the Time be long, nor the shortness of the Time if the distance be short.   

THEOR. 13. There can be no moving in Action made more violent then with a piece of Ordnance.  
The volume or extent of the rarefaction being ten times as much when it becometh fire as it was when it was earth, Fire being ten times more rare than Earth: 
By the 5. Max. By the 4. Theor  and of all Nature's Agents the fire, and of all the Qualities beat carrieth away the prize for violence, seeing the generation of fire in the Powder is momentary. Therefore the time of the rarefaction is extremely short, as being of one only instant, if any moment before that generation begin not to drive out the Bullet, the stroke must then be extremely violent, seeing that the distance is very great in respect of the shortness of the Time, 
Ariss. 2. Meteor  unto which we may add the quickness of the flame, which is such, that it will not stay here below the least part of time but will fly away.   

THEOR. 14. The longer the Chase of the Piece the stronger the streak.  
The generation of this fire being made in an instant, the rarity arriveth at once, the violence pressed to chase out the shot, the flame flieth making it issue out, 
By the tenth theorem.  and Air to come in to prevent emptiness, and all as it were in an instant. Therefore the longer the Chase of the Piece is (being fortified and loaded accordingly) the more effectual shall the Action be, and the stroke the more violent, whereby it cometh to pass that long Culuerings carry further then great Canons although with less powder: yet the force is better entertained by their greater length and better fortification to endure the full charge of powder.   

THEOR. 15. A Piece reverseth when it dischargeth.  
When the ignition beginneth at the bottom of the concave of the Piece, at the Touch hole, the piece reverseth at the instant of the rarefaction, the vent it can find, being only forth of the Touchhole, beateth back until the shot be gone out. And this maketh a Piece Mounted to shoot from allow upwards, to reverse more then upon the level or from aloft downwards: for that the Shot which is heavy, and consequently violent in his natural descending when it is forced upwards, it resisteth more than either shot downwards or level; and so the more the weight of the Bullet resisteth, the force that driveth out the shot, which at last it is constrained to obey and to yield the more to the reverse. But the Metal suffereth the more when it is resisted, as some men cause it by making a Rampart behind the breech of the Piece, against which it may stay, thereby to augment the force of the shot. From whence we may gather that the impression of Reverse is only whileft the shot is within the Piece: besides the Touchhole being made near the bottom of the concave doth not only augment the reverse more than if the Touchhole were in the midst of the powder, or rather more forwards whereby the powder would fire together in the less time, and little or none go out unfired, reverse less, and make the fury of the Shot the greater: And this maketh the small Pistols so pierced, to out shoot those that have their touch-holes pierced at the bottom of their bores.   

THEOR. 16. A Piece of Ordnance sheoteth further in a right line, from a low upwards, then from above downwards, except Perpendicularly.  
To the shot made upwards, there is greater resistance of the bullet, but when a shot is made downwards, the force doth not only work, but the weight of the shot also by its natural heaviness, the bullet easily descends from the straight line, falling under expectation; whence it cometh, that the right Range is further in Mountures, then in any Imbasure, for this proposition is not to be understood so at the going out of the shot, (for all right Ranges, are all equally straight;) nevertheless, that it is shortest shooting from aloft downwards, and longest upwards, and the level being the mean between them both.   

THEOR. 17.  
There are three chief most material and efficient causes of the greater violence of any shot made out of great Ordnance, viz. the Powder, the Piece, and the weight of the Bullet.   

THEOR. 18.  
Powder is compounded of three Principles, or Elements, Saltpetre, Sulphur, and Cole, whereof Saltpetre is it that gives the chiefest violence.   

THEOR. 19  
Albeit Saltpetre be indeed the only, or most material cause of the violence; And that Powder commonly found most forcible that is richest of Petre, yet is there a certain proportion of Perfection of these three Components. And that in such sort, as if you add more or less Petre, the violence shall abate.   

THEOR. 20.  
Although Powder be also the most efficient cause of the force and violence of any shot, yet is there such a proportional charge of Powder to be found for every several Piece, in regard of the proportion of her charged and vacant Cylinders, as giving more, or less, than the same proportional charges, it shall diminish, and not increase the violence of the shot.   

THEOR. 21.  
If any two Bullets of equal quantity, but unequal weight, be let fall from any lofty place to the Horizon, the more weighty, shall ever fall the more swiftly: albeit, not porportionally to their weight; which Axiom is indeed erroneous, albeit, a great Philosopher hath averred the same.   

THEOR. 22.  
If two equal Bullets of different weight, be shot out of one and the same Piece directly to the Zenith, both Bullets being of massy mettle, and charged with one quantity and kind of Powder, the lighter shall always outfly the heavier. But such kind of Bullets they may be charged with all, as the heavier shall outfly the lighter, although they be both discharged with the same Piece, and quantity of the same Powder.   

THEOR. 23.  
There is such a convenient weight to be found of the Bullet, in respect of the Powder and Piece, as the Bullets mettle being either heavier or lighter than that weight, shall rather hinder then further the violence or fare range of the shot.   

THEOR. 24.  
There is such a convenient Proportion to be found of the length of every Piece to his Boar or Bullets Diametre in respect of the Powder, and weight of the Ball, as either increasing or diminishing that proportion it shall abate also, and hinder the violence of the shot.   

THEOR. 25.  
This proportion exactly found in any one Piece, doth not hold in all other, and yet the difference and alteration is such, as may be reduced to rules certain.   

THEOR. 26.  
Besides these three most material causes of violence, the Randons' also and different Mounts of Pieces, cause a great alteration, not only of the fare shooting of all Pieces, but also of their violent Battery. And albeit the different alterations are very intricate and strange, yet have they a Theericke certain.   

THEOR. 27.  
There are also many other Accidental alterations happening by reason of the wind, the thickness or thinness of the Air, the heating or cooling of the Piece, the different manner of charging by Ramming fast or lose the Powder, by close or lose rolling or lying of the Bullet, by the unequal recoil of the Piece in his Carriage or deformity of the Axtree, with diverse other such like, whereof no rules certain can be prescribed, to reduce these uncertain differences to any certain proportions: but all these are by Practice, Discretion, and judgement to be considered, and uniformly guided and performed in their best perfection.   

THEOR. 28.  
Any Piece mounted 90. grades above the Horizon, throweth his Bullet most violently immediately after the discharge, and then the motion groweth flower, till the Bullet be come to his utmost Altitude, and then by Perpendicular falling, increaseth by little and little, his swiftness again, even till it come to the Horizon. But at all other Randons', it falleth not so out.   

THEOR. 29.  
Albeit in the subtlety of Geometrical Demonstration, no part of the Bullets violent motion, can be truly averred a right or direct line, save only the Perpendicular: yet in these experiments Mechanical, That first part of the violent motion (I mean so fare as the piece is said to carry Pointblank) being so near the direct, is, and may well be termed the direct line. As all water levels are accounted in all Mechanical operations, the perfectest levels and directest lines. Albeit the subtlety of Geometrical Demonstration, doth find them not right or direct, but curve or Circular.   

THEOR. 30.  
When any Piece is mounted directly to the Zenith. Then doth his motion violent (being in that situation directly opposite to the natural) carry the Bullet in a perfect right line, directly upward, till the force of the violence be spent, and the Natural motion have gotten the victory. And then doth the Natural return the Bullet downward again, by the very same perpendicular line. And so is the whole motion of the Bullet in this case a very direct perpendicular to the Horizon.   

THEOR. 31.  
But if any piece be discharged upon any Angle of Randon, albeit the violent motion contend to carry the Bullet directly by the line diagonal; Yet the perpendicular motion being not directly opposite, doth though unsensibly, even from the beginning by little and little, draw it from that direct and diagonal course. And as the violent doth decay, so doth the natural increase: and of these two right lined motions, is made that mixed curve Helicall Circuit of the Bullet.   

THEOR. 32.  
Any piece therefore discharged at any Mount or Randon, first throweth forth her Bullet directly a certain distance, called of some Gunners their Pointblank Range, and then it maketh a curve declining Ark, and after finisheth either in a direct line, or nigh inclining towards it.   

THEOR. 33.  
The further that any piece shooteth in her direct line, commonly called Pointblank, the deeper also she pierceth in her battery, if the bullet be not of substance brickle or frangeable.   

THEOR. 34.  
The more ponderous a Bullet is, the more it shaketh in Battery, albeit, it pierce not always so deep, as the lighter or lesser shot conveniently charged.   

THEOR. 35.  
Any two Pieces of Battery Ordinance, charged with one kind of bullet, and shot into one Rampire of massy uniform kind of Substance, shall ever make their profundities of piercing proportional, to their level Ranges horizontal; and if they be discharged, either level or at one grave of random, and at like distance.   

THEOR. 36.  
Any two Pieces of Battery, discharged into any Rampart, of uniform massy substance, shall ever make their piercing depths proportional to their lines diagonal, albeit these Pieces be discharged from different Randons', so as they batter at like distance.   

THEOR. 37.  
As Archimedes' line Helicall or spiral, is made by the direct motion of a point carried in a right line, while that right line is Circularly turned as Semidiameter upon his Circles Centre: So is this Artillery Helicall line of the bullets Circuit created only by two right lined motions, becoming more or less curve according to the difference of their Angles, occasioned by the several Angles of the Random. Whereupon by demonstration Geometrical, a Theoric may be framed, that shall deliver a true and perfect description of those Helicall lines at all Angles made between the Horizon and the Peeces-lines diagonal.   

THEOR. 38.  
These direct or diagonal lines, are always longest when the Pieces Axis is directed to the Zenith. And always as the Pieces Axis declineth more and more to the Horizon. So do the diagonal lines grow shorter, and at the level horizontal, shortest of all.   

THEOR. 39  
These direct lines diagonal, albeit they increase in length at every grave of Random from the Horizon to the Zenith, yet is not their increase uniform or proportional, either to their degrees of Randon, or horizontal Ranges, nor yet to their Circuits or Altitudes, and yet such as may be reduced to a Theoric certain.   

THEOR. 40.  
The middle curve Arks of the bullets Circuits, compounded of the violent and natural motions of the bullet, albeit they be indeed mere Helicall, yet have they a very great resemblance of the Arkes conical. And in Randons' above 45. they do much resemble the Hyperbole, and in all under the Ellipsis: But exactly they never accord, being indeed spiral mixed and Helicall.   

THEOR. 41.  
Any Piece discharged at any one Random with like bullets, and several charges of powder, shall make both their lines diagonal, and curve Circuits of different longitude, but the curve Arkes shall always be as Parallels, and their Longitudes proportional to their lines diagonal.   

THEOR. 42.  
The last declining line of the Bullets Circuit, albeit, it seems to approach some what to the nature of a direct line again, yet is it indeed still Helicall and mixed, so long as there remaineth any part of the motion violent. But after that is clean spent, the rest of his course to the Horizon is direct, and Perpendicular, and a perfect right line indeed, which is best discerned in those Grades of Randon, which are between the Zenith and the Mount or Randon Aequorizontall.   

THEOR. 43.  
This declining line doth always make a greater and greater Angle with the Horizon, As you raise the Piece to a greater Mount, till you come to the Mount Aequorizantall, about which point the same declining line becometh Perpendicular before the Bullet fall to the Horizon.   

THEOR. 44.  
The horizontal Ranges in all Pieces mounted from the Horizon toward the Zenith, doth not still increase, but at every Grade of Randon are longer, till you come to the point or mount Tropical, commonly called the utmost Random, which hath been generally thought to be the grave 45. but is not so. An from that Tropical grave upward, the Ranges decrease again till you come to the grave Aequorizontall, so called because the Bullet than falleth a like disrance to the level Ranges.   

THEOR. 45.  
This Aequorizontall Grade is as fare distant from the Zenith, as that Grade is from the Horizon, which shall cause the piece to shoot in the horizontal plane, a distance equal to his highest Altitude, or longest line diagonal.   

THEOR. 46.  
The mounting of any piece above his Aequorizontall grave, doth still decrease her horizontal Ranges, even till it come to the Zenith. But in a proportion different from any of the former, her Bullet ending every of those Circuits in a direct line perpendicular.   

THEOR. 47.  
The Gradual increase and decrease of these Ranges horizontal, albeit they are equal in the Quadrant, yet are they neither equal nor proportional in the Horizon, neither the Ranges nor their intervals. Neither compared between themselves, nor yet conferred with the Chords or sins of their Arkes. And yet is there such a kind of proportional increase and decrease of the proportion of their intervals, as may be reduced to a Theoric certain.   

THEOR. 48.  
The Tropical Grade commonly called the utmost Random, is not as hath been generally supposed the Medium, or Middle between the Horizon and the Zenith, viz. 45. but rather between the Horizon and the Grade Aequorizontall, which will fall out much nigher 50. from the Zenith, and 40. from the Horizon.   

THEOR. 49.  
The highest Altitude of any Bullets Circuit is farthest distant from the Piece, when she is discharged at her utmost Random, and at all other Randons' either above or beneath that Tropical Point: That highest Altitude is ever least distant, and the bases of these Triangles do ever increase to the Random Tropical, and decrease after, even as the Horizont all Ranges; but in proportion more different every one from other.   

THEOR. 50.  
The Altitudes of the Circuits of Randons' do not increase and decrease as their Ranges Reciprocally, but from the Horizon in every Grade to the Zenith, do still increase, but yet neither equally nor proportionally, neither conferred between themselves, neither yet with sins or Chords of their Arkes of Randon. And yet the increase and decrease of their intervals proportions, such as may be reduced to a Theorieke certain.   

THEOR. 51.  
The Hypethenusall lines of all these different Circuits carry a mixed proportion of the composition of the proportions of these Altitudes and Bases by addition of their Squares; But are not proportional to the lines diagonal of their corresponding Angles of Randon.   

THEOR. 52.  
Any two pieces of Ordinance being mounted to any one Grade of Randon, shall make their Horizontall Ranges of their Bullets proportional to the Altitudes of their Circuits.   

THEOR. 53.  
The Ranges horizontal of any two Pieces discharged at one Randon, will be always proportional to their lives diagonal of the same Pieces Circuits.   

THEOR. 54.  
The horizontal level Ranges of any two Pieces of Artillery are ever proportional to the utmost Ranges horizontal of the same Pieces.   

THEOR. 55.  
And two pieces whatsoever, discharged at one Randon, do ever make their lines diagonal, and lines of Altitude proportional, howsoever the proportions of their charges vary.   

THEOR. 56.  
And two pieces whatsoever, discharged at one grave of Random upon any inclining or declining plane: shall nevertheless make their Ranges proportional to their lines diagonal, and Altitudes of those their different Ranges. Albeit the pieces be charged with a different kind of proportion of Powder and Bullet, so as the shot be made in a fair Calm day, as is in these cases always presupposed, because for such uncertain Accidents there cannot certaine Rules Artificial be prescribed.   

THEOR. 57  
One Piece discharged, at several Randons' under the utmost Random, being a like charged and discharged, and the Piece also of one temper, at both times, shall ever make several Ranges. But if she be discharged at several Randons', the one above the Tropic point, the other under. Then may their Ranges be equal notwithstanding their Randous, Lines diagonal, Altitudes, Bases, and Lines Hypothenufall, be all different.   

THEOR. 58.  
When any Piece (being twice discharged at several Randons', the one above, the other beneath the Tropic point) shall make the same or equal Ranges in a horizontal plane. The middle grave between those several Mounts, is very night the grave of utmost Random: and the Piece Mounted to that middle grave, shall then make very nigh his utmost horizontal Range.   

THEOR. 59  
The grave of utmost Random or point Tropical of any Piece in a Plane horizontal, shall not be the Tropical grave of that Piece, in a plane declining or inclining, but an other Peculiar to that Angle of Inclination or Declination.   

THEOR. 60.  
Any Piece discharged at his grave of utmost advantage horizontal upon a Plane inclining, shall not make so great a Range as on his Plain horizontal: But contrariwise on a Plane descending shall make a farther Range.   

THEOR. 61.  
A Piece discharged first at his due level, and again at his Aequorizontall grave, albeit in the plain horizontal they make equal Ranges, yet in Planes declining they shall not so do, but always the Level Ranges shall ever out-shoot in all declining Planes the Range of that grave Aequorizontall.   

THEOR. 62.  
A Piece discharged at any grave from the Zenith to the grave Aequorizontall, shall always make a greater Range in any Plane inclining or declining, then on the Plane horizontal.   

THEOR. 63.  
In all Planes inclining at all Randons' between the horizontal Level and point Tropical, all Pieces shoot farther in their Planes horizontal, then on any Planes inclining, and contrariwise in Planes declining: But above the Tropic grave not always so, but sometimes, and not always contrary.   

THEOR. 64.  
In any Plane whether it be inclining or declining, if any Piece of Ordnance be discharged, being Parallel or Equidistant to that Plane, and the first graze or bond noted. If the same Piece be with like charge uniformly charged and discharged at such an high grave of Randon, as may cause the Bullet Range the former Distance: That middle grave of the Quadrant, which lieth between these two Mounts, shall be very nigh the grave of utmost advantage, for that inclining or declining plane. The which in all planes inclining, will be above the utmost Range horizontal, and in all declinings under.   

THEOR. 65.  
In all inclining or declining planes, as the grave Tropike of greatest advantage doth vatie; So doth also the proportions of their Ranges, at every grave of Randon differ, whether they be accounted from the Zenith, or Horizon Planes, inclining or declining. But yet in such an assured and certain manner as may be reduced to a Theoric perfect.   

THEOR. 66.  
In all Grades of Randons', & in all manner of Pieces, whether the planes be horizontal, or vary by Inclination or Declination, the diagonal Lines are still proportional to those of the planes horizontal, respectively taken by Graduation from the Zenith, in all Pieces whatsoever. But the Lines of Altitudes, their Bases and Lines Hipethenusalls are ever different in every several Angle, both of Inclination and Declination, and vary by such a different Proportion from the horizontal, as they are to be discovered by a several Method of Calculation.   

THEOR. 67.  
Such Theorikes, Scales, and Instruments, may be framed for the Invention of these strange proportions of Altitudes, Lines diagonal, and Ranges horizontal, as thereby with the aid of Calculations Arithmetical, and some Rules Geometrical, a man may exactly and readily discover the true Circuits and Ranges of the Bullets of all Pieces of Ordnance whatsoever, mounted howsoever; and upon all grounds or planes inclining, or declining, that can be Imagined.    

DEFINITION OF ARITHMETIC.  
Arithmetic is the Art to number well, and is the ground of the Mathematics.  

Of Notation or Numeration.  
The Characters are 9 significant, as 1, 2, 3, 4, 5, 6, 7, 8, 9, and 0, a cipher, Remembering only One, Ten, a Hundred, reckon all your figures or places from the right hand towards the left, always making a prick or dash over every third figure, omitting the first: As suppose this number were to be valued, 4-6 7 2-3 5 6. So herein you find two pricks; then reckoning back again from the last figures on the left hand towards the right hand, name after each figure pricked so many times a thousand as there are pricks towards the right hand, saying 4 with his prick, and the next prick is four thousand thousand, then say six hundred seventy two thousand, three hundred fifty six, and so of all others be the places never so many, you shall name their true values to their numeration, being the common beginning is known well enough: This shall suffice.   

The four Principles of Arithmetic in whole Numbers.  

Addition.  
TO add is to Collect or assemble many Sums into one total beginning at the right hand, and so proceeding towards the left: as by the example following. To add 2356 with 5876, place them so under one another, that all the first figures of the sums towards the right hand stand right under one another: and likewise all the second figures and third, etc. of each sum directly under his fellow first, second, or third, etc. Thus, as 6 under 6, & 7 under 5, and 8 under 3, and 5 under the 2, and then saying 6 and 6 make 12, whereof set down the two under the two six, and carry one for the other ten unto the next sum to add to 7 and 5, saying one and seven are eight, and siue makes 13, place the 3 thereof under the 7 and 5, and carry one again for the other ten to the next place, saying one that I carry and 8, make 9, and 3 make 12: Of which I set down the two, and for the ten again I likewise carry one unto the next place, saying, one (that I carried) and five make six, and two make eight: which being the last, I set it right under the five, & 2. and find that they make totally 8232.   

Substraction.  
TO Subtract is to take a lesser sum out of a greater, and to note the remainder or difference, beginning also at the right hand, and proceeding towards the left. As to subtract 5876 from 8232 placing as before in Addition each first, second, and third figure of the other thus As 6 under 2, and 7 under 3, and 8 under 2, and 5 under 8. And then saying 6 out of 2, cannot be, but borrowing ten from the next place maketh the 2 to be 12, then 6 out of 12 there remaineth 6: which set down under 6 and 2, then say 7 out of 3 less one that was borrowed cannot be done, but 7 out of 12, that is 1 ten borrowed out of the next place and 3 less 1, that is 2 making 12 remaineth 5: which also set down under 7 and 3. Then say 8 out of 2 cannot be, but 8 out of 11, that is, one ten borrowed of the next, and one lent out of the 2, maketh together 3 to remain. Lastly, say 5 out of 8 less one lent, that is 5 out of 7 resteth 2. And so you shall find that 5876, being taken from 8232 will leave 2356, which the precedent Addition proveth true for the remainder.   

Multiplication.  
TO Multiply signifieth to augment a sum by itself, or by some other number, placing the lesser which we commonly name the Multiplicator undermost, so that no figure towards the right hand outreach other, (except Ciphers) and then beginning at the right hand, and proceeding towards the left, still multiplying every figure of the uppermost sum by each figure of the lower, and set the products under the line: as the example here following will demonstrate to the eye. And for the more easy solution of this proposition, it will be necessary to know by memory the products of the multiplication of the 9 simple Characters, 1.2.3.4.5.6.7.8.9. amongst themselves. As five times 7. make 35, and 9 times six make 54, etc. Now 4563 are given to be multiplied by 327. Place the lesser number under the greater with the first of it towards the right hand under the first of the other, & then draw a line under them thus, And say 7 times 3 make 21. Place the 1 under the 7 and 3, and carry 2 for the 2 ten unto the next place, and say 3 time 6 make 18, and 2 that I carried in memory make 20: whereof I set down the 0, and carry the 2 to the next, saying 7 times 5 make 35, and the 2 I bore in mind make 37: whereof I set the 7 under the 5 and 3, and carry 3 to the next place, saying 7 times 4 make 28, and 3 make 31, which I set down also, so I have done with the 7, and cancel it, and begin with the 2, saying 2 times 3 make 6, which I set down under the 2, and carry 1 to the next, saying 2 times 5 make 10, and 1 that I carried make 11: whereof I set down 1 and carry 1, and say 2 times 4 make 8 and 1 maketh it 9, which I set down also, and so I have done with the 2. Lastly, beginning with the 3 remaining, I say first, 3 times 3 make 9, which I set down right under the 3: And again say 3 times 6 make 18, whereof I set down the 8 and carry the 1 to the next place where say 3 times 5 make 15, and 1 that I carried make 16, whereof I set down the 6 and carry 1 to the next, saying 3 times 4 make 12, and 1 that I carried makes 13, and so I have ended, only adding the numbers under the line as you were showed to do before in Addition, and you shall find the Products will be 1491861: which having set down, may be enclosed between 2 lines as the Operation requireth.   

Division.  
To divide is to search how many times one some is contained in another, as if I would know how often 234 were contained in 5382, Place the greater first, and the first of the less towards the right hand under the first of the greater, thus, making a crooked line for the Quotient: and then say how often I have 2 in 5, say two times, which 2 set behind the crooked line, or Quotient, and there will remain 1, Then say 2 times 3 make 6, which taken from 13, there will rmaine 7, which set over the 3. Then say 2 times 4 makes 8, which take out of the 78 above it, and there will rest the 70, so putting out the 8 and the 234, you must remove the 234 one place nearer to the right hand as above is seen, Saying how many times two can I have in 7, say 3 times, and yet there will remain 1, Set the 3 in the Quotient, and the 1 over the 7, and put out the 2 underneath. And then again say 3 times 3 make 9, which taken from 10 over it, there will rest 1, which I set over the 0, and put out the 10 and the 3 under it. Lastly, I say three times 4 maketh 12, which being taken out of the 12, there will remain nothing. Wherefore you finding 23 in the Quotient, or behind the crooked line, may conclude that 234 is 23 times contained in 5382, which was desired to be known. If any temainder had been, it would have made a Numeratour to to the Divisour, etc.    

To extract the Square root.  
TO extract the true square root (or the nearest that may be found) is to search out a number, that being once multiplied in itself (with the remainder if any be) will produce the number assigned. As suppose it were required to find the square root of 4489, put under the 9 one prick, and under the next 4 another prick, thus leaving one figure between the two pricks, and so always if there were more figures, and after take the square number or nearest thereunto of the number over the last prick, namely of 44, which is the square 36, which taken from 44, there will remain 8, which place above the pricked 4, and take the square root of the 36, which is 6, then double the 6, and it maketh 12, which take as oft as you can out of 88, so as that the square of the second number to be produced, may also be extracted, and it will be found to be 7: which being multiplied by 12, will make 84, which taken from 88, there will remain 4, which set above the 8, and multiply the 7 in itself, and that will produce 49: which taken from the 49 over it there will rest nothing, and so you shall find 67 to be the square root of 4489; for multiply 67 it in self, it will produce 4489.   

To extract the Cubic root.  
To extract the Cubic root of any number is to find that number, that being multiplied in itself, and the product again by the same number, will make the number assigned (or the nearest thereto if the number be not a Cubic number.) So to extract the Cubic number of 3 2 7 6 8, place one prick under the first figure 8, and another under the fourth figure 2, and so further if there be more to leave two figures between each two pricks, and look (as before for the square root) how many pricks there be so made, so many figures there will be in the Quotient, and then seek the Cubic root (or the nearest to it) unto 32, which will be found to be 3, which multiplied in itself maketh 9, and that product again multiplied by 3, produceth 27 out of 32, substracting 27, there will remain 5, and that may be set over the 2, and the Quotient 3 also by itself. And then to find the 2 figure of the Quotient, put down 3 and his square 9, & his Cube 27. Now we must take a new number in the Quotient, so that when the 27 shallbe multiplied by the same number, which is 2 and the 9 by the square of 2 which is 4. and again the new number cubickely in itself, and placing the 3 products in order, as the operation here set down showeth, and the same Agregate substracted from the remainder of the division, that in this extraction there shall want nothing, so the Quotient will be found to be 32, which multiplied cubickely will make his Cube 32768.   

By the square root all sorts of Battalions are framed thus. viz.  

To make a square battalion of Men.  
EXtract the square root of the number of men proposed, and it will yield the number both for Rank and also for File.   

To make a battalion square of ground.  
Allow 3 foot in breadth, and 7 in length, which is the space that every Soldier occupyeth marching, Multiply the number of men proposed by 3, and dividing the products by 7, then extract the Square root of the Quotient, and that will be the number of men for the Files. By which then dividing the said number proposed, and the Quotient will be the number of men in Rank.   

To make a battalion whereof the Front shall be to the Flank in any proportion given.  
Multiply the number of men proposed by the proportion appointed for the Flank, and from the product extract the Square root, which will be the number of men for the Files or Flancke. And again to find the number of men for the Front, Multiply the proposed number of men by the proportion assigned for the Front, and from the product thereof, extract the Square root, which root will be the number of men for Front.   

To make a doubled Batallion.  
Double the number of men propounded, and extract the square root of that, and it will be the number of men in Front: Then half that number, and it will be the number of men for Flancke.   

To make a Batallion of a great Front.  
Divide the number of men propounded by the number of men assigned for the Front, and the Quotient will be the number of men for the Flank.  
The Batallions square of men, or square of ground, are weak in Front, and those of great Front, are weak in Flank.  
The Spaniards most commonly use the doubled Batallia.  
And the Hollanders the great Front, for they usually make their Flank consist but of ten Ranks.  
By the extraction of this Cubic root you may find the solid capacity of any Shot, Ordnance and such like solides: hereof we will speak more hereafter in his place.    


A Table showing the Square root unto 3844, and the Cubic root unto 238328. Calculated by the Author R. Norton.   1  4 2 8 9 3 27 16 4 64 25 5 125 36 6 216 49 7 343 64 8 512 81 9 729 100 10 1000 121 11 1331 144 12 1728 169 13 2197 196 14 2744 225 15 3375 256 16 4096 289 17 51●3 324 18 5832 361 19 6859 400 20 8000 441 21 9261 484 22 10648 529 23 11197 576 24 13824 625 25 15625 676 26 17576 729 27 19683 784 28 21952 841 29 24389 900 30 27000 961 31 29791 1024 32 32768 1084 33 35772 1156 34 39204 1225 35 42875 1296 36 46656 1369 37 50653 1444 38 54872 1521 39 59319 1600 40 64000 1681 41 68921 1764 42 74088 1849 43 81307 1936 44 85184 2025 45 87120 2116 46 97336 2209 47 103823 2304 48 110592 2401 49 117649 2500 50 125000 2601 51 132651 2704 52 140608 2809 53 148877 2916 54 156464 3025 55 166375 3136 56 175616 3249 57 185193 3364 58 195092 3481 59 208179 3600 60 216000 3721 61 226981 3844 62 238328   

To find the Fractions Quantity, when the number given is not a square number.  
When you have extracted the Square root of any number, and that yet there resteth something after the extraction made, that showeth the number not to be a Square number, and being very difficult to find the root of a number, not square, exactly, but to come near it: double the root for denominicator, and take the remainder for numerator. Example, I would find the square root of 10, the greatest Root in 10 is 3, and 3 times 3 maketh 9, so the remainder is 1 for Numberator, and I double 6 for denominator. so the nearest square root of 10 is 3 ⅙ which is 1/36 part too little. But if I should add 1 to the double of the Root for denominator, and take the remainder for Numerator, that would make the root of 10 to be 3 ●, which is too much by ¼, part.   

Of Fractions.  

What a Fraction is, and to reduce Fractions.  
A Fraction is a part of a whole number, and the proportion thereof is to the whole number as the Numberator is to the Denominator of the same. And where the Numerators and Denominators are great numbers, they are to be reduced into their least denomination: which to do, is to find the greatest number that will divide them both. As I would abbreviate ●●1/300, I find 5 the number that is common to divide them both, and thereby I first divide 225, and thereof cometh 45 for numerator, than I divide 30 by 5, and that produceth 60. I say then 45/60 valueth as much as 225/300. But to find the smallest fraction, take 225 out of 300, and there will rest 75, and then I take 75 out of 225, and there rest 150: then I take 75 out of 150, and there rest 75, which is the number I seek, whereby I first divide 225, and the Quotient will be 3, than I divide 300 by 75, and the quotient will be 4, so ¼ and 15/60 and 225/300, are of one and the same value equal amongst themselves, and one to another. And so you may do with any other fraction to reduce it to the last denomination.  
Again, some fractions cannot be abreviated, as 1●/20, out of such a fraction take 2 or 3 unities from the Numerator, that is, take ●/12 from 11/12, and there will rest 6/1●, and reduce the ●/●2 to ⅙, so ●/12, and ⅙ is equal in value 11/12.  
To reduce many diverse Fractions into one denomination, There can but two of them be reduced at once; as I would reduce ⅚ and 4/8 into one denomination I set them thus, ●4/68: And multiply the two denominators together, and they make 48, which shall be the denominator, than I multiply 6, the first denominator by 4 the second numerator, and thereof cometh 24 which I set apart for the first, than I multiply 8, the second denominatour by 5, the first Numerator which produceth 40, which I also set apart for the second Numerator, each set over the denominator 48, will be so reduced to 24/48 and 40/41 or 64/48 or 1 and 24/41 equal to ¼ and 4/●.   

Addition of Fractions.  
But if all the Denominators be a like, add all the Denominators together, and set their common Denominator under the sums of them, as ⅙ 2/6 ⅚ make 20/9 or 1 4/6.   

Substraction of Fractions.  
To subtract one Fraction from an other, first (if they be not) reduce them to one Denomination, as to take ⅔ from ¼ which reduced, make 8/62, for ⅔ and 9/12 for ¾, then subtract 2/12 from 9/12 rests 1/12 the remainder sought.   

Multiplication of Fractions.  
To Multiply Fractions, you must Multiply the Numerators together for a new Numerator, and also the 2 Denominators together for a new Denominator, as 3/6 by 4/● produce 12/48 or ●/24 or 1/12 or ¼.   

Division of Fractions.  
To divide Fractions one by an other the easiest way, is to make one of the Denominators to stand as Numerator, and the Numerator thereof as Denominator, and then to work as you did in Multiplication of Fractions: As I would Divide ¾ by ⅔ I changing one, they stand thus ¾ and 3/2 and say 3 times 3 make 9, and that 4 is Numerator for the Quotient, and 4 times two makes 8 for Denominator thereof: So ¾ Divided by ⅔ make 9/8 the Quotient sought.     

Definitions.  

Geometry is the Art to measure well, and is the Sinews of the Art of Artillery.  
GEometry hath her Original from Points, rights, crooked lines, right and obliqne Angles, Superficies, and Bodies, etc.   various geometric angles 
A Point is a thing that cannot be divided as A.  
A Line is a thing that hath Length without breadth, & serveth for lengths, breadths, heights, and depths, as B.  
An Angle is the meeting of two lines, so as they make not one line, and are either right lined Sphaeticall, or mixed Angles, as C.  
And an Angle is a right angle, a blunt, or a sharp Angle.  
An angle greater than a right angle, is a blunt or abtuse angle, as D.  
An angle lesser than a right angle, is a sharp or acute angle, as E.  
A superficies is that which hath only Length and Breadth, as a Quadrate or Triangle, &. as E. E.   various geometric figures 
A triangle is a superficies, made only with three lines, and is either right lined, or Spliaericall, as G.  
A Quadrat or square is a superficies quadranguled, made of sour lines, as H  
A Circle is a plane Figure, contained under one line, which is called the circumference thereof. as I  
A Centre of a Circle is a point in the midst thereof, from which all right lines drawn to the circumference, are equal, as I. also  
A Trapezia, is a right lined figure of four unequal sides, as K:  
The especial things belonging to a Gunner, being Arithmetic (which we have heercin briefly touched) and Geometry which we now purpose to point at, and Perspective whereof hereafter a word for taking distances: And of each of them in as brief manner as I can, because they are not by necessity to be accounted any real parts of this Art and Practice of Artillery, but only necessary apendants thereto: For it is necessary that the Gunner should know what a line, a superficies, and a body is, and how to measure each of them; as well the right as the crooked, the level hypothenusal & perpendicular & diametral lines, and the Angles they can make right or obliques. And measure the Triangles, Squares, and Circles, the Globes, Columns, and Cillinders: And in effect to carry in his memory these Definitions, Demands. and Common sentences, of Eclids Elements: and especially the first Propositian of the same which teacheth.   

How to make an Equilateral Triangle.  
EUCLID. I. PROPO. I.  
Which is Upon the given right line Ab, to make the Equilateral Triangle a b c.   equilateral triangle drawn by linking points on the perimeters of two overlapping circles 
And then the 3. PRO. I.  
Two unequal right lines being given, to cut from the greater a right line equal to the lesser.  
From the Centre B, with the distance A 
* 2.1.15. Def. 1.  cut C B in D, so will B D be equal to A.  
And the 9 PROPO. I.  
To divide an angle given by a right line in the midst, or into two equal parts.   various geometric figures and angles, with labeled points 
From a b 
* 3.1.  cut a d at pleasure, and also 
* 1.1.  e equal thereunto, and draw the right line D C, and make the Equilater triangle D E F, and join A F, which will half the given angle.  
And the 10. PROPO. I.  
To half a given right line as A. B.  
Upon the right line A B, make the triangle A C B, the angle C 
* 1.1.  halfed. 
* 9.1.   
And the 11. PROPO. I.  
To raise a prependicular line C F upon a right line E D from a point C therein given.  
Upon the point C set the Compasses, and on each side thereof in the line E D take equal distances at pleasure, and upon them make 
* 1.1.  an equilater Tryangle D E F, and then draw the line F C which shall be perpendicular to E D upon the point C.  
And the 12. PROPO. I.  
Upon an infinite right line a b given, from a point C without the same, to let fall a perpendicular right line C F.  
Upon the Centre C the Arch of a circle described, will cut the right line A B in D and E, divide D E into 
* 10.1.  half at F, join C to F, and so C F will be perpendicularly let fall at F upon A B.  
And the 13. PROPO. I.  
A right line a b falling upon another right line c d, maketh either two right angles, or else angel's equal to two right angles.  
In the perpendicularity of E B to C D, it is sufficiently manifest; but if A B be not perpendicular in the point B 
* 11.1.  erect the perpendicular E B: so we see the angle A B C and the angle A B D taken together, to occupy the place of the two right angles EBC and EBBED.  
And the 21. PROPO. 1.  
If within a Triangle abc in the side bc, from the extremes of two right lines bd and cd, they are less than the sides AB and AC, but the angle D that subtends it, will be greater than the angle A.   various geometric figures and angles, with labeled points 
And the 31. PROPO. 1.  
By a point given A to the given right line BE to draw a right line parallel.  
Draw AD 
* 23.1.2  that it make the alterne angle ADC equal to DAF, and continue FAVORINA to E, and the Alternates being equals, 
* 29.1.  the lines must be parallel.  
And the 32. PROPO. 1.  
Every Triangle as ACB with one side produced AB to D, The external angle CBD, will be equal to the 2 internal opposite Angles A and E, the three angles of a triangle being equal to two right angles.  
To the side AC 
* 31.1.  make the parallel line by the point B namely BE in these two parallels AC and BE, the line of incidence CB maketh 
* 29.1.  CBE equal to EBBED, and B equal to A: so the whole extern angle is equal to the two intern angles, to which let the third CBA the common angle, 
* 13.1.  and the three angles of the Triangle equal to two right angles.  
And the 46. PROPO. 1.  
Upon a right line AB given to make the square of equal sides, and equal angles ABCD.  
From either extreme as A of the given line, let the perpendicular line AD be 
* 11.1.  erected equal to the given line, and by D make to AB 
* 31.1.  parallel and equal the line DC, join C and B equal, and parallel ABCD joining DA and CB, they will be equal. And the Parelellogram made 
* 1 Axiom. 1.  equilateral, and because the Angles C and B opofite to the right angles A and D, it is a rectangle and 
*⁎* 30.1.  a square.  
And the 47. PROPO. 1.  
In the trectangled Triangle ABC, the square that is made of the side AC, subtended by the right angle ABC being described, will be equal to the Squares A-BED and BCGF, which are described of the sides containing the rectangle.  
Let the three Squares AH, A, and CF be described, and in a direct line let AB, BF, and CB, BF lie, and draw BL parallel to AI, and draw also BH, BY, AGNOSTUS, and CD.  
The common angle ABC being added to the rectangles DAB and JAC, are 
* 2. Axiom.  equal to the Angles JAB and DAC, 
* 4.1.  and also to the tryangles.  
And the 5 PROPO. 4.  
About a triangle to describe a circle.  
Divide any two of the sides into the 
* 10.1.  midst by perpendicular lines meeting in F, from whence draw a right line to each angle, and by their distance describe the circle, FAVORINA, FB, and FC, will be 
* 4.1.  equal, and upon the 
* 9.3.  centre B a circle is described about the triangle.  
1. 
* 31.3.  If the centre fall in the side the triangle is rectangled if within Acute, if without obtuse angled.  
2. By three points not being in a right line to describe a circle by this proportion, for join the 3 points and you have a triangle.  
And the corollaries and the Scholion thereof, viz.  
To every regular figure that is equilateral and equiangled, a circle maybe as well 
* 4.  inscribed by the distance of the perpendicular, 
* 6.1.  as subscribed with the distance to the Angles, and those cut in halves.  
And the 10 PROPO. 4.  
To make an Isosceles Triangle that may have either of the angles at the Base double to the rest.  
Any 
* 11.21.  given line as AB, that the rectangle under AB and CB, may be equal to the square of AC, and by the distance of AB if a circle be described, it will 
* 11.2  make BD equal to AC, then join CD and AD, and the Tryangle ACD may be 
* 1.4 5.4  circumscribed by a circle.   various geometric figures and angles, with labeled points 
And the 4 PROPO. 6.  
Of the equiangles ABC, DEF of the Triangles the sides are proportionals, as AB to BC, so is CD to DE, and as BC to CA, so CE to ED, and as BA to AC, so is CD to DE, which about equal angles B and DE, EBCA and E, A and D are Homogeneal sides AB to DC, BC to CE, and AC to DE, which subtend BCA, and BASILIUS, and CD, Band DCE  
Let the Bases of the Tryangles be BC and CE, 
* 11.1  & according to the quantity of the angles like situate in one direct line, and BASILIUS and EP meet extended in F: Therefore because the angles ACB and E, and DCB and B, are equal, BF and CB will be parallels, and also AC, and OF, and ACDF 
* 28.6,  a parallelogram.  
And the 12 PROPO. 6.  
Three lines being given to find a fourth proportional.   various geometric figures and angles, with labeled points 
And the 13 PROPO. 6.  
Two right lines AB, BC, being given to find a mean proportional between them.  
Set the two right lines given in one direct live as AB, BC, upon all that line AC, describe the semicircle ADC, and from B 
* 11.1  raise the perpendicular line BD, and draw AD, CD: therefore ADC is a right angle (being in a semicircle) and BD the perpendicular maketh two triangles ABDELLA and CBD 
* 8.6.  equiangled, and therefore proportional: Therefore BD is the mean proportional.  
And the 17 PROPO. 6.  
If three right lines be proportional, as A to B, sa B to C, than that rectangle that is made of the extremes A and C, shall be equal to that which is made of the Mean B.  
Because the mean proportional B is twice put, it will be as in the 16. Pro. that 4 right lines about 4 right equal angles, are 
* 1. Def. 6. 14.6.  reciprocally proportionals, Therefore rectangled and equal: and contrariwise being equally rectangled about right angles, they have their sides reciprocally proportionals, viz. as A to B, so is the same B to D, which was to be showed.  
And the 25 PROPO. 6.  
Any right lined figure given a like, and in like sort placed, to make another equal to the given.   various geometric figures and angles, with labeled points 
And lastly the 14. PROPO. 11.  
To what planes soever ED and OF, the same right line figure AB is right they are parallels,  
If they be not Parallels being produced, they will concur to the parts C, E, and 
* 3.11.  make the Section GH a right line, in which any where take the point I, and draw IA, IB in the planes GCD and GEF. And so when as AB is placed right to either, it will be the plane of the Triangle AIB, the angel's LABERNELE and JAB would beright, which are nevertheless 
* 17.1.  lesser than right angles.   

To measure inaccessible Heights, Breadths and Distances, and take a plat by my Cosmodelite with the description thereof.  
Upon the semicircle under the Cosmodelyte there are two squares Geometrical, each side of them being divided into 120 equal parts, and upon the Centre of that Semicircle a Rule or Index with the two sights over or parallel unto the fiducial edge thereof. As suppose I were to measure the distance from me to a Tree, to do which, place the Semicircle, so that the Index laid upon the Dyametrall line may direct with the sight to the tree or mark, then laying the Index upon the Semidiametre that is perpendicular to the Dyametrall line, and choose some mark of competent distance whereunto the sights dírect, or else measure 20 or 100 yards, paces, or feet in that line, and there set a mark, and then leaving a mark where you first stood, remone your instrument thither, and by the Semidiametrall line looking back to the first station or mark, thereby you may place the Semicircle in the first position; which done, turn the Index unto the Tree or Mark whose distance you are to measure, and see what number of those 120 parts it cutteth, then, say by the Rule of 3, If 120 all the parts, the parts cut, as suppose it were 80. What shall 300 yards which I imagine was measured between the first and second Stations give, multiplying the third number 300 by 80, the second number produceth 8000, which dividing by 120, the first number yields 66 yards 2/3 the distance so right.  several instruments for measuring and surveying   

To measure the breadth of a Breach.  
LAy on the Index upon the Dyametral line, and turn that to one side of the Breach, and the instrument remaining in that position, note the number the Index will cut when it is turned with his sights to respect the other side of the Breach, then go forwards or backwards until you see the last side of the breach by some other number of parts (letting a convenient distance between the Stations) and noting the difference of those parts, and the distance of the Stations measured, suppose, 50 yards and the difference of parts to 20. Say by the rule of three, if 120, all the parts give 20, the parts cut by aspect of the Index, what shall 50 yards give, multiplying 70 by 50 produceth 3500; which dividing by 120, yields 20 yards, and 〈◊〉 parts of a yard, the breadth of the Breach sought. A height is taken in the same manner, only reversing the Plane of the Instrument perpendicular, which before did lie Horizontally, imitating the rest of the work as aforesaid.  two horsemen with a wheeled measuring device   

To measure the height of any Tower, or other thing by the shadow is maketh, the Sun shining.  
TAke a staff and place it perpendicularly near the shadow you desire to measure, mark the two shadows of the Tower and of the Staff, than such as the shadow of the Staff hath proportion to the staff, such hath the shadow of the Tower to the Tower's height. Example. Let us suppose the length of the shadow of the staff to be 12 hand-breadths, and the shadow of the Tower to be 45 foot; the staff was 8 hand breadths. Then say by the Rule of proportion: if 12 give 8, what shall 45 give: work and ye shall have 30 foot for the height of the Tower sought.   

To measure the height of a Tower by a lookingglass, or the shadow thereof in a puddle of water.  
SVppose there is a Tree or Tower whose height we desire to know: Take a flat Mirror, or Looking-glass, and lay it level or Horizontally upon the ground some distance from the Tree or Tower, and then go backwards until in beholding in the Glass you thereby see the top of the Tree or Tower, your distance from the glass hath proportion to the height of your eye, such as the distance from the glass unto the point right under the top of the Tree or Tower, is to the height of the said Tree or Tower, As for example, suppose the distance between the Glass and the Tower were 48 foot, and the distance between you and the Glass be 4 foot, and the height of your eye above the level of the glass to be 6 foot, say, if 4 give 6, what will 48 give, multiplying 48 by 6, produceth 288: which divide by 4 giveat in the Quotient 72 for the height of the Tree, or Tower sought.   

To find any distance, height, or breadth by resolving the Triangle made by Stations and Marks.   a right triangle, with several labeled points 
Suppose that B, C, in the Triangle, A, B, C, be the height of a Tower, and let it be required to find the measure thereof, and of the hypothenusal line AB, First measure the distance from A to C supposed 40 paces, then by the Cosmodelite or other instrument planted at A, take the quantity of the angle BAC 30 degrees, then by consequent the angle ABC will be the compliment thereof 60 degrees (the angle at C being a right angle) and all the sides of a right line triangle being equal to two right angles, so there is already had 4 of the 6; namely, the; angles and the side AC. Then finding the Logarithmes of the Angles. As for the Angle sixty degrees, and for the angle 30 degrees, and for the rectangle C 90 degrees. Then say by the Rule of proportion, if AC the sign of the Angle ABC give BC the sign of the angle BAC, what gives AC 40 paces, and the Logarithme of AC to the Log of BC; and thence subtract the Logarithme of ABC, and the Log: of the sign remaining will be 23 27/43 for BC sought.  
And for AB, the Hypothenuse say, if AC giue AB, what will AC 40 paces give facit, 46 ●/5 fere.  
The like may be done for all distances and breadths whatsoever.  
Thus much shall suffice for the apendants. Now to the principal matter itself.   

The Description of the Horselitter, and the Cosmodelite, and to Delineate by either of them any Champion assigned.  
THis Instrument, the Cosmodelits is so plainly demonstrated to the Eye by the Figure thereof, that it needeth few words for further description; Only, you may perceive it to have so many several bend, that it may at once represent any two or three planes assigned: It consisting of two concentric Circles divided, one into 360 equal parts as at A: The other into 24 and a semicircle, each Quadrant divided into 90 equal degrees as B: and within each Quadrant is a geometrical Square, each side thereof divided into 120 parts; It hath an Indez with sights, as C playing upon a Center-pinne, under a box with a Magnetical Needle therein as P: Upon the bottom of the Box is pasted a Chart of the 32 Points, and a Limb of 360 degrees: It hath also a Circle with joints at the knee, with an Index as F, to incline or reclyne the Instrument to any Angle assigned, the Cheeks, the square hole of the half slitts between D and E being the Index & moving of the suporters of the said Semicircle & circle B and A as its and altogether considered, are represented at N to the eye very apparently.  
It is an excellent and general justrument, if it be well made, understood, and used as it ought to be: This shall suffice, with the former Figure in the 31 for the Description, and some uses thereof; Only a word or two, how to describe a Champion in plain by it, and a whole Region by the Horselitter, whose Figure is also in the 32 Page hereof showed.   

To make and Delineate in Platte any Champion, or Region assigned.  
THe Horselitter travelling of purpose, with the motion of the Wheel hanged in steel Springs, roaling on the way, The other Wheels which it turneth, giveth the Measures of Paces, Yeards, or Feet, contained between every two angles, and the Compass within, delivereth to the Obseruor (sitting within the Litter) the alteration of angles from time to time, which he diligently noting in a Book, with all observable things, as Towns, Villages, Hills, Woods, Rivers, Valleys, Parks, Wastes and Enclosures in his way notable, to protract by the degrees of the Needle, or points cut and measures found between angle and angle, with the observable Circumstances not forgotten; And by the Cosmodelites Index and Needle noting the degree cut, it respecting each observable Mark, at the first, second, third station, etc. If need be of so many noted, and the distance of each station from other being measured with a Chain, Lyne, or two Poles, or such like, in known Measures also protracted, the true Platte of a whole Region, Manor, Champion or Field, may be easily Described, by practising duly what hath been already said, & all Distances, Heights, Breadths, & Profundities accessible or inaccessible also measured: As Master Diggs in his Pantometria, and Master Rathorne in his third Book of the Surveyor have largely (with variety) described, which with great ease, the diligent Practician may well apply to either of these Instruments, which let suffice.    

THE PRACTICE OF ARTILLERY.  

CHAP. I. Of the general definition and distinguishing of Ordnance and Artillery.  
ARtillery generally taken, comprehendeth all manner of artificial Engines for the Wars, divised or used at any time, either to hurl Stones or Darts, or to shoot Arrows or Bullets, or such like things, to, or at any remote Object; and that with greater violence and more certain direction, then by the natural strength of any one man's hand can possibly be otherwise performed: Whereby it appeareth also, that Artillery differeth from all other Engines. First, for that all other Engines exercise their violence either upon Objects at hand, or such as are either near joined unto themselves, without whose presence or contingency they effect nothing at all: whereas Artillery exerciseth her force and violence upon things fare off, even when the Object is not present or near it. Secondly, in the exercise of other engines, the special thing required is strength and labour, rather than any great Art or Skill. Whereas in the use and exercise of Artillery, the principal thing required is Art and Skill how to direct and bend the same unto the assigned service: without which they do altogether work in vain. Thirdly, the proper use of other engines, is either to draw some thing unto them as, Capstaynes do; to thrust or to remove some thing from them, as Skrewes; to heave up, as Pumps and Pulleys; or to press down, as Presses, etc. which most commonly serve at home for private uses, whereas Artillery serveth to shoot and cast forth Bullets, Balls, Arrows, Darts, Stones, and diverse sorts of Shot, serving for the public wars both at home and abroad, aswell desensively to repulse and destroy the assaulting Enemy, as offensively to spoil, kill, annoy, beat and weaken the Common Adversary in his Towns, Forts, Armies, Fleets, Ships, Ports, Subjects and designs. Artillery therefore according to the times may be divided into two sorts: namely, Ancient and Modern. Each of which according to Magnitude may be again subdivided into two sorts also; namely, Great and Small. The Ancient Great Artillery were the Catapult, Balista, Scorpion and Ram, The Ancient small Artillery, the Longbow, Crossbow, Sling, & Slurre-bow. The Modern great Artillery are the great Ordnance, being the principal Subject both of this and the former Treatise, which in their places are at large particularly described, & distinguished; herein the small modern Artillery are, the Longbow and the Handgunnes. As the Harquebuse, Musket, Caliver, Carbyne, Petronell and Pistol, the particular uses of them as they appertain, not necessively to the Gunner's Office to manage or practice, being no way exacted fro any accounted within the compass of the Train of Artillery: So I therefore forbear to say much of them referring their Practices and Postures to the judicious instructions of Valiant and Worthy Gentlemen, who have delighted in the profession, use, and practise of those Arms. For the Longbow, although it be now grown some what out of warlike use, since the invention of small guns, yet bows and arrows being both ancient and general warlike instruments, and were of two sorts, viz. the Longbow and the Crossbow. The Longbow is so well known that it needeth no description: which doubtless of the two it was first invented and practised in the Wars, as being the more simple Engine of the twain, whose antiquity is surely very great, and seemeth to have been before Noah's Flood: For Almighty God promising to Noah and his sons, that he would no more destroy all flesh with the waters of a flood, he giveth the Rainbow for a sure token thereof, which he there called his Bow, distinguishing the same from men's bows, as things then familiarly known to Noah and his sons. And as it is ancient, so it is also of great force, by reason that all things therein almost do work secundum naturam. For first the Natural and proper work of the Chords, sinews and ligaments of Man's arm are to draw and pull unto itself, rather than to relate themselves to thrust off. Secondly, the matter whereof the Bow is made, be it of wood or steel, by nature stiff and stark, being bend with the string and drawn compass with the arm, whilst it flieth out to the straightness which it naturally hath, and so fulfilleth his natural work, Thirdly, the Arrow artificially made, and proportioned to the strength of the Bow easily hangeth in the air, and swiftly and gently slideth through the same. The general use of it in all warlike nations may appear, That the bow was in special use among the Hebrews. 
Mach. 9.11. Tit. Liu. lib. 7.  Many places of Scripture verify, and the place of their service was in the Front of the battle; and amongst the Philistims, for Saul was sore wounded with the shooters of the Philistims. 
Chron 25.23.24. Esay 21.27.  And amongst the Egyptians, king josias was hurt with the shooters of Phare Necho king of Egypt: & amongst the Assyrians, Achas was slain with one of their arrows: amongst the Citizens of Rabbah the Amonites their shooters shot from their walls against the army of joab: amongst the men of Cedar, Arabians and Ismaelites, 
jerem. 46.9.  whose strong archers God threatneth should be fewer. Amongst the Lydians whom God calleth forthwith their Bows against the disobedient children of juda: amongst the Assyrians; 
judeth 2.15.  Holophernes having in his army 12000 archers on horseback. And to be short, if we shall read the ancient Histories of the Greeks and Romans we shall find the bow and arrows every where so usual a weapon, that most nations have continually used them: amongst whom our English Nation hath been equal to the best, as all Christendom can bear us witness in many battles; especially that which our Nation did for Ferdinand king of Castille under the leading of the Earl of Bedford, who with 10000 English bowmen, armed besides their bows and arrows, with battell-axes that hang at their backs, whereby he obtained so great a victory, that he & his successors have ever since carried the sheaves of arrows, and the longbow in their shield, and also on their coined half royals.  
The second sort of Bowes is the Crossbow, which Titus Livius calleth Scorpionius modicum, partly by reason it hath the likeness of that beast when the arrow is placed therein, and partly by reason of the like manner of hurting, watching all occasions when and where to strike surest.   

CHAP. II. Wherein is discoursed who were the Inventors of Guns and Gunpowder.  
Having undertaken in the former book, called the Art of Great Artillery, to show by Definitions, Theorems, and certain Questions, the Speculative part of the Art of a Canonier, I have now also thought fit in the second part by the rule of reason to demonstrate the Practice part thereof, and to describe all sorts of Ordnance, aswell such as are, and have been used in foreign Nations, as those that are founded in England, and both the ancient and the modern of both: wherefore I hold it needful for compiling of the whole work as complete as I can, to declare by whom, and how this so devilish an invention was first brought to light. Vffano reporteth, that the invention and use aswell of Ordnance as of Gunpowder, was in the 85 year of our Lord, made known and practised in the great and ingenious Kingdom of China, and that in the Maratyne Provinces thereof, there yet remain certain Pceces of Ordnance, both of Iron and Brass, with the memory of their years of Founding ingraued upon them, and the Arms of King Vitey who he saith was their inventor. And it well appeareth also in ancient and credible Histories, that the said King Vitey was a great Enchanter and Necromancer, who one time (being vexed with cruel wars by the Tartarians.) conjured an evil spirit that shown him the use and making of Guns and Powder. the which he put in Warlike practice in the Realm of Pegn, and in the conquest of the East-Indies, and thereby quieted the Tartars. The same being confirmed by certain Portugese's that have traveled and Navigated those quarters, and also affirmed by a letter sent from Captain Artred written to the King of Spain: wherein recounting very diligently all the particulars of China, said, that they long since used there both Ordnance and Powder: and affirming further, that there he found ancient ill-shapen Pieces, and that those of later Founding are of fare better fashion and mettle than their ancient were. Some also imagine that Powder and Ordnance were invented by the famous Mathematitian Archimedes, who made use of them at the siege of Syracuse in Sicilia, and they ground that supposition upon Vitrunius, who reporteth that one of his engines with a terrible noise did shoot forth great Bullets of stone: which by reason of that report could neither be supposed the Catapulta, Balista, Scorpion, nor any other of his known engines. Others say that Ordnance and Powder were used in the time of Alexander the Great, who having a purpose to besiege a City near the river Ganges, was dissuaded from it by some of his good friends that told him, the Citizens thereof were so much favoured of Inpiter, that he usually sent Lightning and Thunder from their walls, that destroyed whosoever offered to assault that City. And indeed if we shall well consider the nature and effect of Powder and Ordnance, we shall find them to come so near unto natural thunder and lightning, that I think we may well say, that as Nature hath long time had her Thunder and Lightning, so Art hath now hers. Dionysius Halic in his first book of Antiquities reporteth, that Alladius the 12. King of the Latins after Aeneas, had invented a means by art to counterfeit Thunder and Lightning, of purpose to make his Subjects believe him to be a God, yet in the practising thereof he burned his house and himself together, each of which may be probably conjectured to be done with the materials of Powder and Ordnance. Others affirm that a Monk of Germany, named Barthold Shewart, otherwise called the Black. Upon a cettatne time (not thinking upon Powder or Ordnance) in the year of our Lord 1300, having in his Mortar a mixture of Sulphur and Niter for another use; by chance a coal of fire falling into the same, caused it so to rarify and blow itself away: that he being therewith astonished, searched into the cause thereof, & upon further trials, he found that the hot and dry qualities of the Sulphur being with coal and moisture combined and wrought together, with the cold and moist qualities of the nitre, was apt by force to be suddenly unlosed with great rarefaction, whereby by little and little he brought that unhappy invention of Gunpowder and Guns to perfection, to make use thereof in Wars: which he revealing in short space made it common. Beraldus saith, that at the first invention of Ordnance they were all called by the name of Bombards (a word compounded of the verbs Bombe, which signifieth to Sound, and of Ardco to burn) and they that used them, they called Bombardiers, which name is yet partly retained. After which, as Bertholdus saith, they were called Turacio and Turrafragis of the breaking down of Towers and Walls: and by john de monte Regio, they were called Tormenti: their Shot Sphara tormentaria, and the Gunners Magistri tormentorum, But now Ordnance are either named at the will of the inventors, either according to his own name (as the Canon was) or by the names of birds and beasts of prey, for their swiftness, or their cruelty: as the Faulconet Falcon, Saker and Culvering, etc. for swiftness of flying, as the Basilisk, Serpentine, Aspic Dragon, Siren, etc. for cruelty, whoseswiftnes, report, and terribleness is properly and wittily expressed by the Latin Poet Forcastorius, as followeth.  
Continue cana terrificis horentia bombis  
Aera & flamifferum, tormenta imitantia fulmen,  
Corripiunt, Vulcan tum dumb Theutonas' armas  
Inventum: dum tela jovis mortalibus afers  
Nec Mora, Signantes certam sibi quisque volucrens  
Inclusum salucrum cineres, sulphurque nitrumque  
Materiam accendunt, Seruatain veste favilla  
Fomite correpta diffusa repente furit vis  
Ignea circumsepta: Simulque cita obice rupto  
Intrusam impellit glander volat illaper auras  
Stridula et exanimes passim per Prata iacebunt  
Deiectae volucres, magno micat ignibus Aer  
Cum Tonitru: quo Silua omnes Ripaque recurua  
Et percussa imo sonuerunt aequora fundo.  
Imitated by the Author, in English thus:  
What Horrid roars proceed from Bombards souls  
By air made fire, Torments of lightning flashes  
From earth exhaled, with vapours: Vulcan howls  
For that now on earth men can make thunder dashes,  
Ingenious Art now Aping Nature's work,  
Gives also name of birds and beasts of prey  
To Guns, wherein main cruelty doth lurk,  
When powdered Peter, Coles and Napths assay  
To force the Spheric shot t'outflye Report,  
And by Report to make the Welkin roar,  
And Sylvan caverns, Echoes loud retort,  
Batter, Sink, Kill, yet aiming mischiefs more:  
For merciless they'll spare nor high nor low,  
Poor, fatherless, nor widows will they know.  
The devil's birds I think were fit names  
To call them by, that spit such cruel flames.   

CHAP. III. Where Ordnance were first used in these parts.  
PAulus Interianus the Ligurian Historiographer, a grave and authentic Author writeth, that in the year of our Lord 1366. when the Wars were hot between the Venetians and the Genoweses, certain Germans presented two Pieces of Iron Ordnance (wrought by hand) unto the signory of Venice, with some provision of Powder and Leaden Shot; who received them very thankfully; especially seeing how that diabolical unknown fury had not only exceedingly feared, but also slain so many of their Enemies, that thereby they prevailed and obtained a wished victory against their adversaries, and accordingly got their own deseignes. And Paulus jovius in his third book reporteth, that the first Field Ordnance that were used in Italy, were in the Wars between the Bannitoes of Florence, and the house of Medici's brought by Bartholmeo Coglioni, and that the Prince of Ferrara having received a hurt in his foot by a Shott, from one of those small Pieces (mounted upon wheels as he noteth.) The Prince earnestly complained, that Coglioni had behaved himself that day very maliciously against him, by using supernatural Barbarism, in making such horrible and unaccustomed Tempests, to beat and spoil his Men with, who had none other Weapons to defend themselves, but only Swords and Spears. Laonicus Chalon in his fifth book, reporteth that Mahomet the great Turk at the Siege of Constantinople, in the year of our Lord 1419, planted against it one piece of Ordnance, that he discharged seven times in one day, which conveyed a bullet of 300 pound weight, and made the ground tremble a furlong round about it (at the discharge) with the report thereof. And he further affirmeth that the Grecians answered him again with Pieces that shot bullets of 150 pound weight. Pollider Virgil in his fifth book of the English History writeth, that in the year of our Lord 1425, in the beginning of the reign of the French King, Charles the seaventh; the English having besieged the Town of Mantz so battered the walls thereof, that they soon fell to the ground. And Munster in his second Volume writeth, that the Duke de Bar 1431, was defeated by the Count de Vademont, by means of the Ordnance that he used (both Canon and Culvering) which was a matter then so new and rare, that the Count himself at the shooting them off, fell always on his face to the ground for fear. Ordnance were also used by the Almains about the Coast of Denmark in the year 1434. Paulus jovius and Guichardine relate that Charles the eighth of France having undertaken the Conquest of Naples, used Ordnance both in the Planes, and upon the tops of high mountains. And the Italians that descrbed his return, said, that with his soldiers, he drew them up over the tops of the Appenyne Mountains, and so from place to place with admirable courage, where by reason of the steepness and roughness of the place, horses and cattles could not be employed to draw them, but his horsemen did then carry the Shot & other Munitions to them  several cannons 
Pierrier. Steinhuchsen. Cap. 3.  
Abatte mur. Maurbrecher.   several cannons 
Cap. 4. Pierrier ou Bombarde Steinbuchse.  
Eschelle a mire.  
Qiel. leittern.   parts of a cannon 
Cap. 5.   section of a fortress wall 
Tract. 2. Cap. 6.  
Tract de l'espaulle avec ses troniers. et explanades.  
Figur der schutrens mitt ihren zangen vnd britschen.  belonging, each of them alittle. Camello Vitelli is said to have invented the Pistols and small Hand-gunues for horsemen, whereby Ferdinand of Arragon discomfited the French and Almains. Muskets were invented for footmen, and first used at the Siege of Rhege in 1521: since which time their inventions have been so infinitely varied as no man can fully express: which now shall suffice me, and I hope will give satisfaction to other men also.   

CHAP. four Of what forms and fashions Ordnance were first made.  
Captain Vffano saith, that at the first invention of Ordnance they made them of iron bars by hand, with iron hoops, and of several fashions, as may appear in the precedent figure at α and β.  
The first was like to the common drinking Cans (used in England) tapring less & less towards one end. having also a tapering screw at the breech to fasten it into a piece of timber: but the same growing wider and wider from the breech to the mouth-wards, made the Shot thereof to scatter and to be of little force and of less (and most uncertain) direction: these long since are quite out of use, and for their fashions they were called Screwed Tapers.  
The second sort were called A batte murs, or Beat walls, and is represented therein at 2, they were not much unlike Bombards, but were laid in Troughes or Trunk carriages with 4 truckes and two timbers that rise up at the breech to stay it in the carriage, and to perform the office of the Trunnions therein.  
The third was called an Elbow piece, and is represented at 3 like a man's arm bended at the Elbow orthe gonally, or at right Angles, whereupon it took that name, but it being also of little force, is likewise left and of no use.  
The fourth was a Bombard chambered which shot round stone shot, and is seldom (without alteration) used.  
The fifth was called Scala mur, or the Scale wall, not much unnlike our Stock fowlers, these two last are represented at a in the said first figure β, differing only in that our carriages which are made to mount, and embase them by a sliding Standard with holes and a truck at the foot thereof.  
And the sixth is like a Chambered Canon Perior, but that the Chamber is made of a Piece by itself skrewed into the Chase, and hath Truunions as is represented at V 1 in the first figure, but by reason of the great trouble to screw it, the same is also out of comen use.  
The seventh Piece is nothing unlike our Portingale-base, which with her Chamber, Tail, and Hand stern, to guide and direct it unto the assigned mark, as is in the same figure represented at 2, being yet with us of use, especially in small vessels at Sea.  
The three last they sometime did work by Forge and Anvil, yet sometime they did cast the two first of these 3 both of Iron and brass. And thus much may serve to have spoken of the Ordnance first form of Antiquity.   

CHAP. V Of former foreign Founding of Ordnance.  
GVnne-Founders about a hundred, or a hundred and fifty years past did use to cast Ordnance more poor, weak, and much slenderer fortified then now, both here and in foreign parts: also the rather because Saltpetre either being ill or not refined, their sulphur unclarified, their coals not of good wood, or else ill burnt; making therewith also their powder cuilly receipted, slenderly wrought, and altogether uncorned, made it prove to be but weak (in respect of the corned powder made now a days) wherefore they also made their Ordnance then accordingly, (that is much weaker than now:) for the powder now being double or triple more than it was in force of rarifaction and quickness; requireth likewise to increase the Mettle twice or thrice more than before for each Piece. For whereas then they allowed for the Canon 80 pound of Mettle for each pound that the Shot weighed, now they allow 200 pound & more for each pound of the Shot: and for Culuerings than they allowed but 100, and for Saker, Falcon, and lesser Pieces they were wont only to allow 150 for one. But now for the Culuerings they allow 300, and for the small Ordnance 400 pounds, for each pound their several shots of cast iron is to weigh. And as for foreign Founding that it may appear how they differ from our English Ordnance, For I say that in Spain, in Germany, and in Italy, they reckoning their Canons and Culuerings by the weight of their iron cast shot, they make at the least ten sorts of either. For they have Canons of 16, 20, 30, 40, 50, 60, 70, 80, 100, and 120, and Culuerings of 14, 20, 30, 40, 50, 60, 70, 80, 100, and 120, calling them Canons or Culuerings of so much as their Shot weigheth, having several heights of their Diametres, wherein although the Canon of 20 or of 30, etc. shoot iron shots of equal weight, with the Culvering of 20 or of 30 being of like numeration, and also of like height of Boar, for the Cannon of 30, shooteth a Shot of 30 pound weight, and so likewise doth the Culvering of 30, & the like is to be understood of the Canon and Culvering of 50, 60, 80, or of 100 pounds, and so of the rest: yet do they differ in the length of their Chases and fortification of their Metals, for the Canons are but about 18 Dyametres of their Boars in length, whereas their Culuerings are about 32 Dyametres of their Boar long. And besides they likewise differ in fortification of Mettle,: the ordinary Canon being in her Chamber but ⅞ of her bore; and at her Trunnion but 5/●, and at her Mouth but 3/● of her bore in thickness of Metal, whereas their ordinary Culuerings are fortified with the whole height of their Boars in their Chamber and with 14/16 at the Trunnions, and with 7/16 of the height of their bores, at their Mouths in thickness of mettle. Now because the Measures and Weights in those aforenamed Dominions do not agree at all with ours their pound Troy being about one ounce and a half lighter than our pound Haberdepoyz, and their feet and inches Brases, and Palms likewise differing among themselves, and much more from our measure of foot and inch of Assize in England, as may appear by the Scale here annexed, with the several Tables; both theirs and our Ordnance are better to be distinguished & understood 
¼ Of a foot in 


Viena 6 a Pace  
Venice & Verona 8 a Pace  
Grecia 10 a Pace  
Bavaria 6 a Pace  
Antwerp 10 a Pace  
Ferrara 8 a Pace  
Lorraine 10 a Pace  
France du Roy 8 a Pace  
England 20 a Geo: Place      

A Table of Heights.  lb. inch. 14 4 ¼ 16 4 ⅘ 20 5 ¼ 30 6 40 6 4/● 50 7 ⅔ 60 7 ●/9 70 8 80 8 190 9 120 9 ●/● in their Weights, Boars, and Measures, than many words can explain, I have first therefore wished, that my Brethren and loving countrymen (English Canoniers) should be also acquainted with those foreign Ordnance; lest perchance being commanded to serve with some of them, they unhappily should at first be dangerously mistaken therein: wherefore I have likewise here annexed a Table, which will nearly reduce the Spanish heights unto our measures of inches, and for the rest in regard their weights are so nigh one & the same among themselves in the pounds, & differing from our pounds Haberdepoyze, etc. it may also tolerably serve for them all in like fort, as the two examples following will I hope satisfy.  

Example 1.  
Admit there be a foreign Canon or Culvering of 40, and the height of the Boar thereof be required.  
Look in this Table against 40, where you shall find 6●, so you may conclude that the Bore thereof is to be 6 inches 〈◊〉 of our English Measures.   

Example 2.  
And in like manner for a Canon or Culvering of 60, you may find seven inches and 1/9. But you must remember to allow ½ part of that height less, for the height of each shot, for the due vent thereof, as shall hereafter be further showed.  
Whereby you may also perceive that the wont allowance of ● of an inch for the shot lower than the Boar of the Piece: for all Pieces Great and Small is no good proportion for allowing the vent generally, being but a general English error, and rejected by understanding Gunners, as hereafter when we show how to find the due vent for every Piece shall more at large appear.  
In France they have usually these 6 Pieces. viz.  Boar. Leng. Shot. deg. d. lb. Canon 6 19 33 Culu. 5 27 16 Bast. 4 28 7 ½ Mini. 2 1/● 36 2 ●/2 Falc. 2 2/1 36 1 ½ Falconet 2 37 ¼  
And 3 sorts of Shot, Stone, Iron and Lead, whereof the first is to the second subtriple, and the second to the third Subsesquitret in weight.    

CHAP. VI Of later Founding for legitimate Ordnauce.  
THe Emperor Charles the fifth, finding the great inconvenience in those confused varieties, consulted thereof with his Council of War, and thereupon commanded. That all his Gunnefounders should thenceforth cast all Cannons of 18 Dyamerres of their Boars in length, and to carry an iron Cast shot of 45 pound and allowed about 7000 weight of Mettle for every of those common Cannons for Battery: but for reinforced Cannons (that is as we term them double fortified Cannons) to give them one height of their Boar in thickness of Mettle at the Touchhole, and 11/16 at the Trunnions, and ●●/16 at the Mouth and to be also in length 18 Dyametres of their Boar, weighing in Mettle about 8000 pound. But for lessened Cannons being of like length he allowed but 6000 pound of Mettle, being ¾ thick at the Touchhole, ●/16 at the Trunnions, and ●/16 at the Mouth.  
Whereupon these observations may well arise, That each sort of Ordnance   cannons of different sizes 
Cap. 6.1.  
Colubrines Legitimes'.  
Ordentliche Vndt rechte Veldtschlangen.   more cannons of different sizes 
Cap. 6.2.  
Coulewrines bastards.  
Falsche Veldtschlangen.  
Monsieur de Mot, Don Lovis de Valasco, and Conned de Bucquoy, late Generals, or Masters of the Ordnance to the King of Spain, considering the utility and benefit of these Imperial Orders, every of them in their several times gave command to the Founders, that they should thenceforth cast all their Ordnance according to the proportions and Rules following.  
Namely, that every Ordinary Canon of battery should be made to shoot an iron round cast shot of 48 pound weight, with 24 pound of fine powder, or 27 of common powder, and to be in length 18 Dyametres of her bore, and fortified in thickness of Mettle with 7/● in her Chamber, and with ⅜ at the Trunnions, and with 7/● at the Mouth, weighing about 6500 pound.  
The reinforced or double fortified Cannons to be fortified the thickness of one Dyametre in Mettle at the Chamber or Pillar of fire, at the Trunnions with ⅜ of a Dyametre, and at the Mouth with ●●/●● of her bore, which were to be charged with 48 pound shot, and 28 pound of fine powder, or 32 pound of common powder, and weighing about 7000 pound, being 18 Dyametres in length.  
The Lessened Canon to be ●/4 of a Dyametre of her bore in thickness of Mettle at the Chamber, and 〈◊〉 at the Trunnions, and ●/16 at the Mouth, shooting 48 pound shot with 20 pound of fine powder, the Chase being also 18 Dyametres of her bore in length, and to weigh about 5700 pound.  
And to make their Demy-cannons as the reinforced to carry iron shot of 24 pound weight, to be 20 Dyametres of the bore in length of their Chases, and weighing about 4500 pound.  
The Quarter Canons (reinforced also) 25 times the Dyametre of their Boars in length, and the shot of 12 pound, and the piece to weigh 2700 pounds.  
Likewise they gave Order to cast their ordinary Culuerings 28 Dyametres of their Boars in length to shoot a shot of 16 pound, with 16 pound of ordinary powder, or 12 pound of fine powder: but for the Lessened with 14 pound of common, or 10 pound ½ of fine powder; and the double fortified or reinforced, with 18 pound of common, or 13 pound of fine powder. And their common demi Culuerings to be 30 Dyametres of their Boars in length, and more rich in mettle then the whole Culuerings, and their shot to weigh 10 pound, with 10 lb. of common powder, or ●/● of fine powder namely: 8 pound. And for the Lessened 9 pound of common, or 7 pound ½ of fine powder: But for the reinforced, 11 pound of common, or 8 pound ●/● of fine powder.  
And their Sakers or quarter Culuerings to be 32 Dyametres of their Boar for length of their Chases, and to shoot 6 pound of iron shot with as much fine powder as the shot weigheth: and the like for the Falcons, Faulconets, Rabinets and Bases which may be from 36 to 50 Diametres of their Boars in length, and the more fortified. And thus much for Modern Legitimate Ordnance: as for Bastard Canons, Bastard Culuerings, etc. they shoot higher shot, but are in Chase fewer of their proper Dyametres in length. And for extraordinary Pieces they are of lower height in their Boars, and in Chase more their proper Dyametres in length, than the Legitimate are. And of both the Bastard Pieces, and of the extraordinary Pieces there are Common fortified, reinforced or double fortified, or less, or lessened fortified Pieces, aswell as of the Legitimate: each of such thickness of mettle in every member in proportion being compared with their proper Dyametres, as the ordinary, reinforced, or Lessened legitimate Pieces are of ● as the particulars with their names, weights, and proportions here under mentioned, with the Tables following will make manifest.  

Ordinary observations in Venice.  
A Piece being of a inches in height the shot weigheth 1 lb.  
At 2 inches and ½, 3 lb. 〈◊〉 At 3 inches 4 lb. At 3 inches one quarter 5 lb. At 3 inches and ¼, 6 lb. At 4 inches, 9 lb. At 4 inches and a half 11 lb. At 5 inches 16 lb. At 5 inches and a half 23 lb.  
And note that all these shoot the full weight of their shot in powder. And also that their pound is but about 14 ounces Haberdepoy zc.  
And their Observations for their greater Pieces appeareth by the Table and discourse following. viz.  Boar. Shot. C Proved. inch. lb. lb. Canons of 6 inches 5 ¼ 26 18 Canons of 7 inches 6 ¼ 38 24 Canons of 8 inches 7 ¼ 64 42 Canons of 9 inches 8 ¼ 110 76 Cannons of 10 inches 9 ¼ 174 136 Canons of 11 inches 10 ¼ 205 146 Canons of 12 inches 11 ¼ 245 162 Canons of 13 inches 12 ¼ 285 190 Canons of 14 inches 13 ¼ 348 232   three crossed ramrods 
You may also further understand, that for the 4 last mentioned Canons, the Ladle described in the midst of this figure serveth, being but one Dyametre and a half in length of the shots height: whereof 4 Ladlefulls maketh up 6 Dyametres, which is ⅔ of nine which is always accounted to contain weight for weight: namely, so much powder as will be of equal weight with the iron cast shot, aswell for these as all other Pieces, which although it be not exactly so, yet may it serve for a general estimate for a sudden service to guess a near proportion.  

A Table of reinforced Legitimate Ordnance.   Weight, Mir. Co. Leu. Best A The Dragon a Double Culvering 14000 714 357 4252 paces. B Whole Culvering 8500 630 315 3703 paces. C Demy Culvering 4600 470 235 2796 paces. D Saker or ½ Culvering 2650 366 283 2181 paces. E Falcon 1500 279 889 1659. paces. F Faulconet 850 215 107 1280 paces. G Rabinet 425 164 82 669 paces. H Base 300 126 63 725 paces.  

A Table of Lessened Legitimate Ordnance.  A The Dragon or double Culvering 11000 650 325 3164 paces. B Whole Culvering 6300 570 285 3391 paces. C Demy Culvering 3150 434 217 2558 paces. D Saker 2000 334 167 1838 paces. E Falcon 1100 254 127 1514 paces. F Falconet 600 196 98 1163 paces. G Rabinet 350 150 75 895 paces. H Base 300 180 40 842 paces.    

CHAP. VIII. Of Founding of Bastard Pieces, with their Names, Weights, and Measures.  
BAstard Pieces are as I have said, Ordinary, Reinformed and Lessened, namely the Ordinary of one Diametre of her Boar in thickness of Mettle at the Touchhole; reinforced of more than one Dyametre, and the Lessened of less than one Dyametre thick there: each of which have the name, the weight, proportion of powder, and of the shot allowed as followeth.  
The ordinary Basilisk or Bastard double Culvering is about 26 Dyametres in length, and shooteth an iron cast shot of 48 pound, with 39 pound of Common, or 30 pound of fine powder, and weigheth 12200 pounds.  
The Serpentine or Bastard Culvering is in length 27 Dyametres of her Boar, and shooteth 24 pound shot with as much common, or 19 pound ● of fine powder.  
The Aspic or Bastard demi Culvering, shooteth 12 pound shot, with 12 pound of fine powder, and is 28 Dyametres long, weighing 4050 pound.  
The Pelican or Bastard quarter Culvering is 29 Dyametres of her Boar in length shooting fix pound, with as much fine powder, weighing 2400 pound.  
The Bastard Falcon shooteth 3 pound shot, with 3 pound of fine powder, and is 30 Dyametres long, and weigheth 1350 pound.  
The Bastard Rabinet shooteth an iron shot of 1 pound ½ with so much fine powder, and is 31 Dyametres of her Boar in length, weighing 750 pound. These aforesaid are Ordinary Bastard Pieces for the Reinforced and Lessened: the Table following will describe.  

A Table of Bastard Pieces reinforced by Mettle.   Waight by mettle Level Best A Basilisk 14660 659 paces. 329 3921 paces. B Serpentyne 8100 590 295 3511 C Aspic 7600 440 220 2618 D Pelican 2550 344 172 2044 E Falcon 1500 261 132 1553 F Rabinet 800 202 101 1198 G Base 450 120 72 916  

A Table of Bastard Pieces Lessened.   Waight by mettle Levelly Best A Basilisk 10500 595 298 3540 B Serpentine 6300 530 265 3153 C Aspyke 3700 400 200 2028 D Pelican 2100 310 155 1844 E Falcon 1200 212 118 1407 F Rabinet 610 182 92 1086 G Base 155 139 70 825  
Thus much for the Common fortified Pieces, and these Tables for Lessened & reinforced, as well for Bastard as for extraordinary Pieces which will further satisfy the Reader in particulars then many words: which because they are plain enough, I think they shall need no further explanation.   

CHAP. IX. Of Founding of Extraordinary Pieces with their Names, Weights and Measures.  
EXtraordinary Pieces having as I said, longer Chases, and lower heights of Boar then either the Legitimate or Bastard Pieces are nevertheless of 3 sorts also; as the Ordinary fortified with one Dyameter thick of Mettle at the Touchhole, and the reinforced with more than one Dyametre, and the Lessened with less than one Dyametre of their proper Boar in thickness there at the Touchhole, even as we have already said both of the Legitimate and Bastard Pieces also. And first the Ordinary have the measures and weight following.  
The Flying Dragons, ordinary or extraordinary Double Culuerings are of 29 Dyametres of their Boar in length of their Chases, and shoot 32 pound of iron cast shot, with 27 pound of Common, or 22 pound ⅘ of fine powder, and weigh about 12200 pound, shooting by mettle, or Mira Com. 638, leveleth 319 paces, best 3790 paces.  
The Siren or extraordinary whole Culuerings are 40 times length, the height of their Boars, weigh 6900 pound, and shoot 16 pound iron shot, with 16 pound of Common, or 12 pound ⅘ of fine powder, shooting by mettle 560 paces, level 250 paces, best 3332 paces.  
The Flying Sparrows, or extraordinary Demy Culuerings are in length 41 times the height of their Boars, shooting 8 pound iron shot, with 9 pound of Common powder, or 7 pound ¼ of fine powder, and weigh 4100 pound, shooting by Mettle 420 paces, level 220 paces, at the best Random 2499 paces.  
The extraordinary Sakers, or Quarter Culuerings extraordinary, are 42 times in length, the height of their Boars: and shoot, a shot of 4 pound of cast iron, with 6 pound of Common, or 4 pound ½ of fine powder, and weigh 2350 pound, shooting by Mettle 316 paces, level 158 paces, Best, 1941 paces.  
The Extraordinary Falcons have 43 times the height of their Boars in length of their Chases, shooting 2 pound of iron shot with 2 pound of fine powder, and weigh 1350 pound, shoot by metal 249 paces, Levelly 124 pac. Best 1481 paces.  
The extraordinary Rabinets, or Passengers, are 44 times their Boar in length, and weigh 775 pound, shooting 1 pound of iron shot, or 1 pound ½ lead, with 1 pound ½ of Common, or 1 pound ¼ of fine powder, shooting by mettle 192 paces, Level 96 paces, Best 1142 paces.  
The extraordinary Bases weigh 450 pound, and are 45 Dyametres, their shot are ½ pound of iron, or ¼ of Lead, with as much fine powder, shooting by the Mettle 147 paces, Level 74 paces, and at their best Random 876 paces.  
The reinforced and Lessened extraordinary Pieces are made apparent by these Table following.  

A Table of reinforced extraordinary Pieces.   Flying By Mettle Level Best Weight A Dragon 658 329 paces. 3936 paces. 14000 lb. B Siren 590 295 3511 81000 C Sparrow 440 220 2618 4600 D Saker 348 174 2044 2600 E Falcon, 261 130 1553 1500 F Rabinet 202 101 1198 800 G Base 154 77 916 500  

A Table of Lessened extraordinary Pieces.   Flying By Mettle Levelly Best Weight A Dragon 595 paces 297 paces. 3540 10500 lb. B Siren 530 265 3153 6300 C Sparrow 400 200 2018 3700 D Saker 310 155 1824 2100 E Falcon 236 118 1407 1200 F Rabinet 183 92 1081 650 G Base 139 69 829 350  
There rests yet another kind of modern Foreign Pieces invented by juan Mauriga Lara that shoot only Stone or Murdering Shot, which are only Taper bored in their Chambers, not much unlike our Drakes, whereof there were 3 sorts.  
The first of them were 15 times the Dyametre of their Boar in length, and called Rebuffes.   cannons of various sizes 
Colubrines extraordinaires.  
Extraordinar Colubrine●…  
The second sort were 16 times their Boars in length called a Cracker.  
And the third were 17 Boars in length, and called Ferrates, all which are represented in the third figure at ●.  
These last mentioned (as also our Drakes) may either be reckoned among the sorts of Canon Periors, (being they are nearer the length of Dyametres) but shooting iron shot, are nearer unto the sorts of Cannons of Battery: wherefore I conceive they may properly be estimated as Bastards to the one, or else as extraordinary to the other of these sorts, for the reasons before alleged. And thus much may suffice to speak of Foreign Founding.   

CHAP. X. Of our English Ordnance distinguished into 4 kinds, and those generally divided into sever all sorts as followeth.  
THe Ordnance that are usually founded in England, may very fitly be divided into four several kinds in respect of the height of their Boars, length of their Chases, Fortification of their Mettle, and the uses for which they are to serve, whose differences each from other I here intent to show in general, beginning with the Greatest; namely, the Canons of Battery, which we reckon to be the first kind, They differ very much from the other three kinds, as will appear by comparing the height of their Boars, with the length of their Chases, The height of their Boars being all between 8 inches ½, and 6 inches Dyametre; and the length of their Chases being between 15 and 22 Dyametres of their proper Boars; in fortification of mettle they differ also, for that they never exceed one Dyametre of their Boars in thickness of Mettle at the Touchhole. They differ in uses, as being only used in Batteries, which the rest are not except the Culuerings (which are sometimes also used to pierce and cut out those ruins that the Canons have loosened and shaken) Cannon shot being heaviest, because greatest, therefore only and most fitly used to batter the Enemy's Walls, Curtains, Bulwarks, and Defences: of the Cannons of Battery there are three sorts: Namely, the double Canon, or Canon Royal, or Canon of 8, whose Boar is 8 inches and upwards, in the height of her Dyametre, and being 15 or 16 Dyametres long in her Chase; the second sort is called the Whole Canon, or Canon of seven, being 7 inches in height, and about 18 Dyametres long. The third sort of this first kind are the Demy Canons, of about 6 inches in height of the shot, and 20 or 22 Dyametres in length, Of this kind may also the Minions and Drakes be reckoned. Of the second kind we reckon the Culuerings and their Consorts which are in height of Boar between 5 inches and ½, and 1 inch ½ Dyametre, and in length of their Chases they may be between 28 and 60 times the Dyametre of their own Boars, and in fortification being never less than one whole Dyametre of Mettle in thickness at their Chambers: Of this kind are many sever all sorts; namely, all such lesser Ordnance as shoot iron shot? As the double Culvering, the whole Culvering, Demy Culvering, Saker, Falcon, Faulconet, Rabinet, and Base, etc. whereof I shall hereafter speak more in particular. The smaller of this kind are of the more Dyametres of their Boars in length, and better fortified in thickness of Mettle, each having also respect to their own proper Boar. Of the third kind are the Periors, or such Pieces as only shoot Stone, or else Murdering Shot, both which, and Fireballs may be likewise shot out of any of the aforementioned Ordnance. And there are also sever all sorts of Pieces of this third kind, all which are distinguished from the Ordnance of the fourth kind, for diverse respects, especially for length, being 8 or more Dyametres of the Boar at the Mouth in length of their Chases. The sorts of this kind are the Canon Perior, the Periera, the Port Piece, the Stock Fowler, the Sling, Bombard, etc. of each of which more shall be said in their proper places hereafter. Of the fourth kind are all sort of Pieces that either shoot stone shot, Fireballes, Murdering shot, or else no shot at all. The sorts of this kind are the Mortar Pieces, Murderers, Pettards, etc. being in length under 6 times the height of the Boar of their Mouths, of each sort of this kind some are bigger, and some lesser according as the assigned service requireth.  

A Table out of Alexander Bianco, each pace two foot and a half for Randons' of the 6 Points of the Gunners Quadrant.   Point Blank. 1 2 3 4 5 6 Faulconet 180 750 1275 1590. 1710 1785 1800 Falcon 260 1100 1870 2332 2508 2618 2640 Minion 240 1000 1650 2046 2340 2412 2440 Saker 300 1250 2125 2650 2850 2957 3000 Demy Culvering 348 1450 2465 3074 3306 3451 3480 Culvering 360 1500 2550 3180 2420 3570 3600 Demy Cannon 312 1300 2210 2756 2964 3094 3120 Canon of 7 324 1350 2295 2865 2978 2213 3240 Canon of 8 360 1500 2550 3180 3420 3570 3600  
This Table seemeth to be Calculated after the Common Pace, which is but ½ if the Geometrical Pace, and must out of doubt be so understood, as he himself in some part of his Book acknowledgeth, which I thought fit to give notice of to avoid misprisions, and for making the matter more plain. Which the Reader may reduce by taking ½ of every number.  
I have here also added another usual Table for English Ordnance, wherein I acknowledge some errors are, because exactness in Tables of this Nature is not to be expected, by reason of the infinite diversities of Materials and Accidents: But it may so become useful nevertheless, because it reasonably pointeth at what should be in this matter expressed precisely, if it were possible, which the courteous Reader I hope will accept of until better come.  

A Table of Ordinary proportions allowed for English Ordnance.   Boar. Height of the Shot. Waight of the Shot. Waight of Serpent: Powder. Ladles length. Ladles breadth Length of the Piece. Waight of the Piece. Waight of Corn powder. Canon Royal, or, Canon of 8 Inches 7 3/6 inch. 63 lb. 40 lb. 24 inch. 14 inch. 12 foot. 8000 lb. 27 lb. Canon of 7 6 ¾ 39 25 22 12 ¼ 11 7000 18 Demy Canon 6 ½ 6 ¼ 30 20 21 11 ½ 10 6000 14 Whole Culue. 5 4 ¾ 15 14 19 9  4300 10 5 ¼ 5 1 ½ 15 20 10 12 4400 12 5 ½ 5 ¼ 20 16 21 11  4600 15 Demy Culue. 4 ¼ 4 9 8 17 7  2200 6 4 ½ 4 ¼ 10 ½ 9 18 8 11 2400 7 3/7 4 ¼ 4 ⅖ 12 ½ 10 19 9  2500 8 Saker 3 ¾ 3 ¾ 5 5 30 9  1400 4 3 ¾ 3 ½ 5 ¼ 5 ½ 31 9 ½ 9 1500 4 ¾ 4 3 ¾ 5 ½ 5 ½ 32 10  1600 5 ½ Minion 3 ¼ 3 3 ¾ 3 ¾ 25 5 ½ 7 ½ 1200 3 Falcon 2 ¾ 2 〈◊〉 2 ½ 2 ½ 22 5 7 700 2 Falconet 2 ¼ 2 1 〈◊〉 12 18 3 3/● 6 500 1 Rabinet 1 ½ 1 ¼ ¼ 5/4 11 ½, 2 ½ 4 300 ½ Base 1 ¾ 1 ½ ½ 9 2 3 ½ 201 〈◊〉  
For the Culuerings whose shot weigheth 18 pound, you must abate 3/6 which is 3 pound, for then the powder must weigh 15 pound.  
For the Canon abate 1/●.  
For a general observation take that a Ladle 9 balls in length, and 2 balls in breadth, will very near contain the just weight in powder, that the iron cast shot for any Piece weigheth.  
And also that the powder here mentioned is for Serpentine powder, which being now out of use, the Corn powder being 1/● stronger, therefore 〈◊〉 of these weights is to be abated, as in the last Column appeareth.   

CHAP. XI. Of the Canons of Battery in particular, or of the first kind, and their sorts.  
IT would be too tedious and long, yea and almost impossible to show all the differences and inequalities in the Weights and Measures of several Pieces of one same kind and sort of Ordnance that have been cast, or yet are at this time remaining in several Fortresses of England and other countries, besides such as are here & there yet daily Founded or usually made either according to the Princes and the Officers of the Ordnance invention and wills, or some Founder's opinions and self conceits. But forasmuch as it is a matter of greatest importance for every Gunner that taketh charge of Ordnance, to know perfectly of what kind and sort every Pecce that is committed unto him to manage and serve with, is; and whether they be sufficiently fortified or not, and to discern and examine whether any defect be amongst them, and so to be able thereby to judge what powder each Piece in loading is able to endure, with safety to perform her uttermost services, considering then withal that Powder is now reduced into a greater perfection for force then formerly it was, wherefore former proportions are to be altered now: otherwise by ignorance or oversight they may more endamage their own side then their Enemies. Some Pieces being but poorly fortified, are too long to bear a sufficient loading, others are too too short to burn their full charge of powder requisite to carry their shot home to the assigned services; some are too light and, and some too heavy in their breeches, by misplacing their Trunnions in making the mould for their foundings, being too light they danger the vawmures, and by being too heavy in their Mettle towards their Breech, they become unwieldy and troublesome to Manage.  
There are three sorts of Canons of Battery, namely, the Canon Royal, or double Canon, they are usually 15 times in length, the Dyametre of their Boars, which is about 8 inches in height.  
The next is the Whole Canon, or (as it is called) the Canon of 7, being about 7 inches in Dyametre of Boar, and in length of their Chases about 18 such Dyametres.  
The third sort is the Demy Canon, which is about 6 inches, and 〈◊〉 in Dyametre of Boar, and their ordinary fortifications for each of these are 7/● of dyametre thick in Mettle at the Chamber, and 〈◊〉 at the Trunnions, and 〈◊〉 at the Coronish, and ⅛ at the Mouth. But of late some Founders have given unto the Demy Canons the full thickness of one whole dyametre in Mettle at their Chambers; allowing for every one pound weight of their shot some 220 or 143 pound of Mettle (for the biggest of this kind) and more, others in proportion for the least.   various cannons and their cannonballs 
Cap. 8.  
Canon de l'Emp. Charles' V doubt derivent les meillieures fontes.  
Kaiss: Mt. Carolj V Carthaunen nach Welchen die beast guss gerichtet sein.   various cannons and their cannonballs 
Cap. 9  
Fonte nowelle de l'Archiducq Albert. Neuw guss Ertzhertzogen Albertj.  
These three are only used in Batteries against strong Walls and defences of the Enemies, because their greater weight of shot doth shake more than the lighter can, namely more than the demi Culvering, (although the same shooteth and pierceth further) as by experience is daily seen. But foreign Canons were formerly, and are in some places, as we have already said, named according to the weight of their shot, being of 20, 30, 40, 50, 60, 70, 80 90, 100 and 120 pound, and most of them 18 times the dyametre of their Boars in length of their Chases.   

CHAP. XII. Of Culuerings, or the second Kind of Ordnance, with their several sorts.  
THe second kind of Ordnance are the Culuerings, of which are five sorts, the Saker, Falcon, Falconet, Rabinet and Base, wherein the Modern founded Culuerings, Sakers, etc. do much differ also from the Ancient, and our modern English also from the former foreign Ordnance, especially in Length, Boar, and Fortification, for that in former foreign Founding, they did as we said before cast the Culuerings to shoot iron shot of 14, 20, 30, 40, 50, 60, 70, 80, 100, and 120 lb. weight, and called them Culuerings of so much as their iron shot was in weight, and they then allowed them not above 150 pound weight of Mettle for each pound weight of their shot, and allowed them also to be but between 24 & 32 dyametres of their shot in the length of their Chases, with one dyametre of thickness of Mettle (at the most) in their Chambers or Columes of fire, each Culvering being now 30 or 32 dyametres of their Boar in the length of their Chases.  
But of late (as I before said) they allow Falcons and Falconets to be 36 or 40 dyametres of their bores in length, & 1 ¼ or 1 ⅓ of metal at their Chambers, with 250 pound, 300 pound, and sometimes more of mettle for each pound their proper shot doth weigh. The sorts of this kind by reason of their greater lengths of more dyametres shoot further & pierce deeper than those of the first kind, being loaded with as much powder as can be burnt in them whilst the shot remaineth within the Cillinder of the Piece, but being loaded with less, it abateth her utmost execution, if with mbre it increaseth their danger of breaking the Piece, and some of the powder will go then out unfired, or it being fired out of her Chases, etc. little or nothing doth further the course or way of the shot. Wherefore the proportional length fitted to their calibres, and the convenient charge of powder in respect thereof, and of the weight of the shot mentioned in the Theorems of my first part of the Art of Artillery will most advance the shot with all advantage possible. And for their uses they differ much, notwithstanding that they be reckoned as of one same Kind, for the Greater sorts: namely, Culnerings and Demy Culnerings serve to pierce & cut out in batteries what the Cannons have shaken and loosed: the Sakers and Falcons serve for Flankers, the other smaller sorts of this kind, for Field Pieces for the assaults, and to shoot at Troops or Companies of men that are near together. All these shoot iron shot, but may shoot stone shot where the marks are but tender, and so they will save much in Amonition, and yet perform as good service as with the iron shot they can do.  
Alexander Biance in his Book entitled Corona e palma millitare de Artiglieria saith, That their Founders in Italy as I conceive, because their Culuerings shoete shot of equal dyametre with their greatest Canons, & therefore would, if those great Culuerings were not unwieldy, shoot further, pierce deeper, and shake and unloose more than their Cannon: for the reasons aforesaid they have of late years cast fewer Canons (and more Culuerings) then heretofore, commending their force and service fare beyond the Canons.  
But Diege Vffano Captain of the Artillery in the Castle of Antwerp, for reasons in his Traicte de Artillery shown, denyeth the Culuerings to be of equal worthiness with the Cannons: which difference groweth by reason that now Batteries are made at shorter distances than heretofore: namely, within the Canons right Range, as at 80, 90, or 100 paces, so their opinions (both being judicious Gunners) I conceive to grow from the alterations also of Founding, according to the Imperial orders before mentioned, which in these parts of Italy were not known as it seemeth by Bianco Chief Gunner of Cremes, in the year 1603, nor altered from the aforenamed foreign Founding; whereby we may conceive that their seeming differences may be easily moderated by theiudicious Reader. Now for the Harquebuse a Crock, being in these days seldom used but at Sea, where especially, with an Arrow, it is a very galling and serviceable Piece, and may safely be discharged 300 times in oneday, or 25 times in an hour: his leaden shot weigheth but three ounces, and it is charged with two ounces of Powder, and by reason of the length thereof, might be also accounted of this kind, but that it is a Handgunne, and so appertaineth not properly to this discourse.   cross-sections of three loaded cannons 
Cap. 6.4.  
Canon enchambre. Carthau ntitt cingesonckter kammern.  
Canon de tuyeau esgal. Carth: mitt gleichem lauff.  
Canm encampane Carth: mitt zugespitzter kammern.   cannons of various sizes 
Cap. 6.5.  
Eber. Verrat.  
Brecant Preller  
Piece de l'Isle de Dio. Stuck auss der insul Dio.  
Rebuf. Sturtzer.   

CHAP. XIII. Of the Cannon Periors and Perieraes, the third kind and their sorts.  
OF this 3 kind are those Ordnance that shoot no Iron or Leaden shot, but only lighter, as Stone, Murdering, or Fire shot: of them there are four especial several sorts. The Canon Perior being the principal, and therefore as the Canon of Battery and Culvering bring the rest to be of their kinds, so for the same reason also may the Canon Perior do the like for hers. The Canon Perior then, for the outside is not much unlike unto the Canon of Battery, but that they are more uncertain in the heights of their Calibers or Boars, some being higher and some lower in dyametre, It is a comely and a serviceable Piece) and for those uses, namely to shoot Stone shot, they are well & sufficiently fortified; so that being duly loaden, the Gunner may therewith safely serve to defend a Breach, keep a passage, murder, and spoil the Enemy being approached near hand. Most foreign Canon Periors are Chambered, being either taper or belbored in their Chambers, the Mouth of which Chamber being but either ⅔ or 3/2 in Calibre of the height or Calibre of the Mouth of the Chase, of the Piece; the difference of which at the Mouth of the Chamber is called the Orloe or Relish, their Chambers are to be in length 4 Dyametres of the Mouth of the said Chamber. But the most of our English Cannon Periors are equal bored through the length of their whole Chases (which I conceive were better to be only taper bored in their Chamber) so as that the Mouth of their Chambers be equal in height with all the rest of her Calibre or Boar forward, towards her Mouth, because it will be thereby the better fortified in the Chamber, and so the more able to resist the force of her due loading in powder: these Pieces are to shoot the ⅔ of the weight of their Stone shot in corn powder, only abating proportionally 5 pound of powder for every 100 pound weight of shot. The Chambered Canon Periors with Relishes (as aforesard) are troublesome to load, for that they are therefore to use a Scafetta, and a Rolling Rammerhead, with a shiver in the Staff.  
The length of these Canon Periors are about 8 Calibres of their Boar at the Mouth of the Chase: they are to be in their Chambers 2/7 in thickness of Mettle at their Touch-holes.  
The Terieraes are the next sort of this third kind, which are in all things like unto the Canon Perior (already mentioned) but that they are much poorer and weaker fortified with Mettle, being allowed for the Canon Perior, 80 pound of Mettle for every pound weight of their Stone shot, and but 60 pound for the Petrieraes, whose Chamber being but ½ in Boar of the Calibre at the Mouth, must be loaded with but ¼ of Corn powder, but if it be 2/7 then with 1/7 of the Stone shot weight.  
The third sort of Ordnance of this third kind being the Port Pieces, and Stock Fowlers which are Brass cast Pieces open at both ends, invented to be loaded with Chambers at the Breech end, fitted close thereinto with a shouldering, even as the wooden Trees for water pipes have tapred ends to let them close one into another; The shot and wadde being first put into the Chase, then is the Chamber to be firmly wedged into the Tail of the Chase and Carriage. Now in stead of round Trunnions, there are 4 square tenants cast joining with the side of the Chase of the Piece, on either side two, which being let into the Block or Carriage, holdeth the whole Chase fast therein; leaving the Cornish lying upon the ledge of the Ships Port, or upon the Vawmure in a Fort, and tryced up with a rope fastened about the muzzle; The Tail of the Carriage is to rest, and to be shored up with an upright post or foot, full of holes to slide up and down in a square Mortice fitted thereunto, having a shiver at the lower end thereof, with two Tressle legs morteized before under the block of the Carriage, the foot with holes hath a pin to stay the Piece upon any Mounture assigned. The fourth sort of this 3 kind are the Slings and Portugal Bases which have Chambers fitted into their Breeches as the Stocke-Fowlers have, but that the Tails that stays their Chambers to wedge them fast (as in one continued Piece of iron whereof they are usually wielded and wrought) unto the Tail whereof there is a long stern handle of iron to direct them to respect the assigned mark: They stand upon a forked Prop or Pintle upon the ends of which the Trunnions resteth, they are loaded with their Chambers as the Stocke-Fowlers are: these shoot either Base and Burr, Musker or any other kind of Murdering Shot, being put up in bags or Lanterns fitted to their Calibres. And being discharged, their Chambers are to be taken out and filled again, and others to be put in ready charged in the place thereof. These Pieces are usually loaded with ¼ or ⅓ of the weight of their shot in corn powder. Port Pieces and Fowlers are usually made of Cast Brass, but Portugal Bases, Slyng, and Murderers, are commonly of wrought iron; the lengths of the Portugal Base is about 30 times her Calibre; the Sling about 12 times, the Murderers, Port Pieces, and Fowlers 8 at the most besides their Chambers, their Chambers about 3 times their Calibre in length, and weigh the 6 or 8 part of the whole Chase.  

A Table concerning Chamber Pieces.   Length Height Powder Stoneshot & weigheth A Chamber 12 inches & ½ 4 inches & ½ 7 lb. 6 ½ inches. 13 lb. stone. 22 inches & ½ 4 inches ½ 7 lb. 6 inches. 10 lb. stone. 24 inches 4 inches ½ 9 lb. 7 inches 17 lb. stone. 17 inches & ½ 3 inches ¼ 5 lb. 5 inches. 9 lb. stone. A Sling ch. 22 inches 2 inches & ½ 3 ½ lb. 2 inches ¼ 2 lb. ½ iron. A Port ch. 16 inches 3 inches ½ 3 ¼ lb. 5 inches ¼ 9 lb. stone. A Base ch. 9 inches ¼ 1 inch ½ ¼ lb. 1 inch ½ 6 oz. iron.   

CHAP. XIIII. Of the fourth Kind of Ordnance, Short Guns, Mortars, and Square Murderers, Pettards and Tortles, and the sorts thereof.  
Mortar Pieces, Square Murderers, Tortles, and Pettards are the sorts of the fourth kind of Ordnance, and do much differ from the former 3 kinds, and in many things also one of them from the other, as may appcare by the several discourses upon their descriptions and uses. The Mortar Pieces are of several grandures and fashions, for some of them are made to shoot a Stone shot of 350 pound weight, and some again are so small that their shot weigheth not above 4, 5, or 6 pound, and may be of any quantity between. And some are of one Cillinder without side, others are of two, one of them lessened without as fare as their Chamber reacheth bat all of them are Chambered, or as some Gunnefounders term it Cambred taperingly, being at the Mouth of the Chamber about the Calibre of ½ the Dyametre of the Mouth of the Piece, and in length ½ thereof or more as the Chase is longer.  
These Mortar Pieces are of great efficacy, aswell for the Assailants as the Besieged or Defendants: for being duly used, they much terrify & trouble the Enemy besieged in a Town, City or Fort; especially by sending upon them Granades either single or double, or great iron stone or leaden shot, and from within when the Enemy should work, or would rest in their Tents and Lodgings, whereunto by reason of some Hill, building, or Wall, they are so hidden that none other Ordnance can be bended against them; for that all other Guns rely principally to convey their shot in a right line, to do effectual service, whereas this fort worketh altogether in obliqne or crooked lines unless the Piece be mounted to 90 degrees, mounting them commonly above 45 degrees: namely to 60, 70, 80, and sometimes more or less, accordingly as the nature of the service requireth. But for the Defendants, these are ordinarily used to shoot forth Fire Balls into the Champion in the night, that they within may see what the Enemy worketh abroad; or else when the Enemy is approached unto the foot of the Wall, to undermine or pierce it, or to enter a Breach already made, & cannot be well repulsed by other means or cannot be offended from aloft, shooting out of a Mortar or other Perior, Balls of stone, old iron, or any other murdering shot or granadoes and Fireworks. Some of them have their Trunnions in the midst, other moreaft, and some even with their Breeches being fortified with mettle about ½ of the height of the Mouth of the Chamber at the Touchhole, and ⅓ of that Calibre at the Mouth of the Piece; They are of several lengths in Chase, for some are two, and others be three Dyametres of their Mouths Bore in length. They may be loaded either with Cartouches or with lose powder, allowing ¼. part of the weight of the Shot, shooting upon any mountare above 40 degrees, but with ½ shooting level or downwards, always putting home a good wadde between the Powder and Shot unless it be a Fireball, which the Powder in the Piece is to fire in her discharge; for then the Firework must lie in the lose powder, and have a wadd before it, and some use for every hundred the Shot weigheth proportionally to abate 5, which Alexander Bianco liketh not: The proportion for loading them must be ordered according to the strength of the Piece and Powder, and weight of the Shot, and is also accordingly as the Mounture and distance is more or less, if the Shot be a Granado made of Potter's earth baked, or of Glass, the 1/20 part of their weight will be sufficient powder to blow them out with little or no danger of breaking: for if they should have so much powder as that the ball is forced to break within the Piece; or if any pinne-hole or vent should chance to be in a mettailine Granado, so as that the powder within it be fired; the Piece would not only break and tear the carriage, but also endanger him that giveth fire, and frustrate the service: As was proved by M. Kenuins' indiscreet practice in his late Majesty's Mortar Piece, breaking it, and also thereby endangering the spectators; wherefore if the Granado be of cast mettle, it were best to be covered over with the ordinary coating, to stop such vents as is hereafter mentioned: Then will 1/10 part of the weight of the Shot in corn powder be sufficient. But if it be loaded with a  Stone shot, than ⅙ or ½ rather of the weight thereof in corn powder may be allowed, the more powder, the less mounted, as we have already said.  
Now having showed the proportion of powder, fitting each sort of Shot and Mounture, it will not be amiss to show how to order and manage the same Morterpeece, Gunner-like.  
First then the Chamber is to be well sponged and cleansed before the putting in of the powder, whether you load it with lose powder or Cartouch turning the Mouth near upright; the powder being so put into the Chamber, there must be a wad put in either of hay or Okam, & after a Tampkin of Willow or other soft Wood; such as may, together with the powder that was first put in, fully fill up the whole Chamber thereof, that there may be no vacuity between the powder and wadd, or wadd and shot; after which the shot shall be also put in at the Mouth with a wadd after it; especially if the Piece be not much mounted, lest the shot go out too soon, and the wadd between the Tampkin and the Shot, is not only to save the shot from the Tampkins breaking of it, but also to avoid vacuities, which are very dangerous for the Piece by second expansions.  
Having then resolved upon the premises concerning the Piece, Shot, & Powder, as before is showed, and upon the distance and Mounture for the Mark, as hereafter the Rules and Tables following shall direct; then for the bending and disposing it to the assigned service: Observe first to lay a strait Ruler upon the mouth of the Piece, and upon it place a Quadrant or other Instrument crossewise to set the Piece upright to avoid wide shooting, and then placing them foreright to elevate it into the resolved degree of Monuture to avoid short or ovetshooting accordingly, as the Tables and examples following will lead you: for having made one shot, you may thereby proportion the rest, considering whether you are to shoot with or against the wind, or whether it blow towards the right or left hand, and whether weakly or strongly; and so accordingly to give or abate the advantage or disadvantage: which judgement, not Rule must induce, and yet by help of the Notes following, of mine own experience late made in one of his Majesty's Mortar Pieces, and by these Tables, any judicious Gunner may with a Shot or two first made out of the Piece he with practice may very much help himself.  

Captain Vffano his Table for a Mortar Piece to shoot therewith by the twelve Points of the Gunneers Quadrant. And  Points Paces 0 100 1 248 2 377 3 468 4 534 5 570 6 583 7 566 8 532 9 468 10 377 11 243 12 000  
Mine own Notes of practice in a Mortar piece that shot a stone shot of 5 inches in Dyametre high. The Mortar Pieces Chamberbeing 2 ½ inches at the Mouth thereof, and three inches deep, and the rest of her Chase being 10 inches deep, which I discharged with three ounces of powder there being little wind.  
degrees yards Scores At 45 750 37 ½ At 50 710 35 ½ At 55 675 33 ½ At 60 620 31 At 65 575 28 ¾ At 70 480 24 At 75 360 18 At 80 270 13  

A Table out of Vffano for the Mortar Pieces, Randons' made for every degree between the Level and 90 degrees.  degr. paces degr. 0 100 89 1 122 88 2 143 87 3 164 86 4 285 85 5 104 84 6 224 83 7 243 82 8 262 81 9 280 80 10 297 79 11 314 78 12 331 77 13 347 76 14 363 75 15 377 74 16 392 73 17 406 72 18 419 71 19 432 70 20 445 69 21 457 68 22 468 67 23 479 66 24 490 65 25 500 64 26 510 63 27 518 62 28 524 61 29 529 60 30 534 59 31 539 58 32 543 57 33 549 56 34 552 55 35 558 54 36 562 53 37 568 52 38 573 51 39 477 50 40 580 49 41 582 48 42 583 47 43 584 46 44 582 46 45 582 46  
The use of the former Table. The use of the Table may be thus explained. Having once made known the distance the Piece did shoot at any Monuture given. As for example: suppose at 53 degrees which conveyed the shot 700. paces, and you desire to know how far she would shoot at 60 degrees. Now because 700 degrees is not at all in this Table, but against 60 degrees there standeth 529 paces. Therefore say by the Rule of 3, if 562 the number against 53 degrees giveth 700 paces, what shall 529 the number against 60 degrees give, multiplying 700 by 529, and divide the product by 562, and the Quotient will be 649 ¼ fere, the number of paces which the said Mortar Piece will shoot at 60 degrees Monuture being alike loaded, and having such like accidents as it had when it was shot off at 52 degrees, and so for any other number of paces or degrees, or distances assigned.  
The second sort of this fourth and last kind of Ordnance, are the Pettards, which are short Pieces of late years devised and practised to make overtures into Towns, Cities and Forts by breaking open their Ports & Gates, and blowing up of Bridges and Walls by means of the force of powder fired. Of these there are of several forms and magnitudes, even as they are of several uses and for different services; especially in grcatnes when great force is requisite. Some of them are cast in shape not much unlike the fashion of a Grocers or Apothecaryes' spice Mortar, and some are tapered much like a Cooper's water pay le, little deeper than the Dyametre of their mouths, but being not above ¼ in Dyametre at their bottom or breech of their mouths Calibre, and in thickness of mettle ½ of the Dyametre at their breech, and lessening in thickness towards their mouths. Their magnitudes are some to hold but one pound of powder or less; and others to hold 50 lb. or more, and they usually allow 4 lb. of Brass, or 5 lb. of iron to cast a Pet. for one pound of powder, and 250 pound of Brass, or 300 pound for a Pettard that shall hold 50 pound of powder, using those proportions diminished for lesser, and augmented for greater. The Pettard is sometimes to be used in places accessible and inaccessible, Suppose then we are to Pettard a Port or Gate unto which we may approach, in that case a skrewed hook is to be let into the Port, upon which the pettard with her Planchier or Matria is to be hanged, as in the 13 figure at ● is representd.  
The Planshier is at least to be 3 inches thick, armed with iron plates to defend it from splitting, it is also to be under propped with the forked Rest, & stayed in the ground at the hinder end to hinder the reverse thereof. Pettards are to be loaded with fine corn powder, the finer corned the better being very hard beaten in, by little and little at once with iron drifts or such like, of the just height of the Dyametre of each places concave of the Pettard, until it be full within one finger breadth of the top, and then some use to make a hole through the powder unto the bottom with apyke head or such like, into which hollowness they put in certain quills filled with raw quicksilver. Lastly, they cover the mouth thereof with a waxed cloth, being cut of the just breadth of the inside of the mouth of it, & fill up also the rest that is yet empty with molten wax, mingled with hemp cut, or with ●oe rather. They   tunneling beneath a fortress wall to place a mine 
Tract. 2. Cap. 3.  
Comment il fault. armer et conduire une mine.  
Wie eine minen zu leitten undt zu verwahren.   the entrance to the tunnel 
gallery.   various tools and devices useful for conducting a siege 
Tract. 2. Cap. 6.  
Form et vsage de quelques instrumens ingenieux pour une enterprise.  
Form undt gebrauch ettlicher instrumenten zu einer empresa nutzlich zu gebrauchen   tools for constructing a petard 
Tract. 2. Cap. 7.  
Comment il fault charger et attacher le petart.  
Wie ein petart zu laden vnd an zu hangon.  
But if we be to Pettard a Port unto which we cannot approach to hang the Pettard thereon, then make a little wooden horse with 4 wheels or Trucks lined with Cloth or Wool to avoid making noise, the Handle whereof is to carry the said Pettard, being at the least 40 foot long, with a Counterpoyze at the other end, having the Planchier fastened close before the mouth of the Pettard, with the crochet or underprop to place the same as close and flat against the Port as is possible, and the aftmost end of the staff or prop made firm against some stake in the ground (to stay the reverse) so always that it belong enough to reach over the dike or drawbridge to be driven close, that the Pettard may be firmed against the Gate. Then so loaded and firegiven to the slow vent or pipe with the slow receipt, the retreat may have time to be oblikely made, lest her reverse surprise the Pettardier before he canget out of the danger thereof. The figures and discourse following as well for the accessible as for the inaccessible Ports here annexed, will make that which we have said the better understood.   placing a petard  

CHAP. XV. Of several ways to prevent the effectual working of Petards.  
diverse and several means there are also to prevent the placing and effectual working of the said Pettards: whereof a word or two in brief. The first is by a kind of strong iron Gridiron or Grate so placed before the Port, somewhat distant, as 3 or 4 feet off, that the Planchier of the Pettard cannot come close enough to the Gate: for that the Air between it and the Pettard will doubtless make the action thereof to be of little or no effect: otherwise to spoil the Pettardier and Assistants near, a falltrap being let go with a buckle tricker when the Pettardier shall either tread upon a drawbridge or board covered with earth, which will pull out the buckle, and so it will let a great circle with iron works by a spring fall violently upon his head; likewise they impeach the hanging and propping Pettards by certain points of iron about 3 feet long placed under the Draw-bridge, which when it is drawn up, stands out and impeacheth, the placing of them against it. In like sort by a trap-draw-bridge which will fall down as soon as the Pettardier shall tread thereon, and slide him and his Pettard into the dyke; so also if a pair of compasses of iron with teeth on the legs have their head with a joint fastened above to the stone work of the Port, so that as soon as the bridge or board which holds the compasses and teeth open, is unloosed by treading thereon, they are forced together by strong springs most violently, which terribly will clasp and tear him in most miserable manner. Another is by two semicircles with sawteeths to clasp together as soon as the Pettardier sets foot on the false board or bridge to unhitch the springholds. Also a cord being fastened to the outpost end of the lose bridge, which by the Pettardiers stepping thereon, unlooseth the hold, so a number of stones will thereby all fall on his head and beat out his brains. So also a false Port with 3 or 4 feet or more of vacuity between it and the true Port, rising higher than the true Port in greves hoist up as a Portcullis, and shall fall when the Pettardier steppeth on the false bridge; likewise by a false or lose bridge which shall pull a tricker that shall let down a snaphance, and give fire unto 20 or 30 loaded muskets, whose mouths shall be seen through the Port, and discharge themselves upon the Pettardier and his assistants, As the figures in the 6, 7, 8, 9, 10, 11, 12, and 13 Chapters of the second book entitled Recuil de plusieurs Machine's millitaires will more manifest unto the eye.   

CHAP. XVI. How and with what instruments you may break the Pyles Palesadoes, Grates, Percallises, and Chaunes, or such like iron or wood-worke to lay them open for entry.  
TO break Palisadees, Grates, Bars, and such like enclosures of any Town, Cassle, Fo●●●or strong house. The instrument that is noted with A, which is a wrench that being aplyed and fastened as the figure showeth, will tear open strong Bars, Or the Saw B, in sawing asunder the joints, Or the Crow C, whose Cloven soot being gotten between the 〈◊〉, will forcibly disjoint them, Or else Axlike wedge D. But if the enterprise be to be secretly executed without noise of strokes of tools, than a fire wheel in such manner fastened, prymed and fired, and fixed as the figure showeth, will soon make way, if it be well ordered, for the purpose, as hereafter in this Chapter shall be directed. The same instruments are to be applied unto Bars of Gates, of Towns and Castles, if they may be approached secretly. For else there can be no better way to make overture then by battery with great Ordnance, which from far will soon make a breach aswell in Ports which are usually fortified with barracadoes and other defences, but may be thereby soon battered to make sufficient breach to enter by, yea were it in bulwarks or Curtains as hereafter shall be showed, more at large. If you would force a great Port of a Town secretly, there is another means besides the Pettard already spoken of, namely the Skrew Nut marked E, and his skrewbarre A, with, which in turning the winlase X, it will soon break open the Port so that the backestay be fast and strong enough. Now if it be strengthened with chains of iron within, although they were great and strong, yet by the screw spindle's 4 and 5, turning the Nut B, by the winlase & spykesthereof, and so in like manner the iron Burrs and Grates may be broken asunder or pulled out with the Pinchers C, and the drawing hammer D, and the mallet of hard-wood I, and the short Axe-wedge 2, Next to those instruments the drift bridge between them represented was invented to reach over a dyke and to put any Town or Fort to the Scalado, it is not much unlike the Cartbridge used for the Pettard, as before may be seen in his Chapter, but that it is not so great and heavy as it.   

CHAP. XVII. How to Dispart any Piece of Ordnance that is truly and equal bored in the midst of the Mettle thereof.  
OF all things belonging unto a Gunner, the chiefest is to bring the Metal of his Piece even; which the Gunners call disparting: wherefore the dispart for any Piece of Ordnance, whose concave Cillinder or Boar lieth equal and truly in the midst of her Metal, is nothing else but to equal the difference between the thickness of the metal that the Base Ring hath in Semidiamette more than the femidyametre at the Muzzle Ring, without which equal difference applied upon the upmost of the metals on the Muxzle Ringeyther had (or guessed at with discretion,) it is impossible to direct a Piece to any mark, to make a shot to an assured good effect: The dispart is many ways to be found. First in such Pieces as are not Chambered by a priming iron, put down to the lower part of the Boar in at the Touchhole, and making a mark upon it even in height with the highest of the mettle upon the Base Ring, then carrying the same measure unto the Mouth, and placing it upright with the lower end of the priming iron just on the lower part of the Boar there; Then look how much the mark, so made on the pryming iron, reacheth higher than the upper part of the mettle of the Muzzle Ring, so much is the length of the dispart to be placed upon the highest of the mettle there: Or else taking the Dyametres of the Base Ring, and also of the Muzzle Ring with a pair of Caliber compasses, or by guyrding or otherwise, and the half of their Dyametres is the true length of the dispart to be placed upon the highest of the mettle on the Muzzle Ring as is aforesaid.  
As for example, suppose the Dyametre of the Base Ring to be 24 inches, and the Dyametre of the Muzzle Ring to be 18 inches, the difference is 6 inches, the half whereof 3 inches, is the length of the dispart sought. Or take the compass in inches & parts at the Basering, and divide it into 3 equal parts, and do the like at the Muzzle-ring. And the half of their difference will be the dispart for any Piece that is truly bored. Or rather having guirded the Piece at the Base and Muzzle ring, look how many times 22 quarter of inches are therein contained, so many times 7 quarters of inches doth the Dyametres contain. And the half of the difference of those two Dyametres is the due dispart sought. Or else take a Rule or staff, and lay it cross upon the Basering of the Piece, and then take a line and plummet, and hold it that it may hang close: first to the one side of the Piece, and then to the other side thereof, marking also upon the Rule or staff, where the line toucheth at both times, that the string only touch the sides of the Piece without any bending, Then lay that Rule and Measure to the mouth: likewise look what the over measure cometh unto, take the half of that measure for the due dispart. Now for Chamber Pieces, there can be no certain general Rule given for their disparts: for they must be ordered according to the form of the Chamber and orelowe or Hall of the Piece; whether it be Sling, Base, Fowler, or Port Piece. But every discreet and under standing Gunner, when he seethe the Piece, may by what hath been said, know what to do therein: for Port Pieces, and Fowlers they only shoot stone, and not iron shot.   

CHAP. XVIII. Of certain faults committed in Foreign Founding of Ordnance.  
THe industrious Gunner may by that which hath been said, take true knowledge of all sorts of Ordnance, as well Ancient as Modern, and also understand the reasons, grounds, and uses of them, and of any others which shall hereafter be serviceably invented, and so be able to judge of the goodness and defects of any Piece whatsoever, to make choice of the best; and in time of need to make use of the worst; yet it is not imposed upon the Gunner's Office to practice Founding of Ordnance, although it be one of the most necessary Sciences of these times in use, which was never bred among the common sort of men, as other handicrafts were, for that they must not only be conversant and expert in the Mathematics, but also trained up thereto from their childhood if they will be excellent for ready handines therein, which makes me and others wondrously marvel, that so necessary a science should be no better respected amongst us, and that that there is no more care taken to bring up expert Founders of Ordnance for times to come, in this warlike age. But if we shall well examine the most used Founding in Europe: namely, those of Lisbon, Malaga, Barcelona, Naples, Sicilia, Cremes, Milan, Genoa, Venice, Mellines and Vtrecht: in which by reason of their continual practice they might easily have become excellent & expert, yet whether it be by negligence ignorance, or else by the too much haste made by those that have the charge and command of those Founding, it is apparent that they commit great and absurd faults therein. Some of their Pieces (and not a few) are bored awry, their Soul not lying in toe widst of the body of Mettle; some are crooked in their Chase, other of unequal bores, some too light towards the Breech turn their mouths downwards in their discharge, and so endanger their own Vawmures and Defences: insomuch that myself and other good Gunners in time of service could hardly find means to remedy that fault, either by hanging weight upon the Pommel or Cascabell, or by wedging it under at the fore Transom of her Carriage: others are too heavy also in their Breech, by placing the Trunnions too much aftwards, that Coins can hardly be drawn, but by the extraordinary strength to manage and weigh them up behind, or lay her under mettle without putting a long leaver in her mouth. Some and a great many Pieces are come forth of the Furnace spoongy, or full of honeycombs and flaws, by reason that the mettle runneth not fine, or that the moulds are not throughly dried, or well nealed: whereby either the Gunner that serveth with them is much endan. gered, they being as bad or worse to serve with, as those that are too weak and poor in mettle: for if they be loaded with so much powder as is ordinary for those sorts of Pieces (as may often happen when such Gunners load them, as are either ignorant or negligent in examining their defects) they will either break, split, or blowingly spring their metals, and (besides that mischief they do) they will be made utterly unserviceable ever after. Wherefore to avoid those dangers & faults, Gun-Founders may do well to confer one with another, and also with understanding and experienced Gunners thereupon, who with the hazard of their lives have often seen into those inconveniences: yet thus much I dare say to the due commendations of our English Gunnefeunders, that the Ordnance which they of late years have cast, as well for neatness, as also for reasonable bestowing and disposing of the mettle, they have far excelled all the former or foreign aforementioned founders. But it is to be feared that there being so few of that profession here employed for Founding of Brass Ordnance; (only Mr. Pitts and his Brother, and Mr. Philip's, and as yet so few or none brought up to learn it under them,) as that it is like that hereafter there may be a great want of honest and skilful Gunnefounders in England, the inconvenience that else may hereafter so befall, I hope will be foreseen and prevented in good time.  
Le Sieur du Praisac in his 13 Chapter of his Military Discourses, adviseth Founders to have a special care for the temper and Alleys of the metals, the inward cleanness of the moulds and nealing of them well, and to their Caps and Cavities to anoint them with clean grease, and to guard and bind them well with iron, to dry them and settle them firmly, and for the due placing of the Trunnions, as is showed in the 22 Chapter hereof, that they may so nearly equiballance one end with the other, that one Gunner with a Lever or Handspyke may raise or embase it upon her Carriage, either for the draining or putting in Coins to direct them, or lay them under metals, The running of the mettle not fine or too cold, and the mould not well nealed, or the metals not well incorporated; either of these causeth flaws, cracks, spungynes, or hony-combs in the mettle of the Piece, whereby great danger often ensueth.   

CHAP. XIX. Concerning the League and Alligation or mixture of Metals to Found great Ordnance.  
FOr the Natural viscuosity, softness, & dulness of the colour of Copper, there hath for the Founding of Ordnance been many Alloyes, Leagues, or Allegations of other metals by several Founders used as their diverse colours and tempers do manifest. True it is, that the proper Alloy for Copper, is fine Cornish Tin, when as you would have your work subject to the Hammer, or else it will not be reduced to such subtlety; as to endure the fire, or to make vessels off. But when as it shall be accompanied as shall herein be hereafter mentioned, it doth not only change the name, also the aspect and Nature thereof, as to be called Ordinary Brass, Bell-mettall, or else Brass for Ordnance, Brass ordinarily is made only by Tin, Copper, and Lapis Caliminaris. Bell mettle with more Tiune and some Latton, for Bells, Mortars, and for Ordnance, As Biringuccio saith, 12 pound of Tin for 100 pound of Copper, for Bells 23 or 20 pound of Tin for 100 pound of Copper to cause the better sound, and accordingly as they are to be greater or less, wherein I intent not here to give any other Rule; but to mix them by weight, and measure, as discretion and judgement shall induce. But more particularly for Ordnance, I have thought fitting to relate the opinions of such worke-masters and Authors as I have received instructions from. Jerome Rosselli, saith, that for 16 lb. of Copper, 10 lb. of Tin, and 8 lb. of Latton, and that the Tin giveth hardness, and sothereth the Copper and Latton, and that the Latton giveth them colour together, adding the more force to resist the vehemency of the powder fired in them, so that they make the Pieces that are cast of that mixture to be fair and strong. Alexander Bianco in his Military saith, that the best Allegations of those Metals for Ordnance, is for 100 lb. of Copper, 20 lb. of Tin, and 5 lb. of Brass or Latton is to be mixed. Diego Vffano in his Instruction de Artillery saith, that the best Legature for Ordnance is 100 lb. of Copper, 8 lb. of Tin, and 5 lb. of Latton, and 10 lb. of Sow-lead, affirming that Lead being tough and cold, maketh it also become hard.  
And Sicur du Prissac in his Military discourses saith, that the French Founders unto every 100 lb. of Copper do either add 20 lb. of Bell mettle, (which is 25 lb. of Tin and Lead, for 100 lb. of Copper or Brass) or else 10 lb. of soft Tin to each 100 pound of Copper.   

CHAP. XX. Of the Powders or Earth's to make the Moulds to cast in Brass Ordnance.  
FOr the Founding of Great Ordnance, there are special sorts of Earth's, whereof the Moulds and Models are compounded either to cast in Brass or iron, whereof it behooveth to seek the best, namely that are able to resist the fire and receive the melted metals, so that they may render them to be cast and Founded neatly without being subject either to be diminished, cracked or peeled when they shall be nealed, which is such a matter as without experience cannot be done well. The rather be cause that Earth in itself generally taken cannot safely be chosen, the colours thereof is no sufficient sign: for we see some earth to be white, some black, some yellow, and others red; and of each some are good, some bad. But none of them can by their colours be assuredly said or chosen for good in effect: for there may be some of each of those colours good; yet all earth's being either fat or lean, or soft, or gross, or viscuous, whereof the lean soon turneth unto dust, without holding together, which also are a long time drying, and are but of little continuance for strength. The Fat and viscous Earth's shrink and chap, and do soon break by their natural brittinesse, and do often grow crooked by the unevenness of their mixture or temper, whereby they become crooked in the Mould, and so warp the pattern itself: so that it is rare that such a Piece should come neatly or well out of the mould: Where upon we may conclude that good Earth's are neither Fat nor Lean, but between both, and of a fine and subtle grain or mould, which soon drieth and remaineth firm, without breaking, being able to resist the vehemency of the fire; and such Earth's are most commonly of a yellow or red colour: but relying not upon the colour, prove the quality of your Earth's with judgement, and so will experience the Mistress of Art be your best Tutor to direct you to the best powders, which must be the first foundation of your work.  
But to find such as are fit for your work, it behooveth you to sink diverse pits or caves under ground, which have not been much stirred. And after you have begun your work, and compounded your Earth's in a bank or heap, and wet and moistened them like a paste, begin then to beat them with a rod of Iron, as the Potter's use to do their Clay. Then take two third parts of the whole quantity, and mix it with lint of Linen cloth and then beat the same again together until they be well incorporated, that they may appear all one substance, and if any small stones should chance to fall amongst it to pick them out or bruise them as small as may be thereby, and so the powders being well tempered may serve for your moulds and forms.  
Some if they cannot have such Earth's as they would, content themselves, with such as they can get, which when they have tempered into paste, they dry, and then beat and remoysten; others mix it with  sand and ashes; others having but weak Earth's, temper them with water wherein  salt is dissolved, mixing therewith Scales or Lymmel of iron finely beaten and seared.  
And lastly, some mix therewith Horse or Ox dung, and some used sedge and straw finely chopped and mealed, each to his best liking, endeavouring to prevent the ill accedents that may hinder the good successes of their works.   

CHAP. XX. Of making of Moulds for the Founding of Ordnance.   man building cannons 
And having so prepared and resolved of what kind, and what sort of that kind the Ordnance is, you intent to Cast you are then first to make a Moddell or perfect pattern thereof, either of Timber, or of Earth (or both) with all the Mouldures, Ornaments, and Compartments, even as you would have the Piece to be, which you must thinnely anoint with soft hog's grease, and then cover it over with a Column of the aforesaid tempered earth, made and dried by little and little, augmenting it until it be of a competent strength & thickness; This Column must be to betaken into two or more parts, to the end to take the said Model or pattern out of it, and it is to be fortified on the out side with Plates of iron as long as the Chase of the Piece, and with iron wires an inch each from other, and lastly with iron hoops a foot or two asunder, to knock off and on as occasion shall require. There must also be a smooth and equal Cillinder, whose Dyametre must be just the height of the Boar, and made of the same earth moulded upon a strong Iron square Bar, and upon a cord woulded about the same, therewith to make the soul or concave hollow Cillinder of the Piece, by placing it (by help of the Base and Muzzle-ring) exactly in the midst of the vacuity of the outermost Column, which when the Pattern or Model shall be taken out, will remain hollow to receive the mettle that must make the body of the Piece. All these must be well joined ted together, polished smooth, and dried and nealed, that the mettle berune fine, may come off, smooth and neat.  
Lastly, the pattern of the Breech, with all the Mouldures, and Cascabell is in like manner to be covered over by little and little with the same tempered earth, which must afterwards be luted neatly and strongly to the Breech end of the outer Column: All which Mouldures, Rings, Arms, Devices, Flowers, Trunnions, Dolphins and Circles may be at pleasure added thereunto, upon the pattern either in wax, earth, or plaster, and so the perfect impression thereof be received by the concavity of the outward Column, keeping still the due prescribed proportion of the Pieces, according to the kind and sort thereof.   

CHAP. XXII. Of the place, measure, and use of the Trunnions.  
THe Trunnions in pieces not Camber bored aught to be thus placed, divide the whole length of the Chase of the piece into 7 equal parts, and at 3 of those parts from the Basering forwards, in the imaginary right line that proceedeth from the lower part of the Mettle at the Breech, to the upper part of the Mettle at her Mouth, must the place of the Centre of the Trunnions be, and so shall there be 4/7 of the length of her Chase from the Centre of her Trunnions forwards to her Muzzle, & 3/7 backwards to her Breech, except it be for a Taper bored or Cambred piece, for which the Trunnions must be placed more backwards, because the thickness of mettle to the breechwards is greater in compared proportion than it is in equal bored Pieces, which would otherwise become breech heavy, & so be troublesome to manage, and it must be so ordered for these sequent reasons. First for her better fortitude, Namely to take hold the more firmly in the Mettle of her body, and not lie directly against the concavo Cillinder of the Boar. Secondly, that being somewhat under it, they will the better support the great: weight of the mettle: and lastly, that thereby they may be only so much heavier towards their Breech as may be sufficient to keep her steady in her discharge, and not be too unwieldy, but conveniently approaching near equiballancing for the mounting and managing thereof, which the German and Spanish Founders do somewhat seem to help, by placing Dolphins somewhat more towards their breeches: and some others have thought to remedy it by placing of strong Rings in Staples of cast metal in stead and lieu of these Dolphins. But for such Pieces as have neither Dolphins nor Rings to mount or dismount by them, a Leaver being put into their Mouths and a rope fastened at the mouth unto theoutward end thereof, and unto the pommel or Cascabell at the breech, thoy are to be thereby equibalancingly slinged tomount or dismount them conveniently. The Trunnions ought next the body to be in Dyametre one Calibre of her proper bore in thickness, and also one in length, only lessening 1/30 of a Calibre, tapering by little and little towards their outward end of them. There are five things especially to be regarded in casting of mettle. The first is to make the forms and moulds duly. The second that they be well nealed with Charcoals or dry wood. The third to place them well in the Pit. The fourth is to melt the mettle to run well and fine. The fift to be sure to put as much mettle into the furnace as may be sufficient to fill the moulds; and every mould (that is to be filled with Brass or any other Mettle) must have spyralls or vents: for there is no place (although called empty) so void, but it is filled with Air, by means whereof if the hot meltes, substance come to meet with the Air there enclosed, not finding breathing vent, it will break the the mould: wherefore it will be fit that as upon the one side of the mould, the mettle is to come into it, upon the other side the moisture and air may breathe out without impeachment, that all the emptiness of the mould may be filled with mettle. And to that end there must be a vent made that may breathe out the air from the top to the bottom of the mould, concluding that by giving the more and the larger enteries unto the moulds and vents, the better and more fair will your matter be cast off. And so much for Founding of Brass Ordnance.   

CHAP. XXII. How to examine, search, and to find whether any piece of Ordnance be well and duly made, and of what Kind, and Sort it is.  
THe principal thing that a Gunner ought to look unto, when he is to take many Pieces of Ordnance into his charge, is first to search and examine how they are Fortified, and whether they be sound and safely serviceable, and whether they be of the kind of Cannons of Battery, Culuerings, or Periors, and then to know of which sort each Piece is of that Kind, and then whether they be ordinary, reinforced, or lessened in their Fortification of Mettle, and whether they be Cambred, either equal or Taper-bored, and with, or without an Orlow or Relish, be they of cast iron or of Brass mettle: and of what heights their Boars are, and how much Powder they are each of them to shoot, with any Shot, be it of Lead, Iron, Stone, Granado, or other Fireworks or Bales.  
Secondly, that he look how the Sponges, Ladles, Rammers, and Waddhookes, are fitted and conditioned, so that there may be no defect or default in them: And finding all those things well, he is to place them all on the right side of the Carriages of the Pieces they belong unto, so that the Ladles and Sponges be turned towards the mouths, and the Rammers and Waddbookes towards the Breech of their proper Pieces.  
Then by putting a Rammer with his staff into the Pieces Concave Cillinder as fare as it will go, to know whether that Piece be clear, loaded, or Cambered, and equal or taper-boared, with Relish, or not, or have any foulness got into her Concave Cillinder, which he shall perceive if he make a mark upon the staff, at the mouth of the Piece, and pulling it out when it will go no further in, and by laying it upon the outside of the Mettle, if it reach to the Touchhole or not, for if it do not reach thither, it is either loaded or cambred, or else some foulness is gotten into her. And if he find or perceive nothing to be within, yet he shall take her Ladle, and put it into her as far as he can, and moving it lightly about the lower part and bottom of her concave, giving two or three jets, to receive into the same, the dust or small stones or foulness if any be in her, which he shall continue, drawing out the Ladle and emptying it, until he perceive there remaineth no more within her to be drawn out: Then placing the Ladle in his place, let him also take her Sponge, and sponge her well; to draw out all the moisture, rust. Verdegreace, or foulness, until she be clean: then search also her Touchhole, with a Pryming-iron, whether she be therein clean, cloyed. or have any foulness gotten into it.  
That done, then may he with a common search upon a staff, having two or three round Pease, pointed springs that bear out, unless they be forced close put into the concave Cillinder unto the bottom, all along to examine her within whether there be any flaws, cracks, honeycombs, pynneholes, cinders, or other faults: and the Sun shining clear, if the mouth be turned against the Sun beams, they may by a Looking-glass well polished, or with a bright sword, be reverberated into her concave Cillinder: so that those faults may be therein most easily discerned; or else in close weather or rooms, a Wax or other Candle lighted, being fastened upon the end of a Cane, staff, or half Pike, her faults may be spied, if the same be put into her hollow Cillinder, and carefully looked for all along, the Gunners eye being therefore employed diligently at the mouth of the Piece.  
Wherein if he espy any crevices, flaws, cracks, or Honeycombs, he may assure himself that Piece is dangerous both for breaking by recharging of her too speedily after her discharge, as well for her debility by means of those defects or faults, disabling her to endure or resist her ordinary loading, or allowance of Powder to be fired in her, as also lest in such Caverns, flaws, or Honeycombs, some of the Wad, Carthouch, foulness, fur, or Powder, lie smothering therein, and so upon recharging, Fire, the Powder that should load her, unless she be well spunged with wet sponges, with a great deal of handiness, care, and diligence, to be assured to have fully extinguished the fire that shall so smother, before you recharge her. Besides, much discretion and judgement is to be used in the allowance of Powder, as in the manner of loading such Pieces, notwithstanding they be otherwise double fortified or reinforced Pieces, yet to allow them (according as they are thereby more or less weakened) so much more or less Powder, as if they were of the lessened poor, or slender, fortified Pieces of the same kind and sort.  
It may many times happen that he may meet with Pieces that are wider at the mouth, then in the rest of her bore within, which is often found in Pieces that have been long, and many times used to shoot Shott of Iron or stone, whereby the mouths become enlarged, worn, and wider, by reason of the frequency and vehemency of their discharges, whereby the Gunner may be deceived, if he take his measure for his Shot by the Callibre of her mouths, for by that means the Callibre of their bores within being lower or lesser, it may cause the Shott to stick by the way, and then a vacuity being in her between the Powder and the Shott, they will endanger the Piece to break, which may soon be examined with the Crossett, described in the 19 Figure α, whereby Shott for such Pieces may be safely chosen serviceable, according to the Callibres of their narrowest places, giving abatement of 1/20 of that height (though the Shott be round, and not oval) for a convenient vent, whereof more hereafter shall be spoken.  
If he chance to meet with a Piece that is crooked in her Chase, which is a hard matter to be otherwise remedred, then by sending her to the Furnace to be new Founded: But if by necessity a Gunner must needs serve with such a Piece, then must he take a Shott for her so low, that it be sure not to be hindered in the going out thereof, in her discharge. And besides, he must accordingly (as the crookedness lieth) lay the Piece so much the contrary way awry, over, or under the direction of the upper part of the Mettle more or less, as her bending and crookedness is more or less; the which after two or three Shotts made in her, the Gunner shall be better directed then by many words.   

CHAP. XXIIII. How to measure or Tertiate any Piece of Ordnance, to know how much Powder she is able to bear for her due Charge.  
THe best understanding experienced Foreign Gunners, doc call the measuring and examining of the fortification of Mettle in a Piece, Tertiating, because it is chief to be measured and examined in the three principal parts of each Piece: namely, at the breech, at their Trunninons, and at the mouth.  
Now that every industrious Gunner may be assured of the fortitude of any Piece of Ordnance, and so the more safely and boldly allow unto her a due loading, and proportion of powder, for proof and service, that she may without danger perform her utmost execution, I have in the 18 figure α described three Cannons, and three Culuerings, with the measures of their metals (their proper Boars being their proper Scale) at their Breeches or Chambers, & at their Trunnions, and at their Mouths. The uppermost of both which, is the figure of a reinforced or double fortified, the two middlemost of an Ordinary, and the two undermost of a Lessened Piece, both Cannons, and Culuerings, with all their measures. By which also their sorts, and all other Ordnance in their due measures, will be the better conceived and manifested.  
As for example there is a Culvering that shooteth an iron shot of 17 lb. weight with 13 lb. of corn powder, which is ⅘ of the weight of her shot; and the question is whether she may be able to bear so much powder, or if need were more, which cannot be well answered without the examining or tertiaring her mettle.  
But having already searched her, as in the precedent Chapter is showed, and found her sound and free, except the defects therein mentioned, you may measure and tertiate her to answer the question as followeth.  
First, with a Ruler, draw a right line upon a paper slate or flat smooth Previous error not modified board, as in the said 18 figure is described from A to B, Then with a pair of Compasses with straight or reversed points, take the Dyametre or wideness of the Boar of the piece, and place that measure from A towards B at C, which space between A and C, you must divide into two equal parts, and then with the compasses opened to one of those parts, set the same upon another right line, as at the point D, and with the other foot draw a circle, which will be truly equal in Dyametre unto the height of the Boar, as may appear by the Circle AFCQ, and equal to the right line AC.  
Then with a pair of Caliber Compasses take the thickness or Dyametre of the mettle of the Breech at the Touchhole: which distance between the points, you must divide into two equal parts, and then the Compasses being opened to one of them (and one foot set in D with the other) describe the other Circle GH, which shall be equal to the circumference of the mettle at the Touchhole, and so the thickness of the mettle or distance between the said 2 circles will show the quantity between F and H, and E and G.  
And seeing that the distance from F to H is equal to the distance from E to F, which is the Dyametre of the height of the Boar, he may be therefore sure that it is an Ordinary or Common fortified Culvering. But whether it be either a Bastard or an extraordinary Culvering, it cannot be known by the fortification, but by the length thereof; being longer than the ordinary, it is called, therefore an extraordinary Culvering, etc. and being shorter than the Ordinary, it is therefore called a Bastard Culvering.  
Now than this being found to be an ordinary Culvering, she will bear 〈◊〉 of the weight of her shot in Canon powder, which amounteth unto 13 lb. 9 oz. But to be more assured of her fortitude, the measure of her mettle may be likewise taken at her Trunnions, and Neck as followeth.  
At the Cornish or Ring before her Trunnions with a pair of Calibre Compasses, you may take the Dyametre of the body of mettle there, as you did before at the Touchhole, and also divide the distance between the points or ends of the compasses into two equal parts: with the compasses opened to one of those parts, setting one foot in D, make with the other the circle IL, and if you find 7/1 of the bore, it is the proportional fortification for an ordinary Culvering; and the like may be done for the Neck, which the circle MN will equalise and represent, and the distance from F to N being ½ of the height of her bore, and the due thickness of the mettle for an ordinary Culvering at the Neck, confirmeth the former measures and proofs.  
But if in taking the Measures aforesaid, there had been found in her Chamber at the Touchhole from F to H the thickness of one Dyametre of the bore, and 〈◊〉 more, it had been a sign the Piece to be double fortified or reinforced, having also at the Trunnions FL 1/16, & at the Neck FN 9/16 of the height or Calibre of her Boar, Then she shooting an Iron shot of 17 lb. would have endured also 17 lb. of Cannon corn powder to be loaded with, and be fired within her without danger. And this would so have conveyed the shot further than the ordinary could have done, upon like degrees of Mounture.  
Contrariwise, if the circles there had been found, that from F to H, but ⅞ of her Calibre of the bore at the Touchhole, and at the Touchhole but ¾ for FL, and at the neck from F to N but 7/16 of the height of her bore. Then she appeareth to be one of the lessened or slender fortified Culuerings, and must be allowed but 12 lb. 9 oz. of Cannon corn to convey her Iron shot of 17 lb. which upon like elevation will not carry a shot so far as the Ordinary, much less as the extraordinary Culuerings could have done.  
In this self same manner all sorts of Pieces of the second kind are to be measured and Tertiated with this consideration and allowance withal, That the Demy Culvering hath 1/16, and the Saker 1/●●, and the Falcon ⅙ more mettle comparatively then the whole Culvering hath. And so much for the sorts of the second kind of Ordnance.  
Likewise upon the other side of the same figure, the Measures of the Ordnance are thus described.   measuring the mouths of various cannons 
Tract. 3. Cap. 2 fig. 1.  
Chambre 1 Calibre.  
Kammer 1 Calibre.  
Canon renforcee.  
gesterkte Carthounen.  
Chamb. ⅞.  
Kammer ⅞.  
Canon comun  
gemeine Carth.  
Chambre ¾  
Kammer ¾  
Canon amoindrt  
veriungte Carth.  
Comment il fault mesurer les pieces d'artillery.  
Wie das geschutz zu viesieren.  
la chambre 1 Calibre.  
die kammer 1 Calibre.  
Colubrince Commune  
Gemeine Colubkine  
Chambre 1 Cal. ⅛  
Kammer 1 Cal. ⅛  
Colubrine renforcee.  
gestärckte Colubri●zc  
Culebrinarrefarcada  
Chambre ⅞  
Kammer ⅞  
Colubrine amoindrie.  
Veriungte Colubrine.  
The double fortified or reinforced Canons of Battery, have one whole Dyametre of their bore in thickness of mettle at her Touchhole, and 11/16 at her Trunnions, and 7/16 at her neck.  
The ordinary Canons of Battery is ⅞ in their Chambers, 〈◊〉 at their Trunnions, and ⅛ at their Necks of the Dyametre of the Boars in thickness of mettle.  
The Lessened Canons of Battery is ¾ at the Chamber, at the Trunnions 9/16 and at the neck 5/16 of the Dyametre of their Boars in thickness of mettle, whose poorness and debility of mettle, although they be to shoot an Iron shot of about 60 lb. yet they cannot endure above 25 lb. ½ of fine powder, or 31 lb. of common powder.  
Whereas the reinforced Canon of Battery can endure to burn 34 lb ½ of fine powder or 43 ½ of common powder.  
And so the Ordinary Canon of Battery will endure 30 lb. of fine, or 39 lb. of common powder.  
But if the Gunner when he should measure or tertiate any Piece, hath not Calibre compasses, he may do it sufficiently with a cord or string, by guirding the Piece at the Touchhole, at the Trunnions and at the Neck, taking ½ part thereof for the Dyametre of the body of her mettle in each places, Thus:  
The Canon or ordinary Culuerings have about 11 Dyametres of their bore about at the Touchhole, and at the Trunnions 8 Dyametres, and at the neck 6 Dyametres in their circumferences.  
But the Common or Ordinary Canons of battery have but 9 Dyametres at the Touchhole, and at their Trunnions 7 ½, and at their necks 5 2/5 in the circumference of their metals there.  
Lastly, the Demy Canons are but ⅞ of their bores in thickness of mettle at the Touchhole: I need not to insist upon the rest of the measures, nor of the reinforced Ordinary or Lessened, only I may say that as they all tend to none other end, but to make known the force and feebleness of any Piece, to allow her a convenient charge of Powder, that they may perform their best and utmost force most safely: for if you give any Piece more than her due charge in powder, you endanger the Piece yourself, and the service expected, but if you give less she cannot do sufficient execution.  
The force and richness, and the defects and poorness of the Powder, is likewise to be well known for 10 lb. of one powder may do more execution than 12 lb. of another, wherefore increase or abatement must be accordingly made to or from the quantity, that is ordinarily allowed, according to the strength thereof, more or less, whereof I intent to speak more particularly in the chapter of the making and proving of Powder.  
But yet I will conclude with a brief and industrious way to measure a Piece as is by the 19 figure α represented: First draw a right line, as the line CD, then take the wideness of the bore of the Piece with a pair of strait pointed compasses, and set both the points in the said right line from C towards D, as CF which will be the height or wideness of the bore of the Piece. Then with a pair of Calibre compasses take the Dyametre of the mettle at the breech, which being also set in the same right line from C towards D as CE. Lastly, divide EE into two equal parts at A, so will FAVORINA or EA be the thickness of the mettle at the breech. The like may be done at the Trunnions or Mouth.   

CHAP. XXV. To find whether the Concave Cillinder of any Piece of Ordnance be in the midst of her mettle, if not where the thickest or thinnest of the Mettle is, and the difference thereof, and of the longest and shortest distances from the Axis of the mettle to the Axis of the bore, with their Largesse and Disparts.  
BEfore I proceed any further, it will not be amiss here to show the use of Parallel Squire described in the 19 figure α, which is an instrument requisite to find & examine whether that any Piece hath more metal upon one side of her then on the other. The same is of two perches or pieces made square of good seasoned wood planed strait and smooth, joined at the end with two travers pieces truly let in and well closed in their joints, so that as one of the pearches may come nearer or go further off from the other as the Piece to be measured shall require always, keeping the two pearches exactly parallel one to the other, and so locked with shrew pins and nuts, as that they may not budge without his will that useth them.  
These pearches have in each of them 5 or 6 screws with pins of brusse or Iron, that the one perch being put into the Cillinder of the bore of a Piece of Ordnance, the pins and screws with their half round heads may so bear upon the lower side of the bore, that it may hold up the perch close to the upper side thereof, all along even to the Touchhole. Then by the Traverses, locking the Perch that is without, that the further end may touch & rest upon the Basering, and the upper pins also touch the Cornish frieze, and other eminent rings of the outside. Then turning the said instrument round about, all the concave or soul within and about the mettle or body without side of the Piece, if you find it to touch all parts equally in such revolution, you may be assured the Piece is truly bored in the midst of the mettle; but if it touch not equally but be stayed or stiff upon one side, and lose, that the pins bear or touch not one the other, it is certain that the side where it is lose, is thinner in mettle, than the other where it goeth stiff or stayeth.   man examining several cannons with various tools 
Tract. 3. Cap. 2. fig. 2.  
Kreutzstenglein. Croisetta.  
Eschelle pour examine le ba●●n de la piece sil et droit ou non  
Eine leitteren darauff erforschet ob der lauff an einem stuck gleich oder ungleich ist.  
Cecijs est explique desoubs chap. 5.  
Disses is't drunder in 5. Cap. erckläret  
Comment il fault mesurer une piece.  
Wie ein stuck soll visieret werden.  
bouche.  
rictal.  
bouche. netal.  
la cueilliers de charge.  
●undloch.  
mor●luch.  
Die ladschauffel.  
Regla pour signer le, lignes droitte.  
Zoll stab daran die serack linien zu zihen.  
The same being done aswell for the Breach as for the Mouth, and transferred accordingly upon a board with Plumets in the centres of each circle, & one in the perpendicular Dynametre of the middle line of the board, whose lower end must be somewhat hollowed, that it may be the better applied upon the roundness of the mettle of the breech and muzzle of the Piece, as the figure thereof may sufficiently explain, it would be too tedious, and not opera pretium further to describe the perpendicill, or to demonstrate the same, although I have prepared for any friends that desire it.  
Note for as much as it is very difficil to reclaimc such Pieces from shooting awry, or over or under, without these curious preparations: And because they are not safely to be shot in, without very good and mature consideration of their weakness and danger, for if an ordinary charge of powder be fired in such a Piece, the weaker fortified part would not be able to resist the force thereof, but be in great danger to break and split: therefore I would advice every Gunner that shall be apppointed to serve with such a Piece, aswell for his safety as for his credit, either with or without reclaiming those Errors, not to load her with more powder than if she were no better fortified in any place than she is in the weakest part, her surplusage at the thickest, being no better help to strengthen the thinnest of her mettle; then if she were in all places weak alike. Yet to examine the mettle of any Piece do thus also, Mount the mouth of the Piece upon a skidde or piece of Timber, and having from the upper part of the mettle, made four marks, or divided the circumference of the Base and Muzzle Riggalls or Rings into 4 quadrants from the mouth to the Breech, having stretched a chalk line laid upon two of those marks each with his match, striking with that line, 4 lines alongst upon the outside of the body of the piece, and having a great care that they betruely lined; Then take a straight rod and put it into the mouth of the Piece, holding it close to the side of the concave directly within it as the lines directeth, the one line whereof lying directly, his opposite will lie directly underneath it, and the other two lines will be stretched on both the sides of the Piece.  
Then take your Quadrant, and place one side thereof even with the rod, and look what degree the perpendicular plumlyne cutteth thereon, and so turning the piece, that one of the side lines may then lie upright, if the plumblyne then fall upon the same degree at each line of such application upon them all, the Piece is then truly bored. Lastly, there may also for that purpose be an Iron or Brass Instrument with a joint in the midst called Double Calibres with four legs like the figure here described, which by putting them into the concave of the Piece, and turning it round within the bore, clasping the other leg without to the mettle of the Piece, the distance between the other two legs without will show the thickness of the Piece in each part, and show, with applying all the openings unto an inch Rule or scale of equal parts, whether the Piece be thicker upon one side then on another, being alike distant from the mouth of the Piece, and how much and where.   measuring the thickness of a cannon 
Which differences of thickness and thinness of her mettle, wry boring or uneven lying, of the concave Cillinder or Soul in her body or Mettle being so made known. The Large line and Large itself, together with her due dispart, and lying of the Axis, for such a Piece may be found as followeth.   

CHAP. XXII. To Dispart a Piece of Ordnance, whose Boar lieth horizontally awry, and the Axis thereof being parallel to the Axis of the Mettle.  
SVppose that the Boar of the Piece lieth awry so much of the horizontal Dyametre square, as w v, or of the circumferences of the mettle at the mouth, as m n, or at the Breech as t r, here represented by the two parallel right lines, one v b m t, being the vertical semidiametre of the middle of the mettle at the Breech, and v b m at the mouth. And w h o u t the other parallel, whereof w h is the vertical semidiametre of the middle of the bore both at Breech and Mouth, and h n the vertical thickness therein of the mettle of the mouth, and h t the vertical thickness of the mettle at the greatest ring at the breech.  
The difference of b m for h n being added unto the difference of m r from t r, augmented by the line of the usual dispart r m (the difference at the upper part of the mettle at the Breech and Mouth) will compound and make the due dispart little or nothing differing from the usual dispart, but must be placed upon n perpendicularly parallel to m r, which shall direct the said Piece to make an assured good shot, the visual line passing from the Gunner's eye by t and n unto the mark to be shot at, by the 10 definition, and the 65 theorem.  
But if the Boar or Soul of the Piece lie awry, the Axis thereof not being parallel with the Axis of the Mettle.  
As if the Boar at the Touchhole were as the circle x bid. and the Boar at the mouth, as e g h f, and the Axis of the Boar passeth from v at the breech unto w at the mouth horizontally level with the Axis of the mettle; Then shall the Dispart be of such length, as in the former ordinary manner, but the dispart line upon the mettle at the breech will pass directly from point z, unto the point n at the mouth of the piece, to make a perfect shot with such a piece at any mark assigned.   

CHAP. XXVII. To Dispart a Piece of Ordnance, whose Centre of the Boar lieth perpendicularly awry, either above or under the Centre of the midst of the mettle, and yet the Boar's Axis being parallel with the Axis of the Mettle.  
SVppose that the bore of the piece assigned lieth awry so much of the perpendicular Dyametre, as a b above the Axis of the mettle, yet being parallel thereunto, or as much as the circumference m o or b n. Herein the two verticalls being in one same line, both of the middle of the bore, and also of the middle of the mettle; therefore the visual dispart must be placed upon the uppermost part of the mettle of the mouth, and the visual line must pass from the Gunner's eye by the upper part of the mettle at the Breech, and by d the upper part of the mettle at the mouth, and will there serve to make a good shot as if the Axis of the Boar had lain in the Axis of the mettle; and so the like may be said if it were in the perpendicular Dyametre, under the Centre of the mettle at the breech and mouth, as a c, which may suffice.  
But if the Concave of the Boar lie awry, and not parallel to the Axis of the mettle; as if the circle r i s t represent the bottom of the bore at the Touchhole, and the circle r k s w represent the bore at the mouth, and the Axis thereof passing from b at the breech to c at the mouth, crossing the Axis of the mettle at a and lying vertically in one same plane therewith.   three sets of concentric and overlapping circles, with various labeled points 
But if the Circle r k s w be the Boar at the breech, and r i s v the bore at the mouth.  
Then shall the thickness of the mettle at the Mouth i d differ the thickness of the mettle at the breech k e the full quantity of d f the true dispart for the same Piece to be set upon the vertical point d. As d f, to make a good shot at a mark assigned. For take i d, the mettle at the mouth out of k e the thickness of mettle at the breech, and there will rest i e equal to d f, for the dispart sought, by the 10 Definition, and the 8 Demand.   

CHAP. XXVIII. To Dispart any Piece of Ordnance, whose Axis of the Boar lieth awry not levelly nor vertically, the Axis of the Mettle not being parallel thereunto.  
AS suppose first that the bore at the breech be represented by the excentricke circle d g e f, and at the mouth by the excentricke circle oh f p g, and the Axis of the bore the right line a d. The outmost circle of the mettle at the breech by the concentricke Circle q r y w x, and the outmost circle of the mettle at the mouth by the concentricke circle s t z: So shall the thickness of the mettle at the breech be 3 q, and the thickness of the mettle at the mouth be 2 t, which space or quantity 2 t being taken out of 3 q leaveth 4 q the dispart required, to be set vertically upon the mouth at the point t, because the same is the point in the outmost metal of the mouth that is vertically over d, the Centre of the bore at the mouth, and the large line shall be q t: for that q is right and vertically over the Centre of the bore upon the outmost mettle at the breech, and q s will be the dispart line and part of the sight line that must pass from the Gunner's eye by the point q on the Mettle at the breech, and by the point 5 the top of the dispart, set upon the point: at the mouth, and so extending itself unto the Centre of the mark assigned to be shot at; The like may be said if b were the Centre of the bore at the Touchhole, and c the Centre of the bore at the mouth: For than would r s be the large line, and r 4 the dispart line, and 4 s the dispart, each reciprocally answering the forenamed measures, being only placed alike on the contrary side which may suffice.  
But if d were the Centre of the bore at the Touchhole, and a were the Centre of the bore at the mouth.  
Then would 3 s be the thickness of the mettle at the mouth, which being taken out of 2 r the thickness of the mettle at the breech, there will rest 6 r to be set vertically upon the upmost mettle of the mouth at s, because s is the vertical point there over d the Centre of the bore at the mouth of the Piece, so shall 6 r or 8, 7 equal thereunto be the length or heigh of the dispart, and r s shall be the large line, upon the mettle passing from the breech to the mouth; and r 7 shall be the dispart line, part of the sight-line that passeth from the Gunner's eye by the points r and 7, and extendeth unto the Centre of the mark assigned, by the 10 definition and the said 8 Demand.   

CHAP. XXIX. Of the Largesse, and the Large Line in wry bored Pieces.  
Having already showed how to find whether the Piece assigned were equally bored in the midst of the mettle, if not where the thickest and thinnest of the mettle lieth, it resteth now to show also how to find her middle line, or highest of her mettle at the breech and muzzle, as also her large and large line in a piece that is bored or cast awry.  
The Middle line is none other thing, but an imaginary Right line supposed to pass upon the highest of the mettle of a Piece of Ordnance from her Base ring to her Muzzle ring, directly and vertically over the Axis of the body of mettle of that Piece, which by the perpendicill aforesaid is easily found by placing the two corners K and L severely upon the Base and Muzzle rings in such sort as that the plummet belonging to the line n, o, may hang directly over the same line, and being let down, until the point thereof do touch upon the surface of the mettle there, make points or pricks at each place, I say then that those points will be directly over the Axis of the Mettle of that Piece, between which points if a Chalk line be stretched and stricken, or a right line imagined to pass, the same shall be the middle line of that Piece.  
Now to find the Large line, and the Large itself, in such Pieces as are bored, or cast a wry: Having found the middle Line, and the Plummet hanging so directly over n. o. upon the said marks; and having found the Excentricke circles of the thickest, and thinnest of the Mettle, at the Breech, and Mouth, and described them upon the Perpendicill, as is afore showed, with their Perpendicular lines parallel to n. o. letting down their Plumets, each in his proper place severally, so that it hang directly over his own Perpendicular line, and that the point of the Plumet also touch the Superficies of the Mettle, and there at each touch, make a mark and stretch a chalke-line between them, from the Base to the Muzzle rings, and strike a line upon the Mettle therewith, or else imagine a right line to pass between them; I say, that line will be Vertically over the Axis of the Boar, of that Piece; and is the Large line sought, and the distance between the extremes of the middle line formely found, and this Large line upon the Base and muzzle rings noted, are the Large itself: and so is that Piece reclaimed and prepared to avoid wide shooting.  
Now it resteth also to reform her over, or under shooting, whose cause may by the former sections be conceined, and by the perpendicill easily, and readily found and performed thus: First, upon the mark under o, where the plumet touched, place a due Dispart for her, as if she were truly bored; then if the Centre of her Boar, at her breech be found by the instrument, to be under the Centre of the Boar, at her Muzzle; the difference thereof, is then to be substracted, from the level height of the Dispart. But if the Centre of the Boar at the breech, be higher than the same at the mouth, than that difference must be added, and placed upon the mark of the Large, at the muzzle, with that addition, or abatement; and so the visual line, must pass from the Large, at the breech, by the top of that Dispart there placed, which will avoid all over, or under shooting in that Piece.   

CHAP. XXX. To find the weight of any Shot by the Diametre thereof, as well Arithmetically, and Geometrically, as Tabularly, and by Scale, and Compass.  
THe weight of the Shot, being a fit Index for the Gunner, to allow any Piece of Ordnance her due charge of powder; is therefore most necessary to be made known, or first sought; and because a Gunner, cannot at all times when the weight of a Shot is required, have Balance and weights about him, to weigh the same; therefore, it shall not be a miss, here to set down, how he may know the same, to a sufficient nearness, by the height of the Dimetre, or circuit of the circomference thereof; And that also for variety sake, as well Arithmetically, and Geometrically, as Tabularly, and by Scale, and Compass.  
The first thing to be done in Arithmetical working, is to find the  square inches, contained in the Ball, or Shot assigned; which may be thus found, multiply the measure of the known inches of the height, or Dyametre thereof Cubickly, and then again multiply that Cube by 11, and divide the last product by 21, and the number in the Quotient, will express how many solid square inches of Mettle, or Stone is contained in the Globall body of that Shot: If then you know, how much one square inch of the Mettle, or Stone assigned weigheth, you may then soon know the whole Shots weight sought, (for cast Iron 4 ounces allowed for each inch square, cometh near the matter) and the proportion of Iron to Lead may be as 30 to 56: And ordinary Stone to Led, as 18 to 72, and Stone to Iron, as 18 to 48, tolerable accepted.  
But to come more precisely near the truth (although spunginess) and the difference of each Mine from other, and infinite accidents, vary the proportions between their capacities, and weights, and do hinder it. The table following will sufficiently help, in the mean space, I will give one example to illustrate the precedent rule. As for example, it is required to find thereby the solid square inches, in a Shot of 4 inches and ½ in height; the near Cube of 4 ½ being near 91, which I multiply by 11, & the product I find to be 1001, which I dividing by 21, find in the Quotient 47 inches, and ⅔ of an inch more, for the solid content of that Shot, which if it were of Iron, by such allowance as aforesaid, it would weigh 11 lb, & about 15 ounces, but by the first Table following, it would be 12 lb. and 12 ounces, and by the sequent triple Table for Lead, Iron, and Stone Shots; it is found to be but 12 lb. and 10 ounces, wherein appeareth also that a Leaden Shot, would be 17 lb. and 15 ounces, which by the first Table, would be found 19 lb. and 12 ounces. But for easiness, some (and because it may for any Iron Shot be wrought by memory, by a man of any small practice) do use only to divide the Cube of the Shot by 8, and take the Quotient for pounds, and each unity of the remainder for 2 ounces, and so the Cube of 4 ½ being 91, as aforesaid, and divided by 8, the Quotient will be 11 lb. and the 3 remaining will be 6 ounces: The like in all kinds may be done for Stone Shot, by the rule of 3 only, saying, if 48 the proportion of Iron, give 202 ounces, what shall 18 the proportion for stone give? 76 ounces, which will be 4 lb. and 12 ounces for the weight of the Stone Shot, that is 4 inches and ½ in height.  
But the most artificial, and exact Arithmetical working of all such questions, for all usual Metals and Stones, is according to the next Table, wherein, I have imitated the Lord Marchistones Table, in his Rabdolagia, applying this unto ounces, and inches, which are our usual known weights and measures: Whereas his was for Cochleas, or Spoonfuls, and drams, more used by Physicians, then known in Gunner's practices; yet, for his two first Theorems, and Problems, I have followed them, because their works are easy, and excellent.  

The first Problem.  
By the inches of the capacity, of the Mettle, or Stone named, to find the ounces of the weight thereof.  

The first theorem.  
As a 1000 to the inches of the capacity, or solid measure of the Mettle, or Stone named; So is the lowest number of the Column, of the same Mettle, or Stone, to the ounces of the weight thereof.   

The first Example.  
Let there be an Iron Shot of 8 inches high, which by solid measuring, (as above is taught) is found to contain 268 inches, and ⅔: By the said first theorem, as 1000, to 268 ½, so is 4333 the lowest number of the Column  measuring several cannonballs 
Tract. 3. cap. 5.  

Measure qui montre le pois des balles selon leur calibre.  
Mas darauff●● gewicht der kugcln nach ●ere. Calibro verzeichnet.   

Patron duquel en haste on peult Calibrer diverses sorts de balls  
Model durch welchen in cill underschiedliche kugeln konuen Calibrert werden   

Pour montrer combien de vent il faillt donner a la ball  
We viel lufft man einer kugcln geben muss.   of Iron, unto 1162 ounces which being divided by 16 (the ounces of the Haberdepoise,) amounteth unto 72 lb, and 10 ounces the weight sought.   

The second Example.  
Let an ordinary Stone shot, of the same height and measure be propounded, containing as aforesaid, 268 inches ⅓, say, by the same first theorem, as 1000 is to 268 ⅕, so will 1420 the lowest number of the Column, of ordinary stone thereof, be to 382 ounces, which the Stone shot weigheth; they being reduced into pounds by division thereof by 16, will amount to 23 lb. 14 ounces, the weight of Stone shot sought.    

The second Problem.  
By the ounces of the weight of any Mettle, or Stone named, to find what number of solid inches it is in capacity.  

The second theorem.  
As 1000 to the ounces of weight of any Mettle, or Stone named, so is the most right hand number of the Line, of the same Mettle, or Stone, to solid inches of the capacity thereof.   

The first Example.  
Let there be a Shot of Iron of 8 inches Dyametre, weighing 1162 ounces, and we desire to know, how many solid inches it containeth: By the second theorem, as 1000 to 1162, so is 230 the most right hand number, in the Line of Iron to 268, fear the solid inches contained therein.   

The second Example.  
Let there be a Shot of ordinary Stone, whose weight by the second example of the first theorem, will be 23 lb. and 14 ounces, whereof the solid inches is required: By the second theorem, as 1000 is to 382 ounces the weight, so is 710 the most right hand number, of the line of ordinary Stone, to 270 fear the solid inches required; exactness by Table, is not to be expected.    


A Table for the Weights, and Measures, of Metals, and Stones.  Gold. 1000 810 670 645 380 420 410 170 130 120 Quicksil. 1392 1000 950 820 678 568 550 210 150 140 Lead. 1650 1150 1000 910 740 675 635 250 160 160 Silver. 1785 1340 1248 1000 820 710 750 270 200 180 Brass. 2225 1680 1448 1345 1000 925 850 320 240 200 Iron. 2588 1930 1670 1535 1190 1000 930 380 260 230 Tin. 2725 2045 1765 1640 1280 1160 1000 420 280 250 Marble. 6780 5120 4278 4090 2216 2784 2642 1000 710 680 Ord. sto. 9960 7415 6405 5948 2650 4020 3828 1530 1000 710  13200 7880 6798 6315 4958 4333 4067 1645 1420 1000    

CHAP. XXXI. The Geometrical finding the Dyametre, for the weight of any Shot assigned.  
Having a Shot of one pound, 2 lb. or 3 lb. weight of the Mettle, or stone assigned; if it be of one pound, divide the Dyametre thereof into 4 equal parts, and 5 such parts, will make a Dyametre for a Shot of the said Mettle, or Stone, that shall weigh just two pound.  
And divide the Dyametre of a Shot, that weigheth just 2 lb. into 7 equal parts, and 8 such parts, will make a Dyametre for a shot of 3 lb. weight.  
And dividing the Dyametre of a shot of 3 lb. weight, into 10 equal parts, and 11 such parts, will make shot of 4 lb. weight.  
And divide the Dyametre of a shot of 4 lb. into 13 parts, 14 such parts, will make a Dyametre for a shot of 5 lb. weight.  
And dividing the Dyametre of a shot of 5 lb. weight, into 16 equal parts, 17 such parts, will make a Dyametre of a shot, that will weigh 6 lb: And so dividing each next Dyametre into 3 parts equal more than the next lesser was divided into, and it will with one part added frame a Dyametre of a shot, that will weigh just one pound more; and so you may proceed infinitely, increasing, or decreasing, by taking one part less, than it is appointed to be divided into, for 1 lb. less, and the next into 3 lb. less, to abate one from the remainder, infinitely decreasing it.  

A second Geometrical way.  
Having exactly the Dyametre of a shot that weigheth one pound; first describe a Circle, whose Dyametre shall be just equal thereunto, and divide it into 4 Quadrants, with two Dyametres, cutting each other in the Centre Orthogonally, then take the Chord of the whole Quadrant, or of 90 Degrees, that is, extend your Compasses, from one extreme of a Dyametre, to the next, as in the figure following: Take the distance A. B, being supposed the Dyametre of a shot, or ball of just one pound weight, which distance being set in the continued right line D. B. f. g. h, and from E. to f, then will D. f. be the Dyametre of a shot of 2 lb, and then opening the Compasses from A. to f, and setting the same from E. to g. Again, taking the distance from A. to g, and setting it from E. to h, so likewise taking the distance A h. with the Compasses, and setting the same from E. to i, and so continuing until you have proceeded as fare as you will: You shall find if D. B. were the Dyametre of 1 lb. that D. f. will be the Dyametre of 2 lb, and D. g. will be the Dyametre of a shot of 3 lb, and D. h. of 4 lb, D. i. 5 lb, D. k. of 6 lb, and D. l. of 7 lb, and D. m. of 8 lb, etc. and lastly, D. q. of 12 lb, whereby you may proceed in like manner infinitely.   ten nested circles 
Or else you having a Dyametre of 1 lb, double that Dyametre will make a Dyametre of 8 lb, and triple the Dyametre of one pound, will make a Dyametre of 27 lb. and the quadruple, or 4 times the same will make a Dyameter of a shot of 64 lb, and 5 Dyametres, will make a Dyametre of a ball of 125 lb: and five times the Dyametre of a shot of 1 lb, will make a Dyametre of a shot, that will weigh 216 lb.  
It resteth now, to show how to find the mean divisions between those extremes, as for the Dyametre of a shot of 2 lb, 3 lb, 4 lb, 5 lb, 6 lb, 7 lb, and more: so as by such progressions, you may proceed from pound to pound, until you come to the last term, for extreme of 216 lb. Nevertheless, the same manner of working will proceed infinitely; the former mentioned six Dyametres, being marked upon one and the same right line, you must at the end of them, draw another right line Orthogonally, and set therein two such Dyametres, as at C, and from thence draw another right line parallel to the first, from C. to K, than put one foot of your Compasses in C, and make a quarter of a Circle from B. to D, that done, plant a pin, or needle in C, and then draw from the Centre C. lines through all the division of the Dyametres, marked upon the right line A. B, so shall you have six divisions to be divided: The first being divided already, abideth as it was, and is the Dyametre of a shot, or ball of one pound; but the second division, is to be in the circumference, divided into 7 parts equally; because it containeth the second Dyametre unto 8, from 1 to 8, for adding 1 to 7, it maketh 8; the third division is into 19 equal parts, which being added to the 8, maketh 27; the fourth, shall be divided into 37 equal parts, which together with the 27, maketh 64; the fift space shall be divided into 61 equal parts, which together with the 64, amount unto 125; and lastly, the sixth space must be divided into 91 equal parts, unto which adding the 125, you shall make a Dyametre, for a shot of 216 lb. justly.   an arc, a small circle, and various labeled points 
Now for as much, as these divisions are deficill, to make well within so small a Quadrant, you may therefore describe a greater, as the Quadrant K. E, wherein the divisions are more distinct, then in the lesser they can be; further you may note, that Fire-balls, Granades, and other Globous Artifices; must have the same proportion in their Grandures, from their Ball of one pound, which may be exactly considered: and so by this method, you may make Balls of Lead, Brass, Stone, Granades, Fire-balls, and all other Spherical works, of what weight you will, having one of one pound first to lead you, according to the precedent instructions.   


A Table whereby, and by the Inch sight-rule, any Piece of Ordnance between six foot, and fifteen foot in length, may be mounted to any Degree of the Quadrant, under twenty Grades as well as by the Quadrant itself, or by any other Instrument whatsoever.   6 Foot. ½ 7 Foot. ½ 8 Foot. ½ 9 Foot. ½ 10 Foot. ½ 11 Foot. ½ 12 Foot. ½ 13 Foot. ½ 14 Foot. ½ 15 Foot. Gr. Inch.  1 1, 2 1, 3 1, 4 1, 5 1, 6 1, 7 1, 8 1, 9 2, 0 2, 1 2, 2 2, 3 2, 4 2, 5 2, 6 2, 7 2, 8 2, 9 3, 0 2 2, 5 2, 7 2, 9 3, 1 3, 3 3, 5 3, 6 3, 8 4, 0 4, 2 4, 5 4, 7 5, 0 5, 2 5, 4 5 6 5, 8 5, 9 6, 0 3 3, 7 4, 0 4, 3 4, 6 4, 9 5, 3 5, 5 5, 7 6, 0 6, 3 6, 7 7, 1 7, 4 7, 7 8, 0 8 4 8, 8 9, 0 9, 2 4 5, 0 5, 4 5, 8 6, 2 6, 5 7, 0 7, 5 7, 9 8, 0 8, 8 9, 2 9, 6 10, 0 10, 4 10, 8 11, 2 11, 6 12, 0 12, 4 5 6, 2 6, 8 7, 4 7, 8 8, 2 8, 7 9, 3 10, 0 10, 5 11, 0 11, 5 12, 0 12, 5 13, 0 13, 6 14, 2 14, 8 15, 2 15, 6 6 7, 5 8, 2 8, 9 9, 4 9, 9 10, 4 11, 0 11, 9 12, 6 13, 4 14, 6 14, 8 15, 0 15, 7 16, 4 17, 1 17, 8 18, 3 18, 8 7 8, 7 9, 5 10, 4 10, 9 11, 7 12, 1 12, 8 13, 8 14, 5 15, 3 16, 0 16, 7 17, 4 18, 2 19, 0 19, 9 20, 8 21, ● 21, 8 8 10, 0 10, 8 11, 9 12, 3 13, 3 13, 8 14, 2 15, 8 16, 6 17, 5 18, 3 19, 2 20, 0 20, 8 21, 6 22, 7 23, 0 24, 2 24, 6 9 11, 3 12, 3 12, 5 13, 7 14, 5 15, 1 15, 5 17, 7 18, 7 19, 7 20, 6 21, 5 22, 4 23, 4 24, 4 25, 0 25, 8 26, 6 27, ● 10 12, 3 13, 0 13, 8 15, 4 16, 7 17, 7 18, 7 19, 8 20, 8 21, 9 22, 9 24, 0 25, 0 26, 0 27, 0 27, 8 27, 9 29, 2 30, 8 11 13, 7 14, 8 16, 3 17, 0 18, 4 19, 4 20, 4 21, 7 21, 7 24, 0 25, 4 26, 8 27, 4 28, 5 29, 6 31, 1 32, 6 33, 3 34, 0 12 15, 0 16, 2 17, 5 18, 7 20, 0 21, 1 22, 2 23, 5 24, 8 26, 2 27, 6 29, 0 30, 0 31, 2 32, 4 33, 7 35, 0 36, 2 37, 4 13 16, 2 17, 6 18, 5 20, 3 21, 6 22, 9 24, 2 25, 6 26, 9 28, 2 30, 0 31, 6 32, 4 33, 9 35, 2 36, 5 37, 8 39, 2 40, 6 14 17, 4 18, 9 20, 3 21, 8 23, 3 24, 6 25, 9 27, 5 28, 9 30, 4 32, 0 33, 6 34, 8 36, 5 37, 8 39, 0 40, 0 41, 9 43, 6 15 18, 6 20, 2 21, 7 23, 3 24, 9 26, 3 28, 1 29, 4 30, 9 32, 8 34, 3 35, 8 37, 2 38, 3 40, 4 41, 9 43, 4 45, 0 46, 6 16 19, 8 21, 5 23, 1 24, 8 26, 5 28, 1 29, 8 31, 4 33, 0 35, 0 36, 8 38, 4 39, 8 41, 5 43, 0 44, 8 46, 2 47, 9 49, 6 17 21, 2 22, 8 24, 0 26, 3 27, 9 29, 8 31, 2 33, 5 34, 9 37, 1 38, 9 40, 0 42, 4 44, 0 45, 8 47, 3 49, 0 50, 8 52, 6 18 22, 4 24, 1 25, 9 27, 8 29, 9 31, 5 33, 0 35, 4 36, 8 38, 9 41, 2 43, 8 44, 8 46, 5 48, 2 50, 0 52, 8 53, 7 55, 6 19 23, 5 25, 3 26, 9 29, 3 31, 4 33, 2 34, 8 37, 5 38, 7 40, 2 43, 5 45, 7 47, 0 48, 8 50, 6 52, 0 52, 9 55, 5 58, 6 20 24, 6 26, 7 28, 7 30, 8 32, 8 34, 9 36, 9 38, 9 41, 0 42, 1 45, 8 47, 6 49, 4 51, 3 53, 4 55, 4 57, 4 59, 5 61, 6  

A Table, showing the Height and Weight of Iron, Led, and Stoneshot, accuratly and newly calculated by the Author, and applied to our assize of English Measure of Inches and Parts, and to the Haberdepoize Weight of 16 Ounces to the Pound: With the Description of my Gunner's Scale.  Ynches high Quarters. Iron pound Ounces. Led pou Ounces. Stone pou Ounces. 1 0 ⅛ 0 0 3 0 1 ¼ 1 ¼ 0 0 6 0 3 2 ⅜ 0 0 9 0 4 ½ 3 1 0 0 13 0 5 1 2 0 1 1 1 11 0 7 1 1 9 2 0 0 9 2 2 2 3 0 0 12 3 2 14 4 3 1 0 3 0 3 12 5 0 1 4 1 4 12 6 9 1 8 2 6 1 8 1 2 0 3 7 5 9 14 2 7 4 0 8 15 11 5 2 13 1 10 10 15 15 3 10 2 12 10 17 15 4 3 3 14 14 21 5 5 9 5 0 17 5 24 12 6 3 1 20 1 30 0 7 8 2 23 2 35 10 8 14 3 26 6 39 9 10 10 6 0 30 0 45 0 11 4 1 34 0 51 0 12 12 2 38 0 57 0 14 3 3 42 0 63 0 15 12 7 0 48 0 72 0 17 10 1 53 0 79 8 19 14 2 58 0 87 0 21 12 3 64 0 96 0 24 0 8 0 72 10 106 8 26 12 1 ●8 0 117 0 28 8 2 87 3 130 8 32 8 3 95 0 141 8 35 10 9 0 101 0 150 0 37 10 1 109 6 161 8 40 4 2 121 10 181 13 44 2 3 132 11 198 5 49 8 10 2 138 0 2●7 0 51 10 0 164 2 246 0 0 0 11 0 184 0 275 8 69 8 2 216 0 324 0 81 0 12 0 240 0 360 0 90 0 13 0 305 0 457 8 114 8 14 0 389 2 583 8 146 8  
THe Use of this Table in the left margin, is to find out the height of your Shot in the two first Collume of inches, and quarters of inches: Then if is be an Iron shot, over against the height so found in the two second Collumes under the titles of Iron pounds and Ounces, you shall find the weight thereof. The like may be understood, if the shot be of Lead, by the two third Collumes, or of Sun, by the two last collumes, each under his proper title, and over against the height assigned. As for example; For, an Iron shot of 8 inches, the weight will appear to be 72. pound 10 ounces; and if it were of Lead, it would be found 106 pound 8 ounces; but if of Stone, then would it be but 26 pound 12 ounces, which may suffice.  
The Description of my Gunners Seal, is to be made in Brass by M. Allen: And in Wood, by M. Nathaniel Gors of Rateliffe. IT is a square Rule of one foot in length, made either of Brass, Box, or other fine grained Wood that will not warp: Upon one side or square whereof I have set the height of all sorts of Iron shot, from 1 pound to 100 pound weight: And of Stone shot to 37 pound: And of Lead shot to 150 pound weight: Each distinguished from an other by the Letter I. for Iron, S. for Sun, and L. for Led shot, and their Weights and Measures accommodated unto our English Haberdepoiz weight of 16 ounces to the pound, and to our Foot of assize of 12 Inches to the Foot. The second side hath twelve Inches of assize, each divided by Parallels and Dianonall lines, into 100 equal parts, distinctly to take any Number from 1 to 1000, from thence, with a pair of Compasses. The third, hath Cynical and Logarithmall devisions, exceeding necessary for the Gunners practise, as hereafter shall more plainly appear. The fourth, hath devisions proportional to the right Ranges and Randons' of any Piece of Ordinance upon any Mounture from degree to degree; and the number of Inches that any Piece between 6 and 15 foot long requireth to mount her to any degree of mounture, under 20 degrees, as well or better then by the Quadrant; as the Table following will also explain.   several tools of measurement 
Tractat. 3. cap. 13 fig. 1  
La facon form de repartement des quadrant;  
Form undt abtheillung der quadranten.    

CHAP. XXXII. Of the rule of Callibres, and of the difference between the heights of the Boar and Shot for any Piece, which is called the vent or due abatement to shoot with safety, and most advantage therewith.  
FOrasmuch as it is an excellent quality in a Gunner to be expert and ready in the Heights and Calibres of Boar and Shot for Ordnance, and to retain them in memory, rather by reason then by roate, they being the ground and Scale from which all the Measures and Proportions for all parts, as well of the Piece and her Carriage, as of the Powder, Shott, and distance, or the way of the Shot are derived and understood, as by the precedent & sequent discourses may appear: But because most English Gunners have hitherto generally as well for the greatest as the smallest, or mean sorts of Ordnance chosen the Shot for them all, one quarter of an inch lower than the height of their Boars; which the best experienced Gunners of late year's disliking, have for a general proportion chosen rather one twentieth part of the height of the Boar to be abated for a due height of the Shot vent, affirming that in the Falcon and small pieces the abatement of ¼ of an inch is too much, and for the Canon ¼ of an inch is too little, and that 1/20 of the Diametre of the Boar will be a reasonable abatement for all Pieces, be they higher, or lower, which being by Arithmetic so easily found, will not require any example.   

CHAP. XXXIII. Of the Gunners, Quadrant, and Triangle, with their Degrees and Points, whereby either to Level, or else to Mount, or Embase any Piece of Ordnance, to any degree or point assigned.  
THe Gunner's Quadrant is a Geometrical Instrument, made of brass or fine grained wood, containing in the circumference one quarter of a circle, divided into 90 equal parts or degrees in the outmost limb, and in the second limb within into the 12 points of the Gunners quadrant, having within the same also a Geometrical Quadrate, with each side divided into 12 equal parts, and those each of them subdivided by means of parallels and Dyagenalls into 10 equal parts, so that each side will be thereby found distinctly divided into 120 equal parts, fitly serving to take all Geometrical Mensurations, of distances, heights, breadthes, and depths, accessible and inaccessible, by the directions hereafter mentioned. The degrees and also the points being principal helps for the Gunners practise, to shoot at the most certainty both by the right line, and also upon the advantage of any Random to and at any Mark assigned, to a probable or assured good effect; as by the Tables, Scale, and directions following, will more plainly appear, and by the 21 Figure hereof marked wherein each Quadrant, (but that which is marked with 4) hath a straight Ruler about 2 foot long, joined either firmly, or by a Grove dove-tayled unto one of the sides of Semidiametres thereof. Now to plant any Piece level, having put the said Ruler in close unto the lower side of the Mettle, within the Coucave Cillinder of the Boar thereof, then mount or embase the Piece in her Carriage, until the plummet fall directly upon the other side of the Quadrants fiducial edge, by means of drawing out, or putting in the Quoyns as reason will direct you: so will the Axis of the Boar or Concave Cillinder thereof, be found to lie directly level, or parallel to the horizontal plane: you may also without a Quadrant level any Piece duly founded by holding a plumb line upright afore the mouth of the Piece, and mounting or embasing her by means of her Quoynes, until the line shall appear only to touch the Flat of the Mettle at the mouth above, and below alike: So will the Axis of the Soul that is to cut the flat of her mouth at right Angles, the plumb line being parallel or equi-touching, the same flat be found to be parallel to the plane of the Horizon, or truly level as was required: But if by the said Quadrant you would mount the piece to any degree or point of the Quadrant, than you are to mount or embase her in her Carriage, by drawing or putting in of her Quoynes more than before so much, until the plumb line of the Quadrant appeareth freely (the Ruler being put into her mouth as before) to hang directly over the degree or point assigned. And the like may be said concerning the embasing of any piece; as in the 21 Figure α at 2 for the 12 points and at 3 for the 90 degrees A B C and E M N, And also concerning the level at 4, to level pieces, and to find the upper part of the mettle: And lastly, to mount and embase the piece by the help of the plumb line; And by the whole circle at 5, divided into 48 equal parts, making in each Quadrant thereof the 12 points of the Gunners quadrant. The like may be done with the sight Rule, by the Table hereof.   

CHAP. XXXIIII. Of a new devise by any Staff, to level, mount, and embase any Piece.  
ALso any Piece may with a field Linstock, Rammer, or Sponge, or other Staff be mounted to any degree of the Quadrant, being thus prepared. First, mark from one end of that Staff a distance, equal unto the height of the pommel or Caskabell of the Piece  the ballistic arc of cannonballs 
Tract. 2. Dial. 9  
Quelle piece sera de plus lointaine portee celle du hault ou celle du pied d'vne tour.  
Welches stuck am weittesten trägt das so oben oder das so unden am thurn abychet   a cannon aimed at a fortification 
Tract. 3. Cap 12 et 15  
Mire common rez les metaux de 1000 pas.  
Gemeine visier uber die frisen auff 1000 schritt.  
Point du niveau de l'ame de 500 pas.  
Visier der wogen auff 500 schritt.  placed level upon her Platform, and then take the distance between the Centre of the Trunions and the pommel or Caskabell, which make or imagine a semidiametre of a Circle, and divide it by Dyagonalls and Parallels, or otherwise into 1000 equal parts. Lastly, out of the Table of Sines, take the number answering unto every degree out of the said 1000 parts, and set that distance from the said mark downwards. And if the total Sign of the Table be 100000, omit the two last figures of each number thereof towards the right hand, and if it be 10000000, then omit four figures of each number you find in that Table, and the remaining number will show how many of those 1000 equal parts are to be set downwards from the mark beneath the said level for each several degree: Then drawing also 10 Parallels and Dyagonalls from the first degree to the second, and from the second to the third, etc. successively continued from each to his next, noting every degree with Arithmetical characters; so may you from 6 minutes to 6 minutes by those right synes mount the Piece, so set forth for any Piece which it shall be prepared for. This may also be described upon such a staff without the Table of synes in a mechanical manner thus: If you describe a Quadrant or Quarter of a circle with a semidiametre, equal to the distance from the centre of the Trunions, to the centre of the pommel or Caskabell, and divide the Arch of that quadrant into 90 equal parts or degrees, and then from each degree, letting a right line fall perpendicularly upon the base side of the said quadrant. And lastly, each of those right lines being thence transferred from the said first mark downwards upon the said staff, and marking them with Arithmetical figures for each degree, thereupon making also Parallels and diagonals, as aforesaid you may thereby Geometrically and mechanically mark the same from 6 to 6 minutes as before. The use of them are plain and easy, for if you bring down the centre of the Caskabell or pommel of the Piece to any number of degrees thereon, so marked, for that piece, you setting the lower end of the staff to the Platform being even, although it be rising or descending backwards: I say then the Axis of the bore of that Piece will be found to be elevated unto the degree assigned: If you be to embase the Piece, those lines and number also set above the first named mark, will perform the like office there in the thing required.   

CHAP. XXXV. How to find the right line or right range of any Shot discharged out of any Piece, for every elevation, by any one Right or dead Range given for the Piece assigned.  
IF the Range given be the right Range, say by the Rule of three if the Tabular number found in the Table of dead Ranges for the degree of the Range given, give the number of known measures in that Range: what shall the Tabular number of the Table of right Ranges, proper to the degree assigned give. And having multiplied and divided them duly, the fourth number will be the right Range, or right line for the Peecesought.  

Example 1.  
SVppose you are to seek the right Range of 30 degrees for that Piece, whose dead Range for 30 degrees is given or known to be 2200 paces by it, multiply the Tabular number of right Ranges for 30 degrees, which is 695, and divide the product by 2150, the Tabular number for 30 degrees in the Table of dead Ranges, and the Quotient will be 711 paces for the line or right Range of that Piece, mounted and discharged at 30 degrees elevation.   

Example 2.  
SVppose the level right Range is given, and the right Range for 30 degrees mounture be sought, say, if 192 the first number in the Table of right Ranges, give 695 the Tabular number thereof for 30 degrees, what shall 197 paces the level right Range given give, multiply the third by the second, and deuiding by the first, and the Quotient, will be 713 paces for the right Ranges sought, the difference is that Tables cannot be so exactly calculated, but by omitting small fractions, small differences will grow apparent, by working one question or example diverse ways, which let suffice.    

CHAP. XXXVI. To find how much of the horizontal line is contained directly under the right line, or right Range of any Shot, made out of any Piece at every elevation assigned.  
Having by the last Chapter found the number of paces, the Piece will carry her Shot in a right line being duly discharged, at any Elevation assigned, multiply the same by the right Sine of the compliment of the degree of Mounture, and divide the product by the whole Sine, and the Quotient will be the number of paces (or such like measures) contained in the level, directly under the right Range sought.  

Example.  
BE it propounded how to find what part of the horizontal line lieth, directly under the right Range of the Piece assigned at 30 degrees elevation, the right Range at 30 grades by the precedent, being found to be 713 paces, and the right sine of 60 grades, the compliment of 30 being 866, being multiplied together, and the product divided by 1000, the whole sine leaveth in the Quotient 617, for the number of paces lying directly under the right Range sought.    

CHAP. XXXVII. To find how much of the horizontal line lieth under the crooked Range of a Shot, made out of any Piece at any Elevation assigned.  
THe crooked range is so much as the course or 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; And may be thus found either by deducting of the level distance contained directly under the right line or right Range of any Shot made, (found by the last Chapter) out of the dead Range thereof found by the Chapter before-going: For the remainder will be the paces or other measures, lying directly under the crooked range.  

Example 1.  
THe Piece supposed to be mounted to 30 degrees, is found to convey the Shot 2300 paces to the dead range or first graze of the Shot, and it also conveyeth the Shot 617 paces in the level under the right Range, which deducted out of the said dead Range, there remaineth 1683 paces, which lieth directly under the Crooked range, in the horizontal line the thing sought.    

CHAP. XXXVIII. 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 suppositions of the second book of Tartaglia his Novascientia, every body equally heavy (as a Globall Shot) in the end of the violent motion thereof, being discharged out of a Piece of Ordnance (so it be not in the perpendicular line right up or down) the crooked Range shall join to the right Range, and to the natural course or Motions, and be between them both: So for example, the right Range being all the line a b of the Figure following, and c d the natural motion. He saith B C will being the mixed or crooked Range join, and be contingent to them both in the points b and c, wherein c will be the furthest part of the crooked course or range from the Piece so directed, and d the end of the natural motion thereof.  
And in his seaventh proposition of the same book he proveth, That every Shot equally heavy great or little, equally elevated above Horizon, or equally obliqne or levelly directed, are among themselves like and proportional in their distances, as the Figure following showeth: as A E F is like and proportional in the right and crooked Ranges, unto A H I, and in their distances or dead Ranges A F unto A I.  
And in his fourth, fifth, and sixth propositions of the same book, he proveth that every Shot made upon the level, hath the crooked range thereof equal to the Arch of a Quadrant, or quarter of a Circle; and if it be made upon any elevation above the level, that then it will make the crooked Range to be more than a Quadrant, and that if it be made embased under the level, that then the crooked Range thereof will be an Arch less than a Quadrant, as the three last figures following do represent.   several ballistic arcs, with inscribed angles 
And lastly in his ninth Proposition of the same book, he undertaketh to prove, if one Piece be shot off twice, the one level and the other at the best of the Random, that the right Range of the level, is but one quarter of the right Range of the best: And that the dead Range of the level is but 1/10 of the dead Range of the best Random, whereto he that desireth further demonstration, may have recourse, and examine his demonstrations of those propositions in his said second book of his Nova Scientia. A Diagram for the Randons' of a Saker upon each of the first six Points, according to Alessandro Bianco.   measuring several ballistic arcs 
Now to find at what distance from the platform whereon the Piece is to be discharged, the course of the Bullet will cut the aspect of every Mounture (which will help when a mark shall be without the right Range of the Piece in the aspect of its elevation, above the Horizon) to make a fair Shot at first by taking a greater advantage of mounture: as suppose a Mark elevated 15 degrees, to be distant 700 paces.  
By the last Diagram open the Compasses, until the aspect cut the point of Mounture, then applying the same unto the scale under it, you shall thereby find at what distance it cutteth the Random required.  


Alexander Bianco his Table of Randons' for the six first Points reduced.   1 2 3 4 5 6 Falconet. 375 637 795 855 892 900 Falcon. 550 935 1166 1254 1309 1320 Minion. 450 765 954 1026 1071 1080 Saker. 625 1062 1325 1425 1487 1500 Demi-Culuering. 725 1232 1537 1653 1725 1740 Culvering. 750 1275 1590. 1710 1785 1800 Demi-Cannon. 625 1062 1325 1425 1487 1500 Whole Cannon of 7. 675 1147 1431 1489 1606 1620 Double Cannon of 8. 750 1275 1690 1710 1785 1800  

A Table of secant ranges.  0 1000 1 1000 2 1000 3 1001 4 1002 5 1003 6 1005 7 1007 8 1009 9 1013 10 1015 11 1018 12 1023 13 1026 14 1030 15 1035 16 1040 17 1045 18 1051 19 1057 20 1064 30 1154 40 1305 50 1555 60 2000 70 3923 80 5758 90 Infinite  

The use of these Tables.  
FIrst by Bianco his Table, having resolved upon the point of Mounture, look against the name of the Piece, and right under that point, in the common Angle, you shall find the number of Paces of her Random sought.  
The Table of Secant Ranges are proportional numbers, whose use by the examples before mentioned, are plainly manifest, which let suffice.     

CHAP. XXXVIII. How to load a Piece of Ordnance Gunner-like.  
THe Piece being mounted, and duly planted on his Platform, and well provided with all things in readiness for service, as of powder, Shot, Ladle, Sponge, Ramer, Wad-hooke, Wadds, and Tampions. The Gunner must place his Linstock to Lee-wards, or under the wind, and having cleared the piece and Touchhole; he must sponge his piece very well standing on the right side of the piece, and drawing out his Sponge, let him give it two or three blows upon the Month on the outside of the piece, to beat off the foulness and dust it hath gathered within: then his assistant declining the powder or budge barrel aside, he shall thrust in his Ladle to fill it, striking off the heaped powder, giving a shogge to shake down the surplus: and it being so filled and striked, put in the Ladle down to the bottom of her Concave Cillinder unto the Touchhole, but at the first putting of the Ladle (so filled) into the Mouth of the piece, slide in the Ladle staff, so that the upper side may keep uppermost all the way, and when it is arrived to the bottom of the Boar, than he laying his right thumb upon the said upper side of Ladle staff, near the Mouth of the piece, and turning the said staff so much, until the said thumb unremoved upon the staff be found directly under the same; then giving two or three shakes, and bearing up the Ladle, that the powder may be turned out, or go out clean, and that the Ladle bring no powder back therewith, for that were a foul fault for a professed Gunner to commit. Then shall he put the powder home softly, with the Rammer that is at the end of the Ladle staff; putting in a good Wadd, and thrust it home to the powder, giving three or four hard strokes, which will gather the scattered powder together, and drive close the same, and the rest to the bottom of the Chamber the Assistant, having a finger upon the Touchhole all the whilst: And then put in the Shot which with a Rammer he must put softly home, and afterwards another Wadd of Hay, Grasse, Weeds, Okham, or such like: And again, give two or three good strokes with the Sponges Rammer head: But if the Piece do require two or three Ladles of powder, it must be all put in before any Wad, in that manner as the first was mentioned, and so in all other things. And then place the Budge or powder barrel to wind-wards, and cover it safe with some Hide, garment, or : always avoiding to stand before the mouth of the Piece, but on the right side thereof in loading her for fear offurther danger. And lastly, the Piece is to be laid to the mark and prymed and fired, and so will his Piece said to be loaded Gunner-like.   

CHAP. XXXIX. Whether the longer Pieces outshoote the shorter, and why the Culuerings shoot farther than the Cannon and the Demy-Culuering than the whole Culuerings, etc.  
Nevertheless, that the eighth Theorem of this book affirmeth, that The longer the Piece the stronger the stroke, which is most true, yet must it require this moderation, that all proportions be agreeable in the longer Pieces, namely that the proportion of the height of bore, and fortitude of mettle, and charge of powder, be correspondent one to the other, as in my Exposition upon one of Mr. Digges his Questions is related: For if the Fortitude of mettle be wanting, and so unable to resist the force of powder due to load your Piece withal, in respect of her length & height, so that the Shot may be come just to her Mouth in that instant, that all the Powder shall be perfectly fired, or that by reason of her shortness (she having fortitude) the Shot be gone out before the powder in her be all perfectly fired, there is neither of them both can perform so much as they otherwise would do, if their proportions of height, length, and fortitude had been correspondent one to another. And there must also be a respect had unto the force of the powder used, that there may be a convenient correspondency between the proportion of it to the rest: For otherwise, a Piece being loaded with a proportional Charge of worse powder, may shoot further, then if she were loaded with as much in weight of better powder, by reason of the disproportionalities afore said. It was experienced, as Luigo Coluado in his 21 Chapter mentioneth, that an extraordinary Culvering of 48 Dyametres of her bore in length, being loaded with a Charge of powder usually allowed to Culuerings (proportioned to the weight of her Shott) did shoot fewer paces, than afterwards when 8 dyametres of her length was cut off from her Mouth to her Breech wards. And then also 6 dyametres more being likewise cut off, and in like sort, she being loaded and discharged at the third time, conveyed her Shot farther than either at the first or second, whereby and by the 14 Theorem hereof, with the said exposition, all will most plainly appear both Theorically and Practically: But the old error of the Rule of Flat, as some Gunners have called it, and taught it to others: I thought fit to warn you of being a sight Rule, divided into inches, to set on the breech of any Piece, to mount her to any angle under 30 degrees, by a like certain number of inches, and parts, for Pieces of all lengthes, which is not only impossible, but also absurd: As I have showed before in the 76 Page, where I shall speak of the good use that may be made of the inch Rule for that purpose, with my Table for the same in the 93 Page.  
 two cannons 
Tract. 2. dial. 20.  
Quelle sera de plus grande portee la Colubrine ou le Canon.  
Welches stuck am weitesten trägt die Colubrina oder du Carthaunen  
En tel poinct la Colubrine portera 7000 pas. quelque peu plus ou moins.  
In solcher erhöhung trägt die Colubrina ungefchrlich 7000 schritt.  
Le canon 6000 pass.  
Die Carthaun 6000 schritt.    

CHAP. XL. Of shooting Mira commune, or by the Metals of the Piece, and the difference between shooting so, and by the due dispart.  
ALthough the difference of making a Shot to a Mark, by the highest of the Mettle at her breech and muzzle, and by the continued aspect of the Axis of her bore, is so uncertain, according to the length of the Piece, and the differences between the Dyameter of the Base and Muzzle Rings, that no certain proportion can be generally assigned: yet for most Pieces it hath been well observed, that the Piece directed by her Mettle, will shoot about twice as fare, when the Mark is level, or the sight line being parallel to the Horizon, as it will do upon the laying it level by the dispart Quadrant or Axis of her Boar, the incertainty thereof depending upon the Angle, it maketh more or less above the Horizon, which for each Piece may best be found, by the differences of the disparts of several Pieces that are of equal lengthes, but is accepted or guessed to be generally to shoot twice the distance Mira commune, as it will do upon the true level Axis: But that Rule is seldom exact, for the difference is sometimes five gr. and other sometimes seven degrees, and sometimes neither, even as the Mounture upon the Mettle, & the level of the Axis will (being precisely examined) make manifest. And therefore to shoot with any Piece Mira commune, or by the Metals, the difference or Mount about the level, which the mettle causeth being considered, and exactly examined, will show the Angle of the Pieces Mounture, with which you must repair to the following Tables of proportional Mountures, for the several Randons' upon each point or degree of the Gunners Quadrant, which is thus easily to to be appropriated unto any Piece, having made one Shot with her at a Mounture certain, and finding her proper dead Range for the same, which reverted to the given Elevation, will soon yield the Range required. As for example, suppose that by examination it be found out, that by reason of the rankness or eminency of the Muzzle ring, and length of the Chase of the Piece, the direction by the Metals at the Breech and Muzzle ring, to mount the Piece higher than it would, if the Azis of her Boar were duly directed by a true dispart, unto any Mark assigned by six degrees, and let it be imagined that the Mark is elevated six gr. above the Horizon, so found by the Quadrant: And lastly, let it be given at that mounture, the Piece did shoot 850 paces for her dead Range: the question is, how fare the same Piece would convey the like Shott with like loading and accidents, if she were by the highest of her Metals at Breech and Muzzle, directed to the same Mark. Say then if 722, the number in the Table of dead Ranges against six gr. give 850 paces, the measure of the Shott made in her at fix degrees mounture, what shall 1394 the number against 12 degrees mounture give, multiplying the third of these three numbers by the second, deuiding the Product by the first, the Quotient 1534 paces, will so much better answer to the question then Mr. Smiths rule can do.   

CHAP. XLI. Of shooting by the Despart or Axis of the Boar (in right hored Pieces, called by some Gunners erroneously the point Blank) as fare as it curreth a Shot in a right line.  
THis kind of shooting called (point blank) is so fare as a mark is within the straight line of the Piece, which for some Elevations or Mountures, is much more than for others, for that the more a Piece is mounted, the farther she conveyeth her Shot in the right range, except it could be shot perpendicularly downwards, which (as I have already in my first book called, The Art of great Artillery showed) may therefore in Piece given, yield infinite point blanks. But be the Mounture given, and the mark within the right line, or right Range of the Bullets course (that is within that space of the Shots right course) as it may be said to go straight (or insensibly crooked) or so fare as it accompanieth the continued Axis of the Metal, in right bored Pieces, or of the Soul in the wry bored (which is the cause that in such a Shots there is more seldomer failing, then in any other manner of shooting whatsoever) this kind of shooting being made by the Dispart, so maketh the error to be no more than the distance between, the visual line directed from the middle point of the said Axis, and the visual line that passeth from the Gunner's eye, except accidents cause the contrary, it being directed by the highest of the Mettle of the Base ring, and by the top of the dispart unto the assigned Mark. Now forasmuch as the length of the Piece and the variety of the Powder by the eighth Theorem, breedeth the difference of force, swiftness, and vehemency of the Shott and stroke of the Bullet: it is therefore impossible to give general certain Rules for the right Ranges, without some experience in that Piece be first made, found thus.  
If many Papers or  be set in the right line or way of the Shot, between the Mouth of the Piece and the Mark, then making an orderly shot with a full Bullet directed to some Mark, setting a stick in each place, with the top thereof right in the Centre of the hole which the shot went through at every paper: You shall thereby perceive where the shot did first begin to decline, and how much at each distance, which being measured, will very much inform the Gunner both for level Batteries, and shooting at random, and upon advantage, in the mean space the Table following will for right ranges help.  

A Table of the proportions of right Ranges, or point blanks.  0 192 1 209 2 227 3 244 4 261 5 278 6 285 7 302 8 320 9 337 10 354 20 424 30 693 40 855 50 1000 60 1140 70 1220 80 1300 90 1350  
The use of the Table, with example. Having foundby experience that at 6 degrees of Mounture the Piece assigned Shot 200 paces in a right, or insencible crooked line, and would know how fare the same Piece will shoot in a straight line, being mounted to 10 degrees, say by the Table, if 278 the number, against 6 gr. giveth 200 paces, what will 354 the number therein against 10 degrees give, 278 paces.   

CHAP. XLII. 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 any Piece at every degree.  
AS in the last Chapter we have said for the right Range, so must we also say for the dead Range, which consisteth of the addition of the right and crooked Ranges together into one, and then called the dead Range, which is the whole distance from the Platform, upon which the Piece assigned is discharged, unto the first fall or graze of the Bullet, upon the level line, or horizontal Plane, by reason the different lengthes of the Pieces, and strength of the powder increaseth or devinceth the course or fury of the Shot, and therefore more difficult to be found, but only by experience, or by Diagrams, Tables, or Scales made from experiments. Now although it be very difficult, and a thing uncertain also, to arrive herein to exactness, without some experiments made with the assigned Piece and Powder: Yet to come to a necessary nearness at first (fare surer than by uncertain guessing) either by the Table here annexed by my Scale or Rule, grounded upon often observations and trial, I having made 200 shot for it, you having the right range, for the Mounture assigned by the former dead Range, of the Shott for the Mounture required. Note where the Shots course cutteth the Angle of every Mounture, for that Piece and powder given in this manner: First, take the right Range of the Piece experimented from the right Range for the Mounture assigned, and divide the remainder in such reason, as the said Angle of Mounture is to the Angle of the compliment thereof, and to the Quotient add the said right Range found, and the off come there of, will be the dead Range for that Piece, Powder, and Mounture assigned. As for example, let it be supposed, that a Piece mounted at 30 degrees, shot 300 paces in the right Range, and 3000 at the dead Range, I desire to know the dead Range at 40 degrees.  

A Table of the proportions of dead Ranges.  Gr. Pa. 0 192 1 298 2 404 3 510 4 610 5 722 6 828 7 934 8 1044 6 1129 10 1214 11 1396 12 1394 13 1469 14 1544 15 1622 16 1686 17 1744 18 1792 19 1849 20 1917 25 2013 30 2185 35 2249 40 2289 42 ½ 2296 45 2289 52 ½ 2283 60 1792 67 ½ 1214 75 1000 85 ½ 192 90 0  
To do this the plainest mechanical way, is to divide that dead Range into any number of parts at pleasure, which set out in a line, at one end of that right line, make an angle by the 23 proposition of the 1 of Euclid demonstrated herein, and from the other end thereof erect a perpendicular line by the 11 proposition also there mentioned, until it intersect the line that framed the Angle given, and note well how many such parts it containeth, and multiply the parts of the dead Range by the parts, that the line that framed the Angle containeth, and then divide the product by the number of parts you divided the line of the dead Range into, and the Quotient will be the Secant Range, which known, (as imagine, for the secant Range was found 1555 paces, and for the dead range 2000 paces given) Say if 1555 give 1000 the whole sine, what shall 1000 the dead range give, 643 ⅕, the right sign of the Angle, the Piece must be mounted unto, upon the advantage, to shoot 1000 paces for her dead range.   

CHAP. XLIII. How to order and direct a Piece, and amend an ill Shott that was made either by the Mettle, level, right line, or advantage, or Mount.  
IF leisure will not permit to use the Ruler and Bevill, than the Gunner may by his judgement, according to the Charge and proportion of the Piece, take such a mark as he guesseth nearest, and likest to be best for the purpose; if it prove to strike on't just, than he hath his desire: for using like Powder, Shott, and having like temper and accidents, he shall always make thereby the like Shot. But if the Shott went too high, he shall then direct the piece in like sort again, and lay some small thing, as discretion will guide him upon the highest of the muzzle ring, and bring it and the highest of the Base ring in one, with the first point or mark, doing so, or more or less until he hit the mark desired, and the same may be tried by bringing the piece upon the first mark, which without doubt he shall attain unto with reasons Rule as afore. And if the first Shott be under or short, he must do as before ordering and directing his piece in like manner, saving that before the piece be removed, he must lay some little thing on the highest part of the mettle at the breech, and then by help of the Quoynes, she being embased or mounted more or less, as occasion requireth, until the highest of the mettle at the Mouth and Breech with that help, and the first mark become together into one right line. And so is the piece ordered for the shooting by Mira Commune, unless fault be by loading of the powder too much or too little, etc. And although other accidents may mislead him therein, yet either of those failings are also to be reform by the Bevell Quadrant represented in the 25 figure. As if the Gunner by the mettle take his mark so, that the Shot fall short: To correct the same, after the piece at the next Shott, is placed as before, he may then by the said Bevell quadrant elevate her one degree or point higher. As if she were formerly at six points or degrees, she may now be set at 7, and then giving fire, if it strike the mark, he may always order it in the same manner afterwards. But if it were too high, little, or much, he must accordingly divide that difference between the sixth and seaventh point or degrees by discretion (by the lighting of the last Shot.) And if it were too low, then proceeding in the same manner, to add to the sixth point, with judgement: and so may assure himself he may be like to get reputation thereby. But if he be to order a piece to shoot by the level of the Soul, or Axis of the Boar horizontally, then place a piece of board, within or upon the bottom of the bore at the muzzle, as in the precedent Chapter between the said long Ruler and Bevell Quadrant, raising or embasing her with Handspeeks and Quoynes, until the plumb line of the said Bevill, hang directly in the midst thereof: So will the Soul or Axis of the Boar lie directly level or parallel with the Horizon. Then taking away the Ruler and Bevill, and taking by the highest of the mettle at the breech and muzzle, direction to lay her right, and to what mark they respect for height; note that for after uses, and giving then fire, he may attain therein his desire.  
Forasmuch as opportunity will not always permit to place the same on the Mouth as aforesaid. The Gunner may keep that thickness or dispart in his hands, and take his level by the mettle as the fashion is, until thereby he discern the mark, and them both to be in one right visual line. And then setting on the dispart upon the muzzle ring duly, and bringing down the mouth of the piece until the said mark, and the top of the dispart, and the highest of the mettle at the Breech become all three in one right visual line: then take off the said dispart, and note what mark will then be in one right line, with the midst or highest of the mettle at the breech & muzzle, which will be much under the first mark, and it will so serve ever after to make a shot, to an assured good effect at the same mark, and with the same piece, from the same platform.  
The like is to be done in shooting at a mark, elevated to any degree about the level: As also for such marks as are beyond the distance of the right line or right range, by allowing an addition of a Minute, Degree, or Point of elevation, for advantage more or less, as need shall be, until the Shot hit right, and as reason will direct. As for example, a Saker is to shoot at a mark elevated unto 15 degrees, it being distant from the platform 1325 Geometrical paces 5 feet to the pace. But being mounted to the second point, or 15 degrees, she will shoot but 1062 paces in her dead range, and in her best Random she will convey a shot but 600 paces, in a right line, wherefore it being almost 300 paces short of the dead range for 15 degrees, and above 700 paces short of her right range upon her best Random, I must by my Gunner's Scale, or by the Diagram of Randons' in the 27 precedent Chapter, by the perpendicular raised from the Base at 1325 paces, find what random crosseth the aspect of the second point, which will be thereby found to be the fifth points Randon. If then I shall mount the said Saker unto the fifth point: so than I may expect her said Random, to strike or come near to that mark, that shall be elevated to the aspect of the second point, or 15 degrees, at the distance of 1325 paces, and so after 2 or 3 shotts at that advantage attain my desire.  
This is the ordinary manner of shooting upon advantage of any Mounture whatsoever, always observing the means how to draw as near the Enemy as can be. In general, you may observe, that in taking aim by the highest of the mettle, without consideration of the disparture, if the visual line thereof aspect the mark, the shot will be always too high within the right range, contrary to the Gunners diseigne, which should be to ruinated the Foot of the defence in Batteries the sooner to overthrew the wall, also to facillate the entry of the Breach, but singly to shoot at a Troop of Horse or Squadron of Foot, and especially in gravely or stony places it were not amiss purposely to shoot short to light upon the stones, to beat them so up, as that the raising of the gravel and stones may do the more execution, entering traverse-wise amongst the Enemy. But in a plain or level Champion, and amongst Battalions of men the Piece should be so bended and directed, as that her shot may pass by the midst or thickest of them, guirdle height: and so it may cut off a hundred, or whole Rank or File of Men at once, and break their Orders and Ranks, whereby those that fall on their Faces will hardly elcape, but shooting over, profiteth nothing at all, but is merely lost.  
To amend a wide shot, if it went too much towards the right hand, then remove the dispart, or take the large of your sight line somewhat more towards the left hand at the muzzle ring, keeping the former height, or letting the Dispart stand as before, and take your mark as before, only remove your eye a little more towards the right hand upon the Base ring: And so likewise do contrariwise, if the fault of the short aforesaid went too much towards the left hand: and so you shall assuredly amend the former shooting, unless some of these overruling causes or accidents cause the contrary, namely her Soul or Concave bore, not being strairt and right, or lying a wry in the body of the mettle, for then the fault is not in the Gunner, but in the Gun, which he must with judgement and good discretion rectify, as hath been already showed in the 44. Chapter hereof. She will shoot wide also if the Trunions lie not directly the one against the other: as also if the platform lie awry one side higher than the other: or if the Gunner take not his aim, so that the visual line that passeth from his eye to the mark: or if one wheel be higher than the other, or if one wheel be stiff and the other jocund, or be squatted with any rub in the reverse of the Piece, or run upon soft, and the other upon hard ground; or if the Cariage-maker have made the Carriage lean, or hang more upon one, than the other side: If the Nave be too wide, that the Piece shake thereby in her discharge, and reverse: or if the tail of the Carriage rest harder on the platform upon one side more than on the other, when the shot is too low for the Piece, and at the delivery toucheth upon one side. And lastly the vehemency of the wind being sidewise, overrules it to the contrary-side-ward, etc. But if the Shot fall to short or too fare, that happeneth by the force or feebleness of the Powder, or unskilfulness of the Gunner, not directing his piece as he ought, or in ignorance, or by mistaking the distance to the mark he would shoot at.   

CHAP. XLIIII. How the Gunner may be assured to make a good Shott.  
SOmetimes the occasions offer to require, that the Piece be curiously directed, and precisely bended to dismount a Piece of the Enemies that galleth shrewdly, or at a single mark, or at the Loope, Tronier, Cassamat, Horseman, Boat, or other secret place assigned, that else would impeach the appointed service and design: For which the Gunner ought to have an entire and perfect knowledge of the condition and quality of his Piece, by experience made by former practices in her; otherwise it will be uncertain and unlikely, that he at the first shot, out of a Piece, wherein they never practised, to make an assured good shot: and then in loading her, to have great care so to put home the Powder, Shott, and Wadd as that the powder may fire at once, that the Piece reverse not unrulily, it being a certain thing, that the more slow the powder is in firing within the Piece, the greater will her reverse be, and the shot also of the less force in execution. And likewise the reasonable putting home of the Shott and Wadds, neither too hard nor too easy, but that the Ball may gently with a convenient vent, only enter in close unto the Powder-wadd. And lastly, he may direct his Piece by the Quadrant Bevill inch rule, or other former directions, taking his aim directly by the highest of the Mettle unto the assigned mark, or with a due dispart placed upon the point of the muzzle ring, which highest parts may there and at the Base ring also, with a small line be noted for the visual line to pass vertically over them: And then giving fire, let him not doubt of an assured good effect, having a diligent hand in preventing the accidents that are to be provided for, as in the 43 Chapter hereof are mentioned, to avoid side, over, or under shooting, and considering well that such a good shot made, gaineth the Gunner much love and honour. The fittest Pieces for that purpose, are either the Culvering, Demy Culvering, and Saker, or the Cannon, Demi-Cannon, and Minion.  
Such a Shott ought to be made known to the General of the Army, who should therefore liberally reward the Gunner that made the same, not only to encourage him, but others also, afterwards to do the like, or better if it were possible. Louis Collado in his Manual Practice of Artillery, writeth, that at the Siege of Sienna there was a Piece lodged upon the great Church, from which the besieging Army received much damage: but in the end a german Gunner made a shot thereat, who at the first did not only dismount the same Piece, but also made the Gunner thereof, and those that were about him, fly together in the air to their destruction: the which Marquis de Martinian, the General of the Army seeing, it pleased him to take a Chain of gold from his own neck, and to give it unto the Gunner that made the shot, for his reward, which did not only rejoice him, but encouraged all the rest of the Gunners to endeavour diligently, so to purchase the like honour and reward, when like occasions were presented.   

CHAP. XLV. How to make Ladles and Sponges for every sort of Ordnance.   various instruments for firing and cleaning cannons 
Tractat. 3. Cap. 3.  

De demij can ronforce  
Zur halben gesterckten Carth.   

De canon renforce.  
Zur gesterckten Carth.  
●ampon  
Der stempfel.   

Canon commun  
gemcine Carthau   

Canon amoindri  
geschwechte Carthaun   

lanade  
amesure et proportion des cuieilliers a charger.  
Lass undt proportion der ladtschauffelen.   

De quart de Canon renforce  
Zum gesterckten quart   

De commun quart.  
Zum gemeinten q.   

Du quart amoindri  
Zu veriungten quart   

De demij canon common  
Zur halben gem. Carth.   

Demi canon amoindri  
halbe geschwechte Carth   

De piece enchambre ou cacampanee.  
Zu veriungten oder zu gespitzten kammern.   
For double fortified Cannons, to charge them with two Ladlefulls, they are to be two dyametres and a half of their Shott in length from the head of the Ladle staff, which shall be one dyamere more of plate, which must go about the said head: The Brass plate must be in breadth two dyametres unto the said head where each side must have half a dyametre more, to enclose the head of the Ladle staff within the plate.  
The Button or head of the Ladle-staffe must be one dyametre, and of such height or thickness, that it together with Brass plate may be equal to the height of the Shott (due vent being abated) for Sponges, their buttons or heads are to be made of soft fast wood, as Asp, Birch, Willow, or such like, and to be one dyametre, and ⅔ in length, & not above ⅔ of a dyametre of the shots height: The rest being covered with rough Sheep's skin wool, and all, be nailed thereon with Copper nails, so that together they may fill the Soul or Cavity of the Piece.  
The Button or head of the Rammer, must be turned of hard wood in length 1 dyametre, and ⅓ of such height or thickness, that it may fitly enter into the Piece the shots vent allowed: it were the better for fashion & strength: if the ⅓ next the staff were handsomely turned with abatement, and a Ferrill, or Circle of Brass fitted thereupon, to save the Head from cleaving, when as with force we shall ram the Shott home. All these Heads or Buttons must be pierced ⅔, with a hole for the staff an inch or more dyametre, whereinto the staff must be fastened: and the staff must ever be so long, that it must be at the least one foot longer than the Cavity or Soul is deep.  
For the ordinary Canon, the Ladle must be of the same breadth, but must not surpass 2¼ dyametres of the shot in length: and for the lessened Cannons two dyametre only to load at twice, all according to the fashion, length, and breadth, as is showed in the 20 figure α, with the manner of fastening them upon the staffs; wherein also the fashions as well of the Heads or Buttons, as of the Ladles and Rammers, are so represented to the eye, that the discreet Gunner shall need no other instruction therein: Where the description for the Demy-Cannons, which are of the same measures and proportion as aforesaid are these, having respect to their own proper Boars.  
The Ladle for Culuerings and Demy-Culuerings, have four dyametres of their proper Shots in length, and two in breadth.  
The Sakers, Falcons, & Falconers, which may with one Ladle fulbe load at once, may have their Ladles of 7 dyametres, & ½ dyametre of their Shots in length, besides that Coverture of the Head of the staff: and of breadth 2, as all the rest have.  
For Periors, which usually have Chambers, with o'er loes ½ or ¼ less in bore, than their Chase containeth, to them 3 times the dyametre of their Chamber may be allowed for length of their Ladles.  
Now if it should chance you were (having no Ladles not Balance ready) commanded to load a Cannon, or any other Piece in haste: First, put the rammer into the Piece up to the Touch hole, and mark, the staff, even with the mettle at the mouth of the Piece, and then pull it out 3 dyametres, for the Cannon, and 3 ½ for the Culvering, and 4 for the Saker Falcon, etc. and mark there another mark, which is the place that the Powder must supply in the Chamber: And then take Paper, Parchment, or Cloth, as long as the distance between the two marks wrapped round, being of height equal to the bore of the Piece, 1/20 less, fasten the same with mouth glue, or sow the sides and bottom, and fill the same with powder, and pour it into the Piece, putting it gently home, do so until you see the last made mark, to be equal to the flat of the mouth, the Rammer head being home unto the Powder, then put in your Wadd and Shott, as elsewhere is taught.   

CHAP. XLVI. How to make Bridges over great or small Rivers, to pass an Army with the Ordnance, and other Carriages over the same.  
OFten times it so happeneth, that passages are stopped, and not to be recovered, especially about Rivers for want of Bridges, or else some Marish or Moorish place interposeth: Wherefore to be prepared in all Accidents, especially to pass the Ordnance over a River, that one Bridge or Moor may be speedily made, either with Boats placed 12 or 14 foot asunder, and moored by Anchors fast a head and a stern, especially where the River ebbeth and floweth, else if they be but fast a head, it may serve they must at such distance be laid in a right line, to ride cross the whole breadth of the River, at the place appointed. And then between each two next Boats, place 3 beams of Timber, being 18 foot in length, whereof 14 foot must be to rear between the 2 next Boats at each end, two foot must be to bear upon the Boat, which Boats must be of even height or nigh, and the Beams are to be laid 6 or 7 foot wide, each from other, that the bridge may be 10 or 12 foot broad, as well to convey over the Horse and Foot as the Ordnance, Cariages, and all other necessaries belonging to the Army, for the surety and strength of which, there must upon every Boat be also three other pieces of Timber of such length, that it may at each end reach 3 foot over the Boats side, unto which the three Beams aforesaid, must be fast pinned with Tree-nayles and iron bolts, with forelockes and keys, to make them fast one to another. These Beams and Timbers are to be conered over with Planks two inches thick, or one inch and a half at least, and 17 or 18 foot in length, the description of which may be seen in the 17 figure at α.  
But if any boggy or muddy space be between the River and the fixed ground, so that the Ordnance cannot be brought nor drawn near enough unto the Bridge, than that part must be filled up with such things as are fittest to make it firm, whether it be with Faggots and Earth, or Chalk or stones, pyling the sides with Timber driven in, until they reach into firm ground at the bottom for foundation, and to revest it then with boards or walls, according to the time intended, it shall last and continue, that thereby the way may be firm land and even. But if any doubt be that the Enemy will surprise this Bridge, to make himself Master of the River then at each end thereof, a half Moon, or Reddout, or Fort, with Ordinance to do murder, and fireworks must be prepared to prevent him, and therein besides the side of the Bridge, may be palissadoed with long strong sharp pointed sparrs fastened, thereto to secure it that way. Also a continual and a careful eye must be cast upon every part of the Bridge, that if any accident of defect be in any place, it may be speedily repaired and amended: and a Rail on each side would be needful for a stay. A Bridge also may in like manner be made with Trunks, as is represented in the said Figure at β And also to be linked upon one great vessel, with a falling defensive pointed palisado, as therein likewise at 4, is represented, and upon Cask, Cables, etc. which I omit, being rather proper understandings for the Engineer.   

CHAP. XLVII. How to defend a Fortress besieged, and the order, and what provisions of Ammunition will be necessary for the defence thereof.  
AFortresse besieged being well defended, may return to enjoy her former liberties, which the better to do, it will be necessary to make plain, cut down, and ruin whatsoever shall be hiding and hurtful, within half a mile or more round about the Fort, be they Banks, hollow ways, Hedges and Dykes, of Lanes, Bushes, Trees, Houses, Mills, Gardens, Conduits, and such like obstacles, as not only hide them, but hurt you also. Next look that the Place be well victualled, according to the number, for man and beast, fitting for defence, and necessary use thereof fix months, which is the longest time a Fort can be like to hold out, without succour or supply from abroad. Also Ammunition must not be wanting, at least so much as may furnish the Flankers and Artillery, which must be as safe and covertly placed as may be, and not to be easily choked or dismounted. For Amunitions, precise proportions cannot be prescribed, because each day ministereth new necessities, and as the Enemy abroad raiseth or maketh new works. Within Men and Munition may be reasonably paralleled with 1/10 of the besiegers. Then to look that the Counterscarp (which is the shield of the Fortress) be duly flanked, covert, and capable, that the false Ports and ways for Sallies, be safe, close, low, and commodious for issue. That the the Parapets be of Turf, or unburned Brick, that the platforms for the Ordnance be even, and the Planks close joined, that their Reverses cause not errors, and be also capable for the Gunners and Labourers to traverse their Ordnance every needful way upon them. The number of your Garrison may also be estimated by the quantities of the places, to be defended by the outworks you would hold, by the intrenchments imagined requisite, and Sallies you purpose to make. Now after the proportion of a Place whereas 60 Pieces will be requisite, 12 of them may be Cannon, to beat down, and batter the Defences and Trenches of the Enemies, and to make therewith Counter-Batteries, to dismount the Enemy's Ordnance; And 8 of them may be Demy Culuerings, & 10 Demy Cannons, they being lighter, are more easy to manage, and 10 Sakers, to keep the Enemy continually play to hinder their works, offend their Sentinels, beat the entrances of the Trenches, impeach their Approaches, and for that they are light, they may be removed easily and quickly from one place to another, yea out of the Ports with some Drakes, to rake the Enemy's trenches, from some part of the Falsebray. And lastly, 20 Falcons and Falconets for Field Pieces, are necessary, and may be able to serve, not only upon the Ramparts and Walls, but also at the entries of a Breach, and at single Marks, Horse, man, or Boat.   

CHAP. XLVIII. To make a Counterbattery upon a Bulwark, from whence without danger of discovering or dismounting the Enemy's Ordnance, abroad may be dismounted.  
Such Counter-batteries are not to be made without great labour and charges, neither can every Bulwark yield a sufficient room for that purpose, without demolishment of some buildings and houses about the same (which in a time of need, must not be stood upon) as in the 10 Figure at β the whole structure thereof is represented. All the place must then be of that capacity, that from the Parapet to the foot of the sholde●  positioning cannons to defend a fortress 
Tract. 2 Dial. II.  
Comrnent il faut ordonner l'artillerie pour la defence dune Ville  
Wie das geschuts Zur Defension einer Stattsoll gestellet Werden.   positioning cannons to attack a fortress 
Tract. 2. Dial. II.  
Comment il fault loger des pieces seeretes en un bastion.  
Wie heimliche stuck in einer pasteijen zu gebrauchen   tracing the ballistic arcs of several cannonballs 
Tractat. 3. Cap. 13. fig. 2.  
Comment il fault appliquer le quadrant.  
Wie der quadrant an zusch lagen.  
Point du nueau.  
Punct der Wagen.  there may 40 foot of ground, and for the thickness thereof it must ●e 21 or 22 foot, with 27 or 30 foot for reverse, for each Piece making almost 100 foot in all, and leaving yet thirty foot more at least from the said reverse to the other Parapet of the same Bulwark, to the end there may he no impeachment, but that the Troops may march and pass to the defences required freely. And having also room to plant three Pieces of Ordnance upon each of the Shoulders of the same, which will also require 65 some of ground at the least: The Trouniers or Loops are to be 3 foot broad within, and distant 20 foot one from another: Having within the Platforms 3 foot of Barb, and without 9 foot of breadth, and every where 8 foot of height. These three loops must have a counter loop at the Parapet of the Bulwark, having in the midst 4 within 6, and without 8 foot in breadth and deep, that it be even with the Terraplene. Now from these Loops there must be, as we have said so much room, that within the Shouldring there may be 3 Pieces distant 20 foot asunder. Now two or three of these Shouldring discharge their three Pieces, traversing croswise to the Enemy's Batteries, beating so upon them, that they must be forced to quit the place: And although the Euemie abroad may beat the Covertures of the outmost Loops, yet can they neither for the inner Loops, not the Pieces within, come to touch any of them: But you may note that such Batteries cannot be made in a narrow or strait place, as I have said without demolishing structures, and raising the ground so, that it be level with the Terraplene of the Bulwark, which would otherwise be too small for that purpose. And having finished them, they are not to serve for one place only, but they may turn those Shouldring and defences, and make the Pieces thunder about on all sides where the Enemy would settle himself.   

CHAP. XLIX. Of certain reasons that causeth a Shott, though well directed to err in her discharge, and be faulty at the Mark wide, short, or over.  
THere are very many causes and accidents that may make a Shott well directed, to deviate from the expected course. The first is, when as the Soul or bore of the Piece lieth awry in the Body or Mettle thereof, or that the Chase or vacant Cillinder (the director of the Shott) is not straight; wherefore the Gunner may receive disgrace, but having examined and found the fault, he is to supply the defect by discretion and skill. And if the Trunions also be not duly placed directly in a dyagonall line with the Axis of the Piece, it will be wide: likewise if the Platform be unequal, as higher upon one side then the other. Also if the Gunner lay the highest of the mettle at mouth and Breech, it will shoot over if it be within distance: if one wheel be higher than another, also if one wheel go stiffer than the other; or if one wheel meet with a squat by a stone, or otherwise when the Naves be one longer & wider then the other, when one wheel reversing goeth on soft ground, the other on harder, when the Carriage or Trunion ears are higher & lower one than another: if the Carriage be too wide, so that the Piece lieth not fast the rain, but starteth in her discharge: if the Shot be not equally round, or the bore of the Piece not lying straight, but more on the one side of the mettle than the other. The vehemency of the wind, with, against, or aside, may drive the Shot forward, back it, or devie-at it, aside, the thickness and thinness of the air, the heating and cooling, the sleight or hard ramming of the Powder, putting home or short the shot. And lastly, the want of skill and experience: All these, and many more, may be causes of the failing of a Shott at an assigned Mark, which I thought fit here to note at last, not to minister matter of excuse to ignorant, negligent, careless Gunners, but to advice the discreet Gunner to have a vigilant eye, and consideration of all, or as many of those accidents with reason, & of the former directions, to avoid or amend them as well as he can at first. To fail at the first shot, if he be not acquainted with the Piece and Mark is passable; and at the second to fail is pardonable, but to fail of a fair shot at the third time, is too much, and argues but little judgement and discretion in such a Gunner.   

CHAP. L. How to conduct a Mine under ground, to blow up a place, and to prepare a Gallery, to pass the Dyke to the foot of the Breach.  
THe use of Mining is ancient, and was commonly used by the Persian, Greek, Parthian, Romans, and other Nations, that have managed great wars, and no marvel, for that the same is the easiest, and most proper means to force a place: But Pietre Navarro a Spaniard, was the first that invented the Fowrne and the use of Powder therein, for which and some other services the Emperor Charles the fifth, gave him the name of a Conde, and great rewards besides. Yet nevertheless, there is nothing more dangerous for such as work in these Mines, by reason the Countermines of the Enemy: so that if there be any suspicion of countermining, it will not be amiss to divert the course with all dexterity, either toward the right or left hand, as the occasion of the Place will permit. And forasmuch as according to the natural effects of fear, it behoveth the besieged to seek out the shortest and nearest way possible, to offend the Enemy abroad by Countermine or otherwise. The Mine-Master than may sink his Mine, and conduct the same either as in the 16 Figure at α, is described by the letters from A by B to C, or as the other 4 square angular course, and there to prepare the Fourne, which may be armed with powder in Barrels, so that giving Fire thereunto by a Train, he blow up the Place and the Enemies above it: And to the end the same hurt not the Pioneers or Workmen that dig and travel therein? it will be needful to line the same with sparres and boards framed accordingly, seven foot in height, and 5 foot in breadth, but it must be covered with 2 inch plank, to keep up the earth: But if the ground be moist or full of Springs, a gutter with 2 descent must be made, that the water may run to some lower evacuation; if that cannot be, a Well at the mouth of the Mine must be made for a receptackle for all the Springs to run into by their gunters, and Pumpsor Forcers, are to be set sufficient to mount the water, that it may after find a current to run away. But if there be any suspicion of Countermining; then always forwards in your intended course, you may boar long holes in the earth with your long ground Awgars used for such purposes, and pierce holes on all sides, also to know upon what part from you the Enemy worketh, which cannot be done so private, but so the noise of their Mattocks and Shovels will soon be hard by those pierced holes, when you come near their works: if by those means you hear nothing by reason that the besieged had ended their Countermines before you began, and he watching them heareth you work, those piercers being but 12 or 15 foot long, will discover the danger by boring through the solid earth, to the hollowness of their Countermine; and so you shall have Counteraduantage of the Enemies counter-minings. My Cosmodelite before represented, is an excellent instrument, and for that purpose I think the best extant.  
Now being come right under the place to be blown up, and made the Fourne arched upwards higher than the Mine place, therein sufficient powder, either in Barrellor Troughes, you must also stop closely and strongly the mouth of the Fourne, very diligently, looking it be so close that no air breath out, but at one small hole wherein the Train runneth in to give fire thereunto; unto which he that giveth fire, must look that the Match of the Train, be not too long before the powder take, as also to see it be not too short, and so to give fire too soon, that is, before he be gotten into some place of safety out of the blast and ruins, lest he pay the wages of improvidence. The means then to set the matter a work, needs no long discourse, being very commonly known, only to advice that the entrance into the Mine for height and breadth as aforesaid, may be as close and secret from the Enemy as may be, and that in his proceeding on, he must diminish those measures in such manner, that in the midst it be but 5 foot high, and 4 foot broad: And the neeret you come to the end, so much the less give in breadth, so that even to the coming in to the Furne it must be close and narrow, that you may only get the powder thereinto.  
Above all things, the Mine-Master before he begin, must be sure to know the true measure and distance, with the height or depth of the place intended to be Mined, be it above or under the level of the place he beginneth, most precisely taking exact notice of all his windings, turning, and angles, which he maketh from the beginning to the end, as well above and under the level of the right line, passing thence right under the Place, as towards the right and left side thereof: Otherwise his labour will not only be deficill, but also uncertain and most dangerous: there being four principal causes to impeach the effectual working thereof. First, the ill stopping of the Fourne: Secondly, the weakness of the sides by countermines or Caverns. Thirdly, by failing of the Train by moisture or ill contriving. And fourthly, the most important, is, that the Frame whereupon the Barrels stand, be not placed too low, as under the level of the entrance, which it must ever exceed, because the quality of fire is always to ascend. And so obserning every 15 or 20 paces, how high, or low, or wide on any side you are gone, above or under the level straight line. Two of the greatest shames to Soldiers, being either to lose any piece of Ordnance, by negligence or ill guarding them: Or the failing of a Mines due effect.  
And for making great or small Galleryes to pass a dyke unto a Breach covertly, be the dyke watered or dry, the manner is described in the precedent Figure with the Mine▪ and may be made ready in several parts, to be set together speedily by joints, fitted for that purpose, for the easier carriage also: And they must be covered over with Faggots, earth, & green Hides to prevent fitting them.   

CHAP. LI. Of the Guindall, Windlas, and Gin; or Martinet, Krow, and Handspyke, and Lever, and the endless Screw.  
THe Guindall or Windlas, is a convenient ingenious inu●●tion, to mount a piece of Ordnance, or heave aloft weighty matters, and is represented in the 24 Figure, with the Crow of Iron, or Goates-footed Handspyke, and Levers, accompanied with the Gin or Martinet, which will lift up the Axtrees, when the Piece is upon her Carriage mounted, to take off, or put on the Wheels, to grease, or ease, or mend what is amiss about them. The Guindall is thus made of a piece of Timber, six inches square in the feet, or with three young dry Oken Sparres, about 12 or 15 foot long, joined together at the top with an iron bolt, passing through Iron Ferrills, upon which bolt a double pulley is hanged, and at the lower end of each Sparre another iron Ferrill, and a Pike of iron is placed to keep the feet from all slipping, almost at the lower end of two of those legs or Sparres, a piece of a Sparre about 4 or 5 foot long, is fastened between them, and also 3 foot from the end, a Roll and Windlas, with half round irons, are clasped to those 2 legs or spartes, and above that 2 or 3 other pieces of sparres: In that Roll, are 4 mortis holes, for Handspykes, pierced through, whereby they with 2 or 4 Handspykes turn that Roll which hath an end of a rope 4 or 5 times, or more about it, and the other end reeved in the said Pulley, so continued unto another double pulley, with a hole or hook to take hold, or seize a Rope that hath slung the Piece, appointed to be mounted into her Carriage: Or else the Frame may  cannon in a sling beneath a system of scaffolds and pulleys 
Instruments pour le seruice des pieces. Tract. 3. cap 8. Der zu dem geschutz gehörig hebzeug.  
Martinet.  
Wind.  
Guindal.  
der bock oder heber.  
Pied de cheure.  
Levies.  
pebel  
gejss fuss.  
Eschelette.  
hebleiterlein.  be of 3 square Tymbers, the head of two of them joining at the top together, and the rest for the other leg and parts, may by the sight of the said 24 Figure, be framed and understood sufficiently.  
 two wheels and an axle driven by a crankshaft  
The Gin or Martinet is another instrument, serving to lift up the Piece with her Carriage, and all her furniture from the ground with one man's strength, when the Gunner would change a bad wheel, or the like, or put a wheeleon upon the Axletree, or take it off for any purpose, the proportion of this Engine for the use of Ordnance, is that it ought to be about 2 foot long, and 8 inches square, or : the Viceron is of iron forked, to take hold, and with his teeth is wound up by a handle, with a spur of few teeth, it will lift a great weight, multiplying the force proportionally, according to the height of the secret wheel, and of the said spur (contained in the distance of the handle, from the centre of the spur) or to semidiametre of the handles circular revolution, dyametrally multiplied by the reasons between the spur and wheel. That Viceron cometh out of the midst of the said square case of wood, at the top thereof, and by his Fork or Esse, taketh hold of whatsoever is fitted to be lifted up. The Scaletta with the rest may be easily made, understood, and used, as in the said 24 Figure is described. And for the same or any the like purpose, the endless Screw of Archimedes here above represented, is of infinite effect being duly applied.   

CHAP. LII. How to draw a Piece of Ordnance up to the top of a steep and rough hill or mountain.  
HOw to get a Piece of Ordnance up to the top of a steep Mountain the best manner is, that which may be seen represented in the 23 Figure, by means of the Capstane: As suppose D to be the top of a Mountain, the Piece being at the foot thereof, ABC to be the crabbed and rough crooked way, by which the Piece must be gotten up, drawn with a long Cable or strong Hawser, by Pullyes or Blocks, with sheevers to make a Battery against the Tower F, between D and C: For the better effecting of which, the Gunner and Engineer after they have taken good notice of the Place, and made the passage smooth and even, they may place the Capstane behind D, fastening it surely that the same may not overmaster the great poise of the Piece: And then in convenient places of the crooked way (if there be no Trees there to serve the turn, which would be great helps if there were) there must great Pyles by force be driven into the ground, to fasten the Hawser in good and strong Pullyes, by or in which the said Cable or Hawser, must pass the upper part thereof, being fastened to the spindle of the Capstane, and the lower end thereof unto the tail transom of the Carriage or Rings near the same, at each side one. Lastly, four or more men turning the Capstane about, with the Bars thereof, shall first make the Piece to mount up unto the first Pulley or Block at A, where it must be first scotched, until the Block be taken away, by taking out the Pin or Axis of the she ever, and then the Piece is to be taversed towards the second Block or Pully B, and so to the third C, and then to the desired place near D. It were also needful to have a small Truck, as well to bear the Tail up from staying against rough stubs or stones in the way, as also to help the motion, Labourers also must be readily attending near unto the Piece, as well to advance and help the Motion, by heaving and shoving the same, as to traverse the Piece the rightest and best way, as occasion shall require, as in the said 23 Figure may be seen. And after each Poultry, hath performed his office, let a man be ready there with grease, vinegar or Lie, to annoyot the end of the Axtree, that it may soak into the Nave, lest the weight of the Piece in that Motion fire, and also to have an eye to each of the Pullyes, that the Cable break not. And if any danger of its breaking be perceived, then to give warning to them above to stay, and to them allow to scotch, until the Cable be changed or amended. But if the hill be so rough and steep, that the means aforesaid will not do it. Then take the Piece out of her Carriage, and either lay it upon a block Carriage, or on a Sled with Trucks, and lay planks along in her way where it is rough, and use then the Capstane and Pullyes as aforesaid. You may also use for the same purpose Archimedes endless Screw, represented in the 51 Chapter.  
 transporting a cannon up a mountain 
Tractat. 3. Cap. 14  
Comment on peult moner une piece d'artillery sur une montaigne  
Wie ein stuck auff einem berg zu zihen.    

CHAP. LIII. How the Train of Artillery and Ordnance should be ordered with their Carriages in a journey, or upon a March.  
THe whole Train of Artillery, one body divided into two parts Van and Rier, is wholly under the command of the Master, or General of the Ordnance, or in his absence under his Lieutenant or Brave, imagine then that the Army be with suspicion according to advice, to be set upon by the way, both in the Van and the Reire. Then were it fit 500 Horse divided into two Troops, should advance, to discover all the Coast of the Champion, with the dangerous ways, Woods, Thickets, and such like, by which the Army must pass, after these 2000 Foot, should march as well for Coverture as guard of the Ordnance. And they also to be divided into two squadrons, furnished with all necessaries of defence. After them the Train of Artillery, with the Ordnance, marching with their Conductors, Wagons, and Carriages of Powder, Shot, and Tanpions, or Wadding, Coins, and Beds, together with a reasonable number of Pioneers, and some Mariners, and such like spare people, to be ready to make Coverts and defences for the Ordnance and Gunners, or to cut wood, to plain the ways for the Van to pass with four field Pieces, ready mounted in their Carriages, with all their necessaris, as Ladles, Sponges, Rammers, Crows, Levers, Ropes, Tables, and breechings, with experienced Gunners, Gentlemen of the Ordnance, Mattrosses', and Conductors. After follow the Munition and Engines, serving for the use and defence of the Rier of Artillery, with the Boats and Bridges, and then again follow 8000 Foot, and after them the great Ordnance, either in the Carriages with fore-Cariages, or else upon block Cariages, whose wheels being higher, makes the draught the easier. And lastly, follow 3 or 4 Field Pieces ready mounted, accompanied with all their necessaries and apurtenances of Powder, Shott, Instruments, and Attendants. After which there march 2000 foot more, that are for Coverture and defence of the Ordnance and Riere of the Train: these are followed with 500 Horse to close up the Army, whose Charge, is, to see that the Rier of the Train be not set upon at unawares, suddenly, or unprovided. The Army then Marching in this Order, The Enemy shall find the Van and Riere, and also the Body furnished with force in all places. And being always so provided with the Train of Artillery divided into 2 parts, yet remaining one Body: so furnished, as that no doubt but a good and a happy issue will succeed such good equipage, well guarded with Horse and Foot, provided for defence of the Artillery, to march without danger, but in large capable Champions. This Train may be shortened, the Van taking the right hand, and the Rier the left, and the Train between both, equal in Front with Van and Rier, and so Marching more compact, it will be the stronger: as in the 6 Figure at α, by the letters ABC is represented to the eye.   

CHAP. LIIII. How to draw Ordnance if Cattles be wanting, by the strength of Pioneers or Labourers.  
ARtillery or Ordnance, being the principal instrument of the Wars, requireth a great strength of Cattles, either of Horse or Oxen, to transport them from place to place, which being wanting, must in a journey be suppled by Pioneers and Labourers: as imagine that 16 Pieces were to be employed against a Place to be forced, consideration must be had (Cattles being wanting) how those Pieces, whereof 6 are Demy-Canons, 4 are Demy-Culuerings, and 6 are Field Pieces, that shoot 6 l. ball, and how all the provision that belongeth unto them, as Powder, Shott, Wadding, and Cordage, etc. may be transported thither, the Place to be forced being situate in a rough, stony, and hilly ground, by Pioneers and Labourers only, sparing the Soldiers for other services. The Ammunition and Persons that must carry them readily, are first to be considered of: As 600 Shott for the Demi-canon at 30 l. each Shott, will be 18000 l. loaded in Wheelbarrows 2 Shot, in a Barrowe which will be 60 l. for a Man, and will require 300 Men to drive them. Also 600 Demy-Culuering Shot of 10 l. loading 8 Shott in a Barrow, will require 75 Men, each man carrying 80 l. And 900 Shot for the 6 Field Pieces of 6 l. each Shot, putting 13 Shot in a Barrow, will be carried by 69 Men, each man carrying 78 l. except 3 of those men, which shall carry 14 Shot a piece, that is, 84 l. each of them: So all the Shot will be carried by 444 Men. The strongest men which carry most, are loaded with the weight of less than a bushel and a half of Wheat for each man in a Wheelebarrow, which he may easily drive. Then for the Demi-canon, loading them with 18 l. of powder for each Shot, will for the 600 Shott amount to 10800 l. every man carrying 80 l. in a bag, will require 135 men.  
And for the 600 Demy-Culuering, allowing each Shott 8 l. of powder, will come to 4800 l. each man carrying 80 l. 60 men will transport the same.  
And for the 900 Shot, for the 6 Field Pieces, allowing 5 l. for each Shott in powder, that will amount unto 4500 l. which at 60 l. for each man to carry, will requite 56 men, & a Boy to carry the odd 20 l. of powder overplus, which will amount almost unto 180 barrels of powder, each barrel containing 112 l. neat.  
And for the Furniture of the Pieces, the Figure 5 α, showeth the manner of drawing them by 3 lines or traces equally divided, according to the number of men that are to draw them, so that the Demi-canon with her Carriage, weighing 6000 l. reckoning 60 l. for every man to draw, it will then require 100 men, and so the six, six hundred men.   a cannon drawn by a team of laborers  a cannon drawn by a team of horses 
Tract. 2. Dial. 3.2.   laborers transporting munitions 
Comment il fault pour f●●te de che●●●dy Condu●●● t●ent les muretion, que l'●●●tillerie. Tract. 2. Dial. 22.  
Wie in mangel der pfer de heides ●●●●ition undt geschutz vart zu bringon.   a cannon atop a cart 
Tract. 2. Dial: 3. Canon en chariot. Carthaun auff einem lastwagen   a train of artillery on the march 
Tract. 2. dial: 5.  
Comment le train de l'artillery doit marcher force en campagne large.  
Wie-das geschutz in einem wei: dem feldt ordentlich bei einan: der zihen soll.   artillery encamped in a laager 
Wie das geschutz mitt seiner zu gehor soll in seinom guartier losiert werden. Tract. 2. Dial. 5.  
Comment le train de l'artillery doit estre loge en son quartier.  
The 4 Demy-Culuering Carriage, and all weighing about 2400 l. will require 40 men, to draw each of them, so 160 men will at 60 l. for each man serve to draw them.  
The 6 Field Pieces with their Carriages, weighing about 2400 l. a Piece, will each of them require 30 men, so the 6 will be drawn by 180 men, each man drawing 60 l.  
Now forasmuch as there may be cause often to dismount and remount a Piece by the way in the journey, it will therefore be fit to have ready the Gyndall or Winlas, and the Martinet or Give, & when they are to be drawn up any steep hill, than also the Capstone Cable & Pullyes in the 2 last Chap. described, must also be carried, all which may be carried by 40 men with ease: so that for the Carriage and transportation of all these Amunitions in any journey (where Cattles are not to be had) may be carried and drawn by 1675 men and a Boy without any difficulty.  
It may also be demanded, because in such an expedition, that many other things will be needful to be transported for the Ordnances use: As Ironworkes, Nails, Crows, Hooes, Fore-Cariages, Grease, and such like: But seeing they may more easily be divided amongst the Labourers, there resteth for them no difficulty of transportation. And for the better drawing of the Ordnance for each Fore-cariage, a long Transome or Whiping-tree must be fastened afore it, as between A and B is described, that the 3 Ropes or Traces may be placed equidistantly, fare enough asunder to avoid trouble, and because the Traces will be some of them too long, an other Travers or Whiping-tree, or two may in the midst, or in convenient places be fastened to those, or else other Traces rather may go between Whiping-tree and Whiping-tree, to keep the so long Traces from swaying, with too much trouble to stagger the men in drawing, and so hinder their draughts. And three men behind would be needful to guide the Carriage in the bend and turnings of the way. Upon the Traces also each man must have a double Cord fastened to the Traces, which he must put over his shoulder Scarff-wise, and laying his next hand on the Tract, he may so draw with all advantage.  
And for Horse or Oxen, allowing each Horse to draw 500 l. and each draught Ox 600 l. The same may easily be thereby found how many Cattles will be requisite to transport the aforesaid, or any other assigned quantity of Munition for any journey. The manner of the Managing, whereof is represented in the said 5 Figure at β. And the carrying of the Shott and powder in Wheelbarrows and Bags, is deciphered in the said 5 Figure at V And lastly, the description of a Piece ready furnished for a journey, with Carriage and Fore-cariage, Ladles, Sponge, Ramers. etc. is in the same Figure represented at δ.   

CHAP. LV. How many Privileges the Train of Artillery have more than ordinary in Marching and Lodging.  
IF it happen that in Marching, any other Carriage offer to advance before any of those of the Trains Carriages (except the Treasurer's Carriage) than the Master of the Ordnance hath power to command & compel the contrary by Privilege, whereof they enjoy more than others, because of the extraordinary weight of the Ordnance and Shott, and for that they have charge of the principal instrument of the Wars, and therefore hath the first Rank, without contradiction, and aught to have the best Quarter and Lodging, and to be first settled therein. And in March in a Champion they of the Train of Artillery, are to match more close and short, then doth the Vant or Reire between which two and the Batallion, they are always ranged or placed, as may appear in the 6 Figure at α. And the General or Master of the Ordnance, is to have care that his Train be timely lodged, to have time to provide all commodities needful. And if it were possible that they may be so lodged, as to discover the whole Champion about them, whereof these advantages would arise: First, that they may discover all approaches: secondly, that the Camp may be the better defended thereby. And thirdly, the Enemy advancing to give an assault to the Camp, they may by them the better be repulsed. But for their Lodging, the order represented in the said 6 figure at β, it must be observed. First, that between the Retrenchments made with certain Chains of the Munition, and with the empty Carriages and Fore-cariages, they may be enclosed, so that there may be room and space, that the Footmen appointed for their guard and defence, may if need be skirmish, which for that purpose, hold the places therein marked ABCD, having 25 paces breadth at the least. And secondly, that the Pieces of Advice, whereof there are always 3 or 4, regarding all the ways of the Enemy's Auenewes which are ever ready charged and fitted in all things. And lastly, that the Carriages of powder be lodged in the middle, as about the centre or midst of the other Carriages, as you may see by the letters FGHIS.   

CHAP. LVI. Showing how to weigh a Piece of Ordnance, or a Ship sunk under water, and the proportions of all Metals and Ordinary stone, what, or how much they will weigh in the Air, and how much in the water.  
IT being a certain thing, that whatsoever is heavier than so much water, as the body of the matter thrusteth out of the place will sink, and being lighter than so much water will swim, as Nicholas Tartaglia hath not only well collected from the learned Archimedes, but also calculated not only the proportions of all the ordinary sorts of Stones and Metals, whether in Air or Water, according as they poise in both; And also notably expressed their surrounded accidents, in his Treatise entitled by him Novo Scientia, wherein he delivereth as followeth. Namely, that ordinary Free stone, weighing 93 l. in the Air, will weigh but 48 l. in the water, which is near as 2 is to 1 between the Free stone and water.  
And that Marble stone that weigheth 7 l. in the Air, will weigh but 5 l. in the water, which is near 7 to two, 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 Iron or Tin is to water, as 19 is to 3.  
And Brass weighing in the Air 65 l, will in Water weigh but 55 l, and so Brass is to water, as 65 to 10.  
And Led and Silver weighing in Air 30 l, will weigh in Water but 27 l, so Led and Silver are to water, as 10 to 1.  
And lastly, Gold in Air being 17 l. weight, will in the Water weigh 16 l. so Gold is to Water as 17 to 1.  
And in the first declaration of his said Book, he showeth how by a Concave Globe of Glass, having a hole to put in a man's head under it, being set in a Frame of Timber in the form of the Frame of an Hourglass, with a Winlas, Rope, and weight thereat to sink. A man entered into that Frame, to the bottom of the Sea, or other deep water, his head being within the said Concave, Glass, Globe (wherein he may both see and breath, being no water can enter into the same.) And when he will again rise to the top or surface of the water, unwinding the Rope (being long enough) the frame and his body in it, will in like manner mount up as he pleaseth: and the weight remaining at the bottom of the water, and the Rope going through the bottom of the Frame, it will guide it to go up upright.  
And in his second declaration thereof, he setteth down the principal impediments, that usually hinder in the weighing of a Ship, or other heavy thing sunk under water.  
First, if it be docked, or have made his bed, or impression at the bottom.  
Secondly, if it be filled or covered with Sand or Oaze, so that sufficient Ropes cannot be fastened thereunto to sling the same.  
Thirdly, how to get the thing sunk, to separate itself from the bottom of the water, where Air cannot come between, which will be harder to cause such separation, in muddy, oazy, or sandy ground, then in gravely or stony rocky bottoms; yea, and with more difficulty to, in very deep then in shallower waters.  
And lastly, that it is harder to weigh things that have been long, than such as are but newly sunk, because it and the bottom will be so joined and closed together, that to separate them, Nature refusing to let vacuity to come between them, they at the first will be found loath to departed. But having fastened Ropes to sling the sunken thing, either by his help sunk in the said Frame, or else by the means here in this 14 figure at β represented, which may be conceived, a man entered into a case of leather made so sight, that no water can soak in, and with a pair of glass Spectacles fast set, and cemented close, with a pipe of leather boyed by bladders blown, at the brim or top of the water, whilst he fastens the Ropes below. Then 2, 3, or 4 vessels being ankered over the place, and firmly fastened together with Timber beams, the slinging Ropes also fastened to a main Timber between the vessels, being deep loaded at the first, fastened of the said slinging Ropes, and after the vessels being unloaded and lightened, will be more boyant, and weigh to their power: Or else if the slinging Ropes be fastened to their stems (they being loaded forward) and afterwards the loading removed aft, towards the stern of the vessels, they will then weigh all their Force: And where the water heightens much, if Ropes be fastened at low-water, at high water, they will have boyed the sunk thing, or done their most force and help they could.   two wheels and an axle driven by a crankshaft 
Tract. 3. Cap. 4.  
De Colubrine  
Lur Colubrinen.  
〈…〉 au default de sa propre cueilliers.  
Form vnd mass der secklein oder patrohnen so in mangel der rechten ladtschauffeln gebraucht werden.  
Pour le Canon  
Zur Caethaunon  
Lastly, also if 4 Vessels be fastened, so that a square space be between, and one or two of Archimedes endless Scrues called Tripastons, here in a lively figure, represented with which, he said he would move the world out of his place, if he had a firm foundation to plant his Engine upon Datum pondus datis viribus movere: There will be therefore no doubt, but industry and diligence joined, will produce the wished effect: and so knowing the lading or weight of the Ordnance in the Air, as each thing would weigh in a pair of Balance, the matter being Mettaline, then Tartag his true proportions will help, or if other goods, than industry will soon find how much all will weigh in water, which let suffice at this time.   

CHAP. LVII. How Moulds, and Formars, and Cartredges are to be made upon them, to Load and Charge any Piece of Ordnance, without any Ladle.  
Having already showed how to load any Piece with, and without a Ladle: Now I will show how to make Cartredges ready for all Pieces, wherewith in time of service any Piece will be more speedily and certainly loaded. Cartredges are either to be made with Canvas Fustian, or other linen cloth, or with thick strong Paper, especially of Paper Royal: which prepared, take the height of the bore of the Piece, without the vent of the Shott, and cut the cloth or paper of the breadth of three such heights; and in length, for the Cannon 3, for the Culvering 4, and for the Saker Falcon, etc. 4 ½ of the heights of their proper Boars, and leaving in the midst at the top and bottom one other such height, at each place to make a cover and bottom for the Cartredge, cutting each side and end, somewhat larger, than the strict measures appointed for the sowing or glewing of the seams thereof, so much as will countervail the same, having also a respect for augmenting and diminishing those measures, as the powder shall be better or worse than ordinary, and also abating with discretion, when as your Pieces shall be already heated in fight, lest else you endanger the breaking or splitting of your Piece. Having resolved then for what sort of Ordnance your Cartredges are to serve, you are accordingly to have a Model or Former of wood turned of the height of the Shot, and of a convenient length, longer than the Cartredge is to be. Then if you make them of Canvas, half a dyametre is to be allowed more in breadth for the seams: but if they be made of Royal paper, then having lapped it once about the Former, leave about ½ inch surplusage more than will compass it, which with Starch, Paste, or mouth Glue, close about the said Former, having some part of the same substance, fitted upon the end of the Former; first for a bottom, which must also be pasted or glued close, and fast to the side of the Cartredge, so that being dry, it may hold the Powder fast, and sure from spilling. And you must remember first to tallow the said Former, so that the Cartredge being so moulded thereon, it may be easily and without tearing, slipped off again. A pattern for these Cartredges is here in this 20 figure represented. Now having showed how the Cartredges are to be proportioned and made, it resteth also to show how a piece of Ordnance is to be loaded with them, wherein we are only to consider, that if the Piece be Chamber-bored, it must be laid in a Scaffeta, or Semicircle, or Cillinder of wood, of the thickness of the Orlow, or different thickness, or height of the Mettle between the Chamber. Also if the Piece were Taper-bored as the Drakes, and some ancient Cannons are, than the Mould, must accordingly be made to taper for the making of Cartredges for her, and her Ladle must also be cut tapering-like, the figure represented at T in the last figure but one; but if the Piece be equal bored, and the Cartredge made of Paper, then there is no more to do, but to put the Cartredge into the mouth of the Piece, and with the Rammerhead, to put it home, to the bottom of the bore of the Piece, with two or three easy strokes: and then with a sharp three squared Pryming Iron, to cut and prime the Cartredge, that the Powder prymed at the touchhole, may give fire to the quick powder thereby. In all other things for wadding before and after the Shot, and ramming home the Shot, you are to perform the usual manner taught in his proper place.   

CHAP. LVIII. The names of the principal members, and parts of a piece of Ordnance, as they are to be called and known by.  
THe names, kinds, and sorts of each Piece of Ordnance, with their differences, weight, measures, and in their fortifications, being already handled in the precedent Chapters hereof, needs not here be repeated. But in regard the most of them have special parts common, and of like names, I will speak a word or two thereof, and so proceed to the manner of making and proportions, belonging to the Carriage of each particular Piece, as in the next Chapter will appear. The whole piece together, or as much thereof as is matter of Mettle, may by the 2 definition of my Book of the Art of Artillery, be called the body of the Piece. The hollow Concave, Cillinder, or Bore of the Piece, may be called the Soul, by the first of the same. The whole length of her shaft or Column, is the Chase. So much of her bore as containeth the Powder and Shott, is the Chamber, or Charged Cillinder, and the rest of the same is called her Guide or vacant Cillinder. The two spindle's or eminencies that come out about the midst of her chase, whereupon she (in her Carriage) is mounted or embased, are called her Trunions. The most afterward pummel at her breech, is called the Casacabell.  several ships 
Tract. 2. Dial. 24. fig. 1  
●●mmont tirer un batteau enfonce en l'eau.  
Wie ein versenckten schiff auss dem wasser zu heben.   a diver retrieving a cannon from underwater 
Tract. 2. Dial. 24. fig. 2.  
La maniere et trace des instruments pour tirer une piece noyee de l'eau.  
●he undt mitt was instrument ein versencktes stuck auss dem wasser zu zihë  The little hole near the breech, whereby she is prymed and fired, before her discharge, is her Touchhole. All the Mettle behind the Touchhole is the Breech. The greatest and most eminent Ring or Circle of Mettle at the Breech, is the Base ring. The next Circle or Ring before between the Trunions and the Touchhole, is the Reinforced ring: the Circle or Ring next before the Trunions, is the Trunion ring. And the Circle which is foremost, and most rank and eminent at her Mouth, is her Muzzle ring. Lastly, the Ring between the Trunion Ring and the Muzzle, is called the Cornish ring, and the part of the Chase of her shaft contained between the Cornish and Muzzle, is called her Neck. And all the Rings, Circles, and eminencies at her Mouth, are called the Freeze, taking these names from Pillars or Columes, which somewhat represent the Chase of Ordnance: being in form of the Scapus, of a Pillar or Column so nearly, that they take the names of some such part of Pillars, as they nearly represent.   

CHAP. LIX. Of the making Proportions and Measures of every part of a Field Carriage for any usual Piece of Ordnance assigned.  
IT being most certainly a matter of great importance for service, to have the Carriages of all the Ordnance, with their Wheels, Axtrees, and their Furnitures to be strong, well proportioned, and neat, and gracefully wrought, so as the Piece mounted therein be every way so duly fitted, as that in the discharge of her Shot, nor in her Reverse she may not remove from the Angle wherein she was directed. We have thought good here to show the due measures and proportions for all Field Cariages, both by figures represented in the 19 figure at β, and also by rules and discourse as followeth. But first, a word or two of the reasons and different opinions of some of the best modern Authors, that have written of this subject. Louis Collado affirmeth, that long Carriages are better than short: first for their more agility in reversing: secondly, for the much less shaking of the Carriage, Axtrees, Wheels and Platform, saying, that Ordnance mounted upon short Carriages in a few times discharging them, make them utterly ruinous and unserviceable by their passions in reverse. But Alexander Bianco commendeth the short rather than the long Carriages: first, because they then require less room to reverse in, and that being loaded, they are sooner brought again to their place of service: And lastly, that a Piece shooteth further, being mounted upon a short, than it would do upon a long Carriage. Both being moderated speak reason, as Pieces are yet accommodated: but because I know that any Piece of Ordnance may without any inconvenience be so fitted, that it with a short Carriage, it shall less shake the Carriage and Platform, shoot further, and reverse less by fare then in these as now they are fitted will do. Therefore although I with Bianco approve of short Carriages, were they fitted for them, and with Collado as they are yet fitted: yet I will here show the measures and proportions of late used, of the best Cariage-makers, and are made according to the directions of the most experienced Gunners, which although it be most particularly appropriated to the Cannon, yet with the destinctions following it may well lead to the proportional, making and measure of a good Carriage, for any usual piece of Artillery whatsoever as followeth. The sides and Cheeks called Limbers, aught to be of Elm or other Plank that is not apt to split and cleave, which for the Cannon must be once and ¼, and for the Culvering and smaller Pieces once and ½ the the length of the Piece, and for each of them, they must be one dyametre of the proper bore of the Piece in thickness and in breadth, at the head of the Carriage, it must be 4 dyametres, at the first bending 3, and at the tail, 2 dyametres of the bore or height of the Piece.  
The Transomes are to be in breadth 1 Calibre, and ½ of the bore, and in thickness one Calibre, except the tail transomes, & coin, which must be 2 Calibres broad, and 5 long, where of ½ Calibre may be let with a mortis into the cheeks at each end, and it must have a bar of iron pass through the midst thereof from side to side, with a hole for the Pintle of the Fore carriage to enter into; on either side of this transome there must pass an iron bolt from one side to the other, with an iron or rose on each out side, to hold them firm together.  
The next Transom forwards is the Coin Transom, which must be 4 Calibres in length, that is 3 Calibres between the Cheeks, and ½ of a Calibre, let in at each end into the cheek, upon this the breech of the Piece is to rest his bed and coins.  
The next forwards is called the bed Transom, because the forepart of the bed resteth thereupon, and the backer part of it resteth upon the coin transom This is also 4 Calibres in length, but ½ Calibre at each end is likewise let into the cheek near to the Axtree, so 3 whole Calibres thereof will be left discovered between the cheeks.  
The foremost is called the head Transom or fore-Transom, which is 3 Calibres, and ⅓ in length, with ½ at each end also let into the cheek, and so leaveth 2 Calibres, and ½ discovered between the sides.  
Through each of these Transoms there must pass an iron bolt (at the least, for the greater sort of Pieces) from side to side: By means of these 4 Transomes all the Carriage is locked fast, as into one entire body, and is plated and bound strongly with iron, that the joints open not with the vehemency of the reverse. And thus is the Carriage in his perfection, so that if it were armed with his Axtree and Wheels, the Piece might be thereon mounted, and ready to do service.   parts of the carriage of a cannon 
Tractat. 3. Cap. 7.   

CHAP. LX. Of the Wheels and Axtree for Carriages for Ordnance.  
THe Wheels should be in height about ½ the length of the Piece, but in that consideration must be had of the height of the Parapet where they are to serve. And for the Saker, Falcon, and smaller Guns, the height of their Wheels must needs exceed that proportion, namely by 1/12 for the Saker and Minion and by 1/6 for the Falcon and Falconet, and by 1 quarter for the base. The Fellows or Circles of Timberwork, must be in length 4 dyametres 11/16 of the bore, whereof there must be 6 to make the whole circumference, and each of them one dyametre in breadth, and one in thickness: For the greater Pieces, they are to be shod with iron strakes, grasped and nailed with 2 or 3 Ranks of great head Nails, as in the figure 19 at β is represented.  
The Nave or head is to be in thickness 3 dyametres, and in length 3 and one half, armed with Circles or Hoops of Iron, and fastened with stays of Iron, that they stir not from their places, nor go round upon the Timber of the Nave. The spokes or Rays are to be in length 3 dyametres, namely so that being let into the Nave one half, and into the Fellows one half, there may be 2 dyametres discovered between the Nave and the Fellows. There must be 12 of these Spokes in each wheel, each one quarter of a dyametre square. The Axtree must be 1 dyametres 2/● in thickness. The Arms thereof shall be in the thickest place one dyametre, and at the ends thereof 2/3 of a dyametre in thickness. And at the place where it pierceth the Lymbers or sides of the Carriage, it must be 1 and a quarter in breadth, and 1 2/3 in height. As by the figure 19 β may appear, wherein also the places where the Mortis for the Transomes, Axis, and Trunions, are marked with A B C D E F.  
And for further explanation of that which hath been already said, I will here set down the particular proportions used therein for the whole Culvering, wherein the measures for the rest may the better be understood: First, for the Culvering, the Carriage shall be once and a half of the length of the Piece, so that if the Piece be 32 dyametres, the Carriage shall be 48 in length, and the Wheels 11 dyametres high. The Nave 4 high and 5 in length, the Spokes 4 besides the one half let in at each end. The Fellows two, and the Arming one. The Axis shall be in length 13 dyametres ⅓, and at the cutting of the Carriage therewith to be 2 in breadth, and 2 in thickness. The Limber Planks or sides of the Carriage must be 4 and a half, or 5 dyametres broad, one thick, at the Trunions 4, and at the Tail 2 and a half; the rest may be conceived in the former figure 19, made for the Cannon.  
Now to make the Carriage for the Demi-Cannon or Demy-Culuering, you may add to their former proportions 1/24, so that in stead of one dyametre let 25/24 be placed, which proportion should be constantly held in all the measures propounded.  
The like may be said for the Saker and Minion, in stead of one take 23/22, and for the Falcon for one take 7/6, and for the Base, etc. in stead of 1 take 10/●. And so these measures being necessarily added, may suffice, as well for gracefully show, as useful service.   

CHAP. LXI. Of the making of Candlesticks and Blinds, and of great Saussons and little Saussons, and little Saucigdes, and of the inventor and service of them first used at Ostend. For biding of Ordnance and men behind them, and to fill watered Dykes to approach a Breach.  
THe Candlesticks are made in the form described in the next figure 15 at y, and are of such height, as being clothed with Blinds, of Canvas, Sedge, or such like light things, they may behind them cover and hide those that work in the Trenches, o● labour in Batteries, having the one Point or Pyramid distant fr●● the other in such sort, that 2023 Saucidges, or more, or Bavins, or bundles o● Sedge, may be placed between them one by another, but of what wood i● shall be best, is not fit to appoint, seeing that if it be good, and sound, and light with all, to transport with them, ready clothed from place to place.  
These Candlesticks are very necessary to make Blinds of proof, as were seen at the Siege of Ostend in Buckuoy his Ramparts, where his double and great Saucedges were not alone able to cover the Fabric.  
They may also serve in overtures of Trenches, or in passing over Dykes, a● was practised at Rhinberg in the Spanish quarter. They being by experience found to be singular good, especially in miry places, in which reuesting them with Faggots, and setting them accordingly, men may pass by without any danger.   angles of cannon fire during the siege of Ostend 
Tract. 2. Cap. 2.  
ostend.  
S Carl  
S. Phdippe  
Comment it fault mowoir le saulsisson  
Wie die salfitzen fort zu bringen   constructing walls of tall grass 
Tract. 2. Cap. 1.—  
Blinds.  
Blinden.   spikes set into posts 
Chandeliers. Leuchter.  
Tract. 2. dial. 13.  
Comment pour plus grande asseurance des pieces se fait une double battery  
Wie zu mehrer verwahrung der stuck eine doppele batteria zumachen.   

CHAP. LXII. How to plant Pieces of Ordnance in secret Batteries, and in double Batteries, so that they may not easily be dismounted by Counter Battering.  
IF the Pieces appointed to make a Battery, be planted upon a platform that descendeth behind, that in their reverses they may go under the vawmure of the Tronier, the Troniers being vaulted, as in the Cassamattes at the 157, and 158 figures of Marlois is represented, they must by strength and by Tackles be brought up again above the vawmure of the Tronier, and the aim to be readily taken before the Tronier be opened, and fire given immediately after the instant of opening it: So will they in their Reverses be again got under the vawmute, and be free from dismounting, so long as the Furne mouth & Vawmure is able to keep from the ruin of Counter-batteris.  
There is also a means to save Pieces from being dismounted, namely by such double defences as are represented in the 22 figure β, with such Battlements or Loops as are there underneath represented, then only observing that they be of equal wideness, both before and next the Piece, and to make them equally deep enough, so as the right line that may discover the Enemy's Pieces, lie right through each Loope one, then 10 foot more backward or forward, make such another Battery: As the said figure will sufficiently demonstrate, so by those two several Loops the Pieces will be so surely defended and hidden, that the Enemy shall very hardly discover them, much less shoot so precisely, as to dismount them through both.   

CHAP. LXIII. How to plant Ordnance, whereas the Rampart is too shallow for their Reverse, and where earth is wanting.  
FOrasmuch as such necessities may often happen, it will not be amiss to show how to supply the same when need shall be: First, for each Piece take 6 Trees, high enough, strong, and strait; if 6 be not sufficient, take 9 or more for each Piece, which driven deep enough into the ground to hold them firm, and making each of them strong to carry their burdens with Braces, Ioyces and Planks, making thereon a Platform 20 foot long, and of sufficient breadth, that the Pieces may both be managed thereon, and also play and reverse freely, remembering that thereon a Piece will more reverse upon this being level, then upon a Platform that riseth behind, and will therefore without sufficient room and care, endanger the Piece by her falling from aloft to the ground.   

CHAP. LXIIII How to make a Battery with Pieces interred.  
THis manner of Battery hath long been used both in Italy and Hungaria, whereof the delineation following is a sufficient illustration, yet a word or two thereof: First, you may mark out as much place upon the side of some Hill or Mount near, and raised of sufficient height, as will suffice to receive your Ordnance, so that they may each stand 20 foot distant from one another. And then by the aid of Pioneers & other Workmen, make a Dyke deep 11 foot, defensible sufficiently, be it forwards, artificially, or naturally, by thickness from the bank or outside of the hill, to the inside thereof, and so broad, as that people may pass behind the Ordnance, when they have reversed. And when you have made Platforms, open Troniers or Loops through the earth of the side of the hill, so high, broad, and deep, as you would have them, which is a way so sure, that the Town walls cannot any way hinder you therein, especially if it be in a natural firm mould of Earth, if the blowing of the Pieces cause any of the earth within the Trunier to fall, a long Colerake will soon draw out the same, and you may also line it with Watlings.  
 cannons firing from a small earthen fort  

Tract. 2. dial. 15.  
●●me on far a 〈◊〉 battery de ●●qs de l'aine.  
Wie von will: sacken eine bat terie sol goe: matched werden.    

CHAP. LXV. How wanting all other means, to make a Battery by Woolsackes.  
WHere none other but gravely earth is to be had, thereto avoid the shottering, that the Enemy's Ordnance may make by the stones, to endanger the Camp, Woolsacks, may make the Shoulders and Troniers in such manner, as this figure 11 is represented. This is no new invention, for it hath long been used by diverse Nations: now it were necessary that these Sacks were 17 foot long, and 7 foot thick: And to resist the Cannon, there should be three in breadth to make the Shoulders or Parapets of the Troniers, and for the Demi-canon 2 and a half: And it is to be understood, that the two outmost of the three Sacks, must be somewhat shorter then that within, to give sufficient overture for the Troniers without, that the blowing of the Pieces endamage them not, upon the said overture 1 or 2 Woolsacks should also be laid to serve in place of Blinds, for the traversing and managing them the more safely: if by chance the Sacks do any where take fire, there must be water and earth ready to quench the same; and to fasten these Woolsacks, they must be Pyled with Pyles driven into ground, all firmly bound together. Also if other Ordnance then the Cannon or Demie, there must be as many more Sacks of Wool for shoulder defences, as that all the Pieces may be well covered: as the undermost of the 11 figure next manifesteth.   

CHAP. LXVI. How to place great Ordnance, both to dismount the Enemy's Artillery, as also how to make a Battery on the Curtin of the Place, and when.  
ALthough it hath been a received opinion, that such Pieces as do lie high on the walls, are in less danger, and have more advantage than such as are allow in the Champion plane, because those aloft may more easily discover those allow then the contrary. Yet it is found otherwise by experience, as in the 9 figure is seen, where the Pieces allow, playing always under the Pieces, aloft, do and may well embouch them, or else not fail to cloy their Platforms, or beat their Carriages Wheels and Axeltrees, and so consequently make them unserviceable, besides that if they take them underneath, they often dismount those aloft, whereas those aloft cannot dismount those allow, for if a Shott should light upon the upper part of the Mettle of a Piece lying under it, it will but glance away with little danger of dismounting, whereas if a Shott light under a Piece from allow, it either dangereth the dismounting thereof, or else the tearing of some part of her Carriage or Wheels.  
Now for that the charge of making Batteries is great, it requireth good husbandry should be therein used, and the cost not vainly spent, for thereby will accrue encouragement to the Enemy, and discouragement to the party. Besides, therein the Scyte and position of the place besieged, is to be well considered before it can be resolved, which is the best way, either to beleaguer or place the Battery thereunto: For a Place may be assaulted in one place, and yet battered in another, and sometimes the Batteries are to be made upon the point of the Bulwarks, and sometimes upon the Curtains, ever aiming at victory, the end of the enterprise undertaken. To batter a place well manned, as Forts and Castles, at the Bulwarks and Cavaleriaes' is best, being places of defence: But in a Town having cloyed their Cassamats and defences, the Curtin is fittest to be battered, because it requireth more entrenchment, and is of less force in the Terraplenes thereof. Grave and Tramont were battered upon the Bulwarks, and Cort and Cambray were battered upon the Curtains, and so each gotten, wherein the best opportunity, and way is to be taken, to obtain the design. And for battering a place upon the Curtin, 18 Pieces will be necessary, namely 8 Cannon, 6 Culuerings, and 4 Demy-Culuerings, placed as in the figure 9 at α is showed, wherein the 8 Cannon playing at right angles, they are to shake and batter, by reason of the weight of their Shot, the Culvering play traversly, and to cut out that which the Cannons have battered, and the Demy-Culuerings to play upon the Flankers and defences, as also to hinder the Sallies of the besieged, and discover and dismount their Ordnance. The distance that a Battery for either should be made, ought not to be above 120 paces, or 150 at the most, or at 80 or 90 paces if possible, the less the better, yea though it were at the edge of the Dyke, for the nearer they are, the greater are their forces: so as the Ordnance may be covert, that the Gunners and Matrosses' may be without danger of Musket shot, which is best at 80 or 100 paces if you may conveniently approach so near.  
Take this by the way into remembrance for a note: That a Cannon at 120 paces, will pierce a wall or Rampart meanly settled 15 or 16 foot, and being well settled only 10 or 12 foot, but in close sandy ground 20 or 24 foot deep. And that a Cannon may being well fortified, and duly and discreetly managed, be discharged 100 times in one day.  
Note also that a Cannon with one shot made well and orderly, will ruin more than 100 Hods of earth can repair: For one man can carry but 100 Hods of earth in an hour, the distance of 130 steps, or not much more.  
Further, you may note that 1000 Shott succiactly made out of 10 Cannons, will ruin more than 1500 Shot can do, being made out of 5 Cannon. And less can the Enemy repair the first, than the last: For a Cannon Shot made every eight part of an hour at 100 paces distance, will make as much ruin as 12 men, can keep in repair.  
Tract 2 Dial. 10.  
Comment il fault battre en 〈◊〉.  
Wie die Cortinen zu † beschiessen.  
Tract. 2. Dial: 8.  
Les pieces sont de plus grand effect celles qui sont logees en la campagne  
●●elles qui se tiennent plus hault aux murailles des villes et forteresses.  
●he stuck am starkesten die undone in feldt oder  
●oben auff der statt mauren stchon.  
But if 12 Cannons be well employed in a Battery together the 96 Shott, that they may make in one hour, will ruin fare more than 144 men can keep in repair.  
For 14 Cannons will ruin more than 12 and 16 more, than 14 spending, but the like quantity of Powder and Shot. Therefore Ramparts ought to be augmented in thickness, according to the Batteries made, but not in proportion, because the inner part of a Rampart suffereth not so much, nor is it so easily ruined, as the forepart thereof may be.   

CHAP. LXVII. How and when to make a Battery upon the point of a Bulwark, and of the defences to be made therein.  
WHen and where the Curtains are short and close, the Battery is to be made upon the point of the Bulwark and Cavaleriaes': But than it requireth as many or rather more Ordnance than before for the Battery of the Curtin was appointed. The 8 Cannon to beat about the point of the Bulwark, the six Culvering traversing more at right angles with the Front thereof, and the four or six Demy-culuerings to play upon the Cassamats, on each side 2 or 3, and they are also to attend other occasions that shall happen, as hath already been said, and as the figure 12 at α representeth together, with such retrenchments and defences, as the besieged may or should make, being forced, of which there is no danger when the Battery is made in the Curtin, wherein the Breach being once made, it may be more easily forced without any other dangers than those of the Bulwarks and Cassamats, which are not only fare off, but also to be cloyed or dismounted aforehand, or else they are opposed and encountered with the Demy-culuerings, and other Pieces placed on the brink of the Dyke, especially where necessity will urge, or occasion require, whereas in the Curtains there can hardly any such retrenchments be made, as in the Necks of Bulwarks, where with half Moons, in the neck thereof, they may make new resistances with a few men, the Bulwark being Myned, and the Town imagined to be gained, yea when fire shall be given to the Train, which may be perchance prevented also by countermines, which cannot be so directly directed on the breach of a Curtin, as on the Bulwark whose neck is narrow, and may soon be defended, and retrenched with less labour, time, and force, and cause the assay lants to present more men in danger of blowing them up by the Enemy's mines.   

CHAP. LXVIII. How the Ordnance are to be placed at the hour of joining of two Armies, to offend the Enemy most.  
THis is a point hard to be handled by me that have not seen many Armies meet; but finding several opinions delivered by others, I have thought fit to recite them, & deliver what to me seems most reasonable, leaving each to choose either of them, or any other way as to him shall seem most fitting. Some say that the Field Pieces should be placed in the Front of the Bands, and some that they should be placed traversly two and two, or three and three together, on the sides or flanks in the form of the Musketeers, covered with the wings of the Horsemen. But it seems to me most expedient, that certain Pieces should be placed in the Front, which may endamage the Enemy on all sides, seeking always the places of most advantage, without danger of losing any of their Ordnance, and certain Pieces also to be placed in the Flank, some to shoot forthright, and some a Travers, each 3, from other distance 50 or 100 paces. And then there is no more danger but in the joining to withdraw the Ordnance, that our Ordnance hurt not our own bands. And that they be always ready to be Traversed, and retreated, as need shall require, which may much conduce to victory: But it will seldom happen, that in a Battle there be such places so commodious to be found as were to be wished, for that most commonly we shall be constrained to conform ourselves, according to the present occasions, as woods, hills, and other uneven places, for which no other rule can begiven, but with great judgement to seek how to get the advantage of the Enemy, without being offended by Sun, wind, or dust, and such like, which though they may be thought to be small things, yet they will be therein found to be of great importance. But I cannot be of their opinion to have all the Pieces on the sides to be best, for so the Squadrons meeting, ours shall be more offended thereby then the Enemies, besides, that thereby this great danger will arise, that when the wings of our Horsemen would be willing to advance speedily, they will be greatly troubled with those Pieces so shot out of the sides: wherefore the General, or Master of the Ordnance, or his Lieutenant, considering these things, must give directions how the Ordnance shall be lodged, either all in Front, all in Flank, or some in both.  
 cannons exchanging fire across a battlefield 
Tract. 2.  
Comment il fault loger l'artillery au point du Combat.  
Wie das geschutz in der schlacht zustellen.  
Dial. 5.    

CHAP. LXIX. How to fill up a wet Dyke, whereby to approach the Breach made.  
Having already showed how a Battery may in diverse sorts be made, and also how to make the Breaches sufficient for entry, we will now show likewise, if the Dyke should be deep, and full of water or mud (that the Soldiers are thereby hindered) how the same may best be filled up. Wherefore, although there be many ways to perform the same, yet this in my judgement is the best; namely, that when a sufficient Breach is once made, that then the Approaches be also immediately made under the covertures of the Trenches, even unto the edge of the Dyke, and then with Faggots, and earth, or Sausages, (whereof we have sufficiently spoken already) to fill it up, having the benefit of the ruins that the Cannons have made of the Wall, and Faggots, and Sausages which cannot be wanting, whereas either Gardens, Trees, or Woods are near hand. Or else if great Trees be thrown into the Dyke, if they swim, being of Fir or dry light would they will, than Planks laid upon them (the Dyke being excessive deep) and on each side of such Floats, blinds being raised to hide the Passengers from sight of the Flanker, they may thereby pass to the foot of the Breach, even as by a Bridge: But over a small River or narrow Dyke a Bridge may be made over upon a Boats, as in the 17 figure at β is represented. But being first well informed of the quality of the Dyke, whether it be of standing or running water: If it be standing water, than a dozen of light Float Bridges will help well; if there be any scarpe on the other side, or else they are worth nothing: But in stead of them Floats being made with two Fir poles or light wood straight about 15 or 20 foot long, about the thickness of a man's leg or thigh, upon which two sides may be nailed crossewise ledges or boards of wood, about 3 foot long all along upon them. And so these may each of them be carried by 6 men; namely 4 at the two ends, and 2 at the mid sides, as a corpse is usually borne to be buried. And at both the ends of those two sides, there must ropes be fastened, by which hese floating bridges shall be launched, and drawn from one side of the Dyke to the other, four or six Soldiers being gotten upon it, resting them upon their Pikes, which being landed and passed over: the Soldiers on the other side may draw, bake the Float by the ropes at the end next them, and then 4 or six more may get upon the same, and the Soldiers already landed, may draw them over by the ropes at their end, and so helping one another from side to side, many men in a little space of time will be transported over. And when as there are a competent number gotten, or the Floats drawn up, may serve for scaling Ladders, or to mount the Breach the better by. But if for the walls these Ladders or Floats be too short, there may at one end of each side be two loops of Iron fastened, and so firmly fitted, that the two other ends of another Float or Ladder may fitly enter thereinto, and so two or more shall make one Ladder, until they be found of sufficient length. And lastly, we will remember you of Ladders, of Cords, or Ropes, with wooden steps like entering Poop Ladders in Ships, having an iron Grapnell to throw over the wall, to hold fast on the Vawnure or Paraper.   

CHAP. LXX. Of the Gunner's service in general.  
NOw forasmuch as Ordnance are Engines of force, reason, weight, and measure: and the Gunner's men exercised and experienced in them, and their apurtenances in making plat forms, with defences, Troniers, Gabbions, Loops, Parapets of earth, and Faggots about 23 or 24 foot high of Faggots 2 foot high of earth, bed upon bed unto eleven foot high, and after 3 foot of Terraplene, to raise the Troniers and Loops, so that for the Cannon it be 3 foot wide in the Barb within, and 12 foot wide without, the lower part thereof to descend scarpwise, the better to discover the Enemy's avenewes, and offend them the more freely, for avoiding the blast, and smoke, and ruin, it would else make: For the Culuerings 2 foot and a half within, and 9 foot without will suffice; and for less Pieces, less measures. If the Battery be to be made with Gabbions', they being filled with earth without stones, moistened and rammed 7 foot a piece in dyametre, 3 ranks between each 2 pieces, if the place will permit, or 2 at the least, and 3 rows also one before another, setting one between two; so if the first rank have 3, the second will have 2, and the third one: But it will be hard to make a safe Battery with Gabbions', Cannon, or Culvering proof: And each platform is to have 30 foot for the reverse of the Cannon, and 27 foot for the Demi-canon, he ought to see that it be leveled, or rising 1 foot for 20 backwards, the better to stay the reverse & facillite, the bringing the Piece being loaded to the Loope: He ought to search and examine the goodness of the Pieces, their Ladles, Rammers, Sponges, and Tampions, fitness, and roundness of the Shot, force and goodness of the Powder and Match: And to see all fitted accordingly, and to place the Powder covertly, hide safe from the fire of his own, as also of the Enemy's Ordnance. To see the Gunners take their marks towards the under part, giving each under Gunner his charge.  
In Platforms, the first plank next the Barb should be 9 foot long: the second 9 and a half; the third 10, etc. every plank increasing half a foot, to spread for the Reverse, as may be seen at the first figure at β.   

CHAP. LXXI. Of the differences of our English measures in Feet and Inches, from the Measures of other Nations. And also of the difference of pounds and hundreds.  
ALmost all Countries agree in this, that 12 inches make a foot, but the length of their several inches do commonly so much differ from one another, as whatsoever they speak or write of Measures in feet and inches, must not without reducement be understood, to agree with our English foot and inch of Assize, as the discourse and Table following will make plain, whereby it will appear how little Foreign translations, without diligent and exact reduction, when they discourse of paces, yards, feet, inches, or other measures, writ they never so well and truly of their own, can avail us.  
For three inches at Vienna is 3 and ●/10 of our English inches.  
And 3 inches at Venice containeth 3 ●/10 of English inches.  
Two Grecian inches is 3 English, they having 8 inches in our foot, so their foot is equal with the English foot of Assize.  
The foot in Bavaria wanteth 4/5 of our inch of the English foot.  
The foot of Antwerp is 6/10 of our inch, shorter than the English foot.  
The foot of Ferrara is 15 9/10 of our English inches.  
The French foot de Roy is one foot and 4/10 of an inch English.  
The Tuscan Brace is 23 English inches.  
The Florentine Brace is 22 and a half of English inches.  
The Bressian Brace is 17 4/10 of English inches.  
The Can of Naples make 20 English inches.  
The Can of Rome make 22 English inches.  
The Milan Brace make 23 English inches.  
The Loraigne foot is 11 ⅖ of our English inches.  
Whereby each man may judge how much confusion would have grown to the Reader, that should have read a French, Italian, German, or Spanish Author, and had no means to understand, that there were any difference in length of the Measures of one same name. And the like may be said of the weights used of several Nations, which with the former of Measures, would not only have a double error, dangerous for practise, but also confounded the Readers that suspected no such thing.  
The pound Troy being about 1 ounce and a half lighter than the pound Auerdepoyze, yet the ounce Troy being heavier than the ounce Auerdepoyze, because Troy hath but 12 ounces, whereas Auerdepoyze hath 16 ounces in the pound. The Kintall of Biscay 150 l. is but 124 l. English. And the great Kintall of Portugal 128 l. English, the lesser Kintall is 112 l. English.  
The hundred subtle or small hundred, is 100 l.  
The great hundred is 112 l.  
One pound Troy weight is 13 ounces 4 d. weight, 19 gr. ½, of a grain of the Haverdepoyze weight. By these are all their Ordnance and Munition weighed. But in several Countries they differ, as you may see in M. Records book of Arithmetic, called I be Ground of Arts, whereby the Reader may judge how necessary these differences are to be known, and that reduction should be duly made lest confusion follow.   

CHAP. LXXII. Of the making of Salpeter, whether it be Naturallor Artificial.  
SAlpetre is a body of Air, transformed into Earth, apt by Moisture to be dissolved, and by Fire to be resolved unto his first state Air, being an Airy substance, fixed in dry Earth, dissolved by Water, and concocted by Heat into a solid substance, and accepted the rich Mine of Princes in this Warlike Age, and by Philosophers accounted a quintessence of Qualities, participating of all, and yet simply no one of them: For being sharp and salt, in Taste hot and dry, it enjoyeth the quality of Fire, and being also hot and moist, easily dissolved into Water, and by fire tesolued into Air, appeareth to be Air itself: And being white and clear cooleth warm Wine in hot weather, being dissolved, and a vessel therewith put therein, it approacheth near Water, cold and moist: And being, it will bruise, and be brought, or be melted into a hard stone: it is also cold and dry of the quality of the Earth, enjoying all the qualities, and a convertible to all the Elements. It so becometh as they say a quinta essentia. Salpetre is of two sorts namely, Artificial and Natural. The Natural Salpetre is that which groweth in continued mines of the Earth, or upon Rocks, or in Vaults, on Walls, and by Nature's work becometh perfect Salpetre, whereof the store is to small too depend upon. The Artificial Salpetre (though naturally growing) also requireth the help of Art to bring it into true and perfect Petre, and is found in so many places, as in Loame-Floores, Mud-walls, Sellers, Dove coats, Stales, Sta les, and such like places, whereas the rain cannot come to dissolve, nor the Sun to dissolve the Air, substance, fixing and growing therein, that with labour and industry with Arts help, to cause abundant procreation, sufficient store may be provided, and Artificially made thereby in this manner. First, for choice of the Earth for finding, it whether sufficient quantity of Petre be therein or not, observe this, Pair the Floores, and dig 3 or 4 inches deep therein: if you find the Earth full of white and yellow specks, and that having put a little thereof upon the top of your tongue: if it yield an Airy biting, or sharp tindge thereon, the Earth is good, and will be rich, and yield store, according to the more biting or tindging taste thereof. Then dig that Floor so deep, as you find the Earth to be good, which in some places will be a yard, and in others not a foot deep, under the upper Floor make the Earth somewhat small. And put it into half Tubs lose, having a Taphole in the bottom of each, which stop with a staff and cover, with a wisp, that the Earth run not out, when the liquor draineth. Then fill the said half Tubs with water a handful higher than the Earth, and so let it stand in soak 24 hours, and then draw out the staff or peg a little, that the water may drop and drain out thereby into another half Tub that must be set under it of purpose to receive the liquor, which Liquor keep, and lay the Earth upon the Floor, which in six or seven years will again breed as much more Petre therein, and in some floors, especially with help, in fare less space. When you have collected a sufficient quantity of such Salpetre liquor (unless you have Mother liquor) you must of some of it make the Mothers thus, boil your Salpetre liquor in a Cauldron, and scum it (which scum reserve) until the liquor being proved with a knife, be found ready to congeal; then take off, or else put 8 or 9 times as much Salpetre liquor thereunto, and having made the scum rise, and taken it off, and reserve it, let it boil a fret, until the liquor be again able to congeal: which if it prove too tender, it is a sign it is no boiled enough; and if it be too hard, then that it is burnt too much, and must for the first be more boiled, and for the latter recovered with more Salpetre liquor, and renew the Work: but being found indifferently between both, take it from the fire, and put it into half Tubs, wherein good wood ashes are placed upon a laying of Straw upon faggot stick, or Laths in the bottom thereof, and let the liquor drain through the same, and put it into coolers, or brass shallow pans to congeal, and let it stand in a cool room, where in two or 3 days it will shoot out like ye sickles, and keep that for Roch Petre, and the liquor that will not congeal, keep for Mothers, to work a new for more as before. And this is the order to make Artificial Salpetre: And the scum that rose in the boiling mixed with water, and sprinkled upon Floores, will exceedingly procreate Salpetre in short time.  
To collect Salpetre that naturally breeds on Walls, on Caves, in t e Ground, or in Vaults. GAther the Petre together, and add thereto ¼ of quick Lyme and ashes, and put them into a half Tub with a hole, to drain out water, then put in warmed water, and let it so stand, until the Petre be dissolved; then let it drain out at the hole by little and little, and filter it if need be, if it come not clear enough: and then boil it until it will congeal as aforesaid.  
To Refine Salpette wet. TAke what quantity of Salpetre you please, and put the same into a clean Cauldron and put thereto a little fair water, and boil them together until it raise the scum, which take off and keep, and let it congeal and shoot in coolers, as at first it did, and what remains, boil again with more clear water until it congeal.  
To know if Salpetre be well refined. TAke of it, lay it on a board, and put a coal to it, if it raise an Azure scum, it is yet greasy; if it leave pearls, it is yet earthy: But if it burn into the board, and leave nothing but a black colour, and rise with a long flamed ventosity and exhalation, it is well refined.  
Of Gunpowder, and to make the usual sorts thereof. FOrasmuch as Powder is the Base and foundation of all Fire-Engins, therefore I will show his preparations. There are ordinarily three sorts of Powder made, whereof one serves for Birding and Fowling, which is quickest, being 7 or 8 of Petre, for one of coal and of Brimstone: The second for Muskets and Pistols, called fine Powder, which is 5 or 6 of Petre for one of Coal and one of Brimstone. The third, called Ordnance Powder, is of 4 or 5 of Petre for one of Coal and sulphur: But for service, there is but two namely, Ordnance Powder, and fine Powder. There are infinite receipts for making of Powder, but most States have enjoined a certain proportion amongst themselves, although much different one from another: wherefore no certainty can be herein generally concluded, but every man must practise for his experience: only a word or two I will say thereof, namely, that before the Receipt assigned be compounded, it is requisite for making of good Powder, to refine the Petre, to purge the Sulphur, and to choose good coals, made either of Hazle, Alder, Willow, or Birch, Wood without Bark or knots therein being well burned. And then to work those three Materials well together: for therein consisteth a greater difference of force, by the difference in working of them, than is credible without experience. It is to be wrought together by a Horsemill, or Water-Mill, or in a Mortar with Pestles, the Materials kept moist.  
The Compositions of Cornepowder. Five pound of Salpetre, one pound of Coals, and one pound of Brimstone, five pound of Salpetre very well refined, as afore is showed, 1 l. of Willow, or Alder Coals well burned, and of Sulphur well purged 12 ounces: Or of six l. of Salpetre, Sulphur and Coal of each one l. Or of Salpetre 7 l. Sulphur prepared with Quicksilver as we have also showed before: Or Floores of Sulphur one pound, & coals of Hazle half a l. Or if you mingle as much quick Lime in powder as Sulphur, you shall make powder that the moisture shall not impeach taking of fire. Now seeing that it will be to little purpose to show the Compositions, unless we also show the manner of making thereof, which though the varieties both in composing and making are many, tending all to one same end, we will therefore show one reasonable way for small quantity. First, put your Composition into a brazen Mortar, or of wood with a brass bottom. And take also a brass pestle, and beat it so well together for the space of six, seven, or eight hours, that in cutting the same with a knife, there can none of the Materials be discerned a part, but all well incorporated into one body, always moistening the same with a little clear water, strong Vinegar, or Aquavitae, so much that the coals dust not, and so little, that the composition in working become not passed. But if you would have your powder very subtle, moisten the same with the distilled water of the outer rynes of Oranges, and let your sulphur be clear Sulphur vine which in the melting had ¼ of Quicksilver put therein, and incorporated, finely beaten, and searsed with coals, quenched with clear water, wherein quickly me hath been slaked, and either let it stand to clear, or else be filtered: and this moistening will make the corns thereof become hard, and not yield to moisture suddenly. After the composition is thus well beaten and wrought together (the more the better) take a Syve with a Velome, or Parchment, or Leather bottom, made full of holes, of the bigness you desire your corns, and put the Receipt or composition therein, with 2 or 3 short Rulers, a little moistening it, that the pousier or dust thereof fly not away. And sifting them upon a long Rowler, over a half Tub, so will the short Rulers driving the composition through the holes, make the corns come out round yet of several 'sizes, which to bring to have all the corns of one bigness, you must pass through several sives, as they use to size Hayleshott: So shall your Corns of every size be equal. And look what in searcing and dusting rests uncorned, must be separated from the rest, and new moistened and beaten, and then again sifted as before; whereof some dust called Ponsier, will still remain uncorned, which may serve excellent well to make Rockets with. And these corns may be dried in the Sun, or in a warm place, safe from fire. The powder being dried must be dusted again to separate the Pousier from the corns. And to the end the powder become not moist, it should be kept also in a dry warm place, Moisture and Age being both enemies to powder: Moisture, by making the Petre descend, or else vapour, whereby one end of a barrel of powder that hath stood long, will be better than the other, and Age by breaking the proportion and incorporating by the Petres growing and increase, and by the coals corrupting together, with the Sulphers decaying by age in quickness to take fire. And so both through moisture and also by Age powder will decay. Next it must be considered whether it be moist or dry, or wholly, or but in part decayed, and so accordingly to use reason, with diligence to renew the same.  
Several ways to know if Powder be decayed or no, whether by moisture or age, and are decayed in part. IT is the real practic part of a Gunner, to know his powder, and whether it be decayed or not, by mutation or corruption. And there are especially three ready ways to find the same. The first, is by the sight; the second, by the feeling: and the third and surest is by firing it. By sight if it be not black and dark, but bright, and inclining to a tawny bluish colour. By feeling grasping it in the fist, if it run through the fingers quickly, and avoideth the handling, and cling not together. By fire, if fired it rise quick, and spread in a moment, smoke little, but riseth in a clear flash, unto which add further, if it leave no feces but carry all away, the powder is good, or else the contrary is to be judged.  
To revive or renew powder, which is in part thereof. OFten times in Forts, but usually at Sea, powder cannot be kept so fare from humid vapours, but that it decayeth the same, and maketh it of little, and sometimes of no use without renewing it. And sometimes it may decay by age as we have said. Let therefore the Gunner first prove the powder by fire, and if it make a flame with a long tail, that is, if it sleep in its burning more or less, then for every 100 l. aside 4 l. or 6 l. as need requires of refined Salpetre thereunto, mixing them well together, and put them to be beat and wrought by the space of 3 hours together, and then moisting, corning, and drying the same as aforesaid, proving it in meal dried, how it will rise by firing: and so doing, the powder may be made serviceable, if the coal be not corrupted.  
Another proof of powder to be renewed, decayed in part. TAke a pint, or quart, or any other measure of good powder prooned and dried well: Then take of decayed powder well dried the like measure, and weigh them both, and look how much the equal measure of good powder weighed more than the decayed powder, add so much Salpetre refined, as the difference of their weights was unto every time, so much of the decayed powder, and moisten, beat corn, and dry it aforesaid, and it may being proved, be found serviceable and good powder: for the Salpetre only wasteth by dissolution, which neither the coal nor brimstone doth, wherefore by the rule of 3, you may find how much Petre any assigned quantity of decayed powder, will require to renew the same.  
To renew powder totally decayed. But if the powder be wholly decayed, lay a Raysin frail or Matt in a bottom topped, bucking Tubb upon Faggots or Lath, set on edge, to keep the Matt from the bottom, and put in straw, laid crossewise, upon which power the decayed powder, then warm water and put thereon, and let it stand and soak 10 or 12 hours, that all the Salpetre may be assuredly dissolved, then let out the liquor at the bottom top, which filter and congeal into Petre, and add thereto a due proportion of coals and Sulphur, and make it into powder as is formerly taught: For the coals and Sulphur dissolving, will remain behind in the Straw, Frail, or Matt: Or else if you put the decayed powder in a bag, and boil, or soak it in warm water, the Petre will soak out, but some will be soaked into the cloth of the bag, and with more labour must be soaked out.  
Another manner to renew powder without new making it. TAke 3 l. of the decayed powder, and divide it into 3 equal parts, which spread thin upon 3 Tables or smooth boards. Then dissolve one ounce of refined Salpetre in a little warm water by itself, and with a hair over-sprinkle it upon one of the third parts. Likewise dissolve 2 z, and sprinkle it upon one other of the third parts. And lastly, so dissolve 3 ounces of Salpetre, and sprinkle upon the third part of the 3 l. of decayed powder. Then dry the said 3 parts or pounds of powder severally, and prove by fire whether there that which had 1 z, or that which had 3 z. of Salpetre sprinkled upon it is best, you may thereby know how much Salpetre will renew all the whole quantity of decayed powder in the same manner, without new making the same.  
To make powder that shall not decay with time. TAke what quantity of powder you will, and mix it well with Aquavitae, and make it up in Balls, and dry them well in the Sun, or in a warm place, and keep them in an earthen pot well glazed, until you have cause to use them. Cateneo saith, this powder will neither decay, nor waste by age.   

CHAP. LXXIII. Of the making of ordinary and extraordinary Matches, to give fire with unto Ordnance, or Artificial Fireworks, and such like.  
TAke Ropes made of Tow, about the bigness of a Man's little finger, being twisted loosely, and Taw and beat them with a Mallet upon a stone, till they be soft and opening: Then put them into a Cauldron full of strong Lee, made with ashes and quick Lyme, wherein also a quantity of Salpetre or Mother's being put, and when they have boiled well ⅔ of the liquor of the Lee consumed. Then draw out the Match, and twist it harder while it is moist, and afterward dry it upon Lynes, but first draw them through a hole, as Wire-drawers do their Wire to make it even.  
To make extraordinary Match of Cotton, Yarn made Bobbinwise, of a finger thickness. TAke as many threads of gross Cotton yarn, that hath not taken Salt-water by transportation or other ill Accident, and work them Bobbinwise of a competent bigness, and boil them in Salpetre-water, and squeeze them, and roll them on a Table, whereon Mealed-Petre, and Sulphur is spread, then draw them through the palm of your hand, and then dry them well.  
To make Match that will resist fire and water. TAke Salpetre refined one part Sulphur part, and put them into a Pot with ½ part of Camphor mealed with the Sulphur, and one part of fine mealed quick Lyme, with so much Lynseed oil, oil of Petre, a little Varnish liquid, to temper them well together. Then take of Cotton bobbin Match as big as your little finger, and put it into the mixture to soak over a sire, until it be well imbybed, and have soaked up the liquor. Then take the Feces or remainder, and put them in the palm of your left hand, and with your right draw the Match through it twice or thrice, clasping close your fist, that the Match may receive the substance of it thereinto. Then dry it upon a line, and keep it for special uses, for Vaults, mines, and moist weather.  
To make a very violent Match. TAke two ounces of Powder, 4 z. of Petre, two ounces of Aqua vitae, dissolve them over fire, and put in your Cotton Match, to soak it up: if you imbibe the Ficelles for your Rockets therein, it will be very proper, you may roll and rub them in Meal Powder upon a Table, dry them and keep them in a dry place, which let suffice at this time.   decorative endpiece   

OF ARTIFICIAL FIRE WORKS FOR Triumph and Service.  
ALthough Gunpowder with the soul Petre, and the life Sulphur, and the body thereof Coale, be indeed, the chief bases and foundations upon which the practice of Artillery, and making of all artificial Fireworks, either for service in the Wars, or for Triumph after Victory, or for delight and pleasure dependeth, whereof we have already spoken sufficiently: yet Fire being the primary cause for performing their sequent effects, we will first briefly define what Fire is, and then show who were the inventors of it, according as Antiquity hath diversely left us their Testimony. Fire is an element hot and dry, the most rare light and piercing, either detained here below by Art, or constrained by Accident: It engenders and feeds upon that, which by Nature it always affecteth and it striveth to get aloft, as unto the natural place and repose thereof, as our first Theorem plainly manifesteth.  
The Poets feigned, that Promethius first stole the Fire from Heaven: But Vitrwius saith, it was accidently found, and happened by the violent agitation of the Winds and Tempest, among the Arms and Branches of Trees, robustly rubbing one against another, which made them kindle fire & burn. Plynie said, that it was found by Soldiers, because they usually give violent strokes upon solid things, oft times striking sparks of fire. Lucretius said, it was engendered from the lightning, and that Vulcan the King of Egypt, was the first that perceived that fire to make use of it amongst humane creatures, wherefore the making of Jove's Thunderbolts was attributed to him. And Orpheus making little or no distinction between Vulcan and fire, in his Hymn singeth.  
Brave valtant Vulcan's living flames on earth remain as yet,  
Where in bright shining fiery Robes his Majesty doth sit, etc.  
Fire being also a thing necessary for man's life, consisting of heat and humidity, simbolizeth generation so nearly, that sage Antiquity therefore feign the marriage between Vulcan and Venus, and attibute the carriage of Nuptial Torches unto him, at such times as the Lovers would embrace each other. Many more were the ancient fictions & opinions concerning this element of fire: but those I leave for brevity's sake, concluding it as I begun, Fire to be a more rare, subtle, and light element of Nature; then the air which is but his Nurse, seeing that if air become compact, and fixed in a strait place, and fire chance to burn such an Airy body, that would either eat or drink, or consume it, and thereby leave the place void, which nature abhorreth, as appeareth by our 4 or 5 Theorems, or else that rarifieth and increaseth the body thereof by the third and 6 Theorem, and so 2 bodies should be in one place contrary to the 7 Theorem hereof; which let suffice, and so I will proceed to the matter, for contriving and composing of some Fireworks, both for Service and Triumph, and conclude this Treatise for this time.  

Of Rockets and their structures.   several rockets 
Tract. 3. cap. 26. fig. 5.  
So then the Rocket N will be 10 Calibres, 9 for the powder, and 1 for the bindings above, & the bond and fucill below. And the Pearcer O must be at least ½ of the length of the Rocket, whereof by the figure you may see both the form and proportion. And also although some would have a pin reach so high from the breech of the Rocket, and of the Drifts fitted with a hollowness to receive it in the driving: yet that fashion being very uncertain and requiring much skill, handiness, and practised experience, to bring it to rise well, I have rather left it to be pierced after the driving.  
For the Receipts, they must be according to their grandures, & to be filled by a little and a little at once, and giving 4 or 5 strokes upon the Drift with a weighty Mallet, continuing so until it be full within a finger or two breadth of the top, and it must be made of strong paper or parchment well rolled about the Former, or else it will be worth nothing, and besides, if it be not also well pierced and prymed, it will never rise well. If the Receipt for small Rockets should be filled into great, the mixture would be too violent, for that experience teacheth that, fire being given to a composition in a large amplitude, and burning a great quantity, in a little space it holdeth not proportion with the little. For the Rockets of one or two ounces of Receipt, 
For one or 2 ounces Rockets.  they may be of the composition following. Either take fine or Harquebus powder one pound, and soft wood coals two ounces: or one pound of fine powder, and another pound of Cannon powder: or take one pound of fine powder, and an ounce ½ of Salpetre, and 1 z. and a half of coal.  
For Rockets of 4 z, and for Serpents in quills take 4 l. of powder, 
For 3 or 4 z. Rocket, and for Serpents.  1 l. of Salpetre, and 4 z of coals, and sometimes ½ ounces of Sulphur may be added thereunto: or take powder 1 l. 2 ounces, and ⅓ l. of Salpetre, 4 ounces and ½ of coals: or experienced, take powder 1 l, Salpetre 4 ounces, and 1 ounce of coals.  
For 6 ounces take 2 l. 5 ounces of powder, Salpetre ½ l, Coals 6 ounces, 
For 6 ounces Rockets. For 8 ounces Rockets or 10 Rockets.  Sulphur and Limmell of Iron of each 2 ounces.  
Take for 8 ounces 16 ounces of powder, 4 ounces of Salpetre, and 3 ounces of Sulphur, with 1 ounce of Coal.  
Take 2 pound of powder, 
For 1 l. Rockets.  5 ounces of Salpetre, 5 ounces of Coals, Sulphur and scales of Iron of each 3 ounces: Or take 1 pound of powder, 3 ounces of Coals, and 1 ounce of Sulphur.  
Take Salpetre 12 ounces, 
For 2 l Rockets.  powder 20 ounces soft, wood Coals 3 ounces, Scales of iron 2 ounces, and Sulphur 1 ounce.  
Take Salpetre 30 ounces, 
For 3 l. Rockets.  Coals 11 ounces, Sulphur 7 ounces ½.  
Take 30 l. of Salpetre, 10 l. of Coals, 4 l. ⅓ of Sulphur.  
Take 8 l. of Salpetre, 
For 4, 5, 6, or 7 l. Rockets.  2 l. of Coals and 12 ounces, Sulphur 1 l. ¼.  
For in the great Rockets you must put no powder, for the reasons aforementioned, 
For 8, 9, and 10 l. Rockets.  as also for that powder having been long time mealed and dry, it fortifieth itself, and groweth too violent. But if you will at every third or 4 driving, dip the end of your Drift in oil, of Petre or Linseed oil boiled to the height to sealed a feather, you may keep such Rockets long good. The great Rockets are to be made of the weaker or slower Receipts. And the simples must be well beaten and sifted in a Searce, and well wrought together to incorporate.  
After the Rocket is filled within two fingers breadth of the top, 
For Breaks.  you may fold 5 or 6 double paper, and pierce it through, and make a Pettard or Breaker therein of an empty Walnut shell or 2 filled with powder, or a coffined Cap rather of tinned iron Plate, which will give the better report, & pierce the Air swifter, in which you may else put in 2 or 3 Star made of Cotton bombast, put in Aquavitae wherein Camphor hath been dissolved, and sprinkled over with Sulphur Vive. 
For Flyers.  The Rocket being thus made, you must bind unto it a Rod that must equibalance it, if it be placed upon your Thumb 2 or 3 dyametres from the Rocket, and it should be 6 7, or 8 times the length of the Rocket, and strait, to con the Rocket as right through the Air as may be: And ever remember to prove some of your Rockets before you go to perform any show, and also at the first making that if the Receipt be too strong or too quick, it may be in time slowed with Oil or Coal: if to slow, with powder or Petre, quickened according to the rising, burning, and arch it maketh.  
Those Rockets that run on lines also, 
For Runners  aught to be very carefully made, whether they are to double, or single, or those that carry Dragons, Men, Ships, or other shapes in Motion, lest they shame their Master. The line must therefore be fine, even, and strong, and being anointed with soft Soap, it will be slippery, and not easily take fire. And these as well as those that turn wheels, may have a further addition of Roch Petre in their receipt, to add pleasure and life to the Aspect, which let suffice for Rockets.   various fireworks 
Tract. 3. cap. 27.   various fireworks 
Tract. 3. cap. 29.   

CHAP. LXXIIII. The Description of certain Wheels of Artificial Fireworks, and of their Structures and Compositions.  
Having already spoken of Rockets sufficiently, we will next speak of Fire-Wheeles, which were wont to be the chief inventions used at Feasts and Triumphs for pleasure, and which by their Motions yield great contentment to the spectators, as they were anciently used. But now of late by joining many Tires between the Rockets that burn, and are moved with variety, the pleasure is much increased. The Works may be framed both for vertical, and also for horizontal Movers, either upon great woollen spinning Wheels, Coach Wheels, or other Wheels, made of purpose easy to run round, and the greater the better show, and must have the Perch or Axis whereon they are to turn, fitted unto the bore of the Nave, which Perch and Wheel should be anointed or revested with some incombustible oil, ointment, or coating, to guard it from firing, which would confound the aspect intended in the 2 figure α following: the first at A is to move Horizontally upon his Perch. The second wheel B moveth vertically upon an Axis, proceeding out of the side of his Perch, their other Structures and Compositions may be both alike, or varied at the Worke-Masters pleasure, only that if the Axis of the second were of iron polished, and fitted to the Nave, it would be surer from breaking and burning, either of which chances would much disgrace the Fire-Master. To Arm them, furnish them with as many Rockets fast bound, and between them as many Tires of coloured Fires, Serpents, breakers, or showers of Gold, as you shall think with time between them fitted, that the Wheel may move from the ending of every Rocket, until the beginning of the next, with a Sulphur Match between them. And when you have done so, cover them over with painted papers, although they be represented naked for the Readers better apprehension. Now to make a Wheel or Vessel that shall move Horizontally, and have standing Fire-Lanterns move round, and flying Rockets mount up into the Air. The forms of the Lantern, and all the rest may well be conceived by the same figures at C, which for the in-workes, may be also covered with painted paper, as well to hide as grace the Aspect by daylight, before it come to be fired.   

CHAP. LXXV. How to make a Rice, and a Castle, and a Trunk of Artificial Fireworks, of great delight.  
THe frame A is like unto Ryces that skeins of silk are usual wound, and is a pleasing invention, being environed with Bandrolls of Rockets, with a continued rank: But yet the half of them being turned with their heads the contrary way, when the other half have spent themselves: Then by a secret Match on purpose they are fired, and suddenly the motion will be made contrary to the former, the last of the first half being spent, it giving Fire to the first of the latter half, which immediately workketh its effect.  
The Frame B is a Castle with 4 Towers and 4 Curtains, and a Cavalariae or domineering Turret in the midst: The structure thereof is with a thick plank or two, joined well together of the bigness of the plane or foundation of the bottom of the Castle, making a great hole in the midst into, with the top of the Perch, which beareth all the Frame is to enter. The Towers are to be turned of good and strong Timber, about which a number of auger holes, and gutters, are to be made to put to Breakers and Pettards, and to carry Trains between, to fire the Work in order, in the midst of each Tower a slow Match is first fired aloft, or an earthen pipe filled with sure and slow receipt, one Tower receiving fire from another until all be spent. The Curtains also giving several rounds of Cane Cannons, which being well Armed and loaded, will yield a good report: there may be placed Runners that shall fire each other, and pass from Tower to Tower, and Flyers, whose Rods may be let down through the Planks, the Roofs of the Towers shall have Turrets arched, and Vanes upon them, with flag and flagge-staffe.  
The figures C and D is form as Cilinder Granado made of turned Timber, as big as you will with a hollow Concave Cillinder in the midst from end to end: That a Match or slow receipt may orderly fire the Rockets and Cannons entered into the hole. And if you would issue a quantity of Flyers aloft, at once to spread and fly every way, place them declining somewhat that way you would have each fly when fire shall be given: So shall you with a small care and handiness give great variety of content to the spectators to your commendations.   various fireworks 
Tract. 3. cap. 19 et 20. ct 2 i ct 25.   various fireworks 

Tract. 3. Cap. 28.   

Tract. 3. Cap. 30.    

CHAP. LXXVII. How to make flying Dragons and Rockets that will run upon a Line and return again, and of Nocturnal Combats in Fireworks.  
THe burning flying Dragon is somewhat busy in the contriving Structure and Compositions thereof, and he must be his Artsmaster that can perform the same well: Although perfection be not required therein, we will show the easiest manner of Framing and Arming them, and putting them in practice, furnishing each of them with one or two Main Rocket of a pound or two of Receipt for that grandeur as aforesaid, according to the way and weight thereof, which must passethrough the bore threof, having a sparkling starry flaming Receipt to burn in the Dragons' mouth, that being fired when the vent at the Tail is fired may make the Dragon seem to breath Fire forwards, and void Fire backwards also: The body thereof being all over furnished with ordetly Tires of Breakers that at last shall break and consume all the body thereof, which being framed with Ribs of dry light wood, or Whale bone, or Crooked Lane Plates, and covered either with Paper or Muscovie Glass, coloured like to a Dragon, may so represent that creature in shape: these are to have either a void Cane, or else certain swiules for a line, freely to enter into that ballasted, it may almost equipoyzedly hung, and be you're to runneupon a line. Now at great Triumphs two of these Dragons may be made to move oppositely unto the midst of the line, whereas a Globe with Sun, Moon, Staries, & Clouds, may appear lively represented, as in the 24 Figure at γ is showed. The line may be made either of Iron or Brass Wyre, or of Whipcord, anointed with Soap, or such like incombustible matter. These Dragons and Globes may be framed with Arches and Circles of thinn Latin, fastened with small lines, until the Body thereof be framed to your mind. And then set up her wings as she were flying, somewhat shaking with small Rackets in them. Also in the same Figure is a double Rocket, coined with a vacant Cane, they are placed once head to the others vent, to the end that when the first hath carried the other to the end of the line, the other may take fire, and return to the place where it first began his Motion. Also it will be a pleasant spectacle to behold to see two men issue forth at country places, armed with small Trunks or Staffs, and Targets furnished with Artificial Fireworks, which putting themselves amongst the People, shall Combat together in Fire. The Targets being of Planks, may spyrally have Fires of Breakers and Rockets: And the Trunks and Staffs furnished with Cane Armed, Rockets & Pettards, no bigger than a quill, and Armed loaded Nutshell: Or in stead of Staffs or Trunks, they may have wooden dulled Swords or Curtlaces, furnished with Fireworks, which will be a pleasant fight.   

CHAP. LXXVIII. How Artificial Fireballs and Granades are to be form and loaded with their mixtures.  
FIreballs and Granades, are upon all occasions very offensive to the Enemy, to vex and trouble them in their Army, or besieged in their Hods, or Houses, Tents, or Trenches, Bulwarks, and Defences. They may be made round many ways, according to their Calibre resolved. First, take strong Canvas, and cut out 2 Circles ⅓ greater, or more in dyamitre then the Calibre, and having turned in the edges of their Peripheries, sow them strongly with Needle and third round about, only leaving a little hole, until you have thereby loaded the Receipt, ramming it in very hard, and working it Globally: Or else cutting the Canvas into 8 quarters, as appeareth at P in the 27 Figure α, or into 4 quarters, with the Compasses as Footballs, with cross quarters: Otherwise some cut them into 12 panes, as the Globes are cauted in their covering papers, but by their too many seams they become tedious, and subject often to open. If you mean to shoot them out of a Mortar or other Piece, you must have a respect unto the bore of the Chase, that lopded, and armed, and coated, it may near fill the Concave Cilli●der. And if you intent to make Balls to stick, and Fire commonly Hedgehogges, you having sleight filled your Ball unto a Mark, must take two cross sharp barbed pointed, hardened, or steeled Irons, that must be put in to the Ball, to appear through on each side, as at 4 therein is represented: Or loading it with Cannon Chambers and Shot as at C. These may be prymed and fired before they be put in to the Piece. The Figure A representeth invention of a Lantern, or case that with a pryming Pipe, firing a quick Receipt at a time lunted, will break and blow up, and tear all near it fired, yea though it were shot or buried in earth or wall.  
The Balls that break made either of hollow mettle glass or clay, baked, and nealed, and loaded with quick Receipts and pipe, to prime with slow receipt for time, are either single or double to break, are commonly called Granades. But Fire-pots and Balls to throw out of a man's hand, or with a Bascula may be made of Potter's Clay baked with Ears, unto which lighted Matches be fastened, and throwing them, to light upon any hard material, when they break, the Matches lighten the powder, and dispierce the pieces (or pistol-shot contrived about them) as at B may be seen. Their mixtures may be of Powder, Petre, Sulphur, and Salarmoniak, of each 1 l, and 40 z. of Camphor pounded, and serced, and mixed well together with molten Pitch, Linseed oil, or oil of Petre, prove it first by burning: if it be too slow, add more powder; and if too quick, more Oil or . The Balls & Pipes A A and I I, show how to make double Balls to light a Champion with one, and when it is thought the force past, it breaketh and teareth all near it: At B and Z the making and loadings are represented.   explosive arrows to be fired by bow or crossbow 
Tract. 3. Cap. 23.   a multi-barreled cannon and a "pyked trunke gunne" 
Tract. 1. Cap. 23.   

CHAP. LXXIX. How to convoy or direct Fire into a place assigned, or upon the Enemy in an Assault.  
BEing desirous to fire any Ship, Bark, House, Barn, or other building combustible, the Crossbow, the Slurbowe, with his Rack or Gafle to bend it, represented in the 25 Figure at α, charged with a Fire Arrow fitted therefore, with a Mixture proper thereunto, by the Barbes on the Arrow heads, it will hang where it strikes, and by the vents made of purpose, it will fire whatsoever combustible matter shall be near it, especially Sails, dry Timbers, or Pitch and Tarred places: the effect of this Instrument was well experimented at the Siege of Ostend and elsewhere, taking great effect. The like may be done with a long Bow, but that the Arrow must be longer, as may appear at A. The Trunk B will be necessary for defence of a Breach, or to keep a narrow passage, or in giving an Assault, or entering a Ship to keep all the Defendants before, or in the night suddenly to set upon Foot or Horse, or in an Onslaught. To the same effect is the Pocket or Bag C filled with fitting Mixtures, whereof we spoke in the last Chapter for resisting the Enemy, assaulting, by fensing or displaying it about on all sides. The Garland D being filled and coated with one of the said Mixtures, will do much damage unto whatsoever it lights upon being combustible. The Arrows, Darts, and Bags are to be prymed by Vents, and Armed with Marling, and coated with the Roch fire before mentioned.  
But if the Enemy be approached to the foot of the wall, and yet covert, in that case, use the Instrument traced at T and S in the 27 Figure α, which is a block of square or round Timber, pierced and loaded with quick Powder, and on the sides round about it having holes bored to the Concave, either to receive pistol-shot or 3 square Irons pointed, that being let down by 2 Ropes from the top of the Wall or Parapet, may by a Snap-hance or Match drawn through a Train or Channel of dry powder. Fire the loading within, which by the bores will give direction to the Shot, to do the Enemy's mischief, when other devices cannot be used to repulse them.   

CHAP. LXXX. Of the Piked Trunk Gun, and quadruple Barrell-Peeces.  
THese latter Pieces represented in the 25 figure at , are to be accounted amongst the number of Bastard Pieces, but are of a new and serviceable invention, not only for their lightness, but also for the great slaughter of the Enemy they will make being duly used. The first of them is 4, 5, or 6 Pieces joined together, lying like Organ-Pypes placed upon a broad Carriage, taking fire all at once by means of a Gutter or Pipe, that conveyeth the train of priming powder, from one touchhole to the next, and all the rest: these are of the proportion of legitimate Culuerings, being 27 Calibres-in length of their Chase, and double fortified, being 1 and a half in thickness at the Calibre of the Boar in Mettle, each carrying 1 l. of Iron cast shot, with ● of powder, or else 1 l. and a half of Lead shot, with as much in weight of fine powder: Or they may be loaded with pease leaden or spelter round shot, which will pierce an Armour of proof 12 score yards off at least, being put in a bag or Cartrouch for each Piece. And some few of these will send to the Enemy a fare off a continual uley, or shower of shot, they are neat and light, for sour of them will not much exceed 2000 l. weight, and to keep a Passage, or defend a Breach, they are of excellent use.  
The second Piece is a Trunk Gun for fashion, like a Fowler, but close breeched, and is discharged with any charge: in the Carriage thereof behind there is a thick Elm Plank Musket proof, with Loops to the end: their Conducts may be safely covert from Muskets before them: Their wheels need not be gross, and the shaft is with cross pins. Behind in the midst of the Carriage to drive it forward by men's force, in the midst thereof, is a Barrel, like the figure, filled with inextinguished fire, and loaded with Cane, Chamber, with Musket or Caliver shot, and fine corn powder, and guarded at the Mouth with two Iron or steeled Pikes, and on each side of the Carriage four long ones fastened, some few of which will exceedingly gall a troop of Horse Charging, and are easily moved; for 2 men with their Muskets are only needful, and for their use, and the structures of them the figure will sufficiently explain▪ for their receipt, it may be any sure one with Roch Petre to flame, and scales of Iron to sparkle which unto Horse by reason of the continual casting out of Fire, and Flame, and Musket shot, or smaller, will exceedingly affright and gall Horse-troop, which let it suffice.   

A Table of Proportions for old Receipts.  

For Firepikes 2 Pound weight a piece for one dozen.  
Pówder 10 pound.  
Peter Roch 2 pound and a half.  
Peter Meald 2 lb. and a half.  
Sulphur 1 lb. and a half.  
Rossen 1 lb and 3 quarters.  
Turpentine half a lb.  
Linseca-Oyle half a lb.  
Som. tot. 19 lb. 4 oz.  

For Coating and Arming.  
Sulphur 3 lb.  
Turpentine a quarter of a lb.  
Thread 1 lb. and a half.  
Som. tot. 4 lb. 12 oz.    

For 2 dozen of Balls, each one lb 3 quarters Dry work.  
Powder 24 lb.  
Sulphur 1 lb. and a half.  
 1 lb and a half.  
Peter Roch 3 lb. and a half.  
Peter meald 1 lb. and a half.  
Som. tot. 32 lb.  

For Coating and Arming.  
Pitch 2 lb. and 3 quarters.  
 3 lb.  
Sulphur 3 lb. 3 quarters.  
Tallow half a lb.  
Marlin 2 lb. and a quarter.  
Canvas 3 quarters of a yard.  
Som. tot. 10. lb. and a quarter.    

For 2 dozen of Balls wet work of 2 lb. a piece.  
Powder 24 lb.  
Peter Roch 8 lb.  
Peter meald 6 lb.  
Pitch 1 lb.  
Rosen Roch 1 lb.  
Turpentine 4 lb and a quarter.  
linseed-oil half a lb.  
Trayne-oyle half a lb.  
Som. tot. 45 lb. and a quarter.  

For Coating and Arming.  
Pitch 7 lb.  
 1 lb.  
Sulphur 4 lb.  
Canvas 1 yard and a half.  
Small Marle 3 lb.  
Som. tot. 15 lb. and a half.    

For Arrows 2 dozen each 1 lb.  
Powder 12 lb.  
Sulphur 3 quarters of a lb.  
 3 quarters of a lb.  
Roch Peter half a lb.  
Peter meald 3 quarters of a lb.  
Som. tot. 15 lb. 3 quarters.  

For Coating.  
Sulphur 5 lb.  
Peter Roch 2 lb.  
Peter meal 1 lb.  
1 Yard of Canvas 1 lb.  
and Marlynes. 1 lb.  
Som. tot. 9 lb.    

For 1 Dozen of Pots, each one lb. and a quarter.  
Corn Powder 1 lb. and a half.  
Sir Powder 9 lb.  
Sulphur 3 lb.  
Peter Roch 1 lb. and a half.  
Som. tot. 15. lb.  

For Capping.  
Canvas 1 yard.  
O●●m● a quarter of a lb.  
Sulphur 3 quarters of a lb.  
Packthread 1 oz.  
Som. tot. 1 lb. 9 oz.    

For Hoops.  
Sir Powder 2 lb.  
Roch Peter 3 oz.  
Petre meald 2 oz.  
 a quarter of a lb.  
Sulphur a quarter of a lb.  
Turpeutine 1 oz.  
linseed-oil 1 oz.  
Trane-oyle 1 oz.  

For Coating.  
Pitch 3 quarters of a lb.  
 a quarter of a lb.  
Sulphur 1 lb.  
Tallow 2 oz.       

The Author's L'envoy.  
SInce now my Book thou art so fare gone on,  
Abroad on God's name, and be better known:  
But had there been now but one quarter done,  
That, nor the rest, should ne'er have seen the Sun:  
To friends be free, open them, thy Treasures store,  
But carping Scoffers let them have no more  
But Scraps, for that's enough and good for such  
As poison all they see, foul all they touch:  
And on Mechanic escapes forge Arts detraction,  
Ere they will wink or mend, which is the faultier Action?  
The Errats' made, they'll not, did I intent it  
For such as not commend, nor can come mend it,  
Not I, and so I end it.