Effigiem spectas; praestat spectare Laborem Ingenio pollet: omnibus Arte praeit. THOMAE BINNING SCOTT VERA EFFICIES Anno Dom 1675. Anno Aetutis suae 55 A Light To the Art of GUNNERY. Wherein the most necessary points belonging to a Gunner either in Sea or land Service are made Practicable, And faithfully set forth By Capt. Tho. Binning. A LIGHT TO THE Art of Gunnery. WHEREIN Is laid down the True Weight of Powder both for Proof and Action, of all sorts of Great Ordnance. Also the True Ball, and allowance for Wind. WITH The most necessary Conclusions for the Practice of Gunnery, either in Sea or Land-Service. LIKEWISE The Ingredients, and making of most necessary Fire-Works: As also many Compositions for the Gunner's Practice, both at Sea and Land. By Capt. THOMAS BINNING, Mariner. Licenced Sept. 28. 1675. Roger L'Estrange. London, Printed by John Derby, for the Author, and are to be sold by Andrew Forester, at his Shop in Kings-street, Westminster, next door to the Mitre-Tavern, 1676. TO THE High, Potent, and Noble Prince JOHN, Duke of Lauderdale, Marquis of March, Earl of Lauderdale and Guildford, Lord Thirselstane, Musleburgh, Bolton and Petersham, Lord Precedent of his Majesty's Most Honourable Privy Council of Scotland, and sole Secretary of State for that Kingdom; one of his Majesty's most Honourable Privy Council of England, Gentleman of his Majesty's Bedchamber, and Knight of the most noble Order of the Garter. May it please your Grace, WHen I consider the many Reasons, and convincing Arguments, both Ancient and Modern, besides the Commands and Examples laid down in Holy Scripture, of the dutiful Obedience Subjects own unto their lawful Kings; not only by the cheerful assistance of their Estates, and Capacities; but, if need require, without fear and doubting to put their Lives in hazard for the maintenance of their Prince's Honour, and the well-being of their Country; I conclude your Grace in your time to have been herein a perfect Pattern: But when I make reflection upon those many unmerited and undeservedly continued Favours (through your Grace's benevolent Aspect) received from His Majesty and Royal Highness: Knowing also that your Grace is a sure Cherisher and Supporter of Art, even in the weakest Endeavours, I have been encouraged to offer to your Gracious Patronage and Protection these my Observations of Gunnery; the use whereof may in time be serviceable to all His Majesty's Subjects, but more especially to those of His Majesty's Ancient Kingdom, my Native Country, the flourishing whereof hath been observed to be your Grace's constant Care; which maugre all oppositions of Envy, hath not wanted its good Effects. The most of what I here present your Grace, are of my own Experience, and have not been formerly published; and which I have so demonstratively laid down, that they will bear the severest trial of Reason and Art. And as they are the humble Offering of a Mind truly grateful, so I question not your Grace's favourable Acceptance, which will be an Encouragement for me to study something further in this Art, more methodically digested. Pardon, I beseech your Grace, this Presumption, being the mere Product of my Loyalty and Duty: And that your Grace may long and happily live, and constantly enjoy the benign Aspects of his Majesty and Royal Highness, shall be the Prayers of him, who resolves always to be Your Grace's Humble and Obedient Servant, Tho. Binning. To the Reader. Judicious Reader. I Am persuaded there are none, though but mean Artists, that will question the worth of the Art of Gunnery, being founded upon the two principal Pillars of the Mathematics, viz. Arithmetic and Geometry. For by this Art, and good Artists, the Artillery hath gained Battles, Towns, Castles, Citadels and Forts; yea, the strong Trenches of a strong Army forced, opened and stormed by the weaker Army, to the ruin of the Entrenched Forces; which was seen at the Battle of Lutzen, This Battle was at Lutzen in November 1631. where the Serene and Potent Gustavus Adolfus King of Sweden was killed; for there the Swedes Gunners did so artifically ply their Ordnance, that the Swedes Army stormed the Imperialists in the most secure Trenches that could be made, and a stronger Army within than those without; and only by the Artificial and Industrious Carriage of the Gunners. By which you may perceive, that there is as much lieth on the using of the Ordnance, either by Sea or Land, to the safety of the Ship, Garrison, or Army, and annoyance of the Enemy, as upon any thing else. In this little Piece you may find the framing those Draughts, the Calculating those Tables for Powder and Ball, and laying out those Height-Rules both for Powder and Shot, with the True Wind of every Gun, with the Dimensions of their Fortifications, in giving Powder, not having regard at all to the Weight of the Piece; further, as for the Draught of the Ordnance, likewise what is useful to a Gunner either by Sea or Land, and how the Gunner may lay or levelly his Piece to shoot at a Mark; also several Questions, a Gunner ought to give some account of ere he be admitted: As also to use his Mortar-Peece and Pattard, with Fire-Works Offensive and Defensive; Whereby I am persuaded, any that will take notice of the use of the Quadrant and Quadrat, and Observations thereon, will find as Artificial Recreations in this little Piece, as in any hath been written hitherto on this Subject. It is visible, the great harm that cometh by breaking of Guns in firing, is the ignorance of those Gunners, and the great allowance of Powder; for if a True-Fortified Piece of Ordnance shall have to 9 lb Ball 7 lb of Powder; the Question is, What ought to be given to a Reinforced Piece shooting the same Ball? This and other such Businesses moved me to write, that thereby Gunners might be more circumspect. I have not done this, that thereby I may add any thing to the Artificial Gunner, but that the younger Brethren may, by reading and observing what is here made plain, learn to do their Duty. If this Piece do instruct any yet ignorant, I shall be glad; if it please the Readers fancy I have content; but if it displease any critical obstinate Maliguer of the Art, I shall take no more notice of him, but desire he may amend himself and this also: Nevertheless conclude as thou findest, and consider the good will of Thy Friend, T. B. To the Praise of his Countryman Capt. Thomas Binning. INto this little Book I plainly see Inventions rare, with Art of Gunnery Grounded upon two Pillars that must stand, While God and Nature Earth and Sea command, Ar'thmetick, Geometry, with new Inventions, Thy King and Countries Good, being thy Intentions. Therefore Minerva claims Ingine and Wit, And Mighty Mars does own this Subject fit. Seeing from our Countryman it doth redound, (Whose Country hath been formerly renowned) Let us not keep from him deserved Bays, Which Strangers would afford as his due praise, Because he hath given a Light to Gunnery; Not craving therefore Gold or other fee. I do conclude, the like hath not been Wrote In any Language till now by a Scot Tho. Orquart. ERRATA. PAge 28, in the Quadrant and Scale, after 60 read 70. Page 96, line 3, for an read and. Page 136, line 34, for ●●/1● read 23/●4 parts. Ditto, Line 35, for 19/18 read 17/18 parts. And the other, for 20/19 read 21/22 parts. AN INTRODUCTION TO THE GUNNER, For his better Understanding. THere are many who do intrude, and also that have obtained the preferment to be Gunners, either of Garrisons or Ships, who never understood any the meanest or least Article (as I may say) in the Gunners A, B, C. I speak not this to discourage any from engaging in the employment of a Gunner; But I am sure, except he be qualified with the Principles and Ground-Rules of Gunnery, he cannot be worthy of the place. And yet there is more than Art or Action to be obtained ere they begin: For which cause I will here begin with those Qualifications, that a Man professing, and dignified with the trust of a Gunners place, aught to have. 1. That he be one that feareth God more than his Enemy. 2. That he be educated, and expert in his Profession: for Experience confirmeth, some say, teacheth Art. 3. That he be Constant, and not given to change. 4. That he be Faithful, True, and Honest. The Reason, wherefore my first Discourse is of Gunners, is only because many times it falleth out, that most Men employed for Gunners are very negligent of the fear of God. Many Examples of this nature might be alleged and produced from the sad experience of preceding times: But I thought good to intimate only this one, for the terrifying of all Godless, and the confirming all Godly Gunners: Which Example I had from Seyger van Reghterne, General of the Land of Overyssel, in his Diurnal from Amsterdam to East-India; the which Diurnal begun on the 8th day of December, in the year 1628., from Texel, and ended there at his return the 12th of July 1633. In the 38th Folio of that Book, he saith, That in the year of our Lord 1631, in the Month of April, There was on the Island Nero, a Gunner, whose Name was Cornelius Slime, but a very godless and profane Man, who at no time could speak but he would be Cursing or Swearing; and when any would ask him what was his hopes after this Life were ended, his Answer was, It may be to Heaven, or it may be to Hell; but, said he, if I do go to Hell, there I will sell Tobacco and Brandy, and that would be good Medicine for the Devils. But one day this Cornelius Slime, in presence of my Author and many more, being Cursing and Swearing, and many times giving himself to the Devil; In the mean time, in presence of all those People, the Devil lift him up in the Air, and let him fall to the Ground, with a great noise; but the second time being taken up by the Devil, he was carried where never Man living could find him: From the like the Lord deliver us all. But if Experience had not taught me, both in this Country and others, what the lives of many Gunners are, I would have said nothing of it here. Now for the Education of Gunners in their Profession, it was manifest that there were not any of the Gunners employed by the Officers of the Army, in our King's and Country's Service, all the while his Majesty was in Scotland, which were capable of their Duty, or knew any thing of Art; and it was no wonder to see our common Gunners so slothful to at attain to perfection in Art, because if there had been a Man able in his Profession, our Officers of Artillery would not employ him, lest he should see, and so reveal their own Insufficiency. Likewise they needed not care what their Abilities were, for those that had charge over them, durst not put them to examination, for fear their own insufficiency should be openly known; but if they were able to put them to it, we might expect to be better Masters of this Art, when now we are scarce good Scholars. Likewise when there were Able Men in the Country, they could have no Employment; and for fear they should be employed, there was one Calumny or another raised to their prejudice; either he is proud, or a Malignant, which was in effect, he was a true Subject, and therefore not to be employed; and any of these two Names were enough to keep him from employment; or if he was in Service, to cause him to be Cashiered, as the Case then stood. But to encourage Ingenious Spirits to study Art, and to practise the same, Remark what is said of the Emperor Domitian, That he was so skilful in shooting, that let a Boy a good distance off hold up his Hand, and stretch forth his Fingers, and he would shoot through betwixt his Fingers with an Arrow, and not touch the Boy. Now I am sure, that although the like may not be done with any great Piece of Ordinance, yet I have seen one, who shooting with a great Piece, within Point Blank of the same Piece, after Observation and Trial of that Piece, would shoot within a hand-breadth of any Mark; yea, set a Drinking-Cup on the end of a Pike, he would take it with a Ball. And because I have been both at Field, and Sea-Service, and have seen such Errors in Gunners, my desire is, That those that are in Place, or shall come to it, may exercise themselves, and study to better their own Credit, and act something for the benefit and good of their Country, and honour of their King. As for the Constancy of Gunners, and others; Hath it not been seen, since the beginning of those comfortless Troubles in these Nations, the unconstancy and instability of Men, how they have varied from the one Party to the other? yea, they have for Ambition, and greediness of Gain, fled from the Army they have been sworn to, and gone to the Enemy, to the great loss of their own Souls, and hazard of the Truth, and an undoubted advantage to the Enemies of his Majesty. For their Honesty, they are not so much to blame as those that have the charge of them; for were they drawn to an account of what they receive, and how they have spent it, than Men durst not but be honest. All the Powder I spent in the Castle, I weighed, and found every Barrel to lack 10 or 12, and some 14 pound. But the Commissary taking from each Barrel 10 or 12 pound weight of Powder, the Gunner finding this, must be let slip with as much; and I think 20 or 24 pound in the hundred, is a large Intromission. Probatum. Now to help this great, and I may say, terrible Theft committed against King and Country; And that the Ammunition may redound to the profit of the Country, which is the only Service his Majesty requires: Choose honest Men for Commissaries, and Keepers of the Magazine, who will require an exact Account of what is gone or spent, and let every Man be content with his Wages. It is a true saying, and the Word of God clears it, Blessed are the Peacemakers, for they shall be called the Children of God, Mat. 5.9. Wherefore every Man ought with all their Hearts, to cry to God for Peace with Truth, the which I pray God to send us. To any versed in Military Affairs, is known the great Gain or Loss which may redound, either to the Country, Army, or Fleet, by the well or bad management of the Great Ordnance, or Train of Artillery; for which cause, I say, it is most necessary to try such Men you choose to be Gunners ere ye trust, either for Land or Sea-Service: And if they be qualified with these forenamed Marks, then are they fit to act the part of a Man: But it is God by whom increase must come. Now if there should chance a Man of good Qualifications to be admitted for a Gunner, and but meanly expert: To them I say, If they follow these following fundamental Rules, and digested Instructions, which I calculated in the year 1648, and 1651, I hope they shall have pleasure and profit. As it is without all question or contradiction, that there is nothing more Holy, more profitable or necessary than a peaceable Condition; for Peace is the nearest thing to God, in regard where Peace is, there is Love, Charity, Faith, and all the Virtues: Therefore we ought to pray for Peace, that so living in obedience to God, our King and Rulers, we may prosper in this World, and live in Bliss eternally. But in regard that the great Princes of the World may observe and seek Peace, we ought to pray, That as God hath placed them in Power, so he may direct them in all their Actions to do nothing contrary to his Glory, or the good of their Subjects. For what division amongst the Kings and Princes in Christendom, hath done to the destruction of Religion, effusion of Blood, and ruining of their Estates, is much in Histories made plain: And what hath been done by our unnatural Divisions within these three Kingdoms, is yet fresh in memory, to the great grief of many good Christians. And in regard that some Princes in Christendom are forced to keep War, for maintaining of the Christian Faith against Turks, Saracens, and barbarous Tartars; As also that amongst themselves, some are either blown up with Pride, or Envy, who would Reign alone, much amusing the minds of Men what they intent to do; so that War is as like to be as ever: Therefore any well-wishing Person ought to study for the advancement of his King's Honour, and good of his Country. Now what may be the Actions done by great Ordnance in time of War, may be thought either needless or hurtful: Because there is nothing thereby to be taught, but to Raze down Fortifications, and other Strengths to ruin: Or how an Army, by cutting off the Soldiers, may be shattered and broken, and an entrenched Leaguer may be broken up and forced. Truly such Men ought to be in esteem, if we will have any respect to these dangerous Times wherein we live, they ought to be encouraged; because no Potentate can be longer in Peace than his Neighbour pleaseth; and that scarce any strength is able to resist the fury of terrible Cannon well managed. And amongst all Arms in time of War the great Ordnance is first in use, whether it be against, or in a beleaguered Place; and especially when they are rightly managed with discretion, they are both helpful and encouraging to their Party. And contrary, when they are not Men of Judgement and Discretion, but slothful, and ignorant, than they produce damage to the owner of them. For, as History declares, the great Ordnance hath been the only Winners of the Battle sometimes, and great Victory, when they have been well managed, while the opposite Party gave their Ordnance only the blame of their flight, because they were not well managed. What a Gunner ought to be, to whom the Charge is committed, and what he ought to know. As it is necessary in all Fortified Places, as well in time of Peace as of War, to have able practised Gunners, who are able to give an account with reason, of the things belonging to their Charge, and that they be such as fear God more than their Enemy; they ought to be honest, and not given to change, as afore is said. The Gunner ought, besides his true shooting, to be learned in Arithmetic and Geometry, which will cause him give advice where a Strength may be most conveniently battered, and what Ordnance is most fitting to accomplish the same. Also he ought to give Directions to the Engineer, what form of Batteries is most convenient at such and such places: Likewise that by his Art he give directions that a Storm be made, where his Party may have the least harm by his playing with Ordinance upon the places where danger is to be feared: likewise if in a Beleaguered Place, the Gunner is to defend the same against opposition of the Enemy, and to order so, as by the assistance of the Ordnance, and by what other means he can, to oppose and destroy the Enemy for defence of the Place. But before all things, and before the Army approach to the Place, to which the Prince, General, or other Officer who commands in chief, do intent to beleaguer or take; It is necessary that the experienced Gunner be one to go before, and view the Place, with the Grounds thereby; the which to do, is best in the breaking of the day in the morning, to know if the Walls be strong or weak, and how and by what means they may be brought down; as likewise to find if that Fort or Garrison be so Fortified, as to annoy the Ground, or what part thereof is most secure for the Army to lay down Leaguer; and what Ground is best to annoy the Enemy most in the Garrison, and also what place of the Walls thereof is best to Batter and Storm, and which way most secure to bring the Scaling Ladders to set up; and to know if there be any Mount, Steeple, or high Building within that is Fortified, to overlook the Leaguer; for by such means great harm may occur, (or near the Leaguer) where the Enemy may overlook and relieve the Besieged, and so cause the Leaguer to rise; except the Ordnance in the Leaguer be capable presently to disorder and deface the same, that after the Leaguer is entrenched, it may be defended by Ordnance, etc. Then he must know if the Ground be diggable, and on what side of the Leaguer the Proviant may be best and most securely brought in, and what fresh Water is thereabout for their relief within command of the Leaguer-place: So when it is known where, on what end of the place or side the Great Ordinance must be placed, and lie from or in the Leaguer, then must the Batteries be drawn out and measured; and because it is hazardous to work on a Plain, to break Ground before an Enemy, but there must Blinds be raised, some must be where you are not to work, as well as where you intent to build your Batteries: But if you be on such Ground where you must begin your Approach at a distance, than you must know at what distance you may with conveniency break Ground to run your Trenches for Approach; and as it is certain the Point-Blank Distance of a Piece of Ordnance is 220, 230, 240, 250 Geometrical Paces, which is also the distance of a Musquet-shot; Therefore the knowing Gunner ought to give the Workmen order, if there be no other Engineer for the Effect; and in this regard the Gunner ought to be acquainted in Surveying for this, as well as for his Batteries and Ordnance placing: For if one would begin an Approach, than he must choose out so many Soldiers used to Work, as may be able to defend themselves and resist a Sally, if any be: Not neglecting to have Parties both of Horse and Foot about the Ground to defend them; in regard they are to carry, besides their ordinary Arms, Shovels, Pickaxes, Gavelocks, Crows, and what is necessary for their Work. At the place commanded to break Ground, it is fitting to cast up a Redoubt or two, from whence the Trenches are to begin; and run the Approaches, that if any sudden Assault come, the Workmen may retire thereto and defend themselves, and work till they have assistance: for if the Workmen had no place of present retreat, they would be forced to run and leave their Work, Tools, and Arms to the Enemy. To this purpose it is to be observed, That the expert Gunner, or Engineer, who is employed in this Work, is to use all the Art, Skill, and Experience they have, to run their Lines in such sort, that those which are in the Trenches and Approaches may not be discovered and seen by the Enemy, so that with safety and expedition they may approach near the place, or part of the Fortress, which the General desires to become Master of. For now in our Modern Fortifications, there are but two parts in a Town, or Fortress, of which one must be battered if they mind to take it in; and these are either a Bulwark or Curtain. When the General or Commander of the Field, by advice of the Council of War, hath resolved either to batter a Bulwark or Curtain, the Gunner or Engineer being present at the breaking of Ground, is to show and inform the Workmen how they are to run their Line, and, as the occasion presents, of divers lengths; for they must be turned at every just occasion, which is most necessary. When the Line is laid out and marked, the Workmen must be divided and placed in order, that one may not hinder another: Then to give to every Workman the length of 4, 5, or 6 foot, and then begin they to hasten into the Ground, for to avoid the danger which they are exposed to, while they stand upon the Earth; Therefore the Earth which they dig, they cast up before them, and as fast as can be make a Hole like a Grave; so when they have digged three foot in the Ground, and three foot broad, then sure they are covered, since from their Basis to the top of the Cast-up-Work there are six foot: When they are under Covert, than they enlarge and deepen the Approaches as they are ordered: Observe, they need not be so deep at the beginning as near to the Fortress; sometimes the Trenches must be made so broad, as that the Canons and Wagons of Provision must be drawn to the Batteries or Galleries. These Works are ordinarily begun in the Night, so when the Night is gone, there are fresh Men sent to relieve the first, and enlarge the Nightwork, and amend what they could not see wrong. After this Night's Work, or the same, there are Corpse of Guard made to contain Soldiers for a Main Guard, which Work aught to be with a Line of Communication with the Trenches, though they be at a distance, viz. four or five paces distance. When one Line is finished as abovesaid, and that it must be run no further that way, the Gunner or Engineer turns it another way, bearing it from the Town or Fort, and placing the Workmen as aforesaid, and so continuing by Turn and Wind, till he hath got something near the place or Fort besieged, and making good the Line continually with Corpse of Guards and Batteries, until they be at the brim or side of the Moat or Ditch of the Fort: Then is the Gunner or Engineer so to order his business, as to begin a Sape or Gallery, or Mine under the Ground, directing his Course by his Compass: as if Impediment of Rocks happen to stop his Course intended; he may make such Lines and Angles about the same, as may bring him to his direct Line again; no resemblance to it, but a Mariners Traverse by cross Winds at Sea. But for the effectuating of a Mine, there must be provision made of divers things necessary thereunto; as Shovels, Spades, Pickaxes, and all kind of Mason-Tools, with all things requisite to pierce a Wall, wherewith the Rampire is made: Then one prepares Props to support and bear up the Mine from falling or sinking, being thick and long, as is requisite; Likewise you must have store of Fir-Planks to line the Mine within that it may not fall down, for it must all be lined if the Ground be frush or brittle. Before you begin to make a Mine, it will be requisite you know the Ground of the place, whether it be vaulted or not, or on what the Foundation thereof is laid: The Miners being to break into a Wall, are to carry their Mine as close and secret as may be, that the Besieged may not hear any noise, or get any notice where the Mine is made, and how it runs; for if they do, questionless they will make a Contra-Mine or Traverse above Ground, to discover and spoil your Mine begun; so that failing, you cannot force the Besieged that way, except you begin a new Mine in another place: Such as was at the Castle of Edinburgh. The Master-Gunner or Engineer that conducts a Mine, aught to be a Man of good Experience, lest he miscarry in his Traverse; for which cause, he ought to be well acquainted with the Mariner's Compass, and also with the Variation thereof; for if there be a Mineral of Iron Over in that Ground, it is like the Compass will vary, and so miscarry the Mine: He ought also, for his Lines of Traverse, to be acquainted with the Line of Chords, or Plain-Scale; otherways with the use of the Protractor, for directing his Course and Traverse in the Mine, that he mistake not himself either in his Course or Distance, Altitude or Profunditude, according to the Ground he works in, and the Foundation of the Rampart. When the Mine is brought to the entry of the place where the Chamber must be: Sometimes order may be given to blow the Rubbish into the Fort besieged, or it may be out, into the Moat or Ditch; either which may be done by making the side thinner, which they would break to, than the other: And our Experience is sufficient proof of this, either in Cannon or Musket; for if you load a Piece of Ordnance, that there be a greater weight put after the Powder than in reason, give fire to the Touchhole, and you will find that Piece fly out either at Side or Breech. The proportion of Chambers are as various as the Wall or Rampart which they are to deface, therefore can have no dimension, but they must be made so large as to contain Powder sufficient. Some would prescribe Rules for a Barrel of Powder to blow up a Rod of Earth; but the Earth being of various ponderosity, and some so much stronger bound than others, that I suppose they must use rather more than less Powder; yet the Chamber would not be made larger than to contain the quantity of Powder ordained to open that Breach. When an Enemy hath besieged a Place, Citadel, Fort, Castle, or other Fortification, and hath approached to Batteries; certainly it behoves the Besieged to look about them, and to do their utmost endeavour to hinder the Enemy. The Defence against these Approaches is, to strive to make some Contre-Approaches; which may be done by stoutly sallying out, but withal, to sally out with discretion, for fear of losing Men, which is to be expected; (but no Dondass for Governor, who would neither permit sally, nor great Gun or Musket to be fired against the Enemy): by which sallying, the least offence you do the Enemy, is to hinder the progress of their Approaches; for if they be beat back, and constrained to fly into their Works, for so long as the Alarm endureth, they cannot advance their Work, nor begin again to work till the Besieged be retreated. Likewise this manner of Defence may be made by Cannon, which may play from all places upon the Workers of the Approaches, to do them what harm imaginable, which may put the Workmen in fear, by seeing their Fellows miserably slain by the * By firing six Cannon together over the Mine at Edinburgh Castle, it fell in. Cannon, which may be a means to make them leave working till there be Batteries made against the Besieged. The Contre-Approaches, by which you resist an Enemy, that they may not become Masters of your Outworks, or Contre-scarf, with their Approaches; These Contre-Approaches, to hinder the Enemy in their approach, are made by casting up some † By the Traverse I came to the Hole. Traverses, as I did at the Castle of Edinburgh against the Approaches of that Rebellious Army, running them so, as to find the Enemy's Mines; These Lines of this Traverse must be cast up toward the Enemy, but left open to the Besieged, or Garrison, because by them they must be defended: This Traverse must be so made, that it give no advantage to the Enemy if they take them in; and be sure they may be flanked both with Cannon and Musket from the Fort or Garrison. So that as there is an Offensive War, there is also a Defensive War, as doth appear by Mines; for the Besieged having discovered them, and got into them, may lawfully kill the Miners: Now when the Besieged have found the Mine out, it is to be known how they may make the way clear before them, and either kill the Miners, or make them fly, without having the least harm. After the causing a Hole fall in their Mine, near to my Traverse, I prepared a Powder-Barrel, with old Rope-yarn, men's Dung dry about the Walls, Powder-mealed, Brimstone, and Verdigrease, with Camphire; all which being mixed together, I caused to be put in the Mine, which made * Then Governor of Edinburgh. Overton and all fly: So we entered peaceably, and brought thereout their Working Tools without any harm. For the Gunners further knowledge, that is yet in his Minority, this Work is begun with Decimal Arithmetic, which is very useful in the Art of Gunnery, the Working and Extracting of the Square and Cube Roots; as also some Definitions and Problems of Geometry: by which the Gunner may the better make use of his Compasses, for which he will have several needful uses; for the whole Matter, I know little in this Book that may be wanting in a Gunner, that may be called a sufficient Gunner. In fine know, that I shall be glad that every Gunner may profit by it, and I wish that some may amend it. However know, that I intent this for your profit and the public Good; for if I had not seen need, I would never have taken the pains, nor been at the Charges; but (understand me right) no Pains can exceed the Duty we own to our King and Native Country. So wishing every good Subject to employ the Talon he hath received of God, to the Honour of his King, and Good of his fellow Subjects: Committing the Book to thee, and thee to God Almighty; desiring that if thou hast occasion to learn any Gunnery needful at present, thou wouldst inquire for Robert Webster at the Six Stars at Wapping, who will teach any thing needful for the young Gunner. I remain thine, to serve thee, THOMAS BINNING. Decimal Arithmetic. CHAP. I. Definitions. A Fraction or broken Number, is a Number less than an Unite, or One; and according to the common way of Fractions, is expressed by two Numbers set one over the other with a small line, thus, ¾; the upper Number is called the Numerator, and the lower the Denominator. The Denominator showeth into how many parts the Unite or Whole of any thing is to be divided. The Numerator showeth how many of these parts are signified by the Fraction. A Decimal Number is that which is expressed by an Unite, with a Cipher, or cyphers, as 10: 100: 1000: 10000: 100000: etc. A Decimal Fraction is that whose Denominator is a Decimal Number, as 3/10: 46/100: 728/1000: 2342/10000: 57689/100000: etc. Decimal Fractions, whether they stand alone, or be joined with Integers, have always a Comma, or a small Rectangular Line before them, to distinguish them from Integers, which is therefore called a Separating Line, as ⌊ 4, ⌊ 36, ⌊ 348, 4 ⌊ 2, 490 ⌊ 086, etc. As in Integers the Value or Denomination of Places do increase by Ten, from the Unite place towards the left hand: So in Decimals the Value or Denomination of places do decrease by Ten, from the Unite place towards the right hand: As in the Table following. The Table. 9 8. 7. 6. 5. 4. 3. 2. 1. 0. 1. 2. 3. 4. 5. 6. 7. 8. 9 Thousand Millions. Hundred Millions. Ten Millions. Millions. Hundred Thousands. Ten Thousands. Thousands. Hundreds. Ten. Vnits. Tenths. Hundredths. Thousandths. Ten Thousandths. Hundred Thousandths. Millionths. Ten Millionths. Hundred Millionths. Thousand Millionths. In Decimal Fractions, the Numerators are only set down, without the Denominators; but the Denominators are easily known, for they are the same with the Denomination of the last Figure of the Numerator. As in the Examples following. Examples. ⌊ 6 is Six. Numerator. Tenths. Denominator. The common way 6/100 ⌊ 42 is Forty two. Numerator. Hundredths. Denominator. The common way 42/100 ⌊ 364 is three Hundred sixty four.. Numerator. Thousandths. Denominator. The common way 364/1000 CHAP. II. Addition and Subduction in Decimals. ADdition and Subduction in Decimals, whether in pure Decimals, or in Integers mixed with Decimals, differ not from Addition and Subduction in Integers, only care must be had to place the separating Lines of the Numbers under one another; as also the places of like denomination under one another; and the separating Lines of the Sum or Difference, must be placed under the separating Lines of the Numbers added, or subducted. See the Examples. Examples in Addition. ⌊ 347 ⌊ 268 ⌊ 149 ⌊ 764 ⌊ 8972 ⌊ 643 ⌊ 8 ⌊ 79 3 ⌊ 1302 346 ⌊ 98 74 ⌊ 2 6 ⌊ 934 ⌊ 8 ⌊ 07 428 ⌊ 984 In Addition and Subduction, let the place of the Fraction remain so many places as they were, and no more. Example. Addition. 35 ⌊ 72 78 ⌊ 05 113 ⌊ 77 Subduction. 78 ⌊ 25 35 ⌊ 75 42 ⌊ 50 Examples in Subduction. ⌊ 724 ⌊ 482 ⌊ 242 ⌊ 89 ⌊ 5796 ⌊ 3104 ⌊ 6427 ⌊ 36 ⌊ 2827 64 ⌊ 279 48 ⌊ 384 15 ⌊ 895 46 ⌊ 2 9 ⌊ 746 36 ⌊ 454 59 ⌊ 872 6 ⌊ 9 52 ⌊ 972 74 ⌊ 0 65 ⌊ 98 8 ⌊ 02 34 ⌊ 2 ⌊ 642 33 ⌊ 558 CHAP. III. Multiplication in Decimals. THe Numbers to be multiplied together, are called Factors; and the Number found out by Multiplication, is called Product. Multiplication, whether in pure Decimals, or in Integers mixed with Decimals, is the same in Operation with Multiplication in Integers: The last Numbers of the Factors must be set one under the other, as if they were Integers, not regarding the placing of the separating Lines under one another, as in Addition and Subduction: And from the Product must be cut off with a separating Line so many of the last Figures, as there are places of Decimals in both the Factors. Examples. If it happen, when the Multiplication is ended, that there be fewer Figures in the Product, than there are places of Decimals in both Factors (which may often occur when the Product is a Fraction) in such case, as many places as are wanting, so many cyphers must be prefixed to the Product on the left hand thereof, and then a separating Line must be prefixed to sign the Product so increased for a Decimal. Examples. In Multiplication with Fractions, cut off so many places as there are Figures of the Fractions, in the Multiplicand and Multiplier. Examples. CHAP. iv Division in Decimals. DIvision, whether in pure Decimals, or Integers mixed with Decimals, is the same in Operation with Division in Integers. But care must be had to give a true denomination to the first Figure of the Quotient; (according to this Rule). The Rule. The first Figure of the Quotient is always of the same denomination with that place of the Dividend, which stands, or is supposed to stand over the Unite of the Divisor. It will happen sometimes, that the Unite place of the Divisor will stand beyond all the significant Figures of the Dividend, towards the right hand, or towards the left. In this case you must put cyphers to the right or left of the Dividend, until you come over the Unite place of the Divisor. As for Example. If 3 ⌊ 47 is to be divided by 0 ⌊ 000462, they must stand thus; 0 ⌊ 000462) 0003 ⌊ 47 (And the denomination of the first Figure of the Quotient will be thousands of Integers. Another Example. If 34 is to be divided by 642 ⌊ 79, they must stand thus; 642 ⌊ 79) 34 ⌊ 0000 (And the denomination of the first Figure of the Quotient will be hundreds of Decimals. Note, That what cyphers are added to the right hand of the Dividend, immediately next the Integers must have a separating Line (or a Comma) before them. In Division, the Fractions being equal, the Work is as whole Numbers are. If unequal, add so many cyphers to the Dividend, as the Fraction of the Divisor exceedeth the Fraction of the Dividend in places, that you may find your Fraction in the Quotient. Examples. Other Examples. Because the Fraction is two Figures in the Divisor; Therefore I add two cyphers to the Dividend. As in this third Example. If in Division I be to divide by a great many Figures, I may make a Table for them. Example. Which is done, first doubling of it, then adding it until nine times, if I will ten, which proves it. 1 52678 2 105356 3 158034 4 210712 5 263390 6 316068 7 368746 8 421424 9 474102 10 526780 Because the Fraction is three Figures in the Divisor, therefore I add three cyphers to the Dividend. As in this last Example. CHAP. V Of the Square Root. A Square Number is that which is made and produced of two equal Numbers multiplied together, or else of one Number multiplied by itself; as 16 is a Square Number, because it is produced of 4 by 4, (which are Numbers equal, or one Number multiplied by itself) likewise 25, 36, 49, are three Square Numbers, for they are Products of the Multiplication of two equal Numbers, or of one Number multiplied by itself, as 5 by 5, 6 by 6, and 7 by 7. For the Products may be understood by their Unites in a Plane, of such kind as shall represent the form and figure of a Geometrical Plane, as you see here under. The Superfice. 4, the side of the Square. The Superfice. 5, the side of the Square. It is evident by the generation of Squares, that you may make a Square of all Numbers given, and that you may extract the Root of all Squares proposed; and that likewise all Numbers proposed may be the side of some Square or another. There is a Double Root and a Double Square, viz. Simple and Compound; The Simple Root is that which hath but one Number, as are 1, 2, 3, 4, 5, 6, 7, 8, and 9; the Squares of which are called Simple Squares. The Compound Root, is that which hath more than one Number, as are 10, 11, 12, 20, 30, etc. the Squares of such are called Compound Squares. And before you will extract the Compound Root, you must know by heart the nine Simple Roots with their Squares, by means of the following Table. A Table of the Simple Roots with their Squares. Simple Roots. 1 2 3 4 5 6 7 8 9 Simple Squares. 1 4 9 16 25 36 49 64 81 To extract all Roots or Sides of Compound Squares. You must well understand and imprint in your memories the following Chapter. CHAP. VI Extraction of the Square Root in Decimals. IN extracting the Root or Side of a Compound Square, you must first mark the Square Number given, with Points or Pricks from the right hand to the left, beginning with the first Figure towards the right hand, marking over that Figure one Prick or Point, than set another over the third Figure, and another over the fifth; and so proceeding continually from the right hand to the left, marking still with a Prick over every third Figure, leaving the other Figures unmarked, until you come to the last Square towards the left hand. First find the Simple Root of the Figure or Figures that remain towards the left hand, multiply that Root in itself subtract it out of the Figures towards the left hand: Then draw down the next two Figures to that Remainder, and say 2 times 5 the Quotient is 10; set 10 under 72, and see how often it may be found in 72, say 6 times; then set 6 under 6, and set 6 also in the Quotient; then multiply 106 by 6, cometh 636, subtract it from 726, there remaineth 90: Then draw down the next two Figures to that Remainder, and say, 2 times 56 in the Quotient is 112; set 112 under 902, and see how often it may be found in 902, say 8 times; then set 8 under 4, and set 8 also in the Quotient, then multiply 1128 by 8 cometh 9024, subtract it from 9024 there remaineth nothing; so that 568 the Quotient is the just Root of the Square Number 322624, etc. Another Example. etc. CHAP. VII. Of the Cube Root. A Cube is a Solid Body, comprehended of six equal Square Superficies, and is like unto the die of a Table-board. Definition. Definition of the Cube Root. Every Number multiplied in itself maketh a Square Number, of which the Root or Side is the Number multiplied; and every Square multiplied by its Root, maketh a Cube Number, (by the 20th Definition of the 7th Book of Euclid): As 4 times 4 makes 16, (a Square Number, of which the Root is 4) the which 16 being multiplied by the Root 4, the Product giveth 64, a Cube Number, of which the Root is 4. Likewise 5 times 5 maketh 25, a Square Number, which being multiplied by its Root 5, the Product giveth 125, a Cube Number, of which the Root is 5, and so of others. And before you can extract the Compound Cube Roots, you must first know the nine Simple Cube Roots, with their Squares and Cubes. As appeareth in the following Table, which is divided in three Lines, whereof the first (which is the uppermost) containeth the nine Simple Roots; and the second Line (which is the middle Line) containeth the nine Squares; and the third Line, which is the lowest, containeth the Cube Numbers. A Table of the Simple Roots, with their Squares and Cubes. Simples. Sides. 1 2 3 4 5 6 7 8 9 Squares. 1 4 9 16 25 36 49 64 81 Cubes. 1 8 27 64 125 216 343 512 729 CHAP. VIII. Extraction of the Cube Root in Decimals. TO prepare a Cube Number for Extraction, put a Point over the first place thereof towards the right hand, (to wit, the place of Unites); then passing over the second and third places, put another point over the fourth; and passing over the fifth and sixth, put another over the seventh, and in that order, (to wit, two places being intermitted between every two adjacent Points) place as many Points as the Number will permit: So 157464 being given, you are to place the Points as here followeth; and so many Points as are in that manner placed, of so many Figures the Root demanded will consist. Having thus prepared your Number, you may see it distributed by the Points into several Cubes: So in the same Example 157 is the first Cube, and 464 the second. First, Find the Simple Cube Root by the preceding Table of 157, which is 5; subscribe the Cube of that Root under the first Cube of the Number given; so 125 being the Cube of 5 the Root, I writ it under 157 the first Cube of the Number given, and subtract this Cube from the first Cube of the Number propounded, placing the remainder orderly underneath the Line: So 125 the Cube of 5 being subtracted from 157, the remainder is 32: to the said remainder, bring down the next Cube of the Number propounded, (to wit, the Figures or cyphers which stand in the three next places) placing the said Cube next after, to wit, on the right hand of the remainder; so the next Cube 464 being placed after the remainder 32, there will be found the Number 32464, which may be called the Resolvend. Having drawn a Line under the Resolvend, square the Root in the Quotient, that is, multiply it by itself, and subscribe the triple of the said Square or Product, under the Resolvend, in such manner, that the first place (to wit, the place of Unites) of the said triple Square, may stand directly under the third place (or place of hundreds) in the Resolvend: So the Square of the Root 5 is 25, the Triple whereof is 75, which I subscribe under the Resolvend in such manner, that the Figure 5, which is in the first place, (to wit, the place of Unites) in the Triple Product 75, may stand under 4, which is seated in the third place of the Resolvend. Triple the Root or Number in the Quotient, and subscribe this Triple Number in such manner that the first place thereof, (to wit, the place of Unites) may stand directly under the second place (to wit, the place of Ten) in the Resolvend: So the triple of the Root 5 is 15, which I subscribe in such manner, that the Figure 5, which is in the first place (to wit, the place of Unites) in the said triple Number, doth stand directly under 6, which is seated in the second place of the Resolvend: The triple Square of the Root, and the triple of the Root being placed one under the other as is directed, draw a Line underneath, and add them together in such order as they are seated, and let the Sum be esteemed as a Divisor: So the Triple Square 75, and the triple Number 15 being added together, as they are ranked in the Work, the Sum will be 765 for a Divisor: Let the whole Resolvend, except the first place thereof towards the right hand, (to wit, the place of Unites) be esteemed as a Dividend; then demanding how often the first Figure (towards the left hand) of the Divisor is contained in the correspondent part of the Dividend, and observing in that behalf the Rules before taught in Division, writ the Answer in the Quotient: So I ask how often 7 (the first Figure of the Divisor towards the left hand) is contained in 32, (the correspondent part of the Dividend placed above) the Answer will be 4, wherefore I writ 4 in the Quotient: Having drawn another Line under the Work, multiply the triple Square before subscribed by the Figure last placed in the Quotient, and subscribe this Product under the said triple Square, (to wit, Unites under Unites, Ten under Ten, etc.) So 75 being multiplied by 4, the Product is 300, which I subscribe under 75 (the triple Square). Multiply the Figure last placed in the Quotient, first by itself, and then the Product by the triple Number before subscribed; this done, subscribe the last Product under the said triple Number, (to wit, Unites under Unites, Ten under Ten, etc.) So 4 being squared or multiplied by itself, the Product is 16, which being multiplied by the triple Number 15, the Product is 240, this therefore I subscribe under the aforesaid triple Number 15. Subscribe the Cube of the Figure last placed in the Quotient, under the Resolvend, in such manner that the first place of this Cube, (to wit, the place of Unites) may stand under the place of Unites in the Resolvend: So 64 being the Cube of 4, I writ it under the Resolvend 32464, in such manner, that the Figure 4, which is in the place of Unites in the Cube 64, may stand under the Figure 4, which is seated in the place of Unites of the Resolvend: Drawing yet another Line under the Work, add the three last Numbers together in the same order as they are seated, and subtract the Sum of them from the Resolvend, placing the Remainder orderly underneath: So the Sum of the three last Numbers, as they are ranked in the Work, is 32464, which if you subtract out of the Resolvend 32464, the Remainder is 0. Thus the whole Work being finished, the Cube Root of 157464, (the Number propounded) is found to be 54. Note 1. When the Sum of the three last Numbers before mentioned is greater than the Resolvend, the Work is erroneous, and then you are to reform it by placing a lesser Figure in the Quotient. Note 2. For every one of the particular Cubes (distinguished by the Points) except the first Cube on the left hand, a Resolvend is to be set apart, by bringing down to the Remainder the next Cube. And as often as a Resolvend is set apart, so often is a new Divisor to be found, by adding the triple of all the Root in the Quotient (consisting of what number of places soever) to the triple of the Square of such Root, after they are orderly placed, according as is abovementioned. Note 3. The Work of the Table of Simple Cubes in Folio 9, for finding the first Figure of the Root, (as before declared) is but once used in the Extraction of the Root of any Number whatsoever; but the Work of all the following Rules, is to be used for the finding of every place in the Root except the first. The practice of these three Notes will be seen, when we describe how to extract the Cube Root of Numbers not Cubical. CHAP. IX. Another Example wrought by the Genitures. SUppose a Number given to be 16387064, of which the Cube Root is required: First, You must cut the Cube given into Ternaries from the right hand to the left, (as was declared in Chap. 8.) Then find the Root of the first Cube from the left hand 16. Whereof the greatest Root is 2, for 2 being multiplied cubically, giveth 8, the which 8 being deducted from 16, the first Cube of the Number propounded, there remaineth 8, than set the Root found 2, with the Square thereof above it, and by the same the Geniture, and then find a second Figure for the Root of the second Cube, and you shall have 5, which ye shall set down with its Square and Cube under it, right against the Geniture towards the right hand; then multiply each one by another, and add the Products together, there cometh 7625, which being subtracted from 8387, there doth remain 762; In the same manner find a Root for the Numbers remaining to be extracted, and it shall be the Root of your third Cube; And the Example will stand thus. And seeing there remaineth nothing, it is manifest that the Number propounded 16387064 is a Cube Number, and the Root thereof is 254. By the 4 th' Proposition of the second, and 20 th' Definition of the seventh Book of Euclid. When we come to calculate the Table of Cubes, by which you may make an Inch Rule for height, or Line of Diameters, the way shall be described how to extract the Cube Root of Numbers not Cubical, or as they are termed Irrational Numbers, from which no true Root can be obtained, yet many times the Error will not be ●/100000 part of an Unite. CHAP. X. Principles of Geometry. THere are divers Reasons which make me to give these few Principles of Geometry, because the whole Work of this Book, is either to be done by Arithmetic or Geometry; and besides that a Gunner cannot obtain to know the truth of a Diameter of a Ball, except he can Geometrically extract the Wind of the Boar of the Piece, and thereby find the Ball fitting such a Piece: And in general will be most useful for any Gunner. Definitions. 1. A Point or Prick, is that which is the least of all Materials, and it is the beginning of Things, as being void of Length, Breadth, and Depth, having neither Part nor Quantity (expressible in Numbers), and therefore it admits of no Division, but that which is mental only. This Point or Prick is represented unto you by the Letter A. Thus A. 2. A Line is a Magnitude extending itself in length, without breath or thickness, (whether it be a strait line or crooked) and (in respect of its length) may be divided into Parts, but will admit of no other division, but in length only. As is set forth to you by the Line BC; the extremities whereof being Points as B and C. 3. A Right or Strait Line, is the nearest Distance that can be betwixt two Points; As is the former Line BC. 4. Circular or Crooked Lines are longer, though they be extended no further than Right Lines, as are the Lines DE and FG. 5. Rightlined Parallels, are two strait Lines, so drawn, as they are equi-distant in all places one from the other; so that although they were infinitely extended, yet could they never meet; as may be seen by the Lines HI and KL. 6. A Circular Parallel, is a Circle drawn either within or without another Circle, upon one and the same Centre, as is seen by the two Circles, viz. NOPQ and RSTV, being both drawn upon the same Centre W, and therefore are parallel one to another. 7. A Superficies is the second kind of Quantity, and to it are attributed two Dimensions, Length and Breadth, but not Thickness, for a Superficies is the term or end of a Body, as a Line is the end and term of a Superficies. As WXYZ is a Superficies. 8. The Extremes of a Superficies are Lines, as the Ends, Limits, or Bounds of a Line, are Points confining the Line; so are Lines the Limits, Bounds and Ends enclosing a Superficies; As in the foregoing Figure you may see the Superficies enclosed with four Lines, viz. YW, WX, XZ, and YZ, which are the Extremes or Limits thereof. 9 A plain Superficies, is that which lieth equally between his Lines, like as a Right Line is the shortest extension or draught from one Point to another; so a plain Superficies is the shortest extension or draught from one Line to another: As in the preceding Figure WXYZ. 10. A Figure is that Magnitude comprehended by one Line, or more Lines than one: Under one Line is a Circle; Under more Lines is a Triangle, Quadrangle, Pentagon, Hexagon; and so forth. 11. A Circle is that Figure which is comprehended under one Line, called the Circumference, as ABCD; in the middle whereof there is a Point called the Centre, as E; from which, to the Circumference, all Lines being drawn are equal; As in the said Circle the Lines EA, EBB, EC, and ED are equal. 12. The Diameter of a Circle, is a Right Line drawn through the Centre thereof, and ending at the Circumference on either side, dividing the Circle into two equal parts: As the Line AEC in this Circle is the Diameter thereof, because it passeth from the Point A to the Point C, and so likewise through the Centre E, and divideth the whole Circle into two equal parts. 13. The Semi-diameter being the half thereof; as A and EC, the one Term whereof being the Centre, and the other the Circumference: It followeth by the 11 th' Definition hereof, that all Lines drawn from the Centre to the Circumference are equal; Therefore is BE and ED likewise Semidiameters. 14. A Semicircle is a Figure which is contained under the Diameter, and under that part of the Circumference which is cut off by the Diameter, as the Semicircle ABC, is contained under the Diameter AC, and also under the part of the Circumference ABC, which is cut off by the Diameter AC. 15. A Quadrant is the fourth part of a Circle, or is contained under two Semidiameters, and the fourth part of the Circumference, as in the preceding Circle AEB or BEC. 16. A Segment of a Circle, is a part of the Circle contained under a Chord-Line, (not being the Diameter) and a part of the Circumference, as FBG being the lesser Segment; and the Remainder to the whole Circle being the greater. 17. A rightlined Angle, is the Inclination, or bowing of one Line to another, which being extended, do concur or meet in a Point, as in the preceding Circle AEB or AEH, etc. the middle Letter signifying always the Angle, as E. 18. Of Rightlined Angles there be three kinds, viz. A Right-Angle, an Obtuse or Blunt-Angle, and an Acute or Sharp-Angle. 19 A Right-Angle is that, when one Line falling upon another maketh the Angles on both sides equal, then either of those Angles is a Right-Angle: and the Right Line which standeth erected, is called a Perpendicular-Line to that upon which it standeth. As upon the Rightline AC, suppose there do stand another Line BE, (as in the preceding Circle) in such sort, that it maketh the Angles on either side thereof equal, namely the Angle AEB on the one side, equal to the Angle BEC on the other side, then are each of those Angles Right Angles, and the Line BE, which standeth erected on the Line AC, is a Perpendicular to the said Line AC. 20. An Obtuse-Angle is that which is greater than a Right-Angle, as the Angle HEB (in the preceding Circle) is greater than the Angle AEB, by the Angle AEH, and therefore is an Obtuse-Angle. 21. An Acute or Sharp-Angle, is that which is less than a Right-Angle, as the Angle AEH is an Acute-Angle, because it is less than the Right-Angle AED, by the other Acute-Angle DEH. Obs. 1 Here you are to observe, That the Circumference of every Circle doth differ from the Circle, as that which is contained, doth differ from that which containeth. Obs. 2 The Circumference of every Circle, is understood to be divided into 360 Parts, called Degrees; and every one of these into 60 other Parts, called Minutes; or into 100 Parts, called Centesms: But the reason of this Division may be demanded, Wherefore into 360, & into no other Number, did the first Artists divide every Circumference? I Answer, That only Magnitude being to be divided into certain parts, the same aught to be divided into the least and best, for dividing as in equal parts: But so it was, that no Number under 360 could be had, as being divisible into more equal parts; and likewise being a Number not very troublesome to the Memory. Therefore not without Cause or Reason they made choice of that Number before any greater or lesser. From hence it follows that every Angle may be measured by an Arch of a Circle actually divided; whether it be Semicircle, Quadrant, or Line of Chords, (the construction of which hereafter followeth); And first by a Semicircle divided into 180 Degrees: First, Lay the Centre of the same upon the Angular Point, and the Diameter upon one of the Lines forming the Angle, the Degrees contained between these two Lines upon your Instrument is the measure of your Angle. As in this Example, The Centre of your Semicircle placed upon the Angular Point A, and the Diameter upon AC, the Arch contained between AB and AC, such is DE, which is the measure of the Angle DAE 36 Degrees. 22. The measure of any Rightlined Angle, may be had by a Line of Chords, which is described upon a Ruler; which Line is virtually the Arch of a Circle; The Projection whereof is as followeth. Let there be a Quadrant, or fourth part of a Circle, as BAC, divided into 90 Degrees; First, Into three parts, each containing 30 Degrees, by taking the Semi-diameter, as AB, with your Compasses; place one foot in C, and with the same wideness set the other foot in F; set again the one foot of your Compasses in B, (the Compasses not being altered) and with the other take the extent BG: So your Quadrant shall be divided into three equal parts, viz. CG 30 Degrees, CF 60, and the rest unto B 90 degrees: Every one of these being again subdivided into three equal parts; so shall you have the Quadrant divided into nine parts, or 90 degrees, each part containing ten degrees: and so into small parts according to the largeness of your Quadrant. The Quadrant being performed and truly divided: you shall draw a Line from B to C, which shall be the Chord of 90 degrees; again you shall place the one foot of your Compasses at C, and extend the other to 10 degrees; the same extension you shall lay off from C to D, upon the Line of Chords; still keeping the one foot of your Compasses at C, again extend your Compasses to 20 degrees, and lay them off from C to E; and so accordingly to all the rest, till you have finished the division of your Line. Which being performed, shall serve you to measure the quantity of all Rightlined Angles, as well as by any Circular Arch; being more portable, and more ready for use, than any Circular Instrument, as Semicircle, Quadrant, etc. as by the following practice is evident. CHAP. XI. Geometrical Problems. Prob. 1. To divide a Line given into two equal Parts, at Right-Angles. Prob. 1 LEt the Line given be AB; having placed the one foot of your Compasses at A or B; extend the other at pleasure, above the half of the Line by estimation, and draw two Arches, the one above the Line, and the other beneath; then keeping the Compasses at the same wideness, place the one foot at the other end of the Line, cutting the former Arches in C and D with the other foot, lay a Ruler at the points C and D; and where the same doth cut the Line AB, as in E, so shall the Line AB be cut into two equal halves at E, which was required; and the Lines CE and ED, shall be both perpendicular to the Line AB, by the 19 th' Definition of this. Prob. 2. An Angle being given, to divide the same into two halves. Let the Angle be ABC, to be divided into two equal halves: Place the one foot of your Compasses at B, and extend the other at your pleasure to D and E; describe two Arches cutting each other in the point F: So shall you divide the Angle ABC into two equal halves, if you draw a Line from B to F, with two Angel's ABF, and FBC, as equal to the whole Angle ABC, being divided into two halves. Prob. 3. From any Point, or from the end of a Line, to erect or raise a Perpendicular. Let there be given the Line AB, and the Point in the same given C, from which a Perpendicular is to be raised. Place the one foot of your Compasses at C, and with the other take at pleasure above the Line, as D; then from the point D, describe the Arch of a Circle, as ECF, cutting the Line AB in F; then lay your Ruler at F and D, and where it cutteth the Arch as in E, draw a Line from C to E, which shall be perpendicular to AB, from the point C. Again from the point A, a Perpendicular is raised the same manner of way; placing one foot of your Compasses at A, extend the other above the Line to the point G; and draw from G the Arch JAH, cutting the Line at H; then laying your Ruler by G and H, and where it cutteth the Arch as in I; from A to I draw a Line, so shall AI be a perpendicular from the end of the Line AB, or from the point A. The same may be performed by the Line of Chords, as by the practice is evident. Prob. 4. From a Point without a Line, to let fall a Perpendicular to a Line given. Let the Line given be AB, and the Point without the same at C: Draw a Line to AB at Obliqne Angles, as CD; which you shall cut (by the first Problem) in two halves at E; then place the one foot of your Compasses at E, extend the other unto C, drawing the Arch CF: and where the same cutteth the Line AB, as in F, from C to F draw a Line, as CF; so shall CF be a Perpendicular let fall from the Point C, upon the Line AB, as was required. Prob. 5. A Line being given, to draw a Parallel to the same, at any Distance required. Let the Line given be AB, and the Distance from C: Extend your Compasses to the length of C, and placing one foot of your Compasses in any Point of the Line, draw two Arches; and by the Compass of these Arches, draw a Line as DE; which shall be parallel to AB required; as CE. The same another way. Let the Line given be AB, and the Point at C: From the Point C, draw a Line at pleasure unto AB, which shall touch in F, which you shall cut (by the first Problem) into two halves at E: take then a Point betwixt F and A at pleasure, which is here G: draw then a right Line from the Point G, through E, and set the Distance DE, equal to the Line EGLANTINE: draw then a Line through the Points CD; so shall the same Line be parallel to the Line AB. Prob. 6. Two Lines being given, to find a third proportional Line. Let A and B be two Lines given, and let it be required to find a third Line in proportion to them. First, Make any Angle as CDH; then set the Line A from D to E, and the Line B from D to F, and also from D to G; then draw OF: that done, by the Point G draw a parallel to OF, as GH: So shall DH, be the third proportional Line required. A. 4. B. 6. DE. 4. DF. 6. DG. 6. DH. 9 Prob. 7. Three Lines being given, to find a fourth in proportion, that is to perform the Rule of Three in Lines. Let AB and C be three Lines given, and it is required to find a fourth proportional Line. First (as in the last Problem) make any Angle at Pleasure, as the Angle EFG; Then take with your Compasses the Line A, and set it from F to H; take also the Line B, and set it from F to I, and draw the Line HI: That done, take the third Line C, and set it upon the Line FG, viz. (always upon the same Line where the first Line A was placed) from F to K; then by K draw a Parallel to HI, as KL, to cut FE in L: So shall FL be the fourth Proportional Line required. FH. 12. FI. 14. FK. 18. FL. 21. Prob. 8. To divide a Line given into two parts, in proportion one to the other, according to two Lines given. Let AB be a Line given, to be divided into two such parts, that the lesser may be in proportion to the greater: As the Line C, to the Line D. From the end A draw the Line A, making the Angle BAE: then set the Line C from A to F, and the Line D from F to E, and draw the Line EBB: Lastly, By the Point F draw a Parallel to EBB, as FG, to cut AB in G: So shall AB be divided in G, as C to D, which was required. AF. 20. FE. 30. AG. 16. GB. 24. Prob. 9 To cut off from a Line given any part or parts required. Let in the last Diagram AB be a Line given, and let it be required to cut off from it ⅖ parts. First, From the end A, draw the Line A, making any Angle as BAE; then set on any five equal parts from A to E, and also two of the same parts from A to F: That done, draw the Line EBB; then by F draw a Parallel thereunto, to cut AB in G: So shall AGNOSTUS be the ⅖ parts of AB, which was required. Prob. 10. To divide a Line in such sort, as another Line is before divided. This Problem differeth not much from the two last Problems. Draw a Right Line at pleasure, as the Line OB, which Line you shall divide into 100 equal parts as exactly as you can; then extend your Compasses to the Distance OB, and describe an Arch; in which arch you are to include the desired Line A; then draw the Line OC, and you have the Angle COB: which we shall hold for a ground-Rule; because the Legs OB and OC, contain each of them 100 or 1000 parts, which is in the Line A. For Example. I would have 35 parts of the Line A, (whose whole length making 100 parts, as the Line OB doth): I number on the Line OB 35 parts from O to F; with this distance I draw the Arch FG; then is the nearest Distance from F to G a Right Line, which is the 35 parts of the Line A. Likewise if it were desired to have 15 parts of the Line A: Then draw from O the Arch ED; which Distance is the desired 15 parts of the Line A; as the Learned Adriani Meti doth teach. And also how to find the Parts of a longer Line, than the Line of Measure itself is; it is done after the same manner; and is of great use to a Gunner. Use. This may be of great use, if the Gunner be to find the first Round Ball in a strange place, and the Weight unequal to Ours. Prob. 11. Between two Lines given, to find a mean Proportion. Let A and B be two Lines given, between the which it is required to find a mean Proportion. Join the Lines A and B so together, that they make one Right Line as CD, being joined together in the Point E: and upon the Line CD describe the Semicircle, viz. CFD: Then upon the Point E, where the Lines A and B being joined together meet, erect a Perpendicular to cut the Limb in F, as OF, which shall be a mean Proportion between the Lines A and B required. The same another way. Again in the same Diagram, let the Lines A and G be given, between the which it is required to find a mean Proportion. Take the Line G, and lay it down from C to D, and draw CD; whereupon describe the Semicircle CFD: Then take the Line A, and set it from D to E; Then upon the Point E, erect a Perpendicular to cut the Limb in F; Lastly, Draw DF, which shall be a mean Proportion between DE and DC, or between the Lines A and G required. And if you draw CF, it shall be a mean between B and G, that is between CE, and CD. Prob. 12. To divide a Line given by Extreme and Mean Proportion. Let AB be a Line given to be divided by Extreme and Mean Proportion. Increase AB at length to C; then upon the Point A erect a Perpendicular as AD, of the length of AB: That done, take half AD, or AB, and set it from A to E, then with the distance ED make the Arch DG: So shall AB be divided by Extreme and Mean Proportion in G, and AG is the greater Segment, and GB the lesser. The same another way. Prob. 13. The greater Segment of a Line divided by Extreme and Mean Proportion, to find the whole Line. Let AB be the greater Segment given, and the whole Line is required. Increase BASILIUS to C; then upon the end B erect a Perpendicular of half the length of AB, as BD; and draw the subtendant side AD; from which subtract DB, rests OF: That done, set OF from A to C; so shall CB be the whole Line required. Prob. 14. To describe a Circle upon any three Points given, not being in a Right Line. Let ABC be three Prob. 14 Points given. Set one foot of the Compasses in the middle Point at B, and open your Compasses to any extension that is above one half of the distance between B, and the farthest of the other two Points, and with that distance draw the blind Arches DE and FH: with the same extent set one foot in C, draw the Arch FH: Again with the same extent, setting one foot in the Point A, draw the Arch DE: than laying a Ruler to the Intersection of these Arches, draw the Lines DG and HG; which will cross each other in the Point G: and there is the Centre of the Circle inquired. Where setting one foot of your Compasses, and extending the other to any of the three Points, you describe the Arch of a Circle, which shall pass through the three Points given, and give the whole Circumference required: which having, you may find the Diameter by the 12 th' Definition of Chap. 10. of this Book. Observation. By a Segment, or a piece of a Ball being found, to know the weight of the whole Ball. Here is to be observed, That if any Town, Fort or Place be Besieged or Blocked up by an Enemy, and the Enemy shooting continually, there are divers Segments or Pieces of their Ball found in the Place; and it is desired to know what Ordnance they do Batter with. The Gunner shall take the Segment or piece of the Ball, and lay it on a piece of Paper, and set there down by the Circumference three Pricks or Points, as ABC in the Figure following, and thereby, and by the preceding Problem, shall find the Diameter, Centre, and Circumference of the Ball, whereby you may know the weight of that Ball; as is described in pag. 54. Prob. 15. How to Reduce a Right Line into the Circumference of a Circle. The Line given being AB, to be reduced into a Circumference. The which Line AB, you shall first divide into three equal parts, and of these three Parts you shall make an Equilateral Triangle, as CDE; the half of CD is F, and the half of the side DE is G; and where they cut one another as in H, that is the Centre of the Triangle CDE: further divide DF into halves with the point I; draw then a right Line from the Centre H, to I, which is HK; and divide the Line HI into four equal parts, of which you shall add one part unto HI, which shall be HK, (which is the same fourth part five times set); set then one foot of your Compasses in the point H, and the other in the point K; and draw with the same distance a round Circle, whose Circumference shall be equal to the Line given, viz. the Line AB, which was required. Prob. 16. How to reduce the Circumference of a Circle given, into a Right Line. The Mean Proportion betwixt DL and AGNOSTUS, the fourth part of the Circumference, giveth the side of a Square equal to the Circle. From DE subtract the half of AC, there remaineth DK, (which is equal to BF) and is the side of a Decagon inscribed in the Circle. Prob. 17. The Diameter of a Circle being given, to find its Proportion to the Circumference, or the Reverse. The true knowledge of this Problem is of great use for Gunnders, both by Sea and Land. Whensoever the Circumference of a Circle is divided into 10000 equal parts, then doth the Diameter thereof contain 3183 of the said parts, saith Adriani Meti. But Archimedes showeth us the easiest and fittest for our purpose; to wit, That if the Circumference be divided into 22 equal parts, than the Diameter doth contain seven of the like parts: as is demonstrated in this Figure, where you may see, that in the Circle ABC, the Circumference is divided into 22 equal parts, and the Diameter AB doth contain seven of the same parts. A Light to the Art of Gunnery. CHAP. XII. How to know the Proportion of a true Fortified Iron Gun. BY the Demonstration of the last Problem, you have the proportion of a true Fortified Iron Piece, for a true Fortified Piece of Ordnance being of Iron, hath 11 Diameters of the Boar about the Breech, measuring at the Touchhole betwixt the Rings; which to describe is thus. In the Diagram of the 17 th' Problem, the Diameter being divided into 7 equal parts, as is the Diameter AB; then take with your Compasses one of the same parts, and set one foot in the Centre, and with the other draw the Circle EGF, then shall the Line OF be the Diameter of the Boar of that Piece of Ordnance, and the Circle ACB, the Circumference of the Breech of the same Piece at the Touchhole: where it followeth that one 22 part of a well proportioned Piece of Ordnance made of Iron, measured about the Breech, is half the Diameter of the Boar of the same Piece; the which is 11 Diameters of the Boar, as aforesaid: And therefore one side Metal, or the thickness of Metal at the Touchhole is 1 ¼ Diameter of the Boar, as appeareth from G to C, which is completely demonstrated by the said Diagram of the 17 th' Problem: Also by the Neck, near the Mussel of the Gun, are seven Diameters of the Boar about; which is near ⅗ parts of the Diameter in Metal. The true proportion of a Gun. If you should take the Diameter of the Breech of this Piece seven times to be the length of the Piece, and allow three of those parts betwixt the Breech and the Meeks, or Trunions, and four of these parts betwixt the Meeks and the Mussel of the said Piece, than that Piece hath her true proportion. The Reason why one Gun must have more, and another less Powder. Tho' there are many Guns that are some shorter, and some longer, yet they ought not to be thinner of Metal; for if they be thinner, than they are not able to have their true proportion of Powder, either for Proof or Action: Likewise know that true Fortified Guns, and true Bored Brass Ordnance, be their Denomination what it will, aught to have at the least 9 Diameters of the Boar about the Breech, measuring at the Touchhole, and at the Meeks 7 Diameters of the Boar, and 5 Diameters about the Mussel at the Neck: if they have less than is abovesaid, they cannot suffer their true proportion of Powder, either for Proof or Action: but this you must help, by what shall be fully described in its proper place. CHAP. XIII. How to Extract the Wind from the Boar of a Piece Geometrically, and thereby to know a fit Ball for the same. A good way to find the Wind of a Piece of Ordnance under four pound Ball. FIrst, You are to draw the Diameter of the Boar BD, and that Line you are to divide into two equal halves, as EBB and ED; then you have the Centre E, by which you draw the Circle ADCB: Which being done, with your Compasses at the same extent draw an Arch from the point D, extended to AEC; then draw the Chord-Line ALC; keeping still your Compasses at the same extent, measure from A to D, then to C, and so to O: then extend your Compasses from D to O, and draw the Arch ON, which cutteth the Diameter in F: then divide the Line FB into three equal parts, and take one of these parts and place under the Centre E in H, extend your Compasses from H to D, and draw the Circle, whose Diameter is DG, and is the Ball fitting for such a Piece, where you are to observe that GB is the Height of the Wind of the Piece. Observation. And though this former Demonstration be approved by many Gunners, yet I find it by my Observation, better to demonstrate the Wind of a Piece, as in the Figure following. First, Draw the Diameter BASILIUS, which being divided into two equal parts at C, extend your Compasses from C to A or B, and draw the Circle 1.2.3.4.5, which here represents the Boar of the Piece: Keeping your Compasses at the same extension, place one foot in A, and draw the Arch 2, A true way to Extract the Wind of a Piece of Ordnance, and thereby to find her true Ball. C, X; then drawing the Chord-Line 2, X, it divides the Semi-diameter of the Boar into two equal parts; than you are to extend your Compasses to the distance AD, or DC: So fixing one foot of your Compasses in A, you are to measure five of these Dimensions about the Circle, as you see them described, 1.2.3.4.5; then you must extend your Compasses from A to 5, and draw the Arch 5, Q, whereof A is the Centre; than you must divide the distance OB into two equal parts, and take one of these parts, and set it upon the Diameter below C in the point E; then you are to extend your Compasses from E to A, keeping one foot in E, draw the Circle, whose Diameter is AEO: and is a Ball fit for such a Piece as hath for Diameter ACB. The same by Calculation. In the following Diagram AB, the height of the Boar of a Piece being given, to find the Diameter of the Ball AO. First, Take the Semi-Radius ALL, and set it off in the Circumference from A towards B five times, as you see here marked with 1.2.3.4. G; or 1.2.3.4. Q: then extend your Compasses from A to G, and draw the Arch GOQ, so is AO the Diameter of the Ball, and BOY the Wind. Now to find this by Calculation, First consider that AGNOSTUS or AQ is equal to AO, and A 1 equal to ALL; then ALL being the Semi-Radius 50000, is equal to the Chord A 1, withal considering that the Chord of an Arch is equal to double the Sine of half that Arch; Now then 25000 the half of ALL is the Sine A, which in the Table of Natural Sins, giveth 14° 29′, for the Arch A, the double whereof giveth 28° 58′, for the quantity of the Arch A 1, which being quintupled, or multiplied by 5, giveth 144° 50′ for the Arch AGNOSTUS or AQ, so that the Arch GBQ is 70° 20′: The Angle ACG may be measured with a Line of Chords from the Plane Scale to be 144° 50′. The Chord whereof AGNOSTUS, is equal to twice the Sine of 72° 25′, viz. 95327; the double whereof is 190654, which is equal to the height of the Ball, in comparison to the Boar AB, 200000, twice the Radius, or the whole Diameter. In Proportion, as Double is to Double, so is Single to Single: Therefore as 190654 is unto the Diameter 200000, so is the half thereof 95327, the Sine of 72° 25′ unto the Radius: I say then, if the height of the Boar of any Piece of Ordnance be divided into 100000 parts, than the Diameter of the Ball is for the same Piece 95327 of the same parts; and the Wind is the Difference, which is 4673 parts, so that the Boar will be about 21 ⅖ times the height of the Wind. If the Height of the Boar be given, to find the Diameter of the Ball. The Proportion is: As the Radius is to the Height of the Bore given: So is the Sine of 72° 25′, unto the Diameter of the Ball required. Or, if the Diameter of the Ball be given to find the Boar: Say then, As the Sine of 72° 25′ is in Proportion to the Diameter of the Ball: So is the Radius to the Height of the Boar. Example 1. I have an Iron Ball whose Diameter is four Inches, and weigheth 9 lb English Weight, and I desire to know what height the Boar of the Piece will be, which this Ball shall fit, the Wind duly extracted. Sine of 72° 25′ 95327 Inches 4 Radius 100000 4 400000 I Answer, The Height of the Boar of such a Piece of Ordnance is 4 Inches and ⅕ part fere. Example 2. I have a Gun whose Boar is 6 Inches Diameter, and I would know what Diameter must the Ball have, that will fit such a Piece, the Wind duly extracted. Radius ● ⌊ 00000 Inches 6 Sine of 72° 25′ 95327 6 5 ⌊ 71962 I Answer, The Diameter of the Ball that will fit such a Piece, must be 5 Inches, and 7/10 parts of an Inch. And so of others. Another way to Extract the Wind of a Gun, as well Geometrically as by Calculation. The Height of the Boar of any Piece of Ordnance being given, as the Boar AK or GM (in the preceding Diagram) to find the Diameter of the Ball: First, With 60° of the Line of Chords, I draw the Circle DEF; then with 72° of the same Line, I draw the Arches EO and OF, which doth meet in the Point O: From O through the Centre P, I draw the Diameter KA: then from the Centre P, I draw Right Lines through the Points E and F, which doth cut the Circle AK in B and C, and the Circle GM in H and I: So that BC is 72° of the Circle KA, and HI is 72° of the Circle GM, as well as OF is of the Circle DEF: then extend the Compasses from A to B, setting one foot in A, with the other draw the Arch BLC; so is ALL the Diameter of a Ball for the Boar AK: Or from G to H, setting one foot in G, with the other draw the Arch HNI; so is GN the Diameter of a Ball for the Boar GM: Or otherwise, not having a Line of Chords to measure 72°, upon the Circumference of the Bore given: As here in the Boar AK, divide the Circumference of the Boar into five equal parts, as BCSAR, and every one of these parts shall be 72 Degrees. Now to Calculate this Arithmetically; the Chord AB being equal to ALL containeth 144°, or twice 72°; the Sine of 72°, is 95105, the double whereof is 190210, for the Chord AB or ALL, which hath such proportion to the height of the Boar AK 200000, as the Diameter of the Ball is to the Boar. I say then, the Boar being 200000, and the Diameter of the Ball 190210, the one being subtracted from the other, the Difference is 9790, which is the height of the Wind: And if you divide the Diameter of the Boar 200000, by the height of the Wind 9790, the Quotient will give the Wind to be somewhat less than the 20 ½ part of the Boar. The Diameter of the Boar 200000 The Diameter of the Ball 190210 The Difference is the Wind 9790 The Quotient giveth 20 42/100 Times, so that it is less than 20 ½ Times. As the Chord of 144°, viz. 190210, is in Proportion to the Diameter 200000; So is the half thereof the Sine of 72°, viz. 95105, unto the Radius 10000 The Diameter of a Boar being given, to find the Ball. Hence it followeth, That as the Radius is in Proportion to the Diameter of the Boar; So is the Sine of 72° 00′ to the Diameter of the Ball. Or if the Diameter of a Ball were given to find the Boar. Then should the Proportion be, as the Sine of 72° 00′, viz. 95105 is unto the Diameter of the Ball: So is the Radius 100000 unto the Height of the Boar. Example 1. There is a Gun whose Boar is 7 Inches Diameter, I would know what Diameter must the Ball have, that will fit such a Piece, the Wind duly extracted. I Answer, The Diameter of the Ball that will fit such a Piece, must be 6 Inches and 65/100 parts of an Inch. Example 2. There is an Iron Ball whose Diameter is 6 Inches, and weigheth 30 lb 6 Ounces, English Weight: I desire to know what height the Boar of a Piece will be, which this Ball shall fit, the Wind duly extracted. Sine of 72° 00′ 95105 Inches 6 Radius 100000 6 600000 I Answer, The Height of the Boar of such a Piece of Ordnance will be 6 Inches and 3/10 parts of an Inch. And so of others. Observation. The Diameter of the Piece ACB is 4 ⅕ Inches very near, which is the Diameter of a Ball of 9 ¼ lb Scots weight. And the Diameter of the Ball which is AEO 4 Inches, is 8 lb Scots weight. Now the aforesaid Diameter ACB of 4 ⅕ Inches, is the Diameter of a Ball of 10 ⅜ lb English weight. And likewise the Diameter AEO; of 4 Inches, is the Diameter of a Ball of 9 lb English weight. There is a Difference between Scots and English Weight, as So that the Difference between Scots and English weight is as 8 is to 9; that is to say,8 is to 9 That 8 lb Scots maketh 9 lb English. For the first Demonstration, the Diameter DB is 3 ⅘ Inches, which is near the Diameter of a Ball of 6 17/20 lb Scots weight, And near the Diameter of a Ball of 7 11/16 lb English weight. And the Diameter DHG is 3 ½ Inches, which is the Diameter of a Ball of 5 lb 6 ⅛ Ounces very near of Scots weight. And the Diameter of 3 ½ Inches, is near 6 lb English weight, not following the Tables of Mr. Smith, nor any other that I have seen as yet set forth; As I intent to Demonstrate in its due place. Examples. Take the just Diameter of the Boar of your Piece, which you divide into two equal parts, and draw the Circle ABE; then the Compasses at the same station, you place one foot in A, and another in B, and draw the Cross Arches ACB: From C draw a Line through the Centre D to E, and then draw the Line A then place one foot of your Compasses in E, and draw the Arch AB: then place one foot of your Compasses in the Centre D, and extend the other to the Arch F, so draw the Circle FG: which he saith is the way to find a true Ball. Answer to the Objection. Here you have the Demonstration of Mr. Henry Hexham, where you see a gross mistake; For as he supposeth FG, or EKE to be the true Ball: And I find IE is the true Ball for that Piece, and have wrought this as you have it in Folio 28. Wherefore I leave the Ingenious Gunner to judge, which of these Experiments are the best and truest. CHAP. XIV. The Demonstration of the Cannon-Bore, and of all other Pieces of Ordnance to the Rabinet, by Letters: As also the Geometrical Extracting or Deducing of the Wind or Vent of those Pieces, whereby you may know the exact Diameter of the true Ball fitting those Pieces. Weight of Ball. lb lb WA is the Boar of the Cannon-Royal; the distance betwixt A and B, is the true Vent or Wind, that aught to be betwixt the Ball B, and the Bore A— 64 72 WC is the Boar of the Cannon-Ordinary; the Distance CD is the Wind; and D the Height of the Ball— 48 54 WE is the Boar of the French-Cannon; OF the Wind; F the Diameter of the Ball— 36 40 ½ WG is the Boar of the Demi-Cannon Royal; GH the Wind; H the Diameter of the Ball— 30 33 ¾ WIDOW is the Boar of the Demi-Cannon Ordinary; IK the Wind; K the Diameter of the Ball— 24 27 WL is the Boar of the Culverin, or Demi-French Cannon; LM the Wind; and M the Diameter of the Boar— 18 20 ¼ WN is the Boar of the Quarter-Cannon Ordinary; NO the Wind; and O the Diameter of the Ball— 12 13 ½ WP is the Boar of the Demiculvering; PQ the Wind; and Q the Diameter of the Ball— 8 9 WR is the Boar of a large Sacker; RS the Wind; and S the Diameter of the Ball— 6 6 ¾ WITH is the Boar of a Sacker; VT the Wind; and V the Height of the Ball— 5 5 ⅝ WX is the Boar of a Minion; XY the Wind; and Y the Height of the Ball— 3 3 ⅜ WZ is the Boar of a Falcon; ZX the Wind; and X the Height of the Ball— 2 2 ¼ W = is the Boar of a Rabinet; = ⊙ the Wind; and ⊙ the Height of the Ball— 1 1 ⅛ Note: In the Column next your left hand you have the Scots Weight of the Ball; and in the Column next your right hand you have the English Weight of the same. The Ancient and Later Rules given for Gunners, to give Powder to great Ordnance of all sorts, that are drawn on Carriages. According to the custom in former times, the loading of Powder. In Ancient times it is said, That the great Chamber'd-Guns, that shot Stone-Ball, had for their ordinary one pound of Powder to three pound and half, or at most four pound weight of their Ball. This was certainly the first Invention of Guns; and in regard they could not cast Iron, they made their Guns, as Cooper's do Cask, with Staves of Iron and Hoops. Likewise that those Guns that shot Iron-Ball, most have to every three pound of Iron-Ball, one pound of Powder; and this they held for a general Rule, not examining the Fortification of their Pieces. Now at this time Powder was made of all the three Ingredients equal, and therefore could not be strong. But afterward it was found, that all sort of Field-Ordnance, not being Chambered, but true Bored, should be loaded in this manner, (to wit) The Gunner shall take the Diameter of the Ball, or the Diameter of the Boar of the Piece with a pair of Compasses; and this Diameter three times the Gunner must set off upon his Gun from the Touchhole toward the Mussel; which distance being filled with Powder, then, said they, One pound of Powder was allowed to two pound of Ball: this was the Rule of the Primitive Gunners. But now in our time Powder is so variously made, and the difference is such, that it is hardly possible to the best Judgement, to give a true Rule what Powder is sufficient either for Proof or Action; and therefore the Gunner ought to try his Powder before he load his Piece; for it is beyond all question, that if the Powder be decayed, there must be more of it used than of fresh dry Powder: but if Powder be of his Majesty's Tower-Proof, as I am informed, that then the Gunner need not take near so much Powder to shoot among a party of Men, not being at a great distance, as the Piece would crave to batter a Fortification, or Wall, or Gate, or Ship. But because the young Gunner, that is not yet experimented in his Practice, may be taught how he shall load all manner of Guns; and that it is to be understood, that ordinarily those that will be called Gunners, though not known in the Art, use to load their Guns with half the weight of the Ball of Powder; this they hold for a general Rule to all Guns, which Rule is not to be slighted on some occasions, with true-Bored, true-Fortified Ordnance, (yet it may be said, they have this by Tradition) to hold this Rule, without adding to reinforced Ordnance, or deducting from those that are lessened of Metal; so that by this they not having any other Rule, discover their own nakedness or emptiness of Art, for I am persuaded that no experienced Gunner, but will hold that the Gunner ought to search, try, and find the Nature and Fortification of a Gun or Guns, before he do hold himself obliged to give a Gun Powder, and thereby to prove a true Charge of Powder for the same. CHAP. XV. The Reasons why I give Guns Powder according to their Fortifications. THese first Rules were derived from the weight of Ball; but since the Rules were made from the weight of the Piece: for they held generally that four ounces of Powder was sufficient for the Gunner to give a Brass Gun, to every hundred weight for Service; and three ounces to every hundred weight of Iron Guns. Neither this nor the other being right, for I have seen Trumpet-bored Iron Guns of 1200 weight, that could not have half the allowed Powder that either of these Rules did allow of. And likewise I read the Cause of the death of King James the second of Scotland, was by the breaking of a great Gun at the Siege of Rosbrugh. For these and the following Reasons, I do not hold with that common received Rule, than which many Gunners know no better, but to give Ordnance Powder by the weight of the Gun. For if there be a Piece of Ordnance of Iron weighing 1600 pound weight, likewise there is another Piece of the same Boar, and of the same weight: Now by the Rule of weight it must have the like Powder. Great Cautions to be observed in giving Guns Powder. But will you consider, for your Instruction, this Piece is longer, and having no more Metal in her than the other, of necessity she must be thinner of Metal; for what she hath of the length, she must want of her thickness, the Boar being both of one denomination; and since she is thinner, it followeth she must not have so much Powder as the other. That Guns ought to be proportioned in length to their Fortification. Likewise if by the Weight of Guns they should have their Powder, why then do not Founders, where they now make them eight foot long, do not make them ten foot? for it is known to the World, that a Piece of ten foot long will shoot farther than a Piece of eight foot long, but not without equal Powder: Wherefore it is to be considered, they must be both of one Fortification; and being alike in strength, the longest of the two ought to shoot farthest, because more of her Powder is spent in Fire before she deliver her Ball. Question. But some may demand what I mean by Fortified Ordnance? This is the true Geometrical Demonstration of the Boars of Ordinance, with the height of their Ball from 1 lib to 64 lib Scots weight, And the true Wind which ought to be betwixt the Diameter of the Boar and the Diameter of the Ball. Likeways of the English weight of the Ball from 1.2 lib. to 72 lib And their Wind betwixt the Diameter of the Ball, and the Diameter of the Boar. This doth not hold with the General Rule that a 1/20 part of the Diameter of the Ball is the Wind for all Guns But if all Ball were Cast or Turned to a true Roundness, then though they did only fit to go home, the less wind the better. Now to be capable of the same Proportion Arithmetically, the Proportion is, as 22 the Circumference is unto 7 the Diameter: So must 11 the number of times which the Diameter of the Bore measured about her Breech be, to a number sought for; which by the Work I find to be 3 ½ Diameters of the Boar, which this Piece is of Diameter at the Touchhole. Cometh 3 and ½ ½ which is equal to ½. Rules to find the thickness of a True Bored Gun in one side Metal, by all the Diameter. Whilst the Boar itself is one of the Diameters, that being deduced from 3 ½, rests 2 ½, whereby 1 ¼ is the thickness of that Piece in one side Metal; and because these be the Ordnance of Iron, by which the Ground-Rule may be and ordinarily is laid down, to give Guns their Powder of other Fortifications; for you must know that there are some lessened, as thinner Fortified, and so cannot have the same proportion of Powder, though they shoot one and the same Ball: Likewise there are reinforced or thicker Ordnance at the charged Cyllinder, which shoot the same Ball, and must have more Powder: So you may see that the Iron Piece is 11 Diameters of the Boar about the Breech, 9 Diameters at the Trunions, and 7 at the Neck. The true Proportion of a true Bored, and true Fortified Piece of Ordnance. Likewise the Brass Piece is no thicker at the Charged Cylinder, than the Iron Piece is at the Trunions, yet shoots the same Ball, and must have the same Powder; her Proportion is 9 Diameters of the Boar about the Breech, 7 about the Ears, and 5 about the Neck. Seeing you have the Proportion of these true Fortified Ordnance; now it followeth of necessity that the Powder of all such Ordnance should be known: And as writing at length would be tedious, therefore I have Calculated Tables both for Proof and Action, not denominating the Names or Weight of these Ordnance. But thus fortified with 11 Diameters of the Boar about the Breeech, if Iron, Ordnance shooting from one pound Ball to 48 pound. Also the same Tables will serve for Brass Ordnance, being Fortified with 9 Diameters of the Boar about the Breech, by what name soever you define them, shooting from one pound Ball, to 48 pound Ball. The Weight of the Ball and Fortification of Ordnance, are true Rules to give Guns their Powder. Hereby it is clear, That we are not to examine the Weight of Ordnance, and thereby to give them Powder; but inspection is to be had to the Fortification of all sorts of Ordnance, as also to their Weight of Ball: To find the Ball fitting a Piece, by extracting the Wind Geometrically, whereby you may have the true Diameter of the Piece, and by the Diameter you may find the Weight of the Ball, as shall be shown at large in its place, in Tables, Scale, or Height-Rule, and also Arithmetically. But in regard there hath never any pains been taken for regulating the true Powder for Ordnance, I have therefore set down these Tables following for Powder, for Proof and Action of true-Bored and true Fortified Ordnance. Table for Proof-Powder, for True-Bored and True-Fortified Ordnance, either of Brass or Iron. B P B P B P 1 1      00 17 11      12 33 22      00 2 2      00 18 12      00 34 22      10 3 3      00 19 12      11 35 23      05 4 4      00 20 13      06 36 24      00 5 5      00 21 14      00 37 24      10 6 6      00 22 14      11 38 25      05 7 7      00 23 15      05 39 26      00 8 8      00 24 16      00 40 26      10 9 8      12 25 16      11 41 27      05 10 9      08 26 17      05 42 28      00 11 10      00 27 18      00 43 28      10 12 10      08 28 18      11 44 29      05 13 10      14 29 19      05 45 30      00 14 11      02 30 20      00 46 30      10 15 11      05 31 20      10 47 31      05 16 11      08 32 21      05 48 32      00 In this Table you have the weight of Ball, in the first, third, and fifth Columns, and is marked with the Letter B; and in the second, fourth, and sixth Columns, the Powder to prove these Guns, which is marked with the Letter P, being true-Bored and Fortified, Brass 9, and Iron 11 Diameters of the Boar about the Breech. Table for Action, of True-Bored and True-Fortified Ordnance, either of Brass or Iron. B P B P B P 1 0      10 17 7      11 33 14      10 2 1      02 18 8      00 34 15      02 3 1      12 19 8      07 35 15      09 4 2      05 20 8      14 36 16      00 5 3      00 21 9      05 37 16      07 6 3      09 22 9      12 38 16      14 7 4      03 23 10      03 39 17      05 8 4      12 24 10      10 40 17      12 9 5      02 25 11      01 41 18      03 10 5      06 26 11      08 42 18      10 11 5      10 27 12      00 43 19      01 12 6      00 28 12      07 44 19      09 13 6      06 29 12      14 45 20      00 14 6      12 30 13      05 46 20      07 15 7      02 31 13      12 47 20      14 16 7      07 32 14      03 48 21      05 In this Table you have the weight of Ball, in the first, third, and fifth Columns, marked with the Letter B; and in the second, fourth, and sixth Columns, being marked with the Letter P, the Powder for Action, for the Guns being Fortified as before-said, either Brass or Iron. The Proportion you find in the Copper print, N′ 1 and N° 2. A Scale you have for Powder, both for English and Scots true-Bored true-Fortified Ordnance, Brass or Iron, for Service, on the Quadrant-Rule. Having shown the Proportion of these Ordnance, and their due Powder, both for Proof and Action, it is now necessary to know the Proportion of their Ladles, Rammers, and Spong-heads. First, Know that all true-Fortified Ordnance have not one Proportion of Powder, as you may see by the foregoing Tables; neither must their Ladles be of equal length or breadth according to their Boar. The Proportion of Powder as supposed. To make this the more clear, know that the Powder doth not lie in one proportioned length in every true-Bored, true-Fortified Piece; For those that shoot from one pound Ball to eight pound, the Powder lieth three Diameters of the Ball in length in a Cartradge, made on a Mould of the Diameter of the Ball. Names of Guns. The names of these Ordnance are these; a Base, a Fauconet, a Falcon, a Minion, a Saker, and a Demiculvering. Proportion of Powder, and names of Guns. Likewise for these Ordnance that shoot from eight pound Ball to eighteen pound, the Powder lieth about two Diameters and a half long in a Cartradge, made on the Diameter of the Ball; their names are Demiculvering, Quarter-Cannon, Culverin, or French Demi-Cannon. Proportion of Powder and names of Ordnance. And for these true-Bored, true-Fortified Ordnance, that shoot from 18 lb Ball to 48 lb, the Powder lieth two Diameters and a quarter long in a Cartradge, made on a Mould of the Diameter of the Ball: The names of these Ordnance, are Culverin, or French Demi-Cannon, Demi-Cannon Ordinary, Demi-Cannon Royal, French-Cannon, and Cannon-Ordinary; and other names they have, as Bazalisks, etc. By what is before taught, you may know that the Ladles of Ordinance, though of one Fortification, ought not to be of one Proportion. Proportion of Ladles. You must make the Ladles for small Ordnance, viz. from one pound to eight, of three Diameters of the Ball in length, with as much as will nail it on the Ladle-head, and the breadth of those Ladles ought to be of 1 ⅚ one Diameter and five sixth parts of the Ball; this Ladle nailed on a wooden head made of purpose, three fills thereof of Powder will serve for Proof, and 2 fills of Powder will serve for Action to these Guns. And the Ladles for true-Bored, true-Fortified Ordnance, shooting from 8 lb Ball to 18, aught to be two Diameters and a half of the Ball long, with as much as will nail it on the Rammer-head; and the Breadth of these Ladles, one and five sixth parts of the Diameter of the Ball: Three of these Ladles full of Powder will serve for Proof, and two full of Powder will serve for Action. Also those Ladles for true-Bored, true-Fortified Ordnance, that shoot from 18 lb Ball to 48 lb, or 64 lb, aught to be two Diameters of the Ball long, and one and five sixth parts of the Diameter of the Ball broad: Three of these Ladles full of Powder will serve for Proof, and two full of Powder will serve for Action. CHAP. XVI. AS there are true-Bored, true-Fortified Ordnance both of Brass and Iron; that is to say, 11 Iron, and 9 Brass: So there are true-Bored Iron Ordnance of 10 Diameters of the Boar in the Breech, and Brass of 8 Diameters of the Boar about the Breech. And because I know that some Gunners are not acquainted with Arithmetic, (for I have been at Sea with a Gunner that could not read) and so such Men not being able to Calculate the Powder of any Guns: Therefore for the public good of all, I have taken the pains to Calculate Tables for their help; these Tables serve for Iron of 10 Diameters of the Breech, and may well serve for Brass of 8 of the Breech, as the Figures hereby showeth; For the Iron Gun is 10 Diameters of the Boar about the Breech, 8 2/11 at the Ears, and 6 4/11 at the Neck. The Brass Piece is 8 2/11 Diameters of the Boar about the Breech, 6 4/11 at the Ears, and 4 6/11 at the Mussel: And their Diameters are wrought by the Rule of Archimedes; that is to say, As 22 is to 7, so is 10, 8 2/11, 6 4/11, or 8 2/11, 6 4/11, 4 6/11, to their Diameters: As you have it clearly demonstrated in its proper place; For by their Fortifications they are to have their Powder, as the Tables following showeth. This Table showeth Proof-Powder for Iron Ordnance of 10 Diameters of the Boar, and for Brass of 8 2/11 Diameters of the Boar about the Breech. B P B P B P 1 0      12 17 8      13 33 16      08 2 1      08 18 9      00 34 17      00 3 2      04 19 9      08 35 17      08 4 3      00 20 10      00 36 18      00 5 3      12 21 10      08 37 18      08 6 4      04 22 11      00 38 19      00 7 5      03 23 11      08 39 19      08 8 6      00 24 12      00 40 20      00 9 6      09 25 12      08 41 20      08 10 7      02 26 13      00 42 21      00 11 7      08 27 13      08 43 21      08 12 7      14 28 14      00 44 22      00 13 8      02 29 14      08 45 22      08 14 8      06 30 15      00 46 23      00 15 8      08 31 15      08 47 23      08 16 8      10 32 16      00 48 24      00 This Table showeth Powder for Action for Iron Ordnance of 10 Diameters of the Boar about the Breech, and for Brass of 8 Diameters about the Breech. B P B P B P 1 0      7 ½ 17 5      12 ½ 33 11      02 2 0      12 18 6      00 34 11      07 3 1      04 19 6      5 ½ 35 11      12 4 1      12 20 6      10 ⅔ 36 12      01 5 2      04 21 6      15 ⅚ 37 12      06 6 2      10 ¾ 22 7      05 38 12      11 7 3      02 23 7      10 ½ 39 13      02 8 3      07 24 7      15 ¼ 40 13      07 9 3      12 25 8      05 41 13      12 10 4      1 ½ 26 8      10 42 14      01 11 4      3 ½ 27 9      00 43 14      06 12 4      8 ½ 28 9      05 44 14      11 13 4      12 ½ 29 9      10 ½ 45 15      00 14 5      1 ¾ 30 10      01 46 15      05 15 5      5 ¾ 31 10      06 47 15      10 16 5      8 ½ 32 10      10 48 16      00 The Proportion you have in the Copper Plates, N° 3 and 4. In the last preceding Tables, the first Table or the Table next your left hand, sheweth the weight of the Ball, in the first, third, and fifth Columns, and is marked with the Letter B; in the second, fourth, and sixth Columns, you have the Powder to prove these Guns, which are marked with the Letter P; being true-Bored and Fortified as before-said. In the right hand Table you have the Weight of the Ball in the first, third, and fifth Columns, marked with the Letter B; and in the second, fourth, and sixth Columns, being marked with the Letter P, the Powder for Action for the Guns, being Fortified as before-said, either of Brass or Iron. Now there are Ordnance of Iron Fortified with 9 Diameters of the Boar about the Breech, and Brass of 7 about; And in regard I have seen divers mistakes about giving them Powder, even of Men professing great Knowledge without Reason; Therefore I will here describe these Tables following, to give them their due Powder. Lower Fortified than 9 of Iron, and 7 of Brass, you shall hardly find a true-Bored Piece of Ordnance; The Iron Ordnance being 9 Diameters of the Boar about the Breech, 7 at the Trunions, and 5 8/11 at the Mussel or Neck; The Brass Ordnance of 7 Diameters of the Boar at the Breech, 5 8/11 about the Trunions, and 4 1/11 at the Neck. This Table is the Proof for Iron Ordnance of 9 Diamet. in the Breech, and Brass of 7. B P B P B P 1 0      8 ½ 17 6      06 33 12      00 2 1      1 ½ 18 6      09 34 12      06 3 1      10 ⅓ 19 6      12 35 12      12 4 2      03 20 7      02 36 13      01 5 2      12 21 7      09 37 13      07 6 3      4 ½ 22 8      00 38 13      13 7 3      13 ½ 23 8      6 ½ 39 14      03 8 4      04 24 8      12 40 14      09 9 4      13 25 9      02 41 14      15 10 5      3 ¼ 26 9      6 ½ 42 15      05 11 5      08 27 9      13 43 15      11 12 5      12 28 10      03 44 16      01 13 5      15 ¼ 29 10      09 45 16      07 14 6      1 ½ 30 10      15 46 16      13 15 6      2 ¾ 31 11      05 47 17      03 16 6      04 32 11      10 ½ 48 17      08 This Table is the Powder for Action, for Iron of 9, and Brass of 7 Dimeters of the Boar about the Breech. B P B P B P 1 0      5 ½ 17 4      3 ½ 33 8      00 2 0      10 18 4      06 34 8      4 ½ 3 0      15 19 4      9 ¾ 35 8      8 ½ 4 1      04 20 4      13 36 8      13 5 1      10 21 5      00 37 9      01 6 1      15 ½ 22 5      05 38 9      04 7 2      05 23 5      09 39 9      08 8 2      09 24 5      13 40 9      11 9 2      12 25 6      0 ¾ 41 9      14 10 2      15 ½ 26 6      4 ¾ 42 10      00 11 3      1 ½ 27 6      09 43 10      03 12 3      4 ½ 28 6      13 44 10      5 ½ 13 3      7 ¾ 29 7      0 ¾ 45 10      08 14 3      11 30 7      4 ½ 46 10      12 ½ 15 3      14 ¼ 31 7      09 47 11      00 16 4      01 32 7      13 ½ 48 11      03 The Proportions you have in the Copper Plate, N° 5 and 6. Now as these are the Tables for true-Fortified, and lessened in Metal, I hold convenient to give Tables for Reinforced Ordnance; these have commonly, being Brass, 10 Diameters of the Boar about the Breech, and Iron 12 about the Breech. And though to some these Tables may seem foolish, I have seen those who have been esteemed Able Gunners, that knew not how to give such Guns Powder; yea, they have in my presence wagered, and not one of them knew what they wagered concerning two such Guns lying at the Head of Ferveer confer; where amongst six Gunners one only understood to give these two Guns their true Powder; as at the Discussion, a Gentleman of the Ordnance to the States did manifest in favour of the one Man. How many Gunners at the Wager, and but one capable. I also have been in contest with one professing great Art, and was a rare Person in Art: Yet in the Castle of Edinburgh, there was a Gally-Gun of Brass that did shoot 28 lb Ball; and thereby he did conclude that Piece to have 13 or 14 lb of Powder for Action: In hearing this Expression I did laugh: This Dispute was between a general Person and a Gunner. The Gentleman was offended, and asked if I could teach him, (it was but in disdain); I answered, Sir, if you know not better than you express, I am sure I am able to teach you in this point: Whereupon he went out at the Castle-Gate, and was ever mine Enemy from that time forth. And to satisfy the Reader, I will give the Dimensions of that Piece: She was but 7 Diameters of the Boar about the Breech, and 5 ½ about the Mussel, for she was plain without Rings, except the Base and Musle-Rings, or Cornish-Rings; so that by her Fortification she could suffer but 6 lb and 13 ounces of Powder; and with so much I have caused her to be discharged divers times, and could do Service with this Piece, What may be done with a lessened piece, as if it were a Morter-Peece. which could not be done with a true-Fortified Piece; for with this Piece I have shot over the Steeple of Edinburgh, and the Ball hath fallen at the next Lodging where Cromwell did lie. And this I did for three times together, till our Governor discharged me to shoot any more for troubling his Friend. Therefore I say, An able Man may be mistaken of a Gun, when he neither knoweth the Fortification nor Proportion how to Work to give a Piece Powder. So to avoid trouble to Artists for Calculating, and to instruct those Gunners that are not capable of Calculation, I have here set down the Demonstration of 〈◊〉 Guns of Iron, having 12 about the Breech, and Brass having near 10 Diameters about the Breech, and are called Reinforced Ordnance. The Figures following Demonstrate the true Proportion of these Reinforced Ordnance, which require more Powder than true-Bored, true-Fortified Ordnance, as you may see by the Tables following; which Tables might have been first of all: but I observe that the Ground-Rule must be put in the first place; And those that do take their Dimensions from it do follow, whether they be Reinforced or lessened of Metal, such as are formerly described. These following Tables, are Tables for Reinforced Ordnance, which are such as have more strength of Fortification, and are more able to endure firing: Such as be the Bazalisks, Serpents, or Slings, etc. and are good to shoot with at a great distance. Having, as I suppose, given a full account of the true allowance of Powder for all sorts of true-Bored Ordnance, both for Proof and Action, whether they be Brass or Iron Guns, it followeth that the Gunner ought to know how to go to work with his Piece, when he is to apply these Tables, by which he is to give fire. These Rules are to be observed. First, He shall take a piece of Twine, which is to be well waxed, as the Shoemakers do their Thread, that it do not stretch nor shrink; then measure the Piece about at the Touchhole betwixt the Rings, and taking with a pair of Compasses the Diameter of the Boar at the Mussel, measure the Twine how many Diameters of the Boar is contained about the Breech of the Piece, that keep in memory. Now you are to know what Ball fits that Piece, as is plainly set down pag. 42. Geometrically; but may be exactly found in the Tables of Height and Weight of Shot, and in the Tables of Diameters of Boars, either Scots or English. When you have found the Diameter of the Ball, if you cannot Arithmetically find the Weight by the Diameter of the Ball, than you may resort to the Tables for such Fortifications, and next the weight of Ball you have the weight of Powder for that Piece: but you must be sure your Piece must be true-bored, as is mentioned in pag. 58. For if the Piece be either Tapered, Chambered, or Trumpet-bored, these Tables will do no service. Proof-Powder for Reinforced Ordnance, or Iron Guns of 12 Diameters of the Boar about the Breech, and Brass Guns near 10 Diameters. B P B P B P 1 1      05 17 15      01 33 28      08 2 2      09 18 15      05 34 29      10 3 3      10 19 16      07 35 30      08 4 5      01 20 17      05 36 31      08 5 6      08 21 18      02 37 32      04 6 8      05 22 18      15 38 33      01 7 9      01 23 20      00 39 34      02 8 10      06 24 20      12 40 35      00 9 11      06 25 21      09 41 35      12 10 12      05 26 22      08 42 36      08 11 12      15 27 23      07 43 37      08 12 13      10 28 24      12 44 38      05 13 14      01 29 25      01 45 39      04 14 14      07 30 26      00 46 40      02 15 14      10 31 26      14 47 41      00 16 14      14 32 27      10 48 41      12 In this Table you have the weight of Ball, in the first, third, and fifth Columns, and is marked with the Letter B; and in the second, fourth, and sixth Columns, you have the Powder to prove these Guns, which is marked with the Letter P; being true-Bored and Fortified, as above written. Powder for Action of Reinforced Ordnance, or Iron Guns of 12 Diameters of the Boar about the Breech; and Brass near 10 Diameters about the Breech. B P B P B P 1 0      13 17 10      02 33 19      04 2 1      7 ½ 18 10      05 34 19      14 3 2      4 ½ 19 11      01 35 20      08 4 3      00 20 11      10 36 21      01 5 3      15 21 12      03 37 21      09 6 4      14 22 12      15 38 22      01 7 5      08 23 13      08 39 22      10 8 6      02 24 14      00 40 23      03 9 6      10 25 14      08 41 23      12 10 7      02 26 15      00 42 24      06 11 7      09 27 15      12 43 24      14 12 7      15 28 16      03 44 25      08 13 8      05 29 16      12 45 26      03 14 8      14 30 17      04 46 26      13 15 9      06 31 18      01 47 27      04 16 9      12 32 18      10 48 28      14 In this Table you have the weight of Ball, in the first, third, and fifth Columns, marked with the Letter B; and in the second, fourth, and sixth Columns, you have the Powder for Action, which is marked with the Letter P; being true-Bored and Fortified, as above written. These Proportions you have in the Copper Plate, N° 7 and 8. CHAP. XVII. To find the Weight of an Iron Ball in English Inches Arithmetically for Scots Weight. FOr those that cannot find the Weight of the Ball by Arithmetic, I will here show them a Rule, and also Tables which I have Calculated, as well Decimally, as in Pounds, Ounces, and Drams, from eight parts to eight of an Inch of the Diameter of a Ball, unto 10 Inches Diameter, both in Scots and English Weight, and also in Scots and English Inches, for the Artificial Gunner his more ease. It falls out many times that the Gunner cannot find Weights and Scales to weigh his Shot; it is therefore necessary the Gunner should know how to find the Weight of his Shot Arithmetically; as thus, If you desire to know the weight of a Ball, whose Diameter is just Inches, without any Fraction or parts of an Inch, than you are to multiply the Diameter Cubically; then double that Product, and divide the Total by 16, you have in the Quotient the Pounds that the Ball weigheth; and what Remainder you have over, you shall know that Remainder is Ounces. Example. There is a Ball of 4 Inches Diameter given, to find his Weight: The Cube of 4 is 64, which being doubled maketh 128; this 128 being divided by 16, (the ounces in a pound) the Quotient giveth 8, which is 8 lb of Scots Weight which that Ball doth weigh. Behold the Work. 4 4 16 4 64 64 128 Eight pound of Scots weight is the true weight of that Ball. An because every Gunner hath not Arithmetic at his finger's ends, and also to ease the Artificial Gunner, I have taken the pains to Calculate these following Tables, both of Scots and English Weight and Measure, etc. as before-said. I do not take them on trust as others do, but have Calculated them myself from the Ground-Rules, and have given credit to none, because I never found any yet truly set forth. Tables for Iron Ball, whose Diameters being measured with English Inches, are exactly Calculated for Scots Weight, from eight parts to eight parts of English Inches, unto ten Inches: Decimally. B Li.        Parts. B Li.        Parts. B Li.        Parts. B Li.        Parts. ⅛ 00       00024 2 ⅝ 02       26099 5 ⅛ 16       82642 7 ⅝ 55       41528 ¼ 00       00195 2 ¾ 02       59961 5 ¼ 18       08789 7 ¾ 58       18555 ⅜ 00       00659 2 ⅞ 02       97046 5 ⅜ 19       41089 7 ⅞ 61       04663 ½ 00       01562 3 03       37500 5 ½ 20       79687 8 64       00000 ⅝ 00       03052 3 ⅛ 03       81470 5 ⅝ 22       24731 8 ⅛ 67       04712 ¾ 00       05273 3 ¼ 04       29102 5 ¾ 23       76367 8 ¼ 70       18945 ⅞ 00       08374 3 ⅜ 04       80542 5 ⅞ 25       34741 8 ⅜ 73       42847 1 00       12500 3 ½ 05       35937 6 27       00000 8 ½ 76       76562 1 ⅛ 00       17798 3 ⅝ 05       95435 6 ⅛ 28       72290 8 ⅝ 80       20240 1 ¼ 00       24414 3 ¾ 06       59180 6 ¼ 30       51758 8 ¾ 83       74023 1 ⅜ 00       32495 3 ⅞ 07       27319 6 ⅜ 32       38550 8 ⅞ 87       38062 1 ½ 00       42187 4 08       00000 6 ½ 34       32812 9 91       12500 1 ⅝ 00       53638 4 ⅛ 08       77368 6 ⅝ 36       34692 9 ⅛ 94       97485 1 ¾ 00       66992 4 ¼ 09       59570 6 ¾ 38       44336 9 ¼ 98       93164 1 ⅞ 00       82397 4 ⅜ 10       46753 6 ⅞ 40       61890 9 ⅜ 102       99683 2 01       00000 4 ½ 11       39062 7 42       87500 9 ½ 107       17187 2 ⅛ 01       19946 4 ⅝ 12       36645 7 ⅛ 45       21313 9 ⅝ 111       45825 2 ¼ 01       42383 4 ¾ 13       39648 7 ¼ 47       63476 9 ¾ 115       85742 2 ⅜ 01       67456 4 ⅞ 14       48218 7 ⅜ 50       14136 9 ⅞ 120       37085 2 ½ 01       95312 5 15       62500 7 ½ 52       73437 10 125       00000 In this Table you have eight Columns; in the first, third, fifth, and seventh Columns, there are the Inches, and eight parts of Inches that the Diameter of the Ball doth contain, and are marked with the Letter B: And in the second, fourth, sixth, and eight Columns, you have the weight of these Diameters of Iron Ball in Scots Weight; under Li. you have Pounds; and under Parts, you have the Decimal parts of Pounds. Tables for Iron Ball, whose Diameters being measured with English Inches, are exactly Calculated for Scots Weight, in Pounds, Ounces and Drams, from eight parts to eights part of English Inches, unto 10 Inches. B Li.        On.        Dr. B Li.        On.        Dr. B Li.        On.        Dr. 1 00      02      00 4 08      00      00 7 42      14      00 1 ⅛ 00      02      14 4 ⅛ 08      12      06 7 ⅛ 45      03      07 1 ¼ 00      03      14 4 ¼ 09      09      08 7 ¼ 47      10      01S 1 ⅜ 00      05      03 4 ⅜ 10      07      08 7 ⅜ 50      02      04 1 ½ 00      06      12 4 ½ 11      06      04 7 ½ 52      11      12 1 ⅝ 00      08      09 4 ⅝ 12      05      14 7 ⅝ 55      06      10 1 ¾ 00      10      11S 4 ¾ 13      06      05 7 ¾ 58      02      15 1 ⅞ 00      13      03 4 ⅞ 14      07      11S 7 ⅞ 61      00      12 2 01      00      00 5 15      10      00 8 64      00      00 2 ⅛ 01      03      03 5 ⅛ 16      13      04 8 ⅛ 67      00      12 2 ¼ 01      06      12 5 ¼ 18      01      06 8 ¼ 70      03      00 2 ⅜ 01      10      13 5 ⅜ 19      06      09 8 ⅜ 73      06      14 2 ½ 01      15      04 5 ½ 20      12      12 8 ½ 76      12      04 2 ⅝ 02      04      03 5 ⅝ 22      03      15 8 ⅝ 80      03      04 2 ¾ 02      09      09 5 ¾ 23      12      03 8 ¾ 83      11      13 2 ⅞ 02      15      08 5 ⅞ 25      05      09 8 ⅞ 87      06      01S 3 03      06      00 6 27      00      00 9 91      02      00 3 ⅛ 03      13      00 6 ⅛ 28      11      09 9 ⅛ 94      15      10 3 ¼ 04      04      10 6 ¼ 30      08      04 9 ¼ 98      14      14 3 ⅜ 04      12      14 6 ⅜ 32      06      03 9 ⅜ 102      15      15 3 ½ 05      05      12 6 ½ 34      05      04 9 ½ 107      02      11S 3 ⅝ 05      15      04 6 ⅝ 36      05      09 9 ⅝ 111      07      05 3 ¾ 06      09      07 6 ¾ 38      07      01S 9 ¾ 115      13      11S 3 ⅞ 07      04      06 6 ⅞ 40      09      14 9 ⅞ 120      05      15 In this Table you have six Columns; in the first, third, an fifth Columns, there are the Inches, and eight parts of Inches, that the Diameter of the Ball doth contain, and are marked with the Letter B; and in the second, fourth, and sixth Columns, you have the Weight of these Diameters of Iron Ball in Scots Weight; under Li. you have Pounds, under On. Ounces, and under Dr. Drams. The Height-Rule you have on the side of the Quadrant, which proves this Table. This Table be Admirable to some Gunners, and especially English, because their Weight and the Scots Weight doth not hold alike; have perused the Tables of Weight by most of the Authors of Gunnery, and I find them all to agree, and hold firm, as Mr. Nye writeth. But indeed I find nothing of ingenuity, for a Man to copy a Table from another's Works, and never examine the Truth of the Work; But I have made use of their own Ground-Rule, and find not one of them to have wrought it, or set the Table down truly. I will here set down the Ground-Rule by which they are to make their Table, that the Ingenious Gunner may Correct it himself at his pleasure. Mr. Nye says, That two Inches Diameter, is 1 pound 1 ounce. Thus they set it down, 2 Inches Diameter give 1 pound 1 ounce. Now having this for a Rule, you may, if you please, make a Table. Behold the Work. Where you see, if 2 Inches give one pound one ounce, 2 ¼ Inches giveth 1 pound, 8 ounces, and 3 drams, whereof 16 make an ounce. And by their Tables, because they would be near the Right, they set down 4 Inches to give 8 pound 15 ounces; where by this Work it will be but 8 pound 8 ounces. The truest Rule. But there is another more sure way, by this Work following: Say, As 2 Inches is to one pound two ounces: So is the Diameter given, unto the Weight required. Behold the Work. For by this Rule I have Calculated the Table following. Tables for Iron Ball, whose Diameters being measured with English Inches, are exactly Calculated Decimally for English Weight; from eight parts to eight parts of English Inches, unto 10 Inches. B Li.        Parts. B Li.        Parts. B Li.        Parts. B Li.        Parts. ⅛ 00      00027 2 ⅝ 02      54361S 5 ⅛ 18      92972 7 ⅝ 62      34219 ¼ 00      00220 2 ¾ 02      92456 5 ¼ 20      34888 7 ¾ 65      45874 ⅜ 00      00742 2 ⅞ 03      34177 5 ⅜ 21      83725 7 ⅞ 68      67746 ½ 00      01758 3 03      79687 5 ½ 23      39648 8 72      00000 ⅝ 00      03433 3 ⅛ 04      29153 5 ⅝ 25      02823 8 ⅛ 75      42801 ¾ 00      05933 3 ¼ 04      82739 5 ¾ 26      73413 8 ¼ 78      96313 ⅞ 00      09421 3 ⅜ 05      40610 5 ⅞ 28      51584 8 ⅜ 82      60703 1 00      14062 3 ½ 06      02930 6 30      37500 8 ½ 86      36133 1 ⅛ 00      20023 3 ⅝ 06      69864 6 ⅛ 32      31336 8 ⅝ 90      22769 1 ¼ 00      27466 3 ¾ 07      41577 6 ¼ 34      33228 8 ¾ 94      20776 1 ⅜ 00      36557 3 ⅞ 08      18234 6 ⅜ 36      43369 8 ⅞ 98      30319 1 ½ 00      47461S 4 09      00000 6 ½ 38      61914 9 102      51562 1 ⅝ 00      60342 4 ⅛ 09      87039 6 ⅝ 40      89029 9 ⅛ 106      84671S 1 ¾ 00      75366 4 ¼ 10      79517 6 ¾ 43      24878 9 ¼ 111      29810 1 ⅞ 00      92697 4 ⅜ 11      77597 6 ⅞ 45      69626 9 ⅜ 115      87143 2 01      12500 4 ½ 12      81445 7 48      23437 9 ½ 120      56836 2 ¼ 01      34940 4 ⅝ 13      91226 7 ⅛ 50      86478 9 ⅝ 125      39053 2 ¼ 01      60181S 4 ¾ 15      07104 7 ¼ 53      58911S 9 ¾ 130      33960 2 ⅜ 01      88388 4 ⅞ 16      29245 7 ⅜ 56      40903 9 ⅞ 135      41721S 2 ½ 02      19727 5 17      57812 7 ½ 59      32617 10 140      62500 In this Table you have eight Columns, in the first, third, fifth, and seventh Columns, are the Inches and eight parts of Inches that the Diameter of the Ball doth contain, and are marked with the Letter B; and in the second, fourth, sixth, and eighth Columns, you have the Weight of these Diameters of Iron Ball in English Weight: under Li. you have Pounds, and under Parts, you have the Decimal Parts of of Pounds. Tables for Iron Ball, whose Diameters being measured with English Inches, are exactly Calculated for English Weight, in Pounds, Ounces, and Drams, from eight parts to eight parts of English Inches, unto 10 Inches. B Li.        On.        Dr. B Li.        On.        Dr. B Li.        On.        Dr. 1 00      02      04 4 09      00      00 7 48      03      12 1 ⅛ 00      03      03 4 ⅛ 09      13      15 7 ⅛ 50      13      13 1 ¼ 00      04      06 4 ¼ 10      12      12 7 ¼ 53      09      07 1 ⅜ 00      05      14 4 ⅜ 11      12      07 7 ⅜ 56      06      09 1 ½ 00      07      10 4 ½ 12      13      00 7 ½ 59      05      03 1 ⅝ 00      09      10 4 ⅝ 13      14      10 7 ⅝ 62      05      08 1 ¾ 00      12      01S 4 ¾ 15      01      02 7 ¾ 65      07      05 1 ⅞ 00      14      13 4 ⅞ 16      04      11S 7 ⅞ 68      10      13 2 01      02      00 5 17      09      04 8 72      00      00 2 ⅛ 01      05      09 5 ⅛ 18      14      14 8 ⅛ 75      06      14 2 ¼ 01      09      10 5 ¼ 20      05      09 8 ¼ 78      15      07 2 ⅜ 01      14      02 5 ⅜ 21      13      06 8 ⅜ 82      09      11S 2 ½ 02      03      03 5 ½ 23      06      05 8 ½ 86      05      13 2 ⅝ 02      08      11S 5 ⅝ 25      00      07 8 ⅝ 90      03      10 2 ¾ 02      14      13 5 ¾ 26      11      12 8 ¾ 94      03      05 2 ⅞ 03      05      07 5 ⅞ 28      08      04 8 ⅞ 98      04      14 3 03      12      12 6 30      06      00 9 102      08      04 3 ⅛ 04      04      11S 6 ⅛ 32      05      00 9 ⅛ 106      13      09 3 ¼ 04      13      04 6 ¼ 34      05      05 9 ¼ 111      04      12 3 ⅜ 05      06      08 6 ⅜ 36      06      15 9 ⅜ 115      13      15 3 ½ 06      00      08 6 ½ 38      09      14 9 ½ 120      09      02 3 ⅝ 06      11      03 6 ⅝ 40      14      04 9 ⅝ 125      05      04 3 ¾ 07      06      10 6 ¾ 43      04      00 9 ¾ 130      05      07 3 ⅞ 08      02      15 6 ⅞ 45      11      02 9 ⅞ 135      06      11S In this Table you have six Columns, in the first, third, and fifth Columns, there are the Inches and eight parts of Inches, that the Diameter of the Ball doth contain, and are marked with the Letter B; and in the second, fourth, and sixth Columns, you have the Weight of these Diameters of Iron Ball in English weight; under Li. you have Pounds, under On. Ounces, and under Dr. you have Drams. This Height-Rule you have on the side of the Quadrant. By which Work and Tables you may examine any other Weight, if you will compare. Example. As in the preceding Example, 3 Inches Diameter giveth 3 pound 12 ounces and 12 drams, as you may see by the Work. Also I demand what giveth 4 Inches of Diameter. Another Example. If 4 Inches of Diameter give 9 pound weight, what shall 8 Inches give? Answer, 72 pound. Another Example with a Fraction. If 4 Inches of Diameter give 9 pound, what shall 6 ¾ Inches give. I Answer, This Ball of 6 ¾ Inches Diameter, weigheth 43 pound 4 ounces fere; which proves both the Work and Tables to be true and just. Observation. The difference betwixt Scots and English Weight. It is to be observed, That as there is a difference betwixt Scots and English Weight, viz. as 8 to 9, which was mentioned in pag. 54. so is there likewise a difference between Scots and English Inches, which is as 9 to 10; that is to say, 9 English Inches make 10 Scots Inches; as it appeareth in the Tables following. Tables for Iron Ball, whose Diameters being measured with Scots Inches, are exactly Calculated Decimally for Scots Weight; from eight parts to eight parts of Scots Inches, unto 10 Inches. B Li.        Parts. B Li.        Parts. B Li.        Parts. B Li.        Parts. ½ 00      00018 2 ⅝ 01      64826 5 ⅛ 12      26646 7 ⅝ 40      39774 ¼ 00      00142 2 ¾ 01      89512 5 ¼ 13      18607 7 ¾ 42      41726 ⅜ 00      00481 2 ⅞ 02      16546 5 ⅜ 14      15054 7 ⅞ 44      50299 ½ 00      01139 3 02      46037 5 ½ 15      16092 8 46      65600 ⅝ 00      02225 3 ⅛ 02      78091S 5 ⅝ 16      21829 8 ⅛ 48      48877 ¾ 00      03844 3 ¼ 03      12815 5 ¾ 17      32372 8 ¼ 51      16811 ⅞ 00      06105 3 ⅜ 03      50315 5 ⅞ 18      47826 8 ⅜ 53      52935 1 00      09112 3 ½ 03      90698 6 19      68300 8 ½ 55      96214 1 ⅛ 00      12975 3 ⅝ 04      34072 6 ⅛ 20      93899 8 ⅝ 58      46754 1 ¼ 00      17798 3 ¾ 04      80542 6 ¼ 22      24731S 8 ¾ 61      04663 1 ⅜ 00      23689 3 ⅞ 05      30216 6 ⅜ 23      60903 8 ⅞ 63      70047 1 ½ 00      30755 4 05      83200 6 ½ 25      02520 9 66      43012 1 ⅝ 00      39102 4 ⅛ 06      39601S 6 ⅝ 26      49691S 9 ⅛ 69      23667 1 ¾ 00      48837 4 ¼ 06      99527 6 ¾ 28      02521S 9 ¼ 72      12117 1 ⅞ 00      60068 4 ⅜ 07      63083 6 ⅞ 29      61118 9 ⅜ 75      08469 2 00      72900 4 ½ 08      30377 7 31      25587 9 ½ 78      12830 2 ⅛ 00      87441S 4 ⅝ 09      01515 7 ⅛ 32      96038 9 ⅝ 81      25307 2 ¼ 01      03797 4 ¾ 09      76604 7 ¼ 34      72574 9 ¾ 84      46006 2 ⅜ 01      22075 4 ⅞ 10      55751S 7 ⅜ 36      55305 9 ⅞ 87      75035 2 ½ 01      42383 5 11      39062 7 ½ 38      44336 10 91      12500 In this Table you have eight Columns, in the first, third, fifth, and seventh Columns, are the Inches and eight parts of Inches that the Diameter of the Ball doth contain, and are marked with the Letter B; and in the second, fourth, sixth, and eighth Columns, you have the Weight of these Diameters of Iron Ball in Scots Weight: under Li. you have Pounds, and under Parts you have the Decimal Parts of of Pounds. Tables for Iron Ball, whose Diameters being measured with Scots Inches, are exactly Calculated for Scots Weight; in Pounds, Ounces and Drams, from eight parts to eight parts of Scots Inches, unto 10 Inches. B Li.        On.        Dr. B Li.        On.        Dr. B Li.        On.        Dr. 1 00      01      07 4 05      13      05 7 31      04      02 1 ⅛ 00      02      01S 4 ⅛ 06      06      05 7 ⅛ 32      15      06 1 ¼ 00      02      14 4 ¼ 06      15      06 7 ¼ 34      11      10 1 ⅜ 00      03      13 4 ⅜ 07      10      01S 7 ⅜ 36      08      14 1 ½ 00      04      15 4 ½ 08      04      14 7 ½ 38      07      02 1 ⅝ 00      06      04 4 ⅝ 09      00      04 7 ⅝ 40      06      06 1 ¾ 00      07      13 4 ¾ 09      12      04 7 ¾ 42      06      11S 1 ⅞ 00      09      10 4 ⅞ 10      08      15 7 ⅞ 44      08      01S 2 00      11      11 5 11      06      04 8 46      10      08 2 ⅛ 00      14      00 5 ⅛ 12      04      05 8 ⅛ 48      07      13 2 ¼ 01      00      10 5 ¾ 13      02      15 8 ¼ 51      02      11S 2 ⅜ 01      03      09 5 ⅜ 14      02      07 8 ⅜ 53      08      08 2 ½ 01      06      13 5 ½ 15      02      09 8 ½ 55      15      06 2 ⅝ 01      10      06 5 ⅝ 16      03      08 8 ⅝ 58      07      08 2 ¾ 01      14      05 5 ¾ 17      05      03 8 ¾ 61      00      12 2 ⅞ 02      02      10 5 ⅞ 18      07      10 8 ⅞ 63      11      03 3 02      07      06 6 19      10      15 9 66      06      14 3 ⅛ 02      12      08 6 ⅛ 20      15      00 9 ⅛ 69      03      13 3 ¼ 03      02      01S 6 ¼ 22      03      15 9 ¼ 72      01      15 3 ⅜ 03      08      01S 6 ⅜ 23      09      12 9 ⅜ 75      01      06 3 ½ 03      14      08 6 ½ 25      00      06 9 ½ 78      02      01S 3 ⅝ 04      05      07 6 ⅝ 26      07      15 9 ⅝ 81      04      01S 3 ¾ 04      12      14 6 ¾ 28      00      06 9 ¾ 84      07      06 3 ⅞ 05      04      13 6 ⅞ 29      09      12 9 ⅞ 87      12      00 In this Table you have six Columns; in the first, third, and fifth Columns, there are the Inches, and eight parts of Inches, that the Diameter of the Ball doth contain, and are marked with the Letter B; and in the second, fourth, and sixth Columns, you have the Weight of these Diameters of Iron Ball in Scots Weight; under Li. you have Pounds, under On. Ounces, and under Dr. Drams. Tables for Iron Ball, whose Diameters being measured with Scots Inches, are exactly Calculated for English Weight, from eight parts to eight parts of Scots Inches, unto ten Inches: Decimally. B Li.        Parts. B Li.        Parts. B Li.        Parts. B Li.        Parts. ⅛ 00      00020 2 ⅝ 01      85429 5 ⅛ 13      79976 7 ⅝ 45      44746 ¼ 00      00160 2 ¾ 02      13200 5 ¼ 14      83433 7 ¾ 47      71942 ⅜ 00      00541 2 ⅞ 02      43615 5 ⅜ 15      91936 7 ⅞ 50      06587 ½ 00      01281 3 02      76792 5 ½ 17      05604 8 52      48800 ⅝ 00      02503 3 ⅛ 03      12853 5 ⅝ 18      24558 8 ⅛ 54      98702 ¾ 00      04325 3 ¼ 03      51917 5 ¾ 19      48918 8 ¼ 57      56413 ⅞ 00      06868 3 ⅜ 03      94105 5 ⅞ 20      78805 8 ⅜ 60      22052 1 00      10252 3 ½ 04      39536 6 22      14337 8 ½ 62      95741S 1 ⅛ 00      14596 3 ⅝ 04      88331S 6 ⅛ 23      55637 8 ⅝ 65      77600 1 ¼ 00      20023 3 ¾ 05      40610 6 ¼ 25      02823 8 ¾ 68      67746 1 ⅜ 00      26650 3 ⅞ 05      96493 6 ⅜ 26      56016 8 ⅞ 71      66303 1 ½ 00      34599 4 06      56100 6 ½ 28      15335 9 74      73389 1 ⅝ 00      43990 4 ⅛ 07      19552 6 ⅝ 29      80902 9 ⅛ 77      89125 1 ¾ 00      54942 4 ¼ 07      86968 6 ¾ 31      52836 9 ¼ 81      13631S 1 ⅞ 00      67576 4 ⅜ 08      58468 6 ⅞ 33      31257 9 ⅜ 84      47027 2 00      82012 4 ½ 09      34174 7 35      16286 9 ½ 87      89433 2 ⅛ 00      98371S 4 ⅝ 10      14204 7 ⅛ 37      08042 9 ⅝ 91      40970 2 ¼ 01      16772 4 ¾ 10      98680 7 ¼ 39      06646 9 ¾ 95      01757 2 ⅜ 01      37335 4 ⅞ 11      87720 7 ⅜ 41      12218 9 ⅞ 98      71914 2 ½ 01      60181S 5 12      81445 7 ½ 43      24878 10 102      51562 In this Table you have eight Columns; in the first, third, fifth, and seventh Columns, there are the Inches, and eight parts of Inches that the Diameter of the Ball doth contain, and are marked with the Letter B: And in the second, fourth, sixth, and eight columns, you have the weight of these Diameters of Iron Ball in English Weight; under Li. you have Pounds; and under Parts, you have the Decimal parts of Pounds. Tables for Iron Ball, whose Diameters being measured with Scots Inches, are exactly Calculated for English Weight, in Pounds, Ounces, and Drams, from eight parts to eight parts of Scots Inches, unto 10 Inches. B Li.        On.        Dr. B Li.        On.        Dr. B Li.        On.        Dr. 1 00      01      10 4 06      09      00 7 35      02      10 1 ⅛ 00      02      05 4 ⅛ 07      03      02 7 ⅛ 37      01      05 1 ¼ 00      03      03 4 ¼ 07      13      15 7 ¼ 39      01      01S 1 ⅜ 00      04      04 4 ⅜ 08      09      06 7 ⅜ 41      01      15 1 ½ 00      05      09 4 ½ 09      05      07 7 ½ 43      04      00 1 ⅝ 00      07      01S 4 ⅝ 10      02      04 7 ⅝ 45      07      03 1 ¾ 00      08      13 4 ¾ 10      15      13 7 ¾ 47      11      08 1 ⅞ 00      10      13 4 ⅞ 11      14      01S 7 ⅞ 50      10      01S 2 00      13      02 5 12      13      00 8 52      07      13 2 ⅛ 00      15      12 5 ⅛ 13      12      13 8 ⅛ 54      15      13 2 ¼ 01      02      11S 5 ¼ 14      13      06 8 ¼ 57      09      00 2 ⅜ 01      06      00 5 ⅜ 15      14      11S 8 ⅜ 60      03      08 2 ½ 01      09      10 5 ½ 17      00      14 8 ½ 62      15      05 2 ⅝ 01      13      11S 5 ⅝ 18      03      15 8 ⅝ 65      12      07 2 ¾ 02      02      02 5 ¾ 19      07      13 8 ¾ 68      10      13 2 ⅞ 02      07      00 5 ⅞ 20      12      10 8 ⅞ 71      10      10 3 02      12      05 6 22      02      05 9 74      11      12 3 ⅛ 03      02      01S 6 ⅛ 23      08      14 9 ⅛ 77      14      04 3 ¼ 03      08      05 6 ¼ 25      00      07 9 ¼ 81      02      03 3 ⅜ 03      15      01S 6 ⅜ 26      08      15 9 ⅜ 84      07      08 3 ½ 04      06      05 6 ½ 28      02      07 9 ½ 87      14      05 3 ⅝ 04      14      02 6 ⅝ 29      12      15 9 ⅝ 91      06      09 3 ¾ 05      06      08 6 ¾ 31      08      07 9 ¾ 95      00      04 3 ⅞ 05      15      07 6 ⅞ 33      05      00 9 ⅞ 98      11      08 In this Table you have six Columns, in the first, third, and fifth Columns, there are the Inches and eight parts of Inches, that the Diameter of the Ball doth contain, and are marked with the Letter B; and in the second, fourth, and sixth Columns, you have the Weight of these Diameters of Iron Ball in English weight; under Li. you have Pounds, under On. Ounces, and under Dr. you have Drams. CHAP. XVII. The Use of the preceding Tables. Use of the Tables of Iron Ball, measured with Scots Inches. IF the Diameter of an Iron Ball be measured with Scots Inches, I would know what the same Ball weigheth in English Weight. Example. There is an Iron Ball, whose Diameter is 5 ½ Scots Inches; I demand what the same Ball weighs in English Weight. Look in the Table in pag. 80. under B in the fifth Column, where you find 5 ½ Inches; and right against it, in the sixth Column, you have 17 pound and 056/1000 pounds, which is the just weight of the same Ball. Or otherwise, Look in the Table in pag. 81. under B, in the third Column, where you find 5 ½ Inches; and right against it, in the fourth Column, you have 17 poound, 00 ounces, and 14 drams, which is also the just Weight of the same Ball. Or if the Diameter of an Iron Ball be measured with Scots Inches; I desire to know what the same Ball weigheth in Scots Weight. Example. There is an Iron Ball whose Diameter is 6 ⅛ Scots Inches; I demand what doth the same Ball weigh in Scots Weight. Look in the Table in pag. 78. under B, in the fifth Column, where you find 6 ⅛ Inches; and right against it, in the sixth Column, you have 20 pound and 938/1000 parts of a pound, which is the just weight of the same Ball in Scots Weight. Or otherwise, Look in the Table in pag. 79. under B, in the third Column, where you find 6 ⅛ Inches; and right against it, in the fourth Column, you have 20 pounds and 15 ounces, which is also the just weight of the same Ball in Scots Weight. And this I will assure you to be truth, because I have calculated all these Tables with my own hand, and they are since revised and truly done, by the laborious pains of Mr. Robert Webster. CHAP. XVIII. To Extract the Cube Root of a Number not Cubical. You have the Diameter and Weight of Scots and English Ball, on the Scale, on the side of the Quadrant: Also the Dimension of one side Metal, both Brass and Iron Ordnance, by which you may give Powder for Action. I Doubt not but Men of Reason will think, that in Calculating all these Tables, I have taken great pains, so that you need to take the less: And because there are many Gunners that cannot use their Pen, and some that cannot understand the use of Tables, I therefore for their help will here set down an Height-Rule for Ball, from one pound to an hundred pound, both in Scots and English Weight. But before this Height-Rule be made, it is needful to set down a Cubical Table, for except you have this Table, the Height-Rule cannot be truly made. To Calculate this Table, it is necessary that you can Extract the Cube Root of Irrational Numbers; which Numbers are so termed, because that from such Numbers you cannot extract a true Cube-Root, and therefore to the Number propounded you must add 3, 6, or 9 Ciphers; by which you may Extract the Cube-Root without sensible error, as it doth appear in the Examples following. Example. Let it be required to extract the Cube-Root of 8302348. Having distributed the Number given into several Cubes by Points, as is directed in Chap. 8. of this. I demand the Cube-Root of 8, (the first Cube on the left hand) which I find to be 2; wherefore placing 2 in the Quotient, and 8 the Cube thereof, under 8 the first Cube, I draw a Line, subtracting 8 out of 8, the Remainder is 0, which I subscribe under the Line. This is always the first Work, and is no more repeated in the whole Extraction, (as was intimated in the third Note of chap. 8.); then bringing down the next Cube, (to wit, the Figures standing in the three following places of the Number propounded) which is 302, I place it after the Remainder 0, so is 302 the Resolvend; this done, having drawn a Line underneath the Resolvend, I seek for the triple of the Square of the Root, viz. The Root in the Quotient is 2, which multiplied by itself produceth the Square 4, the triple whereof is 12; this I subscribe under the Resolvend, in such manner, that the Figure 2 in the Unites place of this triple Square 12, may stand directly under the Figure 3, which is seated in the third place of the Resolvend, (to wit, the place of Hundreds): Again, I triple the Root 2, which produceth 6, and subscribe this triple Number 6 under the second place (or place of Ten) in the Resolvend, to wit, under 0; then drawing a Line under the Work, and adding together the said two Numbers last subscribed, as they are ranked, the Sum of them is 126 for a Divisor: That done, esteeming 30, to wit, all the places except the first or place of Unites in the Resolvend, as a Dividend, I demand how often the Divisor 126 is contained in 30, and not finding it once contained therein, I writ 0 in the Quotient; and now because the sum of the three Numbers which ought to have been produced (according as was mentioned in Chap. 8.) by the multiplication of 0, (which was last placed in the Quotient) amounts to 0, the Resolvend 302, out of which the said Sum should have been subtracted, remains the same without alteration; wherefore having drawn a Line under the Work, I writ down anew the old Resolvend 302, and bringing down the next Cube 348, I annex it to the said 302, so there will be a new Resolvend, to wit, 302348. Then squaring the Root 20, (that is, multiplying of it by itself) the Product is 400; which I triple or multiply by 3, and subscribe the Product 1200 under the new Resolvend in such manner, that the place of Unites in this triple Quadrate 1200 may stand under the place of Hundreds, or third place of the Resolvend 302348, to wit, under 3: Again, I subscribe the triple of the Root 20, which is 60, in such manner, that the place of Unites in this triple Root 60 may stand under the place of Ten or second place of the Resolved; then adding together the two Number's last subscribed, to wit, 1200 and 60, in such order as they are ranked in the Work, the Sum is 12060 for a Divisor. Again, esteeming the whole Resolvend, except the first place, (or place of Unites) as a Dividend, to wit, 30234, I demand how often 1 (the first Figure of the Divisor towards the left hand) is contained in 3, the corespondent part of the Dividend; and though it be three times contained in it, yet (according to the first Note in Chap. 8.) I dare take but 2; (for if I should take 3, and proceed according as was declared in Chap. 8. a Number would arise greater than the Resolvend, from which such Numbers arising aught to be subtracted) wherefore I writ 2 in the Quotient. Then multiplying the triple Square 1200 before subscribed by 2, (the Figure last placed in the Quotient) the Product is 2400, which I subscribe under the said 1200, (to wit, Unites under Unites, and Ten under Ten, etc.) Also multiplying the triple Root 60, before subscribed by 4, (the Quadrate of 2, the Figure last placed in the Quotient) the Product is 240, which I subscribe under the said triple Root 60; last of all I subscribe 8 the Cube of the said new Root 2, under the place of Unites, or first place of the Resolvend, to wit, under 8; and having added together those three Numbers last subscribed, to wit, 2400, 240, and 8, as they stand in Ranks in the Work, the sum of them is 242408, which being deducted from the Resolvend 302348, there will remain 59940. Wherefore the Work being finished, I find 202 to be the number of Unites contained in the Cube-Root of 8302348 the Number propounded: and because, after the Extraction is ended, there happens to be a Remainder, to wit, 59940, I conclude that the Cube-Root sought is greater than the said 202, but less than 203; yet how much it is greater than 202, no Rules of Art hitherto known will exactly discover, although we may proceed infinitely near, as by the following Rule will be manifest. To find the Fractional part of the Root very near. Ternaries of cyphers, to wit, 000,000000, or 000000000, etc. are to be annexed to the Number first propounded; then esteeming the Number propounded with the cyphers annexed to be but one entire Number, the Extraction is to be made according as hath been prescribed in this Chapter; and look how many Points were placed over the Number first given, so many of the foremost places in the Quotient are the Integers or Unites contained in the Cube-Root sought, and the rest of the places in the Quotient are to be esteemed as the Numerator of a Decimal Fraction; which Numerator consists of so many places as there were Points over the cyphers first annexed: so if 8302348 were given as before to find the Cube-Root thereof, (according to this Rule) annex cyphers as you here see in the Work. And then if you prosecute the Extraction according to the Rules foregoing, you shall find the Cube-Root sought to be 202 ⌊ 48, etc. that is, 202 48/100 and more; wherefore you may conclude that 202 48/100 is less than the true Root, but 202 49/100 is greater than it; So that by annexing two Ternaries of cyphers, to wit, six cyphers to the number propounded, you will not miss 1/100 part of an Unite of the true Root; as also by annexing three Ternaries of cyphers, to wit, 9 cyphers, you will not miss 1/1000 part of an Unite of the true Root; and in that order you may proceed infinitely near, when you cannot obtain the true Root. The whole Operation of the said Example you have in the next page, where you may observe, that for the more certain and easy placing, as well of the Numbers, which constitute the several Divisors, as of those which constitute the Ablatitious Numbers to be subtracted from the several and respective Resolvends, down right Lines are drawn between the particular Cubes of the Number propounded, first distinguished by Points as below. Another Example wrought by the Genitures. In like manner the Cube-Root of 2, will be found to be near equal to 1 ⌊ 25992, etc. that is, 1 25992/100000 parts and more. And the Work will stand thus. The Proof of the Cube-Root. The Extraction of the Cube-Root is proved by multiplying the Root Cubically; to wit, the Root being first multiplied by itself, the Product shall give a Square Number, the which Square being multiplied again by the said Root, the Number arising, or last Product (in case there be no Remainder after the Extraction is finished) will be equal to the Number propounded: So in the Example of Chap. 8. the Cube-Root 54 being multiplied first by itself, produceth 2916, which is a Square Number, than the said Square 2916, being multiplied by the Root 54, produceth 157464, which is a Cube Number equal to the number propounded, whose Cube-Root was required. So that the Extraction is right, and the same Root found is the true Cube-Root of the Number proposed. But when after the Extraction is finished, there happens to be a Remainder, and that the Root is found as near as you please in Integers and Decimal parts, (by annexing cyphers as in this Chapter) than such mixed Number expressing the Root, being multiplied Cubically, must produce a mixed Number less than the Number first propounded; yet so near unto it, that if the Figure standing in the last place of the Decimal Fraction in the Root be made greater by 1, and the mixed number so increased be multiplied Cubically, the Product must be greater than the Number first propounded: so in the first Example of this Chapter, if 202 ⌊ 48 be multiplied Cubically, it produceth 8301305 ⌊ 49, etc. which is less than the propounded Number 8302348; but if 202 ⌊ 49 be multiplied Cubically, therewill arise 8302535 ⌊ 49, etc. which is greater than the said given Number. Behold the Work. The Table of Cubes, whereby the Height-Rule is made. This Height-Rule you have on the side of the Quadrant Rule, both for Scots and English Ball. A B A B A B A B A B 1 1000 26 2962 51 3708 76 4235 101 4657 2 1259 27 3000 52 3732 77 4254 102 4672 3 1442 28 3036 53 3756 78 4272 103 4687 4 1587. 29 3072 54 3779 79 4290 104 4702 5 1709 30 3107 55 3802 80 4308 105 4717 6 1817 31 3141 56 3825 81 4326 106 4732 7 1912 32 3174 57 3848 82 4344 107 4747 8 2000 33 3207 58 3870 83 4362 108 4762 9 2080 34 3239 59 3892 84 4379 109 4776 10 2154 35 3271 60 3914 85 4396 110 4791 11 2223 36 3301 61 3936 86 4413 111 4805 12 2289 37 3332 62 3957 87 4430 112 4820 13 2351 38 3361 63 3979 88 4447 113 4834 14 2410 39 3391 64 4000 89 4464 114 4847 15 2466 40 3419 65 4020 90 4485 115 4862 16 2519 41 3448 66 4041 91 4497 116 4877 17 2571 42 3476 67 4061 92 4514 117 4890 18 2620 43 3503 68 4081 93 4530 118 4904 19 2668 44 3530 69 4101 94 4546 119 4918 20 2714 45 3556 70 4121 95 4562 120 4931 21 2758 46 3583 71 4140 96 4578 121 4946 22 2802 47 3608 72 4160 97 4594 122 4959 23 2843 48 3634 73 4179 98 4610 123 4973 24 2884 49 3659 74 4198 99 4626 124 4986 25 2924 50 3689 75 4217 100 4642 125 5000 In this Table you have ten Columns, in the 1st, 3d, 5th, 7th, and 9th Columns, you have the Weight of the Ball, from 1 lb to 125 lb, and are marked with the Letter A; and in the 2d, 4th, 6th, 8th, and 10th Columns, you have the Cube-Roots and Parts correspondent to the Weight of Ball, which are marked with the Letter B; as shall appear in the Examples following. CHAP. XIX. The way to find the Diameter of the first pound Ball. NOw if any Artificial Gunner desire to make a Height-Rule or Scale to know the Weight of his Shot, by measuring the Diameter of the Ball, and by this Cubical Table: First he must know the exact Diameter of a Ball of one pound weight, of what sort of Metal or Stone he desires his Height-Rule or Scale for; the which to do, observe these Rules following. First, Search until you find a Ball of that Metal very smooth, of any size or weight, and take the Diameter exactly of that Ball, with a pair of Callabassero Compasses. Then draw that Diameter on a piece of Paper, or plain Board, and divide it in as many equal parts as you please; then weigh that Ball exactly well, which being done, multiply the Divisions of the Diameter of the Ball Cubically, and divide that Product by the weight of the Ball; so from that Quotient of your Division, you are to extract the Cube-Root, and the Quotient is the parts of that Ball which weigheth one pound weight of that Metal. Example. The Ball given is a Ball of Iron, whose weight is 12 lb; and his Diameter is divided into 300 equal part; which done, work as followeth. By which I find 131 parts of the Ball given to be the just Diameter of a Ball of one pound weight, of that Country-Weight. As you may see by the Diameters herewith annexed; the Line AB the Diameter of the Ball given, and the Line CD the Ball found for one pound. After you have found the true Diameter of one pound Ball, you must divide the same into 1000 equal parts; or make a Diagonal Scale of the same Diameter of the one pound Ball, and so resort to the Table of Cubical Numbers; and having a Scale of Paper or Wood ready, you may set the Diameter of the Ball on it, from one pound as far as the Table doth run. The Demonstration and Diameter of a Ball of 12 pound being given, the Diameter of one pound Ball is also given, as in pag. 92. And that I may make it the more plain, behold the Diameter of a Ball of 12 pound; and from that, by working as is before taught, you may have the Diameter of one pound Ball, which is here found, and true in every Condition. Thus having the Table of Cubical Numbers, wherein you find the first pound is 1000 in its Root, and the second 1259 of the parts of one pound Ball, which is 259 parts more than the Ball of one pound; which added to the Diameter of one pound, gives the Diameter of a Ball of 2 pound; which place on your Ruler, than the Table gives 1442, for the Diameter of a Ball of 3 pound; and if you take 442, and add to the Diameter of one pound Ball, you have the Diameter of a Ball of 3 pound: And thus you may increase and go upward till you have a complete Height-Rule of what height you please. So making it, as you are taught, you may answer any Question demanded of the Weight of Ball, of the Metal and Weights of the place it is made for. For all places have not one Weight, as you see by the Table following. The Proof of the Height-Rule. Now every Height-Rule for Ball, of what Metal soever it be made for, is proved in manner following: That when you extend your Compasses to the height of one pound, and with the same extension turn your Compasses, you shall reach 8 pound; and if you take the Diameter of a 2 pound Ball, and turn the Compasses about, must fall in 16 pound Ball; and of 3 pound to 24 pound: So that all Ball being twice the Diameter of the other, must carry 8 times the weight of the other. Further-more, By the Cubical Table, with the Diagonal Scale of the height of one pound Ball, you may give an account to make Height-Rules, showing the Weight of Iron Ball in any Place or Country, knowing the proportion it beareth with our own Scots or English Weight: So that here it will be very requisite, in regard ordinarily every Country have their own dinstinct Weights and Measures, to give a Catalogue of some several Places and their Weights compared with ours as you see, and as shall be further demonstrated for the Gunner's more ease. Table of the Weights of several Places being compared with ours of Edinburgh. 100 pounds at Edinburgh maketh at lb. London 112 Antwerp 108 Bollogne, betwixt 139 and 140 Catalogne 160 Cullen 102 Cureland 98 Dantzick 122 Florence 142 Lubeck 110 Lions 120 Genua, betwixt 152 and 153 Amsterdam 100 Venetia, great Weight 106 Prague 62 Lublin 128 A Rule to rectify the Weights of divers Places with ours. Ile set here for Example; There is a Gun in Edinburgh, measured by the Height-Rule, and is found to shoot 36 lb Ball; Now the Question is, What weight of Ball the same Piece doth shoot at London: And comparing the Weights together, you will find it stand thus. And that Piece which shooteth 36 lb Ball at Edinburgh, will require at London a Ball of 40 lb 5 ounces English weight. Another Example. Likewise if there were a Piece at Edinburgh, which shoots 9 lb Ball; I would know what the Weight of a Ball fit for that Piece shall be of Dantzick Weight. Behold the Work. You see that of that Weight it will be 10 pound 15 ounces, and 68/100 parts of an ounce. And so generally the Gunner may fit himself with Ball in all Places. And as there is a diversity in the Weights of several Places, so is there likewise a diversity in the Foot: And that here it will be necessary to give a Catalogue of some several places, and their Feet compared with our Foot. A Catalogue of the Feet of several Places compared with ours of Edinburgh. 100 foot of Edinburgh maketh Foot. Of the Ancient Romans 87 ⌊ 19 Of the Ancient Greeks 83 ⌊ 14 Of the Ancient Babylonians 74 ⌊ 38 Of Alexandria 72 ⌊ 73 Of the Isle Samos 72 ⌊ 73 Of Arabia 81 ⌊ 82 Of London 90 ⌊ 00 Of Paris 82 ⌊ 64 Of Leyden 87 ⌊ 19 Of Antwerp 95 ⌊ 87 Of Copenhagen 90 ⌊ 00 Of Venice 77 ⌊ 60 Of Toledo 100 ⌊ 00 Of Stratsburg 94 ⌊ 22 Example. There is a Gun in Edinburgh, whose Diameter of the Boar is measured by the Height-Rule to be 6 ¼ Inches; I demand how many Inches of London shall the Diameter of the Boar of the same Piece be. I Answer, That Piece whose Diameter of the Boar is 6 ¾ Inches at Edinburgh, is but 5 ⅝ Inches of Diameter at London. Another Example. There is a Gun at London which shooteth a Ball of 6 ¾ Inches Diameter; I demand of how many Inches Diameter shall a Ball be at Edinburgh which shall fit the same Piece. I Answer, That Piece which shooteth a Ball of 6 ¾ Inches Diameter at London, shall certainly require a Ball to fit her at Edinburgh of 7 ½ Inches. Any Ingenious Gunner observing all the Rules that hath been described in this Chapter, may make an Height-Rule for any Metal of Ball. For more clearing of this, I shall set here a Table of equal Diameters and different Weight. The Diameters of Ball of one Country Weight to be found by equal and several Divisions of several Metals and Stones, as they are compared with Iron. Iron is in Proportion to The Proportion of Iron Ball compared with other Metals and Stones. Copper— as 8 is to 09 Silver— as 24 is to 31 Led— as 16 is to 23 Quicksilver— as 56 is to 95 Gold— as 8 is to 19 Tin— as 120 is to 111 Marble— as 96 is to 43 Sclate— as 48 is to 13 Stone— as 144 is to 35 Brick— as 288 is to 65 Example. There is a Gun which shooteth a Ball of Iron weighing 24 pounds; I demand what shall a Ball of Lead of the same Diameter weigh. I Answer, This Piece shall require a Ball of Lead which weigheth 34 lb and 8 ounces, which shall be of the same Diameter as was the Iron Ball of 24 pounds. Another Example. There is a Gun which shooteth a Ball of Iron weighing 36 pounds; I demand what shall a Ball of Stone of the same Diameter weigh. I Answer, This Piece shall require a Ball of Stone which weigheth but 8 lb and 12 ounces, which shall be of the same Diameter as was the Iron Ball of 36 lb. CHAP. XX. FOr the Gunners further ease, I have set down Tables both of Scots and English Weight of Iron Ball, from 1 lb to 100 lb; with the Diameters of the Ball both in Scots and English Inches, and parts of Inches; together with the Height of the Boars of the Ordnance that the same Ball shall fit in the like Inches: So that he may take the Diameter of a Ball, (only knowing the Weight); as also the Height of the Boar of the Piece, which the same Ball shall fit, from any Diagonal Scale of Inches, divided into Decimal parts. Tables for Iron Ball, wherein you have the Weight of every Ball given in Scots Weight, from 1 lb to 100 lb; together with the Diameters or Height of every Ball in Scots Inches and parts of Inches; exactly Calculated to each pound Weight abovementioned. A B A B A B A B 1 2.2222 26 6.5833 51 8.2410 76 9.4129 2 2.7998 27 6.6667 52 8.2944 77 9.4540 3 3.2049 28 6.7480 53 8.3473 78 9.4948 4 3.5276 29 6.8273 54 8.3994 79 9.5351 5 3.8000 30 6.9050 55 8.4510 80 9.5752 6 4.0380 31 6.9808 56 8.5019 81 9.6150 7 4.2509 32 7.0551 57 8.5522 82 9.6544 8 4.4444 33 7.1279 58 8.6019 83 9.6934 9 4.6223 34 7.1991 59 8.6511 84 9.7322 10 4.7876 35 7.2694 60 8.6997 85 9.7708 11 4 9421 36 7.3377 61 8.7478 86 9.8089 12 5.0877 37 7.4050 62 8.7953 87 9.8468 13 5.2251 38 7.4709 63 8.8423 88 9.8843 14 5.3559 39 7.5360 64 8.8889 89 9.9217 15 5.4804 40 7.5999 65 8.9349 90 9 9587 16 5.5997 41 7.6627 66 8.9806 91 9.9954 17 5.7140 42 7.7246 67 9.0257 92 10.0319 18 5.8238 43 7.7853 68 9.0703 93 10.0681 19 5.9298 44 7.8452 69 9.1146 94 10.1041 20 6.0320 45 7.9042 70 9.1584 95 10.1398 21 6.1310 46 7.9623 71 9.2018 96 10.1752 22 6.2268 47 8.0196 72 9.2448 97 10.2104 23 6.3197 48 8.0761 73 9 2874 98 10.2454 24 6.4100 49 8.1318 74 9.3297 99 10.2801 25 6.4978 50 8.1868 75 9.3714 100 10.3147 In this Table you have eight Columns, in the 1st, 3d, 5th, and 7th Columns, marked with the Letter A, is the Weight of the Ball in Scots Weight; and in the 2d, 4th, 6th, and 8th Columns, marked with the Letter B, you have the Diameter of the Ball in Scots Inches, and Decimal parts of Inches. The Geometrical Demonstration of these two Tables is in pag. 54. Tables for Iron Ball, wherein you have the Weight of every Ball given in Scots Weight, from 1 lb to 100 lb; together with the Height of the Boar of each Piece answering to those Balls, given in Scots Inches and parts of Inches, Exactly Calculated to each pound weight of Ball above mentioned, the Wind being truly extracted. A B A B A B A B 1 2.3529 26 6 8695 51 8.5993 70 9.8223 2 2.9645 27 6.9566 52 8.6550 77 9.8650 3 3.3934 28 7.0414 53 8.7102 78 9.9076 4 3.7351 29 7.1241 54 8.7645 79 9 9497 5 4.0235 30 7.2052 55 8 8184 80 9.9915 6 4.2754 31 7.2843 56 8.8715 81 10.0330 7 4.5010 32 7.3618 57 8.9240 82 10.0742 8 4.7058 33 7.4378 58 8.9759 83 10.1149 9 4.8424 34 7.5121 59 9.0272 84 10.1553 10 5.0156 35 7.5855 60 9.0779 85 10.1956 11 5.1774 36 7.6567 61 9.1281 86 10.2354 12 5.3300 37 7.7270 62 9.1777 87 10.2749 13 5.4739 38 7.7957 63 9.2267 88 10.3141 14 5.6109 39 7.8637 64 9.2754 89 10.3531 15 5.7414 40 7.9303 65 9.3234 90 10.3917 16 5.8664 41 7.9959 66 9.3711 91 10.4300 17 5 9861 42 8.0605 67 9 4181 92 10.4681 18 6.1011 43 8.1238 68 9.4647 93 10.5058 19 6.1876 44 8.1863 69 9.5109 94 10.5434 20 6.2943 45 8.2479 70 9.5566 95 10.5807 21 6.3976 46 8.3085 71 9.6016 96 10.6176 22 6.4975 47 8.3683 72 9.6467 97 10.6543 23 6.5945 48 8.4272 73 9.6912 98 10.6909 24 6.6887 49 8.4854 74 9.7353 99 10.7271 25 6.7803 50 8.5427 75 9.7788 100 10.7632 In this Table you have eight Columns, in the 1st, 3d, 5th, and 7th Columns, marked with the Letter A, is the weight of Ball in Scots Weight; and in the 2d, 4th, 6th, and 8th Columns, marked with the Letter B, you have the Height of the Boar of each Piece, which those Balls shall fit, the Wind truly Extracted, in Scots Inches, and Decimal parts of Inches: Which you have in the Copper Plate, pag. 56, 57 Tables for Iron Ball, wherein you have the Weight of every Ball given in English Weight, from 1 lb to 100 lb; together with the Diameter or Height of every Ball in English Inches and parts of Inches; exactly Calculated to each pound Weight of Ball abovementioned. A B A B A B A B 1 1.9230 26 5.6969 51 7.1313 76 8.1455 2 2.4228 27 5.7690 52 7 1776 77 8.1811 3 2.7735 28 5.8394 53 7.2233 78 8.2163 4 3.0526 29 5.9081 54 7.2685 79 8.2513 5 3.2883 30 5.9752 55 7.3131 80 8.2860 6 3.4943 31 6.0409 56 7.3571 81 8.3203 7 3 6786 32 6.1051 57 7.4007 82 8.3544 8 3.8460 33 6.1681 58 7.4437 83 8.3883 9 4.0000 34 6.2298 59 7.4862 84 8.4218 10 4.1430 35 6.2903 60 7.5283 85 8.4551 11 4.2767 36 6.3496 61 7.5699 86 8.4881 12 4.4026 37 6.4079 62 7.6110 87 8.5209 13 4.5216 38 6.4651 63 7.6517 88 8.5534 14 4.6347 39 6.5223 64 7.6920 89 8.5857 15 4.7425 40 6.5766 65 7.7318 90 8.6177 16 4.8457 41 6.6309 66 7.7712 91 8.6495 17 4 9446 42 6.6844 67 7.8104 92 8.6811 18 5.0397 43 6.7370 68 7.8490 93 8.7124 19 5.1313 44 6.7888 69 7.8873 94 8.7436 20 5.2198 45 6.8399 70 7.9252 95 8.7744 21 5.3054 46 6.8902 71 7.9628 96 8.8051 22 5.3883 47 6.9398 72 8.0000 97 8.8356 23 5.4688 48 6.9886 73 8.0369 98 8.8658 24 5 5469 49 7.0368 74 8.0734 99 8.8959 25 5.6229 50 7.0844 75 8.1096 100 8.9258 In this Table you have eight Columns, in the 1st, 3d, 5th, and 7th Columns, marked with the letter A, is the Weight of the Ball in English Weight; and in the 2d, 4th, 6th, and 8th Columns, marked with the Letter B, you have the Diameter of the Ball in English Inches, and Decimal parts of Inches. Tables for Iron Ball, wherein you have the Weight of every Ball given in English Weight, from 1 lb to 100 lb; together with the Height of the Boar of each Piece answering to those Balls, given in English Inches and parts of Inches; Exactly Calculated to each pound weight of Ball abovementioned, the Wind being truly extracted. A B A B A B A B 1 2.0362 26 5.9446 51 7.4414 76 8.4997 2 2.5653 27 6.0198 52 7.4897 77 8.5368 3 2.9371 28 6.0933 53 7.5374 78 8.5735 4 3.2322 29 6.1650 54 7.5845 79 8.6101 5 3.4817 30 6.2350 55 7.6311 80 8.6463 6 3.6998 31 6.3035 56 7.6770 81 8.6821 7 3.8950 32 6.3705 57 7.7225 82 8.7176 8 4.0722 33 6.4363 58 7.7673 83 8.7530 9 4.2353 34 6.5007 59 7.8117 84 8.7880 10 4 3403 35 6.5638 60 7.8556 85 8.8227 11 4.4804 36 6.6257 61 7.8990 86 8.8571 12 4.6123 37 6.6865 62 7.9419 87 8.8914 13 4.7369 38 6.7462 63 7.9844 88 8.9253 14 4.8554 39 6.8059 64 8.0264 89 8.9590 15 4.9683 40 6.8625 65 8.0680 90 8.9924 16 5.0764 41 6.9192 66 8.1091 91 9.0256 17 5.1801 42 6.9750 67 8.1500 92 9.0585 18 5.2797 43 7.0299 68 8.1903 93 9.0912 19 5.3544 44 7.0840 69 8 2302 94 9.1238 20 5.4467 45 7.1373 70 8.2698 95 9.1559 21 5.5361 46 7.1898 71 8.3090 96 9.1879 22 5.6226 47 7.2415 72 8.3478 97 9.2198 23 5.7066 48 7.2925 73 8.3863 98 9.2513 24 5.7881 49 7.3427 74 8.4244 99 9.2827 25 5.8630 50 7.3924 75 8.4622 100 9.3139 In this Table you have eight Columns, in the 1st, 3d, 5th, and 7th Columns, marked with the Letter A, is the weight of Ball in English Weight; and in the 2d, 4th, 6th, and 8th Columns, marked with the Letter B, you have the Height of the Boar of each Piece, which those Balls shall sit, the Wind truly Extracted, in English Inches, and Decimal parts of Inches: Which you have in the Copper Piece herewith. Thus having both Arithmetically, and by Tables, given Instructions how to make an Height or Diameter-Rule for Ball; and likewise having shown both Arithmetically, Geometrically, and by Tables, how to deduct the Wind from the Boar of a Piece, thereby to know her true Diameter of Ball; and having given Tables of the Weight of Ball by their Diameters: Therefore it follows, by the Weight of the Ball and Fortification of the Piece, that all Ordnance have their Powder either for Proof or Action. And, as I have shown by the Tables, all Brass or Iron Ordnance ought to have their Powder to their Proof; for True-Bored Ordnance, and True-Fortified, the Weight of their Ball from 1 lb to 8 lb, and from 8 to 18 three quarters of their Balls Weight; and from 18 to 48, two third parts of the Weight of the Ball, and so infinitely. For their Ordinary, follow the Tables where you may serve sufficiently, and save Powder. For Powder in Service or Action, it is to be referred to the Gunners discretion; and here I will give you Tables, whereby the Gunner may give Powder to Taper-Bored Ordnance, either for Proof or Action, or any hot Service, from 1 lb Ball to 36 lb Ball. CHAP. XXI. AS formerly I have shown, all Ordnance are not true-bored; therefore I suppose it will be necessary for the Young Gunner to know how to give Taper-Bored Guns their Powder; and though they are not ordinarily in these Countries, yet it may happen sometime the Gunner may be ordered to make use of such. In my Judgement there are no Guns more fit to go in the Head of Regiments in an Army than Taper-Bored Guns are: I mean not Leather Guns, by which the King and Country hath been cheated, but such as they make in Holland of Brass, Cast Ordnance. Neither do I mean those Tapered Guns, with which the Hollanders cheat the World, being Plates of Brass within and without, betwixt the Skins there are Bars and Hoops of Iron. A Table of Powder for Taper-Bored Ordnance, both for Proof, Action, and Storm; from one pound Iron Ball, to 36 pound. Iron Ball Proof. Action. Storm. lb lb      on lb      on.       dr. lb      on lb      on.       dr. lb      on lb      on.       dr. 1 00      05      05 00      04      00 00      03      00 2 00      10      11 00      08      00 00      06      00 3 01      00      00 00      12      00 00      09      00 4 01      05      05 01      00      00 00      12      00 5 01      10      11 01      04      00 00      15      00 6 02      00      00 01      08      00 01      02      00 7 02      05      05 01      12      00 01      05      00 8 02      10      11 02      00      00 01      08      00 9 03      00      00 02      04      00 01      11      00 10 03      05      05 02      08      00 01      14      00 11 03      10      11 02      12      00 02      01      00 12 04      00      00 03      00      00 02      04      00 13 04      05      05 03      04      00 02      07      00 14 04      10      11 03      08      00 02      10      00 15 05      00      00 03      12      00 02      13      00 16 05      05      05 04      00      00 03      00      00 17 05      10      11 04      04      00 03      03      00 18 06      00      00 04      08      00 03      06      00 19 06      05      05 04      12      00 03      09      00 20 06      10      11 05      00      00 03      12      00 21 07      00      00 05      04      00 03      15      00 22 07      05      05 05      08      00 04      02      00 23 07      10      11 05      12      00 04      05      00 24 08      00      00 06      00      00 04      08      00 25 08      05      05 06      04      00 04      11      00 26 08      10      11 06      08      00 04      14      00 27 09      00      00 06      12      00 05      01      00 28 09      05      05 07      00      00 05      04      00 29 09      10      11 07      04      00 05      07      00 30 10      00      00 07      08      00 05      10      00 31 10      05      05 07      12      00 05      13      00 32 10      10      11 08      00      00 06      00      00 33 11      00      00 08      04      00 06      03      00 34 11      05      05 08      08      00 06      06      00 35 11      10      11 08      12      00 06      09      00 36 12      00      00 09      00      00 06      12      00 In this Table is four Columns, in the first, under Iron Ball, is the Weight of the Ball that these Guns ordinarily shoot; in the second, under Proof, is the Weight of Powder for Proof; in the third, under Action, is the Weight of Powder for Action; and in the fourth Column, under Storm, is the Powder for Service. The right order of all Gun-Founders is, That for every 6 lb Ball the Piece shoots, they allow 1 lb for the Wind. This is the Goe 〈…〉 stration of the Diameter of Ball, And the Diameter of the Boars of Ordinance From one 〈…〉 weight: And as I am informed, commonly used in England by which Demon 〈…〉 of the Diameter of the Boar is Sufficient wind for all Guns. CHAP. XXII. To find the Diameter and Length of the Tapered Chamber of a Piece. Most necessary. PRovide a Tamken to the Boar or Height of the Ball; put it on the end of an Half-Pike, and put it up till it stop at the Chamber or top; take that out again, having before marked the Half Pike; then put up the Half-Pike in the Gun to the Breech, and mark the Half-Pike again; then take a Piece of bowed Wire, and put it in at the Touchhole to the lower part of the Chamber, and mark the Wire above the Gun; then hale it up till it hack at the upper part of the Chamber, and mark the Wire there again; so measuring betwixt these two Marks of the Wire, you have the small end of the Taper-bore; then measuring the Diameter of the Tamken, and so you have the great End: Then taking the Distance between the marks of the Half-Pike, so having both Diameters and Length, (if you will) you may draw the form of a Tapered Chamber on Paper, and extract the Wind from it, for the Cartrage going up with more ease. CHAP. XXIII. For Chamber-Bored Guns. THese Guns are tried with ¼ part of their Balls weight of Powder; So that a Piece shooting 24 lb Ball, is proved with 6 lb Powder: For Ordinary, there is allowed for every pound of Ball 3 ounces of Powder, so that there needs no Table to those Ordnance, for there is not many of those to be found but Mortar-Peeces. Chamber-Bored Guns were of old as is supposed. But certainly those Pieces must be ancient since their Foundation; That Josephus in his Antiquities of the Jews doth say, That there were Stones shot into Jerusalem at the Siege of great weight; that at one time one of these Stones shot off the Head of a Man, and carried it several furlongs from the Body. As I am here to speak of Chamber-Bored Ordnance, so I do remember that in Holland they use to boar their Guns of 6 lb Ball to 8 lb, and that there may come of these Guns to be made use of. Three sorts of Chambered Ordnance. Now know that of Chamber-Bored Guns, there are three sorts; to wit, first, Those that shoot Iron Ball; Secondly, Those that shoot Stone Ball; and thirdly, Those that shoot Granades and Fire-Works. First, Know that it is a Chamber-Bored Piece which hath two right and true Boars; the one is the vacant Cylinder, all from the Mussel till you come to the Charged Cylinder; the Charged Cylinder is from the Touchhole to the great Boar, called the Chamber, because it is not so great a Boar as the other. But if this Chamber be too long and narrow, or small to continue Powder for this sort of Pieces, than the Ball may be delivered before all the Powder be fired, and do little Execution; For it is without controversy, that the vehemency of any Ball struck from a Piece, is by virtue of the Powder fired in the Piece before it come out, and is rather hindered than furthered by any Powder that is fired after it is out. Likewise there be Chambers short and wide, which may be harmful; for the Powder all firing suddenly, before it lose the Ball, the strength thereof many times doth burst the Piece; Therefore it is best in this, as in all other cases, a true Proportion be kept. Things incident ought to be with diligence observed for fear of danger. CHAP. XXIV. To know the true Proportion of the Chambers of Ordnance. The true Proportion of Right Chambers in Pieces. ANd first of them which shoot Iron Ball; a well proportioned Chamber for a Piece that shooteth Iron Ball, aught to be three Diameters of the great Boar long in the Chamber, and three quarters of the Diameter of the Ball, the Diameter of the Chamber: Having this Proportion, they ought to have one pound Powder for every three pound of Ball for Proof; and for Action three quarters of a pound; this being so plain it needs no Tables. The true Proportion of a Chamber in a Chamber-Bored Piece that shooteth Stone, is once and a half the Diameter of the Ball long, and the Diameter of the Chamber is two third parts of the Diameter of the Ball; having this Proportion, one pound of Powder will serve to prove a Piece that shooteth 4 pound of Ball, and three quarters of a Pound for Action, the Ball being Stone. Now I suppose, and I hope that I need not doubt, but hitherto there is enough written and declared to the use of great Ordnance of most sorts that are used, and how with caution they ought to be handled. I was a Gunner when the Spanish ships came to the Downs, in the year 1639. And because I in my Youth have served for a Gunner both by Sea and Land, not doubting that any need Instruction that are undertakers to be Gunners, (but as aforesaid) it may be some Friends may prefer some Young Men before they be capable, even to be Gunners of good Ships, who never knew how to shoot a Gun in anger. CHAP. XXV. Therefore I will here give some needful Observations for Gunners of Ships. 1. THe first is, That the careful Gunner coming into a new Ship, diligently and carefully measure his Guns, to know whether they, or any of them, be full Fortified, Reinforced, or lessened in Metal. 2. Then he shall with a Ladle and Sponge draw and make clean all his Guns within, that there remain not any old Powder, Stones, Iron, or any other thing that may do harm. 3. That he shall search all his Guns within, to know if they be Tapered, Chambered, or true-Bored, or whether they be cracked, flawed, or Hony-combed within: And finding what Ball she shoots, to make the Weight of the Ball above the Port; that thereby he may set the same Mark or Number upon the Cartrage and Case, that in time of Service, those who bring the Powder may not go wrong. 4. The Guns being dimensioned and clean as aforesaid, the Gunner shall take half a Ladle of Powder for every Gun, and blow them off, Sponge them well; and finding them clean, Load then the Piece or Guns with their respective Cartrages and Powder; which being rammed home, with a straight Wad after it, then let the Ball roll home to the Wad, and set a Wad close home to the Ball, that the Ball roll not out with the tumbling of the Ship; then must he Tamken that Piece at the Mussel or Boar, with a Wooden Tampken, which he must Tallow with hard Tallow round about for preserving the Powder from Water; Likewise make a little Tapon of Ockam for the Touch hole, which must be tallowed also for Water, before the Leaden Apron be put over; then make your Piece fast as occasion best presents. 5. The Piece loaded and fast, than the Gunner is to have to every Piece 24 Cartrages at least ready made; to wit, 12 filled, and 12 empty in sort: Likewise he must be careful, so long as the Gunner's Crew are busy with the Powder, that there be no burning Match or other fire in the Ship; also to lay his Cartrages in Barrels or Chests in sort, that when there is occasion to be brought, it be without abuse. Most needful, for great hurt may come by a Ball too high. 6. The Gunner must see that he sort his Ball very well, and lay every sort by themselves in several Cases, and upon every Case set the weight of one of the Shot which is in them. Also he ought to make the Bags for H●il, for the Guns above, ready betime, and fill them with Stones, Small Shot, or pieces of old Iron, which may do great damage to the Enemies Men. 7. If it fall out that any new Ports must be cut out in the Ship, the Gunner must be careful that they be above a Beam, or close by if possible; also that they be not higher or lower than the Ports before; Likewise that there be room for the Guns to play, because if one Gun should be dismounted, there might be another brought to her place: And observe, that the Carriage standing on her Truckes, the uppermost part of the Carriage must come to stand in the middle of the Port up and down, that a Man may lay his Piece as he pleaseth. 8. The Gunner must be careful that the Powder in the Room be well covered with Hides; also that the Axtrees of the Truckes be well smeared with Soap; These not to be neglected. also that his Ropes, Rammers, and Sponges be ready at hand; and he must not let the Powder lie unturned above one month, otherwise the Salt-Peter will descend to the lower part of the Barrel, which is to be feared if Men should make use of that Powder: And he must every Month draw the Ordnance, if he fear they have got any Wet or Moist to the Powder, also for fear of the Salt-Peter dissolving, which may prejudice the Piece. And he must be careful of the Candle and Fire about the Gun-Room and Powder-Room, that there come no disaster. Likewise he must keep a good Account of all Materials that belong to the Guns, as Ball, Match, and Powder, what part thereof he spends, and also what now remains, that he may give a good account what is become of them. 9 A Gunner must use all diligence before he Rencounter with his Enemy, to set a bailey of Water betwixt every two Guns, that when they see conveniency, they may dip the Sponges for cooling of the Pieces, and fear of Fire remaining, which may do hurt: And that he be careful not to shoot except he hit, for it is sure, when the Enemy sees that he is not hurt, it gives him more courage: But to encourage Young Gunners, I will counsel them at Sea, not to use a Lont-Staff in Service, but first observing the way of both Ships, whether the one heave and the other set, or both heave and set together; and also the sailing of the Ships, if both one way, or on several Tacks, whereby he shoot not in vain: Now if the Gunner have a small piece of light Match, he standing at the left side of the Piece, shall set his right foot in the Carriage, looking over the Piece, and according as he sees occasion give fire, and at the fire giving, retire his right foot, and before the Piece be recoiling the Gunner is free; and by trying his Dexterity, will make a good Experiment, and that he will do good Service: But if the Ball have not done to your expectation, you may help the next; for when you see from the Breech of your Piece to the Mussel, and so to the Mark, you have a sight of three things; so Euclid avers, that seeing over any three things, you have a right Line from the first to the third, through the second; for there is no Man dare promise to make a good Shot at Sea, if he have no experience of the Piece, and observation of the Ships motion. 10. Also the Gunner must be sure that there be no melted Stuff for Fire-Works done in the Ship but on Shore, for it is dangerous for a Gunner, and great hazard for Ship and Goods, yea and men's lives: Likewise there may no Firework be brought above in the Round-house or Cabin to stand, for fear of shot, but must be kept below till time of need, either in the Powder-Room, or Steward-Room: By the hazard of such things there hath been many and cruel Examples. Of Necessaries that a Sea-Gunner ought to have for his Ordnance. Necessaries that a Gunner ought to have for his Ordnance are many, and the quantity is according to the quantity and quality of his Guns; and also if he be in a Man of War, or a Merchantman, than there is difference of Provisions, only I will here name them, let every Gunner take what he thinks will fit, and at the Voyage end give an account what is spent, and what he hath, and how he spent that which is gone. I leave to the Gunners own discretion the quantity of necessaries. Powder. Round Shot in sort. Double-heads in sort. Cut Iron of foot or foot and half long. Wooden Tampkens in sort. Cartrage-Paper. Thread, Needles, Twine, and Starch. Match. Mallets, Hand-Spoaks, Rammer-heads, Worms, Ladles. Sponge-heads, and Staves to place them on. Beds and Coins in sort. Old Strouds for Breeching, and twice laid Stuff for Tackles. Lashers, double and single Blocks, new Rope for Double Tackles, some old Strouds for Sponges, some Lines. Marline, tarred Twine, Port-Ropes. Moulds for Cartrages in sort, Axeltrees and Truckes. Budg-Barrels, and Lint-spindles', Crows, Splice-Irons. Primes, Staples and Rings, Tackle-Hooks, Nails. Thimbles, Port-Bands, Sheet-Lead, and Lead-Shot. Old Canvas, Seals and Weights in sort. Lanterns, Dark-Lanthorns, Powder-Measures. Soap, Horns, and Prime-Irons, Height-board. Height-Ruler and Compasses. With what other Instruments he finds needful. CHAP. XXVI. How to Dispart a Piece of Ordnance. AN easy way to Dispart a Piece of Ordnance. First, Take the Diameter of the Piece upon the thickest part at the Breech with a pair of Callabasser Compasses, and likewise at the Mussel at the thickest part thereof; then draw upon a Paper or Board both Diameters: So laying a Ruler through the Centre, draw the Diameter, and then you may the easier take the Difference betwixt them. Example. The only way to Dispart a Piece of Ordnance. The Diameter of the Breech (in the preceding Figure) is OF, the Diameter at the Mussel CD, and the Diameter of the Boar AB; so you see the Difference betwixt the two Circles is DF or EC, which is the true Dispart of that Piece. If you take a piece of Wax, or Straw, or Stick, of the length DF, and set on the Muslle at D, you have a true Dispart: I have made them of Iron and screwed them on. CHAP. XXVII. How to levelly a Piece of Ordnance to shoot at Blank. What Point-Blank Distance is. SHooting Point-Blank is a term very much misconstrued amongst our Gunners, for I have heard some say, they have shot a mile and more Point-Blank; the which is contrary to the nature of Great Ordnance, for it is observed, that it is much to shoot 350 Paces Blank, accounting 5 foot to a Pace, which is little over the ⅓ part of a mile. But to shoot Point-Blank, is to be understood, that then the hollow Cylinder of the Piece lieth upon a level Line, so that the Ruler of the Quadrant being put into the Mouth of the Piece, the Plumb-Line hangeth perpendicular, than that Piece lieth to shoot Point-Blank. To know how to make a good Shot at a Mark, within Point-Blank-reach of the Piece. The Piece lying as is before shown, set the Dispart of the Piece at the place required on the Mussel, than a Ruler from the Dispart to the Breech of the Piece; so turning your Piece to the Mark, you looking from the Breech alongst the Ruler to the Mark desired; fire your Piece, and if there be nothing defective in the Piece, or Carriage, or Platform, you make a good Shot: But if the Piece lie so, that the Ruler of the Quadrant being in her Concavity, and the Plumb-Line cut any of the Quadrant, then is that Piece said to be clevated, and will shoot further than when she lieth level, except there be some Object which lieth higher than the Piece to stop it. And if that Piece lie so, that when the Ruler of the Quadrant is in her, the Plumb-Line hang without the Line of Level, than that Piece is said to lie under Metal, and will not shoot so far as if the Piece were lying level, except there be a very great descent under the Piece. Moreover it is certain, if Men have time, and the Object lying within Point-Blank-reach of the Piece, that the industrious Gunner observing these Rules, may do good Service at the first or second Shot: for it is certain, that if a Man look along any three things or marks on one Line, then betwixt the first and third there is a right Line over the second; so that if a Man look from the Breech of a Piece, over the end of his Dispart on the Mussel of the Piece, and to the Mark he is to shoot at, than the Breech of that Piece and that Mark lieth on a right Line through the Dispart: Therefore it is imagined, the Mark being within Blank-Reach of the Piece, if the Piece be loaded and fired she will make a good shoot, all impediments being removed. CHAP. XXVIII. IF the Ball err, contrary to your expectation, either above the Mark or below, or on either side, follow the Rules following to help the next. Rule 1. If the Shot err too high or too low, help it thus, When you have done as is described, and that the Shot hath carried too high as in D, or too low as in E, the Mark you shoot at being in C; having loaded your Piece, you are to find the middle of the Boar of the Piece, and the places on the Base-Ring and Musle-Ring corresponding, than you are to set the Dispart, so you cause traverse your Piece till you bring the Breech of the Piece A to the top of the Dispart at the Mussel B, and the Mark C in a Line; after Fire given, you hold this for a Rule. But the Gunner may lay his Piece very artificially, and yet the Shot may carry contrary to expectation several ways; if it be too high as in D, help it thus; having laid your Piece as at first, in the Line ABC, and found the Ball in D; then lengthen your Dispart on the Musle-Ring, till looking over the Piece you find ABDELLA; this done, you are to cause lift the Breech of your Piece, till over your Piece and Dispart you find the appointed Mark C; then fire, and you will hit your desired Mark. Observe the Copper Piece, Numb. 1. Likewise if your Shot at first had been below the Mark, as in E; you are to Load her and bring her to her first station, and then you are to take from your Dispart so much, till you have the Line ABE; this done, you are to lower the Metal of your Piece, till you find your desired Mark ABC; fire your Piece and you do good service. Now if the Ball should come to light on either side of the Mark, as (in the second Figure of the Copper Piece) in E to the right hand; to help the next, lay your Piece in all points as before, with her Dispart; than you are to go to the Breech of your Piece, and find at your conveniency a place on the Base-Ring, looking over the Dispart, you see the mark of the shot at E; mark narrowly that place of the Base-Ring, (with Chalk or what you please) keeping that mark to look over your Piece, than you cause traverse your Piece till looking over your mark on the Breech, your Dispart, and behold C your desired Mark in a Line; fire that Piece and you have your desire. And if to the left hand, you may help in the same manner. Observe the figure in the Copper Piece, Numb. 2. But if you were to shoot at any known distance, without the Blank-reach of the Piece, upon any degree of Random, first measure the distance to the Object, and as you find it in proportion to the Blank-reach of the Piece, the same quantity you may take from the Dispart. For if your distance be ¼ farther than the Blank-reach of the Piece, then take from the Dispart ¼ part of its length; by holding this proportion, if the Object be on a right Line from you, you will do good service. Many times it falls out, that when a Gunner enters a Battery, Castle, or other Fortification; before he can have time to observe Rules, orders are given to fire some Ordnance; it may be in all his Life he hath not seen the like before that time, therefore he must lay his Piece by the discretion of his Eye and former experience; if then his Ball strike the Mark, his experience and discretion is a good Rule; but if the Ball go besides expectation, you may help as is before taught. For if the Gunner observe these Rules cautiously, he shall find both pleasure and profit, and have praise of the Spectators. CHAP. XXIX. The way to Shoot a Ball from a Hill to a Valley, or from a Valley to a Hill. I suppose mistakes, or trusting to other men's Works, makes one beget another. MAny and divers Opinions are there of shooting from Height to Valleys, as Nicholas Tartaglia in his first Book of Colloquies, and 26 th' Colloquy, affirmeth, That though the Mark be within Blank-reach of a Piece, the Ball shot under Metal will strike above the Mark aimed at. Likewise one William Claes, in his Book called the Practic Busketrie, pag 94. affirmeth the same by many Instances, That a Ball shot from a Height will over-shoot the Mark, though there be no impediment. But I cannot blame the Hollander, in regard his Country is very plain, and no remarkable Height, whereby he might have confirmed what he saith by practice. But I rather adhere to Luigui Callado; for in his Practic manual de Arteyleria, Chap. 8. he informs, That a Ball being shot from a Height, will strike below the Mark; as I myself by practice have found divers times. By Experience. For in the year 1650, I was in the Castle of Edinburgh, when that Army of Rebels to our King did beleaguer that Castle, so that many times I had occasion to shoot so far under Metal, or below the Level-Range, that I have been forced to cut the Brestband of the Carriage quite out, and so to elevate the Breech of the Piece, that it hath been supposed she would fall over the Wall; and though in this case I durst not coin my Piece with fast Bed and Coin, yet always I found the Ball to hit below the Mark till I helped it. A Remarkable Instance. One remarkable instance I had of this, in shooting at that Mirror of his time for loyalty and gallantry, James Marquis of Montr●ss his Head, standing on the Pinnacle of the Tolbooth of Edinburgh, with which the Enemy reproach us, as counting loyalty a sin worthy of death. Now at this time I was by the Governor commanded, that there should not a Gun be shot in the Castle; which I took as an ill Omen of what followed; I demanded a reason for it: he told me I had too much Blood on my Head already: I being somewhat troubled, lest his Majesty, and those that loved him, both abroad and in the Castle, should suppose me a helper to the Treachery, desired the Governor to give me Orders in presence of all the Soldiers, otherwise I would not desist. When a Sheep is General of an Army of Lions they may be beat. So he sent for me, and on the Head of the Parado, commanded me that no Ordnance should be shot in the Castle; for if any Gunner should do it, I should suffer a Counsel of War. Nevertheless, being curious to have down the Head, which deserved Honour above what I can write, I laid a Piece of 24 lb Ball; and because I durst not be accessary to any Acting, far less to that, I desired Thomas Kniblo, who was Keeper of the Magazine, that he should fire that Piece, after he saw the Governor and I gone to walk; which he did. The Governor hearing a Shot, and I in his company, inquired who had shot that Gun: I answered, I knew not; so that one returned to the Wall to know who it was, and whereat he shot; the young Man answered, Sir, I thought that it was sin in you and the Master Gunner to suffer these Men to fortify themselves, and raise Batteries before your Nose, and you not stop them, wherefore I shot at this, meaning the Battery. But that Providence had ordered that Head to be taken down with more Honour, I admired of its abiding, for the Ball took the Stone joining to the Stone whereon it stood; which Stone fell down, and killed a Drummer, and a Soldier or two, on their march betwixt the Lucken-Booths and the Church, and the Head remained, till by his Majesty it was caused to be taken down, and buried with such honour as was due to it. The Reasons of their former mistakes. Now any that knows the Place, knoweth that betwixt the Fore-wall of the Castle and the Tolbooth is not a quarter of a mile; so that it was in Blank-reach of a Demi-Cannon: Yet the Piece lying higher than the Mark shot at, shot lower than the Mark: And I am of Opinion, that Reason must give it to be so, in regard that the Parallel Line made betwixt the Breech and the Dispart, lay 8 Inches near above the Boar of the Piece; and if it carried about so far below the Mark, I am sure she perfected the Line, the Boar made parallel to the Imaginary Line above: Behold the Figure AC. So much for shooting from a Height to a Valley, which may be helped, by laying your Piece so as your Imaginary Line parallel to the Boar, direct you half a foot above the Mark, than you shall do good Service. It is also to be observed, that shooting from a Valley to a Height, that a Ball will over-shoot the Mark, if it lie within point-Blank-reach of the Piece: Reason should give it so: for the Piece being elevated to a great Height, the Ball with the force and exaltation of the Powder, doth elevate above the true Line, which the Boar maketh to the Mark, in regard of the Wind or Vacancy that is betwixt the Ball and the Piece: As was found by shooting at the Castle of Edinburgh, where the Gunners shooting to dismount our Ordnance, most of their Shot flew over the whole Castle, till observed by the Gunners and helped. But when we come to treat of Observations of Heights, Depths, and Distances, by the Quadrant, you will have further satisfaction. CHAP. XXX. To know how to make as good a Shot by Night as by Day. First, You are to lay your Piece by day, as is formerly taught, being loaded with Powder and Shot, as if you were to make presently your execution at the place. Good Observations if followed. Then take a Mariner's Compass, and set that on the Breech of the Piece, and looking over the Piece you see the Mark, and observe how the place bears off you, so that in the Night you may know how, and on what Point of the Compass the Place bears off you, when you are to give Fire; then take a Line and plummet at the Mussel of the Piece, and right over the middle of the Mussel let the Plummet hang to the Platform; so you shall remark, or make a mark on the Line where it cutteth with the lower edge of the Boar of the Piece at the Mussel; and likewise remark where the Plummet toucheth the Platform: And for your more assurance, you may let the Piece be fired in the day time at the same Mark; and as you find that Shot to prosecute, you may proceed as is before-taught, and in the Night you may do good Service. In the Night as by Day. First, Set your Piece as is before shown by the Compass, causing your Matross or Pioneer to traverse the Piece to your desire; then go to the Mussel with your Plumb-Line, causing them to elevate or abase the Metal, till you find the Plumb-Line and Plumb fall in their former stations: So in firing that Piece you may do good Service by Night or by Day. But withal you must observe the distance to the Mark, if you be to shoot beyond Blank-reach of the Piece, also how the Wind is, whether with or against you, or on which side; for by these means the Ball may change her Course; and so if you have a Dark Lantern, that you may see your Compass and Plumb-Line, observing all these things, you may shoot by Night as well as by day. But to know whether you shoot right in the Night or not. To be sure you will see where your Ball Lights. It shall be requisite to take some Butter, or Tallow, and melt them in some Kettle, wherein you shall dip your Ball that is to be shot, and roll the same Ball in fine Powder, that the Powder may stick fast to it; and when you have done, put home the Powder in your Piece; and observe you put no Wad betwixt the Powder and the Ball; so when you give fire, the Ball will flame as a Candle; and where the Ball doth light, the mixture will fly on the Object, by the light whereof you will see whether you have hit the Object or not. CHAP. XXXI. To know how far any Piece will shoot at any degree of Random. Uncertain to find exact truth in Random Tables. THis task is so difficult as there are Proportions of Ordnance, yea it will alter by the alteration of Wether; likewise if the place lie higher, the Piece shall shoot farther over a Valley at the same Random, than she shall from a Valley to a Height; for these Reasons, I have found none that ever made Tables for great Ordnance, that would or could make them good on all Accounts and all Degrees. Now the only Rule by which a Gunner may know how many Paces his Piece will shoot, in elevating from Degree to Degree, is to take good notice how far she shoots Point-Blank, as also Horizontal with the Metal; which Distance being marked to be ⅓ part, or a half, or ⅔ parts farther than Point-Blank, then hath he a convenient Proportion to work by, and to find his desire reasonably near. This Table I had from William Class in his Practice of Gunnery. A Random-Table for a Demi-Cannon to 45 Degrees. 1 298 16 1528 31 2308 2 394 17 1594 32 2344 3 488 18 1658 33 2378 4 580 19 1720 34 2410 5 670 20 1780 35 2440 6 758 21 1838 36 2468 7 844 22 1894 37 2493 8 928 23 1948 38 2515 9 1010 24 2000 39 2534 10 1090 25 2050 40 2550 11 1168 26 2098 41 2563 12 1244 27 2144 42 2573 13 1318 28 2188 43 2580 14 1390 29 2230 44 2584 15 1460 30 2270 45 2585 This is now a brief way of making a Table of Randoms for a Demi-Cannon, which may be done in like manner for any Piece of Ordnance whatsoever; first knowing the true Distance she shoots at Point-Blank, and the Distance she shoots lying Horizontal by the Metal, compute Difference, and work as before, you have your desire. As this Table is for a Demi-Cannon, so there must be one for every sort of Ordnance the Gunner makes use of; And he shall hardly find truth. CHAP. XXXII. The Geometrical Quadrant, with the Uses in Measuring Distances, Heights, and Depths, and Distances most useful for a Gunner. First, To measure the Height of any Tower, Wall, or Castle, or any other Body, standing on a Plane, if you have access to it, by the Gunter 's Quadrant. SEt the Ruler of the Quadrant so to your Eye, that you see through the Sights, from the place where you stand, the mark you desire to observe; then note what part of Vmbra Recta, or Versa, your Thread cuts, and you shall find the Height in this manner. 1. If the Thread of the Plummet fall on 100, then is the Height desired equal to the Distance betwixt the Observers foot, and the Ground or Root of the thing observed. Conclusions and Observations done by the Quadrant 2. Otherways, if the Thread fall on the parts of Vmbra Recta, or Right Shadow, then is the distance betwixt the Observers foot and the ground of the thing observed, less than the Height of the Body observed, according as the parts cut off Right Shadow by the Thread is to 100; Therefore use the Rule of Proportion, otherwise called the Rule of Three, and set the parts of Right Shadow in the first place, cut by the Thread or Plummet-Line, and the 100 in the second, and the Distance you are from the Root, or foot of the Mark, in the third, and the fourth place will show the desired Height; as you may see in the Example following. 3. But if the Gunner cannot Cipher, then do this; go so far back or fore, till you see the Mark desired, and that the Plummet-Line of your Quadrant (being still observing) fall on the parts of Right Shadow: And know that if the Line fall on 100, the Distance is equal to the Height: If the Line fall on 75 parts, than the Distance is three-quarters of the Height; if it fall on 66 ¾ parts, then is the Distance ⅔ parts of the Height; if on 50 parts, the half of the Height: if on 33 ⅓ parts, one third part of the Height; and if on 25 parts, one, quarter of the Height; by which you may conclude the Height of what you observe. 4. But in observing, if the Thread fall in parts of Vmbra Versa, or Contrary Shadow, then know that the Distance of the Ground to the Place observed, is more than the Height of the same: And the Proportion is, as 100 parts is more than the parts cut off the Contrary Shadow; so is the Distance from the Mark, unto the Height of the thing observed. Example. Suppose the Thread to fall on 25 parts of Vmbra Versa, and the Distance betwixt your Foot and the Wall be 300 foot: Then say, As 100 parts is to 25 parts of Contrary shadow; so is 300 foot the Distance given, to 75 foot the Height required. To which if you add the Distance betwixt the Observers Eye and the Ground, you shall have the true Height. 5. And if you cannot Cipher, then go so far backward or forward, always seeing the Mark desired, till the Thread fall on what parts of Contrary Shadow you would have it; and if it be 100, then is the Distance and Height equal; if it fall on 75 parts, then is the Distance one quarter more than the Height; if it fall on 66 ⅔ parts, then is the Distance one third part more than the Height; if the Thread fall on 50, then is the Distance one half more than the Height; if it fall on 33 ⅓, then is the Distance ⅔ more than the Height; if on 25, then is the Distance three quarters more than the Height: Ever adding the length from your eye to your foot, than you shall certainly have the true Height. 6. This manner is used to measure the Height of any thing, whereto you may have access: If it were that you must measure the Height of a Wall, or any other thing standing on the side of a River, than you must have two Observations; in manner following: First, Measure the distance from your station to the side of the River; being come to the brim of the Water, stand perpendicularly upright, draw down the brim of your Hat before your face, till you looking by the brim of your Hat, see the Foot or Root of the place you would measure; then turn yourself about, observing in all things your gesture, till you see on that side of the River where you stand, some Hill, Down, House, or any other Mark; thus you shall measure with your foot the distance to it, and then Work as is before shown. Secondly; To measure the Height of any thing standing on a Plane from you, when you can have no access to it, or were hindered by the Enemy to come near it. 1. To this Work you must have two several Observations, as followeth: Put the Ruler of the Quadrant to your eye, in such manner, that through the Sights you see the Mark desired; To know how far, or what Distance you are from the Enemy's Forts, or Strengths, is most necessary for a Gunner. take notice then what parts of Contrary, or Right Shadow is cut by the Thread or Plummer-Line, and then where you stand set up a Staff; than you are to go a remarkable distance backward or forward, and take there your second station; and observe your Mark as before, then note well what parts of Contrary or Right Shadow your Line cutteth; note that also down: Now if it be so, that in both your stations the Plummet-Line hath fallen on parts of Right Shadow, then deduce the lesser from the greater, and keep the Difference: Then say by the Rule of Three, As the Difference in the parts of Vmbra Recta, is to 100 parts in the Quadrant; So is the Distance between the two Stations to the desired Height of that Body: But it is to be understood, that you must not forget to add the Height of your Eye from the Ground. Example. In the first place, when you find the Thread fall in 25 parts of the Right Shadow, and in the second on 50; then let the distance betwixt the stations be 30 foot. Say then by the Rule of Three; As 25, the difference of the parts of Observation, is to 100 parts in the Quadrant; So is 30 foot the distance of the Stations, to 120 foot the Height required; to which add the Height of your Eye. 2. But if at one Station (or possibly at both Stations) the Thread falls on parts of Contrary Shadow, than the parts must be converted to parts of Right Shadow, as shall be shown in the following Example. Example. Experience is the best Schoolmaster. Suppose there were placed some Guns on the top of a Hill, as in the Figure by A; by which the Gunners in the Valley B have a great deal of loss and trouble; wherefore order is given to one of them, to do his endeavour to dismount these Pieces at A: Now to do this with understanding, and what hast convenient; First, He must know the height of the Hill AD, with the distance BD: Then he may by Prop. 47. of the first Book of Euclid, find the length of the Hypothenusal Line AB; to be assured how many degrees of the Quadrant his Piece must be elevated to the Mark. Take for Example. We say that the first Station observed, the Thread fell on 25 parts of Contrary Shadow, and at the second on 90 parts of Right Shadow; than you cannot take 90 parts from 25 parts; therefore you must alter the 25 parts of Contrary Shadow to parts of Right Shadow, in manner following: Multiply 100, the one side of the Quadrat by itself, and you have 10000; this you divide by 25 the parts of Contrary Shadow, and you have in the Quotient 400 parts of Right Shadow, which is equal to 25 parts of Contrary Shadow; then take 90 parts from 400 parts, there remain 310 for the Difference: Also let the Distance betwixt the two Stations, from B to C, be 200 foot: Then say by the Rule of Three; As 310 is to 100 parts in the Quadrant; So is 200 foot the Distance of the Stations, to 64 16/31, which is very near 64 ½ foot, the Height of the Hill AD: We should now show the way to find the Distance AB and BD; that those who cannot Cipher, may understand this. Thirdly; Therefore we will give one Example or two, that they may do such without Arithmetic. These must search out their Stations, in which the Thread may fall on all such parts of the Right and Contrary Shadow as they desire, which is easy to be done, if they go discretly forward or backward, and measure the Distance betwixt the Stations, till the Thread fall where they desire. 1. If the Thread fall at the first Station upon 100, and at the second on 50 parts of Right Shadow, then is the Distance half the Height. 2. Or if the Thread fall at the first Station upon 100, and at the second on 66 ⅔ of Right Shadow, then is the Distance betwixt your Stations one third part of the desired Height. 3. And if the Thread fall at the first Station on 100, and at the second on 75 of Right Shadow, then is your Distance just one quarter of the desired Height. 4. Likewise if at the first Station the Thread fall on 100, and at the second on 66 ⅔ parts of Contrary Shadow, then is the Distance half the Height. 5. Or if the Thread fall at the first Station on 100, and at the second on 50 parts of Contrary Shadow, then is the Distance equal to the Height desired. 6. The same it shall be, if at the first Station the Thread fall on 50 parts of Right Shadow, and the second on 66 ⅔ of Contrary Shadow: But still remember to add the Height of your Eye above the Ground. Fourthly; To measure the Distance to any place, or the Breadth and Length of any Plane or Water. By what hath been said before, it appears plainly that in the measuring the Height of any thing, there must be once a known Distance, to wit, some length of the Plane whereon the Height is erected: Likewise in measuring any Distances, as the length of a Field, it is very necessary to know the Height of something thereby; which may be easily done: for if you were to measure the Distance to a Fort, Battery, Trinal, or Bulwark, which you desire to know; if the Distance be not great, in that case you need know no Height but your Eye from the Ground where you stand; But if the Distance you would measure be great, than it is needful to have a known Height to stand upon, which Height you must add to the Height of your Eye, which may be done with a Plumb-Line, whose Marks you know: Then Work as followeth. Example. Take for Example, that you desire to measure the Distance from B to D; then turn the Centre of your Quadrant to your Eye, and observe through both your Sights the Point D; remark well what part of Right or Contrary Shadow the Thread cutteth; If it happen to fall on 100 parts, than ought the Distance to be equal to your Height: But if the Thread fall on parts of Contrary Shadow, which in such Cases is ordinary, then is your desired Length more than your known Height, so much in proportion as 100 is more than the parts cut of Contrary Shadow, which the Line showeth. Therefore say by the Rule of Three; As the parts of Contrary Shadow, which the Plumb-Line showeth, is to 100; So is the known Height unto the Distance required. Example. The Thread cutteth 1 ⅓ parts of Contrary Shadow, and the Height from the Eye to the Ground is 5 foot: Then work as followeth, and you will find the length BD to be 375 foot. Now having the Perpendicular AD, and the Base BD, you may easily find the Hypothenusal AB, to be near 380 foot: But here you are to extract the Square Root, for Euclid in the 47 Prop. of the first Book of his Elements, hath proved by Demonstration, That in Rightangled Triangles, the Square which is made of the side subtending the Right Angle, is equal to the Squares which are made of the sides containing the Right Angle. Where if two sides be given, we may find the third side thus; in the Rightangled Triangle ADB, you have AD 64 ½ foot, and you have the Base BD 375 foot; whose Squares being added, and the Square-Root extracted, you shall have the Square-Root near to be 380 ½ foot for the Hypothenusal AB: For Extracting the Square Root, it is described in Chap. 6, and 7. This I have done for the use of Young Gunners, that when occasion may present, they may lay their Pieces at a reasonable Degree, thereby to come near the Mark at the first Shot; And always may observe a greater distance from a Height to a Valley. Example. There is a Castle, as the Figure showeth, and in the Battery there lies a Piece of Ordnance; If it were desired of the Gunner to know if this Piece might be of service to dismount the Piece in the Battery C: Now the Gunner must desire time to measure the Distance from him to the Battery C; whereby he may the more assuredly Answer. Then shall he take a Line and measure the Height AB; then standing at A, shall take the Quadrant with the Centre to his Eye, and beholding through the Sights the Mark C, Remark narrowly the parts cut by the Plumb-Line, which is without fail parts of the Contrary Shadow: Then say, As the parts of Contrary Shadow are to 100; So is my Height from the low Battery to the Distance required. Let the Height AB be 95 foot, and the parts of Contrary Shadow 5 ¼ and you will find the Facit to be 1809 ½ foot, or 362 Geometrical Paces very near. But if you please to reduce the Distance to Paces, divide the Quotient by 5, for 5 foot make a Pace, and you have as aforesaid. This is so clear, that I think any Gunner may perceive, that if he in the Battery C, elevate his Piece two Degrees above the Level, that then he might do good Service, and by once firing, if the Ball go beyond expectation, you may help the second. Necessary Observations for Gunners either by Sea or Land. The like may the Gunner in the Battery B do, and also the Gunner in the Battery A to C: and so each to other, for they have double Advantages of the Gunner at Sea, except he be lying in a River; and let his Ship lie never so still, so long as she is afloat, she hath ever a Motion, nevertheless the Observant Gunner in a Ship may do good Service. For I myself in the year 1652, or 53, being forced from Scotland, when the War began betwixt the States of Holland, and the (then) State of England; and as many better than I were in necessity, I put myself in a Frigate of Terveer, one Jaques Wolves Captain, I served there for a Gunner, and in our Voyage to Shetland to bring home the Hollands East-India Fleet, we met with a Storm, where we lost above 20 Sail of our Fleet, our Ship was called Prince Rupert; but with this Ship we were forced to come to Anchor betwixt Fulla and Shetland, and by providence road the Storm out; when we had fair Wether, we went to Brasa Sound in Shetland, and there riding at Anchor with three Ships of our Fleet: the Commander or Corporal of the Soldiers and I fell at Dispute concerning his Men, that they could not shoot at a Mark; whereupon he told me, That I could not shoot so well with a great Gun, as any of them did with their Musket; at last I wagered with him that I would shoot as near with a great Gun, as he himself with a Musket; whereupon we agreed, (the Wager was two Rix Dollars): I sent the Quartermaster to our Captain, who was aboard one of his Consorts at Dinner, for liberty to shoot; which was granted: The Mark we were to shoot at, was the Buoy of the Anchor of the same Ship our Captain was aboard of; so that we had the four Captains for Judges: I brought a Sacker-Cut, from the breast of the Steerage to the Mainmast; I disparted and loaded her, and set her to the Port, I set her to the middle-Port of the Ship; then we were at a contest who should shoot first; I gave him that privilege: So after he shot, he found he came not near by three yards, as it was alleged; and that he might be better pleased, I gave him liberty to shoot again, This is true, and can be witnessed. where he made little mends: Then I laid my Gun to the Port, and observing the ranging of the Ship, I gave fire at my conveniency, and struck the Buoy, which lay about 150 paces from us; there are Men here in London that did see it. I say, good Service may be done aboard a Ship, if the Gunner be cautious. And by this I would have you know, that I would have Gunners to consider, that the middle of a Ship is the only place for to make a good shot, though by accident there may be some made either afore or after; as I will give an Example. Example. In the Figure, Num. 133. Suppose there is a Ship in a River or smooth Road a pretty distance off, as this Ship E F: The Gunner is demanded if he could do any good Service with his Guns at the Battery on the Shore G, which only could wrong them. The Piece he is to use here, is a Demi-Cannon, which shoots Point-blank 200 Paces. This you must consider, could not be answered, till he knew what distance he lay off; therefore he must observe as followeth: First, With a Lead-Line measure the length from your Topmast-Head to the Water, as from E to F; then go to the Topmast-Head in F, and observe with the Centre of your Quadrant to the Eye, that through the Sights you see the Battery G, and in all things doing as in the Battery A for clearing. Example. Let the Height from the Water to the Topmast-Head be 90 foot, the parts cut of Contrary Shadow 5; so set it on the the Rule as followeth. which is 360 Geometrical Paces. At a Degrees the Demi-Cannon shoots 394 Paces. Suppose the Gunner in the Ship had a Demi-Cannon, which shooteth Point-Blank 200 Paces; Therefore may the Gunner conclude to elevate his Piece 2 Degrees, and thereby at the first shot be pretty near the Mark; by which he may help the second: Even so may the Gunner in the Valley at the Battery G, observe to do good service on the Ship E F: Likewise the Gunner in the Battery A, may do good Service every where round about, if he observe what is before set down: Nevertheless my desire is to set down another Example of observing by the Cross-Staff. Example. It is desired to know the Breadth of the Bulwark ABC: First, You are to observe the Distance to the same, as from D to B, which we suppose to be 750 foot: Take the Cross-Staff as EFG, having thus on the end of your Staff a Cross, as FG, at such distance as you may see by the Transom F in C, and G in A; The Breadth or Length of a Curtain or Bulwark is all to be done in one manner. then divide the length of your Staff in as many equal parts as you please: As here let be 15 parts, and the Cross FG, we make 7 of the same parts: Then say by the Rule of Three, As 15 parts the length of the Staff, is to 750 foot E B; So is 7 parts the length of the Cross, to 350 foot for the Bulwark ABC: Do the like with all others, and give good heed to the following Questions and Answers, which are useful for all Commanders, Captains, or practised Gunners, as well in Offensive as Defensive Service by Sea or Land. If a Man were on the top of a Rock or Hill, on the side of a River, and on the other side saw a Tree, and would know the distance over to that Tree, as the Figure CAB: To do this you have two Observations, the one is the Line of Level; then going on a Right Line from A to C, you observe, and find the Thread cut 54 parts of Right Shadow; then measuring your distance AC, and finding it 68 foot, you follow the Ground-Rules, 54 gives 100, what 63 foot Difference of Stations. CHAP. XXXIII. Questions for the Practice of what hath been formerly taught. Quest. 1. WHen a General with his Army hath besieged a strong Fort, Castle, or Town, and hath secured his Army by Intrenchments, and hath taken notice of the most fitting places for Approaches: Now the Question is to the Gunner, How near they may approach the place with Batteries, and at what Distance the Cannon will do best service, that there they may be planted and made. Answer. If I were to answer, I would desire to approach as near as it were possible to come, and to plant the Batteries about 100, and some 50 foot from one another; and if it were possible, even to the Counterscarp; not only thereby to give the place most damage by the Guns, but also to frustrate the Enemy from sallying out, as likewise to do them most prejudice at their Casements, to Guns and Gunners, by which they might be forced not to dare to show a Head above the Wall. Question 2. This Resolution is good, but very dangerous to perform; for as the Proverb is, It is dangerous to chase a Dog out of his Nest; for if there be a brave Enemy within, how could you approach so near, but it should cost many a brave Soldier his life? Answer. As it is without controversy, where Carpenters work there must fall Chips; but that will never cool the courage of a brave generous Spirit, ever considering, wherever we are, we are in the Hand of God; yea, the danger is not in all places alike, for if you be where there is Earth enough to work, there you begin to cast up Trenches and Mounts against the Town to save yourselves from harm; for the higher the Earth is, the deeper is the Trench to be made, to save you from the sight of the Enemy. Question 3. When you are approached so near the Enemy's strength, that the Cannon is to do service, Whether should you choose a Bulwark or a Curtain, for your storm-place to play upon? Answer. That must be according to the greatness of the place; if the Bulworks be of great distance one from another, in that case I would rather choose a Bulwark than a Curtain, there to make my Breach, thinking that I should come sooner to my advancement there, because the Bulwark is better fortified than the Curtain, and is a principal Strength: And if you make your Breach for Men to enter, you find them sometimes cut off, so that you may begin to fortify there anew, where you are as it were in the Enemy's Bosom; this occasion you have not in a Curtain. See Capt. Hexham. Question 4. If you did storm this Bulwark, and found there some Guns that before you had not seen the like, and that you must presently use them against the Enemy, and know not what Ball they shoot; What is the quickest way to find their true Powder and Ball? Answer. If the Piece be left loaded, she must be drawn; for the Enemy in policy might so leave a Piece, on purpose to split about their ears that take her: When drawn, a piece of bowed Wire being put in at the Touchhole down to the bottom of the Concave, upon the Metal mark that Wire with a Knife; hale the Wire up till it hack on the upper part of the Metal in the Chamber, and mark as before your Wire; take the distance betwixt the two marks, and that is the Diameter of the Boar: And see if it be the Diameter of the Boar at the Mussel: if you find her a true-bored Piece, then take your Compasses, and extend them to the length betwixt the lower mark and the hack of the Wire; this Extension being taken on the Scale of Powder gives you her Powder; and extending your Compasses betwixt the marks, lay that to the Height-Rule, and you will have the Height of the Ball: Otherwise finding the Weight of the Ball, resort to the Table of Powder for that Fortification, and where you find her Weight of Ball, you will find the Weight of Powder for that Piece, for having the Diameter of the Boar and one side Metal, double the one side Metal, and add the Boar to it, you have the Diameter of the whole Piece: Then say, As 7 is to 22; So is the Diameter of the Piece to her Circumference: And having one side Metal at the Breech and Mussel, you have a Dispart: So presently you may do good Service. Question 5. When you have the Diameter of the Boar of a Piece, How do you know what Ball will serve that Piece to shoot, and neither be too high, thereby to hurt the Piece; neither too low, to miscarry by reason of the too much Wind? Answer. As it is convenient the Ball be something lower than the Boar of the Gun that it serves for; and some have thought fit to declare one quarter of an Inch to be a sufficient Wind to all Balls; and others have declared, that a twentieth part of the Diameter of the Ball, is a sufficient Wind for all Guns: I hold that quarter of an Inch to be altogether absurd; because except a Man can give the true Demonstration, as you are taught, and is set forth in pag. 42, to 52. he shall never know how to extract the Wind betwixt the Boar of a Piece and her Ball. For if you please to try for fancy; A Cannon of 8 Inches in the Boar, shall have the Wind for her Ball 1/●● ⅛ part of the Diameter; as also a Base of two Inches in the Diameter of the Boar, hath but ●/1● part of the Diameter of the Boar; for if a Piece of 1 lb Ball shall have proportionable to 9 lb Ball, she would have no Wind at all; and if a Gun of 63 lb Ball had proportionable Wind as a Gun of 9 lb Ball, she would have too much by ●/1● part; behold the Demonstration, Folio 102. and a Piece of 4 ¼ Inches in the Boar, hath just 1/20 part of the Diameter of her Boar, for the Wind to her Ball: which will never stand as a general Rule, except it be Geometrically demonstrated, where you will find the Height of the Cannon-Ball just 2●/1● parts of her Boar, the small Ball ●●/1● parts, and the other 20/19 parts: Wherefore I aver, all that hath been writ to this purpose, is but Supposition and no real Rule; but Geometrically you have your desire, and need not to follow any other Rule for extracting the Wind to find the True Ball. Question 6. When you have obtained Geometrically the True Diameter of a Ball to fit a Piece, the Question is, How shall you know the Weight of that Ball it being Iron? Answer. Some receive this by a common Opinion, that 4 Inches Diameter of a Cast Iron Ball is 9 lb Averdupoise Weight, as you may see by Dr. Weybard's Tactimetria; wherefore I say that is the most certain Rule. Now if 4 Inches Diameter weighs 9 lb; What shall two Inches weigh? you will find the work stand thus. And it is a general Rule; behold you see a Ball of 2 Inches Diameter weigheth 1 lb 2 ounces: If you hold this for a Rule, you may Work and Correct all Tables of this kind that are made in England: Likewise, I say, you may find the Weight of any Iron Ball thus; Say, It hath been ever observed for good, that the Tables of Mr. Norton, Smith, and Nye; and therefore Capt. Sturmy in his Magazine for Mariners, doth follow the same Rule, and gives us the same Tables of Mr. Nye, as he supposeth refined: for he sayeth, Two Inches and a quarter of a Ball, weigheth 1 lb 5 ounces: I will let you see the Error. Now here a Ball of 4 Inches Diameter by his Tables, weighs but 7 lb 6 ounces: But I praise Mr. Norton, who says, We must not expect truth from his Tables. But Capt. Sturmy affirms his translation of Nye to be truly Calculated; if they be true, I must be quite wrong. Mr. Nye saith. Now you may perceive, that they err only by neglecting to Calculate their Tables; But as the Blind lead the Blind, so they both fall in the Ditch; for he gives 8 ½ lb, or 8 lb 8 ounces. And by Capt. Sturmy his Tables, I find a Ball of 8 Inches Diameter to be 58 lb 14 ounces; and yet he hath set down in his Tables a Ball of 7 ¼ Inches for 58 lb. And by the Tables of Mr. Nye, though he hath placed 71 lb, I can find by his working but 68 lb for the weight of a Ball of 8 Inches Diameter. So this will be proved by the Line of Numbers, for if you say 4 Inches gives 9 lb, what shall 2 Inches give; place one foot of your Compasses in four Inches, and the other in 2 Inches, keeping the Compasses at the same extent, set one foot in 9, and measure downwards 3 of these Extents, which will reach to 1 lb 2 ounces; likewise say, if 2 Inches give 1 lb 2 ounces, what shall 8 Inches weigh; extend your Compasses from 2 to 8 Inches; the Compasses at the same extent, place one foot in 1 ⅛ part, and three of these Extents will strike at 72 lb: But if the Weight of a Ball should be demanded in Scotland, you shall find a Ball of 1 lb is 2 Inches; and one of 4 Inches 8 lb; and 8 Inches Diameter (if you observe the Work of the Table) 64 lb; you will find the same by using the Line of Numbers; in saying, a Inches Diameter gives 1 lb, what 4 Inches; and by laying one foot of your Compasses in 2, the other in 4 Inches Diameter, and with the same extent set one foot in 1, and with three of these extents you shall find 8 lb weight: thus you may do in finding the Weight of Ball, knowing their Diameter to what Height you will; and find the true Weight either Scots or English, without being beholden to Tables; though you have in pag. 100, exact Tables Calculated Arithmetically, from eight parts to eight parts of Inches unto 10 Inches Scots Weight; And in pag. 102 you have the like number of Inches Calculated for Ball in English Weight: This is the quickest way, and reasonable true; if there be not holes in the Ball, or, as I have seen some, a great Ring about them, which might have taken up the Wind of the Piece. Question 6. Pray you what Cautions or Circumspections would you use in order to your Approaches making, that thereby the Army might have the least hazard, and greatest speed to come to the Places where the Batteries are to be made for the Cannon, thereby to be more certain of a hopeful and good success over the Enemy? Answer. But not Dundass Governor. To Answer this, you must know you may have many hindrances, if there be a resolute Enemy in the Strength; Nevertheless observe; 1. You must be careful of your Leaguer, that it be well trenched and secure from fear of the Enemy, in all Quarters, by Trenches and Flank-works; then choose to set your Batteries most conveniently in the opposition of their Strengths, and observe that there be no Hill, nor deep Ditch to hinder the Soldiers, if occasion offer to an Assault. 2. That your Approaches be entrenched to open or shut, and to make such a way to come to the Batteries, and be sure it be well covered and guarded with Men to keep it. 3. That the Platforms be large enough for the Guns to Reverse, and also to command the Place they shoot at. 4. If there be Earth enough, that you make the Trenches deep and wide enough, and well flanked. 5. That with advice and deliberation, you Batter all the high Flankers, the while you are making your Approach-Trenches. 6. When you have brought your Trenches to the Counterscarp, then make your Platform and Beds for your Pieces by the Point of the Counterscarp, by which you may hurt their Low-Flankers, and take them away; and so continuing your Battery that you bring down their Counterscarp, and the body or face of their Work. Question 8. When you are approached so near as you can, how shall you then Storm and Breach a Bulwark at the Point, that is both Offensive and Defensive? Answer. If you use thereto 18 or 20 Pieces, all Whole or Half-Cannon, and plant them so as they may shoot Right Angular, and cross one the other; and if the Approach be so near as aught to be, I would have 4 of my Guns only play to dismount the Enemy's Ordnance in their Places, wherever I could perceive they lay, and by this means make my Storm more free. Question 9 If you were to shoot at a distance, what Gun would you choose, a Reinforc'd-Gun, or a True-Fortified? Answer. It is true, that if you elevate a Reinforc'd-Gun to 45 Degrees, and the True-Fortified to the same, shooting both one Ball, that then the Reinforced Piece will drive his Ball more violently, and shall fly farther than the Ball of the True-Fortified Piece: And great reason for it, the Reinforced is long and well Fortified; they of Brass are 10 Diameters of the Boar about the Breech, and his Proof of Powder is ⅚ parts of his Balls weight, and some the whole Balls weight; and the True-Fortified but 9 Diameters of the Boar, which gives a great difference in Powder, for she is proved with ⅔ parts of her Balls weight of Powder; besides the one is longer by half as long again as is the other; for the one being 18, and some 20 foot long, the other is but 10 or 12 foot long: by these Reasons, being better Fortified, hath more Powder, more length, and but equal Ball; she must burn more of the Powder before the Ball be delivered, which must of necessity more violently drive the Ball farther than the True-Fortified Gun. Question 10. Thus it followeth, that the longer a Piece is, the more strength she hath, and doth violently carry her Ball farther. Answer. This is so to appearance; for as we say any thing conveyed through a Pipe or Boar, hath his Course more violent according as the Boar is long, and hath been found so to do by some: But I say experience teacheth otherwise now, for I have seen a Demi-Cannon tried, being of a reasonable length, and broke a foot and a half at the Mussel; yet when the Piece was tried again and again, did carry her Ball as far as she did before. Question 11. How is this, that a Sling doth shoot farther than a True-Fortied Piece, or other suchlike Piece, which is shorter than a Sling? Answer. I hold that which Reason and Experience both showeth: Namely, that the strength of any Piece is so much more as the Piece is longer; but being fortified accordingly, and with this restriction, that it is done with an indifferent length; for from 8 to 12 foot long, being of the same Boar and Fortification, the Piece shall add to the flight of her Ball: But from 12 to 20 foot long, you shall see them abate of the Balls flight; the reason is, in all those too long Guns, the Powder is burned before she deliver her Ball, whereby the flame and strength of the Balls flight is abated. This is strange, and opposeth the thoughts of many Gunners; but by my Experience here in England by Saltwich. I found it so, and therefore not to be controverted. Question 12. But if you load a long Piece with so much more Powder, and being thereto Fortified, should not that give strength to the fire, that thereby the Ball should more vehemently be farther driven? Answer. It is without all question, that a Piece doth most harm having its greatest Loading; yet it is found ordinarily, that in all Guns having Powder above half the Balls weight, all taketh not fire; yea, I myself at Saltash in Cornwall, gave a Quarter-Cannon, shooting 12 lb Ball, more than her ordinary allowance, and laying 6 pair of Sheets on the Ground, on the descent of the Ground; and after fire given, I found two ounces of the Powder whole, by which you may guests what more was burnt after it came out of the Piece by the flame; and so I suppose the Balls flight is not increased but diminished: Whereby you may understand that too much Powder is disadvantageous for Ordnance, and that there ought inspection to be had to their Loading: And for these reasons I have Calculated these Tables, which I am sure is the nearest Truth to give Ordnance their Powder, of any yet given out by any other. But I know some Gunners will be offended to think that by these Tables, the Fortification of their Guns considered, they should be drawn to an Account of what Powder they have spent. Question 13. If you were to shoot from the Battery G, in the Figure 133, to the Ship E; if you had your choice, whether would you use a Demi-Cannon or a Bazilisk? Answer. If it were a calm day, and the Sky clear, and the distance betwixt both about 300 or 400 Paces, than I would hold little or no difference which of the two to choose; but if it were a little Wind, the Sky thick, and the Air damp and moist, I would rather choose a Demi-Cannon than a Sling, or rather a Whole-Cannon than a Demi-Cannon. My Reason is this, That the Wind, and Mist, or Rain, hath not so much strength to divert a great Ball as a small, which is found Experimentally: for divers times I have shot from the Castle of Edinburgh to the Links of Leith, when the Enemy was exercising; but when there was a gale of Wind on either side, or against, I found the small Ball to err; but the Demi-Cannon came much nearer my expectation. Question 14. If you were to shoot from a Valley, as at the Point B, against the Hill A, or from the top of the Hill A to the Valley B; is there any difference in laying of the Ordnance? Answer. There are divers Opinions about shooting of this nature, for most do say, that shooting against the Hill from a Valley, the Ball will be below the Mark; and likewise shooting from the Hill to the Valley, that the Ball will strike below the Mark; but as I have shown by my own Experience, these Authors are not to be owned: for I doubt it is with divers that have writ of Gunnery, as that the Proverb will hold good, viz. Many Men speak of Robin Hood, that never shot in his Bow. So I doubt some have writ they know not what themselves, never being experimented. Question 15. By this I perceive there is no Rule, or Fundamental Ground can be made, by which you can make a Table of Randoms, whereby the Gunner may lay his Piece to shoot such Distance by such Degrees of the Quadrant being thereto elevated. Answer. This I affirm, and my Reasons you have in pag. 122, which if any Man will truly consider, he will either not think to aver Random-Tables, or otherwise to make Tables for every Gun that is made, and also for every Wind and Wether that is, when they are to make use of the Guns; and he must not forget to make Tables for every Ground he is to shoot over: Which will keep them at work all their lives, and never conclude to any good purpose. Question 16. Is it possible to give a general Rule, that instantly you may plant your Ordnance on a March against the Enemy in the Field, when the General intends to give Battle? Answer. I believe not, because of the many hindrances and impediments that do many times follow; for the Rule of Discretion is that which must then be observed, and the Order of the General, and therefore is carried a competency of Field-Pieces, which are to be planted at the Head of the Battle, and some betwixt the Vant and the Middleward, by 2 or 3 together on the Flanks and Wings of the Musqueteers, being covered with the Wings of Horsemen, or as occasion presents and suffers them; some of these on the Front of the Army, playing with diligence on the Enemy's Brigades; and if the Fields be plain and even, then as the Army hath by them Cannon, Demi-Cannon, Field-pieces and Slings, which may be planted for the greater annoyance of the Enemy at a greater distance; for every Regiment ought to have 2 or 3 Field-pieces, which must be planted at the Head of the Leaguer, and must stand a little elevated with Earth, (if possible); all these will cool the Enemy before the Battles draw near; and some of these Field-pieces may be removed as occasion will serve, where they may gall the Enemy so, that Gunners being Men expert, and having good Attendants, may be very advantageous to an Army. CHAP. XXXIV. The Order and Necessaries for Guns to March by Land, they having six Demi-Cannons, six Sakers or Demiculverings, with two Whole-Cannons, besides their Field-Ordnance. BEfore the Train doth march, there goeth out Pioners, each of which is furnished with either a Shovel, Scoop, Pickax, Crow or Handspike; having for their Commanders, a Captain, Lieutenant, and two Corporals, with a Drum to every Company; who are to make plain the way for the Cannon. After them first follow the 6 Sackers or Demiculverings, drawn with their respective Horses, with their Provision of Ball in Wagons, and their Powder in Wagons, besides there must be at the Rear of the Cannon, if any whelm, help sufficient to mount them again. Next follow them six Demi-Cannon, with their Shot and Powder conform; Then 2 Whole Cannon, with their Powder and Ball accordingly. Then the Carriage of Ladles, Sponges, and Rammers, Match, Crows, and Handspiks, and Budg-barrels: These besides the Field-pieces for the respective Regiments, take a great many Horses, Wagons, and Men, for their Attendants. Now when the Cannons are on their March, every Gunner to his respective place, must march at the right side of his Piece, and by them their Harbingers, who take notice of all the Ropes, and other Provisions for Draught, and help them if defective: and also to see that the Axtrees be well soped or tallowed, that thereby the Train may march without stop: The Wagon-Master must have spare Horses by his Draught, if any fail either in Wagons, or in Draughts of the Ordnance. Several have given Rules for so many Horses to a Piece of such a Weight; as thus, every 500 lb of Metal for a Horse-Draught; where the Guns alone, besides the Carriages, must have 120 Horses: So I reckon for Guns, Carriages, and spare Horses, there will be 180 Horses: Now for Powder, Ball, and other Provisions, 100 Horses more with Wagons, besides Wagons for the Officers. This is supposed to be for so many Cannon in fine plain Way; but the Horses in every Country are not all alike, for I have been drawing Cannon, and allowed but to every Horse 350 lb, and hardly able to perform; but sure it is, where Horses are to be pressed, there need no halt to be made for Draught, if the Conductors be provident. But if there should fortune Cannon to be drawn in places where Horses or Oxen (for if you order a Yoke of Oxen for a Horse-Draught it will be equal) are not to be found; Therefore I will set down a general Rule, how these Guns may be drawn by the strength of Men. And the Calculation shall be made for the forenamed 14 Guns; by which may be reckoned any other Draught having the Weight. First, It is conceived an indifferent Man will draw 100 lb for his part, (but on a plain way); therefore for ordinary, I do allow a Man to draw 80 lb weight: And you will find, counting the weight of these 14 Pieces thus; The Cannon 7000 lb, a piece, is 14000 lb for them two; then the Demi-Cannon 4500 lb, and these 6 are 27000 lb; for the 6 Demi-culverins 3200 lb a piece, and these will weigh 19200 lb; which in all is 60200 lb: which sum being divided by 80, (the pounds of draught for one Man) will make 752 Men to draw the 14 Pieces of Cannon. Now these 752 Men to employ with discretion and good order, that every Man may do his endeavour, you are to make fast your Ropes in this manner, on either side of the Carriage; before on the Hacks one Rope, and on the middle of the Bolt or Brestband one; And upon every Rope, shall be so many Ropes so made fast, as every Man may have 2 ½ foot distance one from another; so that the Draught-Ropes for a Demiculvering must be 17 fathom long: Now for the Demi-Cannon and Cannon, they may be reckoned by their proportion; so the Men are set to Work, as the Figure hereby doth show. This will be thought a new Invention, but I used the same in my Lord Middleton his Service from Aberdene to Fyvie, where I caused them to make these Sled-feets, as you see fast to the Carriage, in this manner; near to the Breech of the Piece there is a Bolt, whereon the end of the Sled-foot is; and under it, at the foot-end of the Carriage, a Square-hack to lay over the Sled-foot, and then a Rope through the Sled-foot: And a Man or two thereby shall steer a Gun by a Height or Hole, in the way where she is to be drawn, so that many times it saves the Guns from falling over. And when you are to meet your Enemy, or make use of your Guns, you may lift up your Sled-feets, and lay them all along the side of the Carriage in manner as you see, on a Hack where they do not trouble, and unhacking the Ropes from the Hacks before, you may use your Gun at your pleasure. CHAP. XXXI. By knowing the Weight of one Piece of Ordnance true-bored, to find the Weight of another true-bored Piece, being of the same Metal. BEcause it falleth out sometimes, that in a Fort or Ship are Guns, not having their Weight described upon them; Therefore in such occasions, not to let the Gunner be to seek, but that he may give her Weight without great trouble, I shall here set down some Examples, whereby the Gunner may with ease find the Weight of any great Ordnance whereby he may be able to show, what store of Horses or Men are competent to draw these Ordnance, if occasion require. These Examples and Rules I intended to have given by a Gauge-Rule; and because these ways are more easy to do, and quicker dispatched, I shall only take by the way to let you know, that I will admit there is a Brass Saker weighing 1900 lb Weight; and as it is given out in other Questions, she is 3 ¾ Inches in the Diameter of the Boar: Now it is commonly found, these Guns are about the Breech, measuring at the Touchhole, 9 Diameters of the Boar: I say then, if I bring 3 ¾ Inches all into Quarters, than I have 15 Quarters; with which I multiply the 9 Diameters of her Breech, and I find them 135 Quarters; which dividing by 4, I bring again to whole Inches, and find 33 ¾, which we will here call 34 Inches, for the Circumference of her Breech: Then I say by the Rule of Three; As 22 is to 7, So is 34 to 10 9/11 Inches. The Work. This 10 9/11 of Inches, is the Diameter of that Saker; if she be true-Bored, she is true-Fortified: And such are the only Guns to make choice of for finding by their Weight, the Weight of any other Brass Piece: Therefore, I say, Example. If a Gun of 11 Inches Diameter at the Chamber weighs 1900 lb; What shall a Piece of 18 Inches Diameter weigh? Thus by the Table of Logarithms. The Logarithm of 11 Inches, is— 1,041393 The Logarithm of the greater, 18 Inches is— 1,255272 Difference Increasing— 213879 3 The Triple whereof is— 641637 The Weight of the known Piece is 1900 lb— 3,278754 Sum is— 3,920391 Which is the Logarithm of 8325 lb, for the Weight of the great Gun. Here you see that this operateth well by the Table of Logarithms, and the Weight of the Piece is found to be 8325 lb. Now to find the same by the Line of Numbers on the Scale, you are to place one foot of your Compasses in 11, and the other in 18; keeping the Compasses at the same extent, set one foot in 1900, and then triple turning the Compasses, the last foot will touch at 8325, as before. Another Example. Also there is a Piece, I know not what her Weight is; but I find the Diameter of this Piece to be 8 ¾ Inches: And I place the Work to find her Weight as before. Behold the Work. The Diameter of the known Piece is 11 Inches— 1,041393 The Logarithm of the Diameter of the other 8 ¼— 0,942008 Difference decreasing— 99385 3 Triple of the Difference is— 298155 Which Subtracted from the Logarithm of 1900— 3,278754 Rests— 2,980599 Which is the Logarithm of 956 ⅓ lb, for the Weight of the lesser Piece, which was required. The Weight thus found by Logarithms, you will find the like by the Line of Numbers, if you extend your Compasses from 11, the known Diameter, to 8 ¾, the Diameter of the Piece whose Weight you would have; the same extent three times from 1900 down the Scale, will reach to 956 ⅓. This former Work you may find on the Line of Numbers, if you place one foot in 9, the Diameter of the Boar that begirts the Piece at the Touchhole, and the other foot in 7, which is most near the Diameter that begirts the other Piece, and the Compasses at the same Extent, place one foot in 1900 the Weight of the known Piece, and three times turned downward, will light on 956 ⅓, as before. CHAP. XXXVI. By knowing the Weight of one Piece of Iron Ordnance, to find the Weight of another Piece of Iron Ordnance. Suppose an Iron Saker of 3 ¾ Inches Diameter of the Boar, this Piece weigheth 1600 lb; I find all such Pieces to have 11 Diameters of the Boar about the Breech; for which cause I work as before, and bring 3 ¾ into quarters, which I multiply by 11 the Diameters of the Boar about the Breech, and I find 165, which I divide by 4, to bring again into Inches, and the Quotient is 41: Then I say, by the Rule of Archimedes; As 22 is to 7, so is 41 to 13 1/22 Inches. The Fraction is so small not to be valued. So that I find 13 Inches to be the Diameter of an Iron Saker, whose Weight is 1600 lb, and that the same is a true-Bored, true-Fortified Piece: Now there is an Iron Piece whose Weight I know not, but I find the Diameter of that Piece at the Touchhole or Charged Cylinder to be 21 Inches: To find the Weight of this Piece Logarithmically. Example. I say, a Piece of Ordnance of Iron, of 13 Inches Diameter, weighing 1600 lb; What shall an Iron Piece of 21 Inches Diameter weigh? The Work will stand thus. The Logarithm of 13 Inches, is— 1,113943 The Logarithm of 21 Inches, is— 1,322219 Difference increasing— 208276 3 Triple of the Difference is— 624828 The Weight of the known Piece 1600, is— 3,204119 Sum is— 3,828947 Which is the Logarithm of 6744 lb, for the Weight of the Piece inquired. If you will Work by the Line of Numbers on the Scale, you will find it near the same; for if you place one foot of your Compasses in 13 inches the Diameter of the known Piece, and the other in 21 inches the Diameter of the Piece whose Weight you desire to know; keeping your Compasses at the same extent, set one foot in 1600, the Weight of the known Piece, turning your Compasses three times up the Scale, and you will find the third extent will reach 6744, which is the weight of the Piece required. Another Example. There is also a Piece of Iron Ordnance, whose Diameter I find in the charged Cylinder to be 8 ¼ inches; the Question is, to find her Weight. The Log. of the known Piece, 13 inches is— 1,113943 The Log. of the other Piece, 8 ¼ inches is— 0,916454 Difference decreasing— 0,197489 3 Triple of the Difference is— 0,592467 Which subtracted from the Log. of 1600— 3,204119 Rests— 2,611652 Which is the Logarithm of 409 lb, for the weight of the Piece inquired. Finding here the weight of this Piece to be 409 lb, you see it followeth, that great or small Ordnance their Weight may be found; yet for variety we will have another Example. Example. I will admit there is a Piece sound, whose Diameter is 10 ½ inches; and the Weight of this Piece I demand. The Log. of the known Piece, 13 inches is— 1,113943 The Log. of the other Piece, 10 ½ inches is— 1,021189 Difference decreasing— 0,092754 3 Triple of the Difference is— 0,278262 Which being subtracted from the Log. of 1600— 3,204119 Rests— 2,925857 Which is the Logarithm of 843 lb, for the weight of the Piece inquired. This and the former is found on the Line of Numbers, if you extend your Compasses from 13, to 8 ¼; and with the same extension turned three times down the Scale, you have 409 lb. If you extend from 13 to 10 ½, and with the same extent from 1600, three times turned down finds 843 lb for the weight of the Piece inquired. And so much for the finding the Weight of Ordnance, thereby to provide what Horses, Oxen, or Men are able to draw them. As the Figure here demonstrates. Having, as I suppose, satisfied the Gunner for what is incumbent for him to act both by Sea and Land, with all sort of great Ordnance, either true-Bored, Tapered, or Chamber-Bored: Now it remains that I satisfy my Friends, who expect to hear something of those Pieces that shoot Granado's, or other Fire-Works; as likewise of the Pattard; and of their Ingredients, Compositions, and the manner of using them. CHAP. XXXVII. Of Powder and its Ingredients. IT is a Paradox to many, to think that Saltpetre, Brimstone, and Coal, being incorporated, should be the only Compositions for Powder: But know this, That whosoever desires to learn to shoot in great Ordnance, or to make Fire-Balls, or any kind of Fire-Works, should learn to know the nature and sympathy of these three. Salt-peter that is pure and of a Crystal Colour is best; the refining whereof is set down by divers Authors, as Mr. Nye, and others; yet the nature of it is to burn downward, but if pure and well refined, will burn upward, with a great deal less noise. Brimstone is hot and loves the fire, and the fire loves it; it is of a sharp nature; when you kindle it, it fireth upward; its colour is of a bright Yellow if it be good. The Coal neither augmenteth nor diminisheth any strength or force of itself, only it soon taketh fire, by which the Saltpetre and Brimstone receiveth the fire, and perfecteth their Work: The best Coal is made of the lightest Wood, and the lighter the Wood is, the Coal shall be the better. And it is obvious to all, that when these two opposites, viz. Salt-peter and Brimstone are incorporate, and fired together, the Coal nourishing the fire, there is nothing can resist the force thereof, until the fire dissolve the whole in the Air. Example. If you load a Gun with Powder, (which is nothing but these Ingredients incorporate) or any other narrow Pipe, so soon as the fire comes to the Body, and the Composition is separate by the fire; then doth it force itself out to the Air so vehemently that nothing can withstand it. Powder is made of divers sorts, as Cannon-Powder, Pistol-Powder, Musquet-Powder, and Powder for Fire-Works. Powder may be tried three manner of ways; First, Put your hand in a quantity of Powder, and gripe it hard, if it crack and make a noise in your hand, you may judge it is good; but if it crack not in your hand, it is either not well wrought, or it is spoiled. The second way, is by taking a little Powder, and put it on a smooth plain Board, or a piece of flat Stone; put fire to it, if it go up quickly to smoke, and leave no marks behind it, you may judge it good; but if it burn slowly, and leave white Corns behind it, than you may suppose it is not well incorporated, and hath too much Saltpetre in it, or that there is too much Dust and Coal therein. The third is by the Taste; if it be too sharp in the taste, it is like to come moist; but if it taste a little Niterish and sweet, and hard-corned, it is good: There are several other ways to try the goodness of Powder, that for brevity I here omit. Of Fire Works. There are several Sorts of Fire-Works, some for Offensive Service, some for Defensive Service, and some for Recreations and Sport: I intent only to speak of those which are to be used in earnest, not minding to meddle with those for Recreation at this time, in regard they are so learnedly treated by divers Authors. Of Fire-Works, and those Ingredients used for Compositions. As there are sundry and numerous Ingredients that may be used in Fire-Works; so Fire-Works are so to be mixed as they may work several effects, according to the several occasions may be produced in War; therefore it is impossible for any Man to lay down Rules, which only must be observed; but that the Gunner may have a taste of every Dish, that are necessary to be used in bringing Enemies to Ruin, and Rebels to the Obedience of their Lawful Princes, observe these following. The Loading and Use of the Mortar-Peece. These Pieces are not to be used as great Ordnance, in shooting at great Distances; but, as it were, to throw a Granade, or Fireball, or Stones, over Walls, or into Garrisons, being seated high or low; or from a Garrison to Cast a Ball into the Enemy's Works or Batteries, thereby to frustrate them of their intents, by taking a way those Men most active in the same. The Mortar-Peece may be elevated to any degree of the Quadrant; but the contrary you may observe in great Ordnance, for they cannot be elevated above 45 degrees; and the nearer you approach to any place to shoot at it, you must deball your Piece under 45 degrees; so that if Tables were to be made for Great Ordnance, they may not exceed 45; and Tables for Mortar-Peeces may be made from 1 to 45 degrees, and from 45 to 90 degrees. Now he that would Load a Mortar-Peece, may elevate her Musse to what degree he will for his own conveniency, the Piece made clean, you put the Powder in the Chamber, and upon the Powder a Wad of Rope-yarn, Hay, or what you can provide; than you put a Turf of Earth cut on purpose, that is large wider than the vacant Cylinder upon the Wad, which fills the Chamber, and then you put the Granade or other Firework above that Turf, and putting Grass or Hay about your Granade, that it may lie as you would in the Mortar, and also to keep the Powder in the Mortar from the fire of the Feusey. The Mortar Piece being thus Loaded, you cannot give fire, with any hope of success, before you observe and know, how far the Distance is betwixt you and the place where you would have your Ball to light, and also know, how far that Mortar-Peece can cast her Ball from Degree to Degree; likewise you must observe the Wether, whether it be calm, or blows hard, or if the Wind be with or against you, or if it be to the right or left of you: Having duly considered these things, the Gunner may do well the first shot; but if he err, he must amend the next. So that it stands to reason, that when you have found the Distance to the place you would lay your Ball at, that you may know by this Table near what Degree of the Quadrant the Piece must be laid to reach thither. 90 0 75 403 60 661 89 80 74 425 59 673 88 124 73 448 58 693 87 148 72 450 57 708 86 171 71 473 56 723 85 195 70 496 55 737 84 219 69 500 54 751 83 243 68 521 53 765 82 267 67 540 52 779 81 289 66 562 51 792 80 291 65 580 50 804 79 313 64 599 49 816 78 335 63 608 48 827 77 359 62 626 47 838 76 381 61 644 46 848 Now if you were with a Mortar-Peece at the back of a Wall near a beleaguered place, and there were a remarkable place, as Magazine, or Store-House, or Corn-Barn, and it is desired to lay the Granade or Fireball in that place, the distance betwixt you and this place being found to be 243 paces, as in the Figure from A to M; Then look in the Table, and see what Degree is opposite to 243, and you will find 83 Degrees, and so the Mortar-Peece A must be elevated to 83 Degrees to cast her Ball or Granade into the House M. Do so with all other. When you would discharge a Mortar-Peece, first you must set fire to the Feusie of the Granade or Firework, and you must see it burn well before you give fire at the Touchhole, and mark narrowly where the fall is, thereby to help the next if need require, in form as aforesaid. The Feusies for Granades or Fire-Balls, may be filled with this Receipt; 1 part Powder, ½ part Salt-peter, ¼ Brimstone, and ¼ part Rosin, being all well beat to Meal, and moistened with Linseed-Oil. Now follows the Proportion of the Pattard, and Use thereof with all things belonging thereto. The best Pattards are made of Copper, to wit, 1/10 part of Brass: they are made of Iron also, some more some less, as the Figures showeth: The Pattard A is 12 Inches long, the Diameter at the Breech is 7 ½ Inches, and the Diameter of the Concave is 5 Inches; then the one side Metal must be 1 ¼ Inches thick; she is at the Mussel ½ inch thick, and the Diameter of the Boar at the Mouth is 10 inches, and weigheth 76 ½ lb. There is another Pattard as B, which is 9 inches long; the Metal at the Mussel is ½ inch thick, and by the Touchhole 1 inch thick; the Diameter of the Boar at the Mouth is 7 inches, and the Boar at the Breech 4 inches. While this Work was intended for the Young Gunner's Instruction, I hold it my duty to show you that there is no Firework that can be invented or made for Offensive Service, but the same will and may be made use of for Defensive Service; but some may be made for Defensive Service, which can hardly be useful in Offensive Service, as Barrels for smoking out of a Mine, or Balls, or Bags to burn the Wood, or Rubbish cast in to fill up a Ditch, Powder-pots, and such like. Granades to shoot out of a Mortar-Peece. The Mortar-Peece shoots all sorts of Fire-Works; First, Granades, the Shells made of Iron; Secondly, Balls or Bags made of Canvas, in form of Granades; Thirdly, A Mortar-Peece may shoot Stones coated with Fire-Works, or Stones in the Night to fall among the Enemy, as if it reigned Stones. 1. For the first the Iron Shell of a Granade must be filled with good Powder, and some well-powdered Brimstone mixed with it, that thereby the Powder may throughly fire the more suddenly. In your Granade you may put some little Balls of unquenchable Composition, that when the Shell breaks and brings down the Rubbish of a House, those little Balls may raise Fire afterward; which is fearful in a Garrison, and is one of the greatest terrors can come among them. Canvas-Balls for Granades. 2. These Balls must be made of strong Canvas; when you have made your Canvas-Ball, you may fill it with Sand, and then take two Iron Rings, and mould your Ball strongly in form as you see the Ball in the Copper Plate N° 3. But if your Ball be of great weight, single Line will not serve to mould your Ball, and therefore you must make it a great deal less than the Boar of your Mortar-Peece, both in regard of the moulding and coating of your Ball. The Ingredients or Composition to fill this Ball. Take Powder, Salt-peter, and Brimstone, of each a like quantity, these you shall beat small, and incorporate them together; moisten them with Linseed-Oil, and work them with your hands till you make a Paste, that it may stick together in small Balls if need be; This is a Slow Composition. Another for the same. To this Composition you must take 4 parts of Powder, 3 of Saltpetre, and 3 of Brimstone; these being severally beat to Meal, moistened with Linseed-Oil, and wrought as aforesaid; This is a good Composition. Another for the same. Take 12 parts of Saltpetre, bray it not very small, and 12 parts of Brimstone not small beat, work them well together, and moisten them with 2 parts of Linseed-Oil; then take 6 parts of good Saltpetre, bray it as small as Currants; incorporate these Ingredients, and make a Ball thereof as big as a Walnut; and if it burn as long as you may tell 30 soberly, then is the Composition both good and strong. When you have found your Composition good, you may fill your Bag at discretion. In moulding, you must have 2 Iron Rings of the thickness of ¼ of an inch each of them; the one 4 inches Diameter, and the other 3; and as you mould the Ball, rive the Line through the Rings; to which you must have a Splice-Iron, or Marlin-Spike of Horn; a tack of Hartshorn is good to do it with: In the largest of your Rings you may set your Feusie; the Feusie may be made of Wood, the Pipe bored; you may boar 3 or 4 small holes near the lower end; it is the custom of Feusies to reach the middle of the Granade or Ball; you may pierce this Ball when filled with Firework, and put therein Iron Pipes, loaded with Powder and Shot; but be sure the Touchhole be wide enough, that Rust doth not stop them from firing; these Pipes must be beat in, till their Musles be equal to the Line. Then you must coat this Bag with these Ingredients following; Take Pitch, melt it, and put therein Oil till it be tough and pliable; then put some Powder in it; and if you take Hurds or Tow, and spread on a Table, run this Stuff upon it; then wrap your Ball therein, and open your great Ring for your Feusie-Hole, and stop it with a Plug. When you are to use this Ball, take out the Plug, and put therein your Feusie filled; then Load your Mortar-Peece, and set your Ball in the Mortar in the same manner you do your Granade; having laid your Piece as she ought to be, than fire the Feusie, and so your Piece: If this Ball fall near any thing that will take fire, it will burn, and do the Enemy great harm. For those Stones, that may be shot from a Mortar-Peece, if you dip them in Composition made for Water-Balls, with Pitch, Rosin, and Wax, When they are coming down (as it were from Heaven) into a Garrison, it puts them in great fear, and makes them gather about the fire. Then you may have a Mortar-Peece loaded, and put therein stones as big as a Man's head; and laying her as the other, these stones falling amongst the people, put them quite out of heart. Another Granade for a Mortar-Peece. If you make a Ball of Canvas, as is before shown, well moulded and filled with Sand, then melt Pitch and Rosin, and dip the Canvas Bag in it; but you may have Musquet-Shot cut in two, and clap them on this Coat as full as the Bag can stand, as you see in the Copper-Peece N° 2; then Coat it again, put in the Feusie; and if you fire it among Men, it will do great harm, the Sand being put out, and the Bag filled with Powder. Another for the same. If you let a Pully-maker or Turner turn of hard Wood two half Balls to join each in other, as the Figure 2 demonstrates; they two being joined make a Spheral Body, as you see, then mould them strongly together with Wire, and with a Goudg cut out little slices of the Wood, as may help lodge half Musquet-Ball; then dip it in melted Pitch and Rosin one dip over, and set shot; then Coat it again; this Ball being filled with fine Powder, and a Feusie put into it, it will serve either to be shot as a Granade, or heaved as a Hand-Granade, and will do good Service. To make a Composition for Fire-Arrows. Take 2 parts of Saltpetre, 2 of Powder, 1 of Rosin, 1 of Brimstone; pound these Ingredients very small, and mix them together; then moisten them with Brandywine and Linseed-Oil, or Oleum Benedictum; then fill your Bag of Canvas made for the purpose, very hard and full, then stick an Arrow-head through the Bag, and make it fast with Twine, Rope-Yarn, or such like; and put a Plug for the Feusie-Hole, where you mind to fire it; then coat it over with Pitch, rub Powder in the Touchhole, give fire to it, and shoot it where you will, and it will burn very well. But if you would not have it burn, till it light at the place appointed, in regard you would not have it seen, you shall take a little good Tinder of a Finger's length, and put it in at the part you mind it shall take fire; put that Tinder in fire, and shoot it where you please. There are Gunners, that when they have moistened their Composition, clap it about the Arrow, and then lay Canvas about it, and few it fast, bore holes, prime it, fire it, and shoot it, where they have a mind; but it must be coated first: The form of an Arrow you have in the Copper plate N 5. You may fill the Hedgehog N° 4, in the Copper piece with this Composition. To make Fire-Trunks. Amongst Fire-Works a Trunk is one, for they may be made with easy charge; First, 'Cause the Block-maker to make a Trunk of hard Wood, and reasonable thick, (though you make the Ball small) you may put two Hoops of Iron about it, and at the great end leave Wood enough to make a Socket for the end of a Pike or Pole. The Compositions for Trunks. Take Brimstone, Pitch, and Wax, alike quantity, melt them over a slow fire, and put thereto 2 parts of Saltpetre mealed, with ¼ part of Verdigrease, and 1/● part of Camphire; all these being mixed together, add ⅛ part of Linseed-Oil, stir it well about, and take Hurds, Tow, or Hemp, and make wet with this Composition, which you shall roll up in form of Balls; these Balls you tie together with Twine, and when they are cold, you bore them cross through, which Holes you prime with Powder-dust; you may make of these Balls as many as you please; you may coat these Balls with melted Pitch, and roll them in Powder-dust. To Load the Trunk. First, Load her with a quantity of Powder, as the Gunner thinks fit to carry out his Ball and not break the Trunk; then put home to the Powder one of those cross-bored Balls, and for his Wad to keep him to the Powder, take a little Meal-Powder moistened with Linseed-Oil and made into Dow; and upon that load Powder and Ball again; then put upon the Ball of this slow Composition; then load Powder, and then Ball, and then of slow Composition again, till your Trunk be full; Then take the Lance and make fast in the Trunk, and set him to your shoulder in form of a Musket; let one fire at the Mouth of the Trunk, and you may shoot these Balls round about where you please, and they will burn. These Balls may be used in Iron-Shell Granades, or in Wooden-shell Granades, if they be so big as to contain them; for when the Granade breaks they will burn furiously. To make Balls to show Light in the Night. Take Antimony 1 lb, Rosin 1 lb, Brimstone 3 lb, Saltpetre 1 lb, Coal 1 lb; make many Balls thereof, bind them up with Tow: If the Enemy lie near your Walls, Ditches, or Trenches, for your own satisfaction, you may fire one or more of these Balls, and throw them over, where you have any suspicion; These Balls will give you light to see, if any be near your Fortification. And if you find the Enemy, you may fire your great Guns of what sort you will for their annoyance, still throwing of these Balls to give light to know the Enemies proceed. To make an Extraordinary Firework, which being put into a Mine, or on a Breach for Storm; shall suffocate or kill those who come in the Smoke of it. Take of Horse Litter, that hath been sufficiently spoiled by the Horses, dry it in the Sun; likewise take some of the dirt that Hogs have lain upon, and dry it also; dried Cow-Gall, old woollen Clouts, chop all these small; then take 1 part of Wax, 1 part of Hogs-Lard, 3 parts of Powder mealed, ¼ part of Ratsbane, ¼ part Orpiment brayed to Meal, ¼ part Verdigreese; mix all these things together, and fill a Bag therewith being well coated, put a Feusie into it, and give fire; heave it among the Enemy, or shoot it to them, it will do excellent Service. But if you fill a Barrel of this Composition, and set it in a Breach where the Enemy is to storm; if the Wind carry the Smoke from you, the more it burns, the more it will smoak; and I am sure no Man can be able to act in that Smoke, so that you may have great advantage of your Enemy in contriving this Smoke; as Figure 8 in the Copper piece showeth. To make a Firework that shall stink fearfully. Take Brimstone 2 lb, Rosin 1 lb, Kitchenstuff 1 lb, Assa Foetida 1 lb; melt these together, then take shave of Horn, or the parings of Horse-Hoofs that are dry, mix a good quantity with the former melted stuff; then take Hemp, Tow, or Rags of Linen, or woollen, or Okam, as much as will drink up the Composition, and make thereof a Fireball; this being rolled in a little Powder mealed, and Man's Dung; set fire to it, and it will stink so, as who comes in the Smoke will rather fly, than abide the Smoke, (if they be able); you may put this in Bags, and make Balls or Hedgehogs thereof at your pleasure. To make by Fire, in time of Storm, a Smoke among the Stormers. Take a large strong Barrel and pitch it close, half full of Quicklime; then set in the middle of the Barrel such a quantity of Powder in a close Cask, that, when fire is given, may blow the great Barrel, and all that is in it to pieces; and be sure you put in this little Barrel a Pipe or Feusie filled with Composition, that may reach through the great Barrel; Then fill the great Barrel full with the aforesaid Lime, and lay it at the Breach, where the Enemy is to storm; and when you see your best advantage, having a Train laid of purpose, you may give fire, and if fire come to the Powder, it will so spoil those about it, that they, by filling their Eyes, Throats, and Noses, shall not be able to see, or walk: by this means the Besieged may have advantage against the Enemy. If Lime were used for cleansing the Decks, instead of Stones, I believe it would give much satisfaction at some times; but Quicklime is dangerous, if Water come to it unawares. This Lime is nothing but Limestone burned, that no Water hath been near; than it must be very well brayed, and made as fine (if possible) as flower; the finer you make it, the greater harm it shall do to the Enemy; and being dry and light, will continue the longer ere the Smoke dissolve. Another Barrel in time of a Storm. But if you would play with your Enemy, you may fill your great Barrel with fine pebble Stones, Musquet-Shot, and pieces of old Iron, in form of our Powder-Chests at Sea; this being fired, while they are thick about it, will make rare sport for the Defendant, and make them afraid of worse to follow; and than if you can ply them with Hail-shot from your Guns, and small shot, Hand Granades may give them cause to retire, if they can, with the greater safety, as the Figure in the Copper piece 10, doth show. The Proportion of Compositions for Offensive Fire-Works. 1. Take one part of good Powder, one part of Saltpetre, and half a part of Brimstone, and a quantity of Sawdust, or old rotten Wood, which will make a great Smoke: These being well mixed with Linseed Oil, and wrought under your hands, until you make the Composition to a Paste, that it may hold together to make Balls. 2. Take gross Cannon-Powder 1 lb, Saltpetre 1 lb, Brimstone ¼ of a lb; pound these very well in a Mortar, or a Powder-Mill, and mix them together; moisten them with Linseed-Oil, and work them well with your hands to a strong Dow or Paste, as is beforesaid. 3. If you take very good Powder, beat it very small, searce it through a Sieve, and moisten it with Linseed-Oil, work it to a Dow or Paste; it is good if you make use of it presently; for this Composition is too strong to be kept, and therefore you may add to it half so much Saltpetre, and a little Brimstone, than it may be kept. 4. If you take of the best Pistol-Powder you can get, beat it very small, searce it through a narrow Sieve, moisten it with Linseed-Oil, work it well as is before taught, and you have the best and strongest Composition without doubt amongst all the others; but it is likewise too strong to be kept long, and fearful, if dry, to be fired. 5. If you take gross Gunpowder, as much as you please, and as much Saltpetre, being moistened with Linseed-Oil, and wrought as the rest, with a little Brimstone. 6. If you take two pound and a half of gross Gunpowder, and 4 lb of Saltpetre, and 1 lb of Brimstone, all well beat, and seared through a Sieve; then being moistened with Linseed-Oil and wrought as before. 7. Take 1 lb and a quarter of Powder, 1 lb of Saltpetre, three quarters of a lb of Brimstone, half a lb of Sponk, the Heart of Willow, or old rotten Wood rubbed small; all these being moistened with Linseed-Oil, work them well with your hands as the other Compositions are. 8. To 4 lb of Powder, take half a lb of Brimstone, and half as much Saltpetre as both the other; all these being well pounded and seared through a Sieve, (as aforesaid) and being moistened with Linseed-Oil, work as the rest. 9 If to 2 lb of Powder you take 1 lb of Saltpetre, half a lb of Brimstone, and half a lb of Coal or rotten Wood, these all being well moistened with Linseed-Oil, and wrought, this will make a good ordinary Composition. 10. Take to 1 lb of gross Powder, 2 lb of Saltpetre, and the quarter part of these two of Brimstone; these being all pounded and seared, and moistened with Linseed-Oil, and wrought as formerly instructed. 11. If you take 1 lb of good Powder, a quarter of a lb of Brimstone, and 6 ounces of Saltpetre; these being all moistened with Linseed-Oil, and well wrought; then you take one fourth part of Spunk, or Sawdust well rubbed, mix this Composition with it, and you have your desire. 12. Take 4 lb of Powder, 1 lb of Saltpetre, ½ a lb of Brimstone; these being moistened with Linseed-Oil, and well wrought; Lastly, Take half a lb of Rosin, and as much Pitch small pounded, and seared through a small Sieve, and then a little Sawdust mixed therewith, with rotten Wood rubbed small in your hands; this is for the flame or smoke: If you would have it to spread abroad, put some brayed Glass therein. This Composition may be used amongst your Recreations, but it is not to be long kept. 13. Take of Musket Powder 12 ounces, Coal 4 ounces, Brimstone 3 ounces, moistened with a little Linseed-Oil; this being well wrought may be likewise used. These following Compositions should not be moistened at all, but made altogether dry, and so used. 1. Take what quantity of Saltpetre you will, and the fourth part of that of Brimstone, with a little Powder, and a little Coal; all these being fively pounded, and seared through a small Sieve; mix therewith some rotten Wood to increase the flame. 2. If you take 1 lb of Saltpetre, ½ a lb of Brimstone, a little Coal, and a little rotten Wood, the best you can have, to make a Smoke; the first two pounded and seared, and the rest mixed therewith. 3. Take 2 ounces of Powder, 1 lb of Saltpetre, 2 ounces of Mercury; these 3 well pounded and seared; then 2 ounces of rotten Wood rubbed between your hands, and 2 ounces of Pitch; these two beaten small not seared, mix them to the other Ingredients. 4. You may take 1 lb of Saltpetre, pounded and seared, a little Spunk, with a little Rosin; work the same as aforesaid, then mix them all together. 5. If you take Salt-peeer and Brimstone, each alike, and a little rotten Wood; this is also a good Composition in Balls or Bags, and will keep long unspoiled, and hath likewise no danger in the firing: It is esteemed to be the best of all Compositions, and gives no strong fire, as the moistened Balls do. 6. Take 3 lb of Saltpetre, 1 lb of Brimstone, mix them with Coal, or rotten Wood which is light; if you use to these Balls Feusies it will not be amiss, or some of the slow Composition moistened with Oil. All these may be made in Cloth-Balls, coated as aforesaid, and made use of as the Gunner pleaseth, for offending of an Enemy. As there is nothing now unlawful, (though never so base) that can be acted against an Enemy; so it is very common for Persons to take upon them to be Spies and Intelligencers, who void of fear will enter with the Enemy in their Army, Leaguer or Garrison, on purpose to betray them. Those Men who will give themselves to be Spies, they must certainly be of an idle and base disposition, void of the fear of God or Man, and subtle, secret, and Masters of all Villainy; yet there are many simple Men, that for love of Money do put themselves out for this use; these Men, although they be instructed in what they are to go about, and how they may carry themselves in the same; nevertheless, either before or after they have done their Business, by some instinct of fear, otherwise by the Justice of Heaven, they are cast down, and by their own simplicity divulge something, which brings them to be apprehended, and through torture confess the Matter, and according to the Law of Arms receive Justice beyond other Malefactors, in regard the Offence of Treachery, under the colour of Friendship, is a Treason, and Treason is as the sin of Witchcraft, which will certainly be punished both by God and Man. But if the Gunner should have occasion to use one of these for his secret Business, he should choose one of those, who had been employed in such business before, and of such a nature, that though he be threatened, and asked questions seeming as though he might have been betrayed; nevertheless he must stand unalterably to his own innocency, without fear to change his colour, or coldness of heart to tremble; but with a merry countenance, dexterity in speech, knowing subtlety to answer what is demanded. I do remember, at the Line at Leith, when his Majesty's Army lay there; one day there came a pretty subtle young Man from Cromwel's Army, making his pretence that he had left his Service of purpose to serve the King; he was brought before General Alexander Leslie, who put the Matter slightly by, and gave the young Man leave and freedom to take Service where he pleased; whereupon he took occasion to go down the Line, see all our Army, and continued two days: I sent for the young Man, and in company I did allege he was a Spy; he put it off with the finest jokes that could be; assuring me, There was not a faithfuller Subject than he in the Army, swearing effectually to the point; but that afternoon he went to the Enemy to receive his Reward; he was a sprightly young Man, but of a solid and discreet behaviour, that indeed I did admire his audacity and impudence; this Fellow was fit for a Spy. Another; when I was in the Castle of Edinburgh, a Soldier came running right up from the Enemy's Works, that if he had been a Runaway, they might have killed him; but this fellow came running into our Moat, and when he was there, feigned himself mad, and would be up; the Governor Dondass desired to have him up; so I caused hale him up by a Rope about his middle, (I am sure the Wall rubbed the Skin off his hand); yet when he came in, he was slabbering, as it is said David did before the King of Gath, 1 Sam. 21. but hear what he would, and see what he would, he answered nothing to that purpose; but after he had been that day and night in the House with the Governor, he found the way back to the Enemy without help: Such as these are worthy to be Spies. Now though I will not encourage any Person to any Action so far below a good ingenious Spirit; nevertheless I will show you what Fire-Balls they use, and the subtlety they use in the perusing those Fire-Works in laying of them: And therefore for Examples-sake, I will here show the use of them, that thereby you may the better guard yourselves from the treachery of Spies. They use these following Fire-Works, when they intent to burn the Barns of Corn, or Storehouses where the Corn of the place lieth, or Powder-Magazines, in regard it is impossible for them to come into them, but that it is useful and necessary they have some Windows or Slits in the Walls, wherein they heave their Firework, which is made in this manner. Take one part of Colophony, or Rosin, two parts of quick-Brimstone, one part of Saltpetre, these three pounded very small and mixed together; put to them so much Linseed-Oil as will make the Composition like a Conserve; then make Balls of the same, and if you will, you may make it for Arrows to shoot out of a Bow, or Crossbow, or by observing what is said of Fire-Trunks, they may be used in the same manner, or they may be heaved by a Man's hand. There are other Fire-Works that they use, as this strong Composition. Take 3 parts of Powder, one part of Brimstone, which being pounded small to Meal, mix them very well in a Bowl, put into them the bigness of a Walnut of Greek Pitch, or Colophony, which must also be small stamped, and in the mixing you shall let some drops of Turpentine fall, as also a spoonful of Linseed-Oil, and then make it to Paste with Brandywine, that if occasion be you may make Balls of it. But if you fill Bags with this Stuff, well packed together, and make therein a Hole, and put a stopper into it; then dip these Bags in the following Composition. Take one part of Brimstone, let it melt, and put into it one quarter part of Wax; when that is melted, put in one part of Pitch, and let that melt, and stir them together, take it from the fire, and mix into it one quarter-part of Powder. Or Coat these Balls with this Composition; Take 3 parts of Brimstone, melt it, and put into it 1 part of Wax, and 1 and a half of Grease, one quarter-part of Turpentine, and as much Vernice; when all is melted, set the Kettle a distance from the Fire, and put therein 3 parts of fine Powder; mix them, or stir them well together: when this is to be used, you shall take the stopper out of the Prime-hole, and in the place thereof, put in a piece of Match as long or short as you please, according as you would have them to do execution. The making of this Match you are taught in pag. 172. To such Actions as these, the Match must be chosen that smokes not, for they use to lie till a certain time, and smoking Match will discover them. Example. I desire a Fire to begin within 3 hours' time, therefore I take a long piece of Match, which I intent to use; and I measure the same exactly; I light that Match, and mark how much of it burns ¼ of an hour; I measure my Match again, by which I know how much is burned in the quarter's time, and 12 times so much must be the measure of Match for the time appointed; it must be laid Serpentlike about the Ball, that the parts touch not other, neither the Bag, as the Figure in the Copper Piece, N° 7. There are some may make use of the Fire-Arrow, which may be made sundry ways; some make them thus. Take Powder ¼ part, 2 parts Brimstone, and 1 part Salt-peter, each well pounded to Meal, and seared; mix these three Materials together, moisten them either with Brandy or Linseed-Oil, and then melt Rosin, and pour it into Water, which makes it hard; then pulverize it, and take one part of it and mix with the former Ingredients; then pound them together very well till they are fit to make Balls of; then may you take of this Composition, and lay about an Arrow-Head, and wrap it about with Fustian or Canvas, and seize it about the shank of the Arrow-Head; this Arrow-Head so armed, you Coat it as other Fire-Works; then make a Priming-hole towards the point of the Arrow; stop it, and when you make use of it, fire and shoot it where you desire: As the Figure in the Copper Piece, N° 5. Here follows Compositions for Fire-Works for Storm, divers manner of ways. 1. Take Powder 4 lb, Saltpetre 3 lb, Brimstone 1 ½ lb, Rosin 1 ½ lb; these being all well beat and mixed together, and moistened with Linseed-Oil. This is a good Composition for Fire-Balls, and burn in the Water. To make Fire-Balls to burn on the Water. 2. Take Powder 15 lb, Saltpetre 10 lb, Brimstone 4 lb, Rosin 2 lb; moistened with Linseed-Oil. 3. Take Powder 10 lb, Saltpetre 8 lb, Brimstone 2 lb, Rosin 1 lb; moistened with Linseed-Oil. 4. Take Powder 4 lb, Saltpetre 6 lb, Brimstone 2 lb, Rosin 1 lb; moistened with Linseed-Oil. 5. Take Salt-peter 8 lb, Brimstone 8 lb, Coal 1 ½ lb, Antimony 1 lb, Amber 1 lb, Camphire 2 lb, Turpentine 1 lb, Rosin 1 ½ lb; all beat small and moistened with Linseed-Oil. Another for Water-Balls. 6. Take Powder 9 lb, Saltpetre 7 lb, Brimstone 2 lb, dry Tanners Lee 1 lb; moistened with Linseed-Oil. 7. Take Powder 3 lb, Saltpetre 2 lb, Brimstone 1 lb, Colophony 1 ½ lb, Amber 1 ½; moistened with Linseed-Oil. 8. Take Powder 6 lb, Saltpetre 6 lb, Brimstone 4 lb, Colophony 3 lb; all small beaten, and moistened in Linseed-Oil. 9 Take Powder 1 lb, Saltpetre 1 lb, Brimstone 2 lb; moistened with Linseed-Oil. 10. Take Powder 2 lb, Saltpetre 1 lb, Brimstone 2 lb; moistened with Linseed-Oil. 11. Take Powder 2 lb, Saltpetre 2 lb, Brimstone 2 lb; all beat small, and moistened with Linseed-Oil: These Balls may be used to Fire-Works and Fire-Balls. 12. Take Powder 2 lb, Saltpetre 5 lb, Rotten Wood, or Tanner's Lee 1 lb, good Brimstone 1 lb, Salt 1 lb; these all beat small and mixed together, moistened with Linseed-Oil. To make a long burning Composition for Fire-Balls. 13. Take Powder 10 lb, Saltpetre 4 lb, Brimstone 6 lb, Filings of Steel 4 lb, Sawdust 4 lb; and after you have moistened the Composition, mix the filings of Steel and Sawdust amongst it; then make Balls of this Composition, and tie them as other Balls. Another that is soften. 14. Take Salt-peter 5 lb, Brimstone 2 lb, Coals 1 lb, Sawdust 1 lb, mixed amongst it. 15. Take Salt-peter 2 lb, Brimstone 1 ½ lb, Powder 1 ½ lb; these being beat small and mixed together; take Turpentine, melt it, and moisten these Ingredients in it. Another Composition for Fire-Arrows. 16. Take Salt 8 lb, Brimstone 3 lb, Coals 1 lb, Sawdust 1 lb. 17. Take Salt-peter 2 lb, Powder 2 lb, Brimstone 1 ½ lb; you may use it to what you please. For Powder-Pots, or Stink-Pots. Take fine Powder, mixed with some Brimstone small beat; put therein some Assa Foetida, some pieces of Verdigreese, and some Camphire: This heaved in a Ships Round-House, Forecastle, or betwixt Decks, will make a fearful stink and smoke. To make Match that shall not Smoke. Take a glazed Earthen Pot, and put therein clean red Sand till it be ⅔ full; coil therein Match, so that no part thereof touch other; then cover it well with the foresaid Sand, and coil Match thereon as before, and then put Sand above it till the Pot be full; which done, you are to put the Cover on the Pot, and lute it close, that no Smoke come forth of it; put this Pot into a Sinder or Charcoal-Fire, and cover it all over; let the Pot stand there till the Fire extinguish of itself; then take it out, shake the Sand off, and your Match is ready. I could infinitely have added, but being straitened, do conclude, That as yet to the Art of Gunnery there is NO END. At the Six Stars in Wapping are Taught these Mathematical Sciences following. Arithmetic in Whole Numbers, Fractions, Decimals, Logarithms; Rules of Practice, or Brief Working, etc. Algebra, or the Working by Cossick Practice and Surd Numbers. An exact and perfect Method for keeping Merchants Books of Accounts, by way of Debtor and Creditor, after the Italian manner. Geometry, to take Altitudes, Latitudes, Longitudes, and Profunditudes; to measure Stone, Timber, Board, Glass, Pavement, Tiling, Brickwork, Plastering, etc. Trigonometry both Plain and Spherical, with its Applications, etc. The three kinds of Navigation, with the Use of the Globes, and all other Instruments necessary or fitting for that Art. Astronomy, with the Projections of the Sphere on any Circle, etc. Surveying of Land, Gauging, Dialling, Fortifications, the Gunner's Art, etc. By Robert Webster.